curtipot_

Version 3.6.1 (March/2012) for MS-Excel® 1997 - 2010

Copyright © 1992 - 2012Prof. Ivano G.R. Gutz

[email protected]

http://www2.iq.usp.br/docente/gutz/Curtipot_.html

This freeware is a courtesy of

Instituto de Química - Universidade de São Paulo, São Paulo, SP, Brazil

Member of the Editorial Boards of Talanta (2005-2007) and Electrochemistry Communications (2005 -->)

Member of the Brazilian Academy of Sciences

Honored with the Commend of the Brazilian Order of Scientific Merit, 2007

Fellow of the International Union of Pure and Applied Chemistry

Research interests, CV, publications, see: www2.iq.usp.br/docente/gutz

CurTiPot was written almost during weekends and holidays, in São Paulo and, sometimes in Guaeca beach

See photos googling for [guaeca panoramio gutz]

Dr. Ivano Gebhardt Rolf Gutz - Full Professor (since 1992)


» generation of curves with data equally spaced in pH or volume

» simulation of experimental random errors in pH and volume

» overlay of multiple simulated curves for comparison

Read the License by placing the mouse on the red dot just at the left cell

To enable the execution of macro-instructions in MS Excel follow instructions at the right -------> -------> -------> -------> -------> ------->

The Solver supplement is required only by the Regression module. Follow activation instructions given in the cell I19 of the module

Experimental pH values are assumed free of calibration, junction potential and alkaline errors of the sensor (to be corrected previously for best results)

The author reserves the right not to be responsible for the correctness, completeness, accuracy and bug-free operation of the freeware CurTiPot

Due to the wide range of screen resolutions in use nowadays, some figure resizing/displacement may be required

Read local instructions in comment boxes by placing the mouse on cells with red marks (like in Q14, Q17 and Q34 at this page);

Save your data, settings and results in Curtipot_anyname.xls files to preserve the original software (optionally deleting unused spreadsheets, with exception of this first one);

CurTiPot main features and uses

• pH calculation of aqueous solutions with activity coefficient and buffer capacity estimation (mixtures of up to seven hexaprotic systems)

• Simulation of simple and complex acid-base titration curves - Virtual Titrator

• Data analysis of real and simulated curves

» Evaluation of curves with enhanced accuracy by interpolation, smoothing and automatic endpoint detection

» determination of concentrations and refinement pKa values by non-linear regression

• Distribution diagrams of species, protonation of bases and buffer capacity vs. pH and vs. added volume

• Database with equilibrium constants (pKa) of 250 acid-base systems (expandable by the user)

Download the latest release of CurTiPot from www2.iq.usp.br/docente/gutz/Curtipot_.html

If you agree with all terms of the License, enable macros and use CurTiPot freely

Ionic strength and activity coefficient calculations are available in the pH_calc and Regression modules

Please report errors and incompatibilities of Curtipot (developed for Excel 9 and 10) to the author;

BEGINNERS should prefer "CurTiPot_i with first steps" freeware, downloadable from http://www2.iq.usp.br/docente/gutz/Curtipot_.html

Enable macros (see cell R16 above); click on the pH_calc tab, at the botton left of this page;

Click on Calculate pH; if you are a high shool student and can't grasp all the stuff at once, look for the pH at the dark blue cell H23; change concentrations to see the effect;

Switch to the Simulation module and repeat the prealoded titration of phosphoric acid; start clicking on the buttons at the left of the figure; change some concentrations afterwards;

Find endpoints of your real or simulated curves with Evaluation. There are buttons to load the last titration curve from Simulation;

Play and learn with the Distribution module; enjoy the Graphs before you advance to the less simple but more powerful Regression to fit concentrations and pKas;

Version 3.6.1 (March/2012) for MS-Excel® 1997 - 2010

Features

Installation

Remarks

Fast Start

http://www2.iq.usp.br/docente/gutz/Curtipot_.html


pH and Acid-Base Titration Curves:

Analysis and Simulation

Q14

End user license agreement Thank you for your interest in the CurTiPot version 3 freeware, a workbook of spreadsheets for Excel (proprietary software of Microsoft), authored by Dr. Ivano G. R. Gutz, Professor of the Institute of Chemistry of the University of São Paulo, São Paulo, Brazil, now on referred as Author of CurTiPot. Please examine the License Agreement before you start using CurTiPot. Personal or Educational Use Only The Author grants you a non-exclusive and non-transferable freeware license of CurTiPot for your personal or educational use at home, in classroom or in academic laboratories. If you intend to make commercial use of CurTiPot, including but not limited to any profitable non-educational activity or selling or distributing CurTiPot for payment, you must obtain a written permission from the Author in advance. Restrictions You may introduce modifications in the spreadsheets to suit your needs, but you are not allowed to remove the original notices about the intellectual property of the workbook and macros, in special but not only from the front page. You shall not distribute copies of modified versions without approval by the Author of the clearly identified changes. Distribution You may share unmodified copies of CurTiPot with students and colleagues that do not have access to the Internet, if they agree to be bound to these Terms and Conditions and as long as you take all reasonable precautions to avoid exposure of your copy to viruses. To minimize risks, it is highly advisable, to use only updated copies obtained from the Author’s download page. Changes to Terms and Conditions The author reserves the right to update CurTiPot and to modify these Terms and Conditions at its sole discretion, without notice or liability to you. You agree to be bound by these Terms and Conditions, as modified. Please download updated versions of CurTiPot from time to time and review the Terms and Conditions. Disclaimer of Warranties The Author disclaims any responsibility for any harm resulting from your use (or use by your colleagues or students) of CurTiPot and third party software used in conjunction with it. CurTiPot is provided "AS IS," with no warranties whatsoever, express, implied, and statutory, including, without limitation, the warranties of merchantability, fitness for a particular purpose, and non-infringement of proprietary rights. The author also disclaims any warranties regarding the security, reliability, accuracy, stability, convergence and performance of CurTiPot. You understand and agree that you download and/or use CurTiPot at your own discretion and risk and that you will be solely responsible for any consequences of incorrect information or results obtained with CurTiPot. This license does not entitle the Licensee to receive from the Author any extra documentation not contained in the program file, support or assistance by any means, or enhancements or updates of CurTiPot other than those made available for download at the Author’s site. Limitation of Liability Under no circumstances shall the Author or his employer be liable to any user on account its use or misuse of CurTiPot. If you accept the terms and conditions given above, you are entitled to use CurTiPot free of charge for unlimited time and number of uses. The Author will enjoy your comments, error reports and suggestions by e-mail.

Read about the name and origins of the program by placing the mouse on the red mark (cell Q34).

Instituto de Química - Universidade de São Paulo, São Paulo, SP, Brazil Version 2, improved and adapted for titrations with coulometric generation of reactants, was released in 1992

Member of the Editorial Boards of Talanta (2005-2007) and Electrochemistry Communications (2005 -->)

Honored with the Commend of the Brazilian Order of Scientific Merit, 2007

Fellow of the International Union of Pure and Applied Chemistry Version 3.3, from January 2008, has a frindlier interface with the Database and includes logarithmic distribution diagram generation overlaid on the titration curve.

Research interests, CV, publications, see: www2.iq.usp.br/docente/gutz Version 3.4, from October 2008, extends Ionic strength and activity coefficient calculations to the Regression module (formerly available only in pH_calc).

CurTiPot was written almost during weekends and holidays, in São Paulo and, sometimes in Guaeca beach

CurTiPot has reached 130 countries with >50 thousand copies and was used and cited in more than fifty papers and thesis (see Google Academics)

The software CurTiPot, version 1.0 for DOS (Borland Turbo Basic and Microsoft Disk Operating System), was created in 1991 and launched in 1992.

- Full Professor (since 1992)

Version 3.0 for Excel, an evolution of the DOS version with added Regression module was released in 2006 (in Portuguese).

Version 3.1 was the first release translated to English. It was launched at May 1st, 2006, at the site www2.iq.usp.br/docente/gutz/Curtipot_.html.

Version 3.2, released in December 2006, includes a separate pH_calc module with activity coefficient estimation.

Version 3.5, Jan/Feb 2010, calculates Buffer Capacity (BC) and medium charge (zm) (pH_calc module) and plots BC and zm and finds the isoelectric point (Distribution module).

Version 3.6, March 2012 - Inflections (endpoints) of real and simulated titrations are located automatically by the improved Evaluation module, with smoothing and interpolation.

HistoryThis freeware is a courtesy of

Q34

The acronym CurTiPot means Potentiometric Titration Curves (in reversed order). Originally written in Turbo Basic for DOS and first demonstrated and distributed during the 15th Annual Meeting of the Brazilian Chemical Society in May 1992, versions 1 and 2 (not translated do English) became widespread in Brazil. Version 3, for Excel - the first to be translated to English - was launched in 2006. Its extra features include a separated pH calculation module and an advanced Regression module, both comprising ionic strength and activity coefficient calculation. Meanwhile CurTiPot was used and cited in fifty puplications and thesis, as can be checked in Google Academics. Sitemeter tracks some thousand downloads monthly to one hundred an thirty countries from the website http://www2.iq.usp.br/docente/gutz/Curtipot_.html. An undetermined number of copies is downloaded from over 300 software distribution sites. Feedback by e-mail with criticism and suggestions is welcomed. If you are really satisfied with CurTiPot, please link to http://www2.iq.usp.br/docente/gutz/Curtipot_.html from your homepage or publications. Ivano G. R. Gutz www2.iq.usp.br/docente/gutz

» generation of curves with data equally spaced in pH or volume

» simulation of experimental random errors in pH and volume

» overlay of multiple simulated curves for comparison

Read the License by placing the mouse on the red dot just at the left cell








CurTiPot main features and uses

• pH calculation of aqueous solutions with activity coefficient and buffer capacity estimation (mixtures of up to seven hexaprotic systems)

• Simulation of simple and complex acid-base titration curves - Virtual Titrator

• Data analysis of real and simulated curves

» Evaluation of curves with enhanced accuracy by interpolation, smoothing and automatic endpoint detection

» determination of concentrations and refinement pKa values by non-linear regression

• Distribution diagrams of species, protonation of bases and buffer capacity vs. pH and vs. added volume

• Database with equilibrium constants (pKa) of 250 acid-base systems (expandable by the user)

Download the latest release of CurTiPot from www2.iq.usp.br/docente/gutz/Curtipot_.html

If you agree with all terms of the License, enable macros and use CurTiPot freely

Ionic strength and activity coefficient calculations are available in the pH_calc and Regression modules

Please report errors and incompatibilities of Curtipot (developed for Excel 9 and 10) to the author;

BEGINNERS should prefer "CurTiPot_i with first steps" freeware, downloadable from http://www2.iq.usp.br/docente/gutz/Curtipot_.html

Enable macros (see cell R16 above); click on the pH_calc tab, at the botton left of this page;

Click on Calculate pH; if you are a high shool student and can't grasp all the stuff at once, look for the pH at the dark blue cell H23; change concentrations to see the effect;

Switch to the Simulation module and repeat the prealoded titration of phosphoric acid; start clicking on the buttons at the left of the figure; change some concentrations afterwards;

Find endpoints of your real or simulated curves with Evaluation. There are buttons to load the last titration curve from Simulation;

Play and learn with the Distribution module; enjoy the Graphs before you advance to the less simple but more powerful Regression to fit concentrations and pKas;


Version 2, improved and adapted for titrations with coulometric generation of reactants, was released in 1992

Version 3.3, from January 2008, has a frindlier interface with the Database and includes logarithmic distribution diagram generation overlaid on the titration curve.

Version 3.4, from October 2008, extends Ionic strength and activity coefficient calculations to the Regression module (formerly available only in pH_calc).


The software CurTiPot, version 1.0 for DOS (Borland Turbo Basic and Microsoft Disk Operating System), was created in 1991 and launched in 1992.

Version 3.0 for Excel, an evolution of the DOS version with added Regression module was released in 2006 (in Portuguese).


Version 3.2, released in December 2006, includes a separate pH_calc module with activity coefficient estimation.

Version 3.5, Jan/Feb 2010, calculates Buffer Capacity (BC) and medium charge (zm) (pH_calc module) and plots BC and zm and finds the isoelectric point (Distribution module).






Use the e-mail: [email protected]




of aqueous solutions with activity coefficient and buffer capacity estimation (mixtures of up to seven hexaprotic systems)

of curves with enhanced accuracy by interpolation, smoothing and automatic endpoint detection

regression

diagrams of species, protonation of bases and buffer capacity vs. pH and vs. added volume

) of 250 acid-base systems (expandable by the user)

Regression modules

(developed for Excel 9 and 10) to the author;

" freeware, downloadable from http://www2.iq.usp.br/docente/gutz/Curtipot_.html

; if you are a high shool student and can't grasp all the stuff at once, look for the pH at the dark blue cell H23; change concentrations to see the effect;

module and repeat the prealoded titration of phosphoric acid; start clicking on the buttons at the left of the figure; change some concentrations afterwards;

. There are buttons to load the last titration curve from Simulation;

before you advance to the less simple but more powerful Regression to fit concentrations and pKas;


Version 2, improved and adapted for titrations with coulometric generation of reactants, was released in 1992

Version 3.3, from January 2008, has a frindlier interface with the Database and includes logarithmic distribution diagram generation overlaid on the titration curve.

Version 3.4, from October 2008, extends Ionic strength and activity coefficient calculations to the Regression module (formerly available only in pH_calc).


version 1.0 for DOS (Borland Turbo Basic and Microsoft Disk Operating System), was created in 1991 and launched in 1992.

module was released in 2006 (in Portuguese).


module with activity coefficient estimation.

) (pH_calc module) and plots BC and zm and finds the isoelectric point (Distribution module).


How to enable the macro-instructions in Excel

Needless to say, the macros of CurTiPot contain no harmful code

and are fully removed by closing the file.


To enable macros in MS Excel 2010:

1. Open Excel and click the File tab (top left corner of screen)

2. Click on "Options" (2010; bottom left; 2007: bottom rigth pop-up)

3. Click on "Trust Center"

4. Click on "Trust Center Settings"

5. Click on "Disable macros with notification"

6. Click OK and OK again

7. Open (or close and reopen) the CurTiPot file

8. When the "Security warning" shows up, click on it to enable content

To enable macros in MS Excel 2007

1. Open Excel 2007

2. Excel 2007: Click the Office Button (top left corner of screen)






8. Open (or close and reopen) the CurTiPot file

9. Click on "Options..." button located by "Security Warning"

10. Select "Enable this content" option.

11. Click OK. You'll be trasfered to the form.

To enable macros in MS Excel 97-2003:

1. Open Excel

2. Go to "Tools "

3. Select "Macro "

4. Select "Security "

5. Select "Security level"

6. Select "Medium "7. Load (or exit and reload) curtipot_i.xls8. When reopen, select Enable Macros




8. When the "Security warning" shows up, click on it to enable content

2. Excel 2007: Click the Office Button (top left corner of screen)


9. Click on "Options..." button located by "Security Warning"

pH Calculator

Fill out concentrations; Enter; Click button B18.

HCl Acetic acid EDTA Hydroxide ion

[B]

[HB] 0.02650

0.02000

0 0 0.0465 0 0

0 0 0.0665 0 0

0 0 -0.073 0 0

Electrolyte Na+ K+ Ca++ Cl- NO3-

0.073

0.073 0 0 0 0

Charge Balance OK

Results at chemical equilibrium

pH 7.001 9.986E-08 1.008E-07

p[H] 6.894 1.277E-07 1.290E-07

"pH" 7.321 4.773E-08 2.110E-07

0.782 0.099501

0.026248 Buffer Strength

Acid / Base HCl Acetic acid EDTA Hydroxide ion

-1.000 -0.996 -1.570 -2.968 0.000

0.000 0.004 1.430 1.032 1.000


[B] 4.057E-07

[HB] 2.650E-02

2.000E-02

2.196E-07

Solution composition - reagents added, in mol/L

Acid / BaseProtonation

Phosphoric acid

[H2B]

[H3B]

[H4B]

[H5B]

[H6B]

S[HiB]

S[H]

SziCi

Ci (mol/L)

ziCi

a H+ a OH-

[H+] [OH-]

"[H+]" "[OH-]"

g H+ Ionic strength (mol/L)

Buffer Capacity (Buffer Index, DC/DpH) mol.L-1.pH-1

Mean charge (zm) and mean protonation (hm) of the equilibrium HiB species at pH

Phosphoric acid

zm

hm

Equilibrium concentration of species, in mol/L

Acid / Base protonation

Phosphoric acid

[H2B]

[H3B]

[H4B]

[H5B]

A3

Gutz: Name of the acid or base (of the conjugated acid). To change it, write in cell K3 or load a different system from the Database

B3

Gutz: See comment in cell M1 on how to change acids ans bases.

A4

Gutz: Leave blank/fill out with the concentration (mol/L) of fully deprotonated base (of a conjugated acid) added to the solution, e.g.: [Na2CO3], [Na3PO4], [NH4OH], [pyridine] or [Na4EDTA]

A5

Gutz: Leave blank/fill out with the concentration (mol/L) of monoprotonated base (or acid, HB) added to the solution, e.g.: [Acetic acid], [NH4+], [pyridonium], [NaHCO3] or [Na2HPO4]

A6

Gutz: Leave blank/fill out with the concentration (mol/L) of biprotonated base (H2B) added to the solution, e.g.: [H2CO3], [H2Na2EDTA] or [NaH2PO4]

A7

Gutz:d Leave blank/fill out with the concentration (mol/L) of triprotonated base (H3B) added to the solution, e.g.: [H3PO4]

A11

Gutz: Sum of concentrations of all forms of the base B introduced in the solution: [HB] + [H2B] + [H3B] + ...

B11

Gutz: Do NOT write in this cell or any other one of the same color, not to corrupt the equations.

A12

Gutz: Maximum H+ concentration available from the full deprotonation of all forms of HiB used in the formulation of the solution: [HB] + 2[H2B] + 3[H3B] + ...

A13

Gutz: Cizi = ion concentration times charge of the ion (e.g., 2[Ca2+]).

A14

Gutz: Fill out with the concentration of counter-ions of the salts of acids and bases, as well as other electrolytes added to the solution (e.g., to adjust ionic strength). This data is not essential but it will reduce the uncertainty of the estimation of activity coefficients and pH. Note: sulfate, a common divalent anion, is only fully dissociated a pH>4 because of its first protonation constant of 100 (= pKa2 2 of sulfuric acid). To deal more accurately with this acid/base system, load sulfuric acid from the Database (instead of defining it as electrolyte).

B14

Gutz: Name of the ion (strong electrolyte). To change it, write in cell K11.

A15

Gutz: To add, e.g., 0.1 mol/L NH4Cl to the solution, write 0.1 in the Cl- column of this line and 0.1 in line 5 of the column loaded with ammonia. For 0.1 mol/L CaCl2 , write 0.1 under Ca++ and 0.2 under Cl-.

A16


A17

Gutz: Electroneutrality is not a must to calculate the pH (by clicking B19). However, there will be some extra uncertainty in the results due to incorrect ionic strength calculation.

A23

Gutz: This is an estimate of the pH = -logarithm of activity of H+ ions or hydronium (see definition in http://www.iupac.org/goldbook/P04524.pdf ) that would be measured by a pH meter for a solution with the given composition, at 25ºC (or another temperature specified for the pKw and pKa values). The potential of potentiometric sensors (like the glass electrode or the H+/H2 electrode) changes linearly with the inverse of the logarithm of the activity of hydrated H+ ions, not the concentration (expressed as p[H] in cell B24). The uncertainty of estimated pH values is never lower than the uncertainty of the pKa values in use, and it grows with the ionic strength, I, due to deficiencies of the Davies equation (more about in cells D26 and K15). It can exceed 0.1 pH unit for I>0.05, specially in solutions with highly charged ions (like PO43--).

C23

Gutz: This and other activity results are based on (uncertain) estimates of activity coefficient made with the Davies equation. Read more in cells A23, D26 and K15.

A24

Gutz: p[H] = -log[H+], calculated with the apparent pKas (cells K25 to Q30), while "pH" (cell B25) is obtained with the thermodinamic pKas, valid only for I=0 (see comment in cell K15), and pH (cell B23) uses estimated activities to come closer to the measurable pH. Although potentiometric sensors respond to activity of species (see comment in B23), it is possible – but not usual – to calibrate a pH meter (a high impedance voltmeter) with H+ concentration standards at a given value of I (to keep the activity coefficients constant) and measure free hydrated proton concentrations directly at this I. Some other techniques like spectrophotometry present a concentration response and may be used to indirectly measure p[H] (e.g., optodes).

A25

Gutz: "pH" is the value found in calculations where concentrations are used in the law of mass action expressions supplied with thermodynamic equilibrium constants – as usual in high school or introductory general chemistry classes and textbooks. Comparison with pH (cell B23) and p[H] (cell B24) reveals that errors are small only for diluted solutions, where ion-ion interactions are less significant and activities depart less from concentrations (see comments in cells A23, D26 and K15).

A26

Gutz: This and other activity coefficients are (uncertain) estimates made with the Davies equation. Read more in cells A23, D26 and K15.

D26

Gutz: The amount of electrostatic interaction between ions in solution is related to the ionic strength, I, a parameter used in the Debye Hückel equation for estimation of activity coefficients and extended versions of this equation, suitable for work at I>0.01 mol/L, where the effective hydrated ion size of the species also becomes relevant. As a general trend, the activity coefficient decreases with the increase of I (due to ion-ion interactions like the formation of ion pairs) down to a minimum in the region of I = 0.3 to 0.7 mol/L. At such high values of I, the association constants of each with all other major ions need to be feed to the equations or empirically fitted, to reduce uncertainty in estimates. The Davies equation, based on the average behavior of the ions and used here to deal with in complex mixtures for witch such constants are not readily available, renders estimates with greater uncertainty. Read also A23 and K15.

C27

Gutz: The Buffer Capacity, BC, (or Buffer Index) can be understood as the concentration of (strong) acid or sodium hydroxide that, when added to the solution under consideration, would shift the pH by one unit, in a hypothetical pH region of constant BC. Since the BC can change rapidly with pH (as shown in Figures 3 and 7 in "Distribution"), estimates of the resistance against acid or base addition are reasonably accurate only for 0.1 DpH or less. For example, a buffer solution of pH 7.000 prepared with 0.0395 mol/L NaH2PO4 and 0.061 mo/L Na2HPO4 presents a BF= 0.055213. i) Addition of acid or base in a BF/10 concentrarion, aiming a DpH of 0.1: Addition of 0.00552 mol/L HCl displaces the computed pH to 6.904, close to the expected 6.900; a similar concentration of NaOH increase the pH to 7.101, practically 7,100. ii) Addition of a concentration equal to BF, aiming DpH of one unit: Addition of [HCl]=0.0552 mol/L renders a pH of 5.62 instead of 5.00 while addition of [NaOHl]=0.0552 mol/L raises the pH to 10.90. This overshot happens because BF changes with pH (see Distribution) and there is more HPO42- than H2PO4- in the buffer). More about, e.g.: Understanding, Deriving, and Computing Buffer Capacity, by Edward T. Urbansky and Michael R. Schock, Journal of Chemical Education, 2000, Vol. 77, 1640-44 and references cited therein.

A30

Gutz: The mean or average charge of a conjugate acid/base system HiB at a given pH is calculated by the equation zm = z + hm where z is the charge of the base B (cells K4 to Q4) and hm is the mean number of protons bound to the base, taking in account the fractional contribution of all species in equilibrium. Refer to the Distribution module to generate complete curves of mean charge versus pH or titrant volume. The isoelectric point (pI or PIE) corresponds to the pH value where polyfunctional species (zwitterions) like amino acids, in average, present no unbalance of positive and negative charges in the molecules, so that the mean charge, zm = 0.

A31

Gutz: hm or h, is the mean number of protons bound with a base B at given pH. For HiB species with stepwise number of protons i coexixting at a given pH, h is the sum of their molar fractions (cells in lines 44 to 50) times the i of each species.

0.000E+00 0.000E+00 4.650E-02 0.000E+00 0.000E+00

for pH 7.001


% B 100.00 99.56 0.00 0.36 0.00

% HB 0.00 0.44 56.99 96.03 100.00

43.01 3.61

0.00 0.00

0.00

0.00

0.00

100.00 100.00 100.00 100.00 100.00

[H6B]

S[HiB]

Species distribution (fractional composition, in %)

Acid / Base protonation

Phosphoric acid

% H2B

% H3B

% H4B

% H5B

% H6B

% S[HiB]

read comment

Fill out concentrations; Enter; Click button B18. 6 1

Ammonia Carbonic acid Acid / Base HCl Acetic acid

Charge of B -1 -1

-7.000 4.757

SS

0 0 4.650E-02 Electrolyte

0 0 6.650E-02 Ion charge 1 1

0 0 -0.073 pKw 13.997

SO4= ClO4- Davies equation parameters

for activity coefficient estimation

0 0 0.073 A 0.509

0 b 0.300

Stepwise apparent constants recalculated for I

pOH 6.996 Acid / Base HCl Acetic acid

p[OH] 6.890 Charge of B -1 -1

"pOH" 6.676 -7.214 4.543

0.782

Buffer Strength 0.011399

7.001

Ammonia Carbonic acid

0.996 -0.852

0.996 1.148 pK'w 1.38E+01

Ammonia Carbonic acid HCl Acetic acid

1.28E-07 0.782 0.782

1.000 1.000

1.29E-07

pKas of the acids and bases in the solution

pKa1

pKa2

pKa3

pKa4

pKa5

pKa6

Na+ K+

pK'an = logK'p1

g OH- pK'an-1 = logK'p2

pK'an-2 = logK'p3

pK'an-3 = logK'p4

pK'an-4 = logK'p5

pK'an-5 = logK'p6

Activity coefficient (g) of species

[H+]Acid / Base protonation

g B

g HB

[OH-] g H2B

g H3B

g H4B

g H5B

G1

pH Calculator - Fast start: This module calculates the pH and buffer capacity of simple or complex aqueous solutions, with correction for ionic strength effect based on the Davies equation. Beginners should download CurTiPot option i -- the same free complete program, but with ballons showing numbered step-by-step guindance of use in each module of the program -- from www2.iq.usp.br/docente/gutz/Curtipot_.html (or first link for curtipot on Google). CurTiPot will not run properly until macros are enabled. See instructions at cell A22 ------> -------> Here are some exercises to become familiar with the main resources: - Click on the button "Calculate pH ..." (cell B19) and check cell B23 for the solution of the default acid-base chemical equilibrium problem: a buffer mixture of NaH2PO4 and Na2HPO4. - Change the default concentrations in cells D5 and D6; press Enter; click Calculate pH. - Copy the concentration in D5 to D4 and clear D5; copy D6 to D7 and clear D6; click Calculate pH. - Change pKa2 (M6), e.g. 7.2 to 9.2, Enter, Calculate pH. If you haven't learned what acid-base dissociation constants are, or whatfor acids are titrated, perhaps you should go through a simple tutorial first, e.g., a flash animated one: http://www2.wwnorton.com/college/chemistry/gilbert/tutorials/ch16.htm - Check the pH of water at 25 ºC: Delete D4 and D7, Enter, Calculate pH. - Compare the values of pH, p[H] and "pH" (B23, B24, B25); have a look at other results in lines 22 to 52 (you don't need to understand all these figures now - some are for advanced users). - Check the Buffer Capacitiy (D28) by adding stron acid or bas to the solution. - Formulate multicomponent mixtures and solve them instantly. - Load other acid/base systems clicking on K2, selecting another acid and clicking on J2. This acid-base pH calculator first appeared as a separated module in the 3.2 Excel version of CurTiPot, an evolution of the 1.0 Turbo Basic version launched in 1992. Prof. Dr. Ivano G. R. Gutz www2.iq.usp.br/docente/gutz

J4

Gutz: Charge of the most deprotonated species of an acid or base in accordance with the highest pKa for the system, e.g., 0 for NH3 or pyridine -1 for acetate/acetic acid -2 for carbonate//carbonic acid -3 for phosphate///phosphoric acid -4 for EDTA

J5

Gutz: Options: a) pKa1 , -logarithm of the dissociation constant of a monoprotic acid or first constant for a polyprotic system. b) logKpi, logarithm of the protonation constant of a (conjugated) base, with i=1 for a monoprotonable base and i= n (most deprotonated species) for polyprotic systems (more about at U5); c) pKw - pKbi, for -log of the dissociation constant of a base, with i=1 for a monoprotonable base and i= n (most deprotonated species) for polyprotonable base. Numerically, values of a, b e c are taken as similar.

J6

Gutz: Options: a) pKa2 , -log of the 2nd dissociation constant of a biprotic or polyprotic acid; b) logKpi, log of the first protonation constant of a biprotonable (conjugated) base or i=n-1 for a system with n protonations; c) pKw - pKbi, with i=1 for a biprotonable base or i=n-1 por a base with n protonations; for a monoprotonable base, leave blank.

I11

Gutz: Total concentration of each base (regardless of the protonation level of the added component) in columns B to H; grand total in column I.

J11

Gutz: Write the name (or formula) of ions of strong electrolytes (not involved in protonation equilibria), like counter-ions of salts of weak acids. In fact, the name is irrelevant; only the charge matters This is required for ionic strength calculation and activity coefficient estimation.

I12

Gutz: Maximum concentration of H+ that could possibly be dissociated from all the components added to the solution.

J12

Gutz: Fill out with the charge of the ion.

I13

Gutz: Summation of Cizi of all acidic and basic ingredients; if not zero, it shoud be neutralized by counterions in the electrolyte.

J13

Gutz: The ionic dissociation product of water changes with temperature and ionic strength, I. For pure water at 25ºC, the accepted value is 13.997 (or 14.00). The program corrects for I variation using the Davies eq. and displays the resulting value in K31.

K15

Gutz: CurTiPot recalculates apparent equilibrium constants at the ionic strength, I, of the solution from thermodynamic constants (I=0) by estimating activity coefficients with help of the Davies equation. The accuracy is good for I<0.05, acceptable for I<0.2 and poor for higher values of I. There is no rigorous means to calculate activity coefficients of individual ions, although there are many equations pursuing the reduction of the uncertainty of the estimates by taking in accountt individual effective ion size parameters and specific ion-ion interactions and/or introducing empirical coefficients fitted to real data. Such parameters are readily available only for the most common inorganic and organic ions, limiting their application range in comparision with the simple and general Davies eq. A compilation of over twenty equations with references to original work is available in the file Ionic St_effects.pdf contained in the package http://www.iupac.org/projects/2000/Aq_Solutions.zip For calculations involving seawater (e.g. ionic strength at different salinities), see: http://ioc.unesco.org/oceanteacher/oceanteacher2/02_InfTchSciCmm/01_CmpTch/05_ocsoft/01_toolbox/OcCalc/OcCalc.htm

I16

Gutz: Summation of Cizi of all electrolytes

J16

Gutz: A and b are parameters of the Davies equation, used for activity coefficient estimation. They depend on temperature, dielectric constant, electrolyte, etc. The recommended values for water at 25ºC are: A=0.509; b=0.300. The Davies eq. does not require the size of different hydrated ions but, to some degree, the A and b parameters may be empirically adjusted to more closely describe a given electrolyte. For example: For NaCl + HCl solutions, A=0.43 and b=0.49 conducts to gH+ values in excellent agreement with those provided (up to 0.5 mol/kg) in http://www.iupac.org/projects/2000/Aq_Solutions.zip on base of more complete equations fitted to experimental data. For phosphate solutions, A=0.51 and b=0.20 seems appropriate at pHs above neutrality.

I17

Gutz: Charge Balance of all Cizi of ingredients added (before equilibrium); if not zero, it shoud be neutralized by adding counterions.

J17

Gutz: Read comment in cell J6 (above) and K15.

G27

Gutz: Buffer Capacity=Buffer Strength x ln(10) where ln(10) ~ 2.303 For a monoprotic acid, e.g., Acetic Acid written in column C, the Buffer Strength is evaluated by the expression: C11 x (C44/100) x (C45/100) + D24+F24

L32

Gutz: These activity coefficients were estimated with the Davies equation and their uncertainty increases with the ionic strength. More information in cells A23, D26 and K15.

SS

0.000E+00 0.000E+00 4.650E-02

and p[H] 6.894 Eletrolyte Na+ K+

Ammonia Carbonic acid 0.782 0.782

0.44 0.08

99.56 84.99

14.92

100.00 100.00

g H6B

gi

I41

Gutz: Summation of the concentrations of all H+ potentially dissociable from reagents available in the solution, coined CHtotal. to be equaled with CHcalc obtained by iteractively changing fitting the pH value.

Click on K2 to Q2; select acids/bases; click on J2; read M1

8 5 7 2 3

Phosphoric acid EDTA Hydroxide ion Ammonia Carbonic acid

-3 -4 -1 0 -2

2.148 0.000 15.745 9.244 6.352

7.199 1.500 10.329

12.350 2.000

2.680

6.110

10.170

Cl-

2 -1 -1 -2 -1

Color coding

D o n o t c h a n g e

C h a n g e c r i t e r i o u s l y

Fill out, change or leave blank

0.09950


-3 -4 -1 0 -2

11.709 9.315 15.531 9.244 9.902

6.772 5.469 6.138

1.934 2.253

1.786

1.500

0.214

for pH 7.001 and I = 0.0995


0.109 0.020 0.782 1.000 0.374

0.374 0.109 1.000 0.782 0.782

0.782 0.374 1.000

1.000 0.782

1.000

0.782

of the acids and bases in the solution

Ca++ NO3- SO4

= ClO4-

M1

Gutz: Selecting/editing names, charges and pKas. Options: a) Write directly in the cells K3 to Q10; b) Click on names in line 2, slide along the list, click on another name; finally, click on J2 to load the constants from the Database. Frequently used acids missing in the Database should be added to it.

0.374

Ca++ Cl- NO3- SO4= ClO4-

0.374 0.782 0.782 0.782

pKa(n) = -log Kd(HB-->B) = log Kp(1)

Acid / Base HCl Acetic acid EDTA Hydroxide ion

Charge of B -1 -1 -3 -4 -1

1.000E-07 5.715E+04 2.239E+12 1.479E+10 5.559E+15

3.540E+19 1.905E+16

4.977E+21 9.120E+18

9.120E+20

2.884E+22

2.884E+22

Kw 1.01E-14

Overall apparent protonation constants recalculated for I 0.09950

Acid / BaseHCl Acetic acid EDTA Hydroxide ion

Charge of B -1 -1 -3 -4 -1

6.11E-08 3.49E+04 5.11E+11 2.07E+09 3.40E+15

3.02E+18 6.08E+14

2.60E+20 1.09E+17

6.65E+18

2.10E+20

3.44E+20

K'w 1.65E-14

Overall protonation constants = bp = SKp (calculated by the program)

Phosphoric acid

bp1

bp2

bp3

bp4

bp5

bp6

Phosphoric acid

b'p1

b'p2

b'p3

b'p4

b'p5

b'p6

R5

Gutz: The betas are cumulative (or global) protonation constants, obtained by multiplying the protonation constants Kp from 1 to i, with i stepping up to n, the maximum number of protons accepted by a (conjugated) base (same as the maximum number os dissociable protons of an acid, but in reversed order). Note that pKa = logKp for a monoprotic acid (because Kp = 1/Kd or pKd = 1/logKd ) and, for multiprotic systems, the first logKp is the last pKa. Protonation constants, Kp, and betas are preferred here in agreement with the most extensive compilations of equilibrium constants, e.g., Critical Stability Constants, Vol. 1–4 (complete references in the Database), and because the equations become unified with those used for metal-ligand-proton equilibria, based on formation (instead of dissociation) constants.

Click on J2 to use these pKas in the pH calculation

Ammonia Carbonic acid Acid / Base HCl Acetic acid

0 -2 Charge of B -1 -1 -3

1.754E+09 2.133E+10 -7.000 4.757 2.148

4.797E+16 7.199

12.350

Temperature 25.0 25.0 25.0

Ionic strength 0.000 0.000 0.000

How to enable the macro-instructions in ExcelAmmonia Carbonic acid


0 -2 and are fully removed by closing the file.

1.75E+09 7.97E+09

1.10E+16 To enable macros in MS Excel 2010:







7. Open (or close and reopen) the CurTiPot file8. When the "Security warning" shows up, click on it to enable contentTo enable macros in MS Excel 20071. Open Excel 20072. Excel 2007: Click the Office Button (top left corner of screen)3. Click on "Options" (2010; bottom left; 2007: bottom rigth pop-up)4. Click on "Trust Center"

pKas loaded from the Database

Phosphoric acid

pKa1 = logKpn

pKa2 = logKpn-1

pKa3 = logKpn-2

pKa4 = logKpn-3

pKa5 = logKpn-4

pKa6 = logKpn-5

Z2

Gutz: The pKas shown here are copied automatically from the Database by changing K2 to Q2. See U5 to understand why pKa1 = -logKpn

Z5

Gutz: See R5 to understand the conversion of pKa in logKp

5. Click on "Trust Center Settings"6. Click on "Disable macros with notification"7. Click OK and OK again

8. Open (or close and reopen) the CurTiPot file9. Click on "Options..." button located by "Security Warning"10. Select "Enable this content" option. 11. Click OK. You'll be trasfered to the form.

To enable macros in MS Excel 97-2003: 1. Open Excel 2. Go to "Tools "3. Select "Macro "4. Select "Security "5. Select "Security level"6. Select "Medium "7. Load (or exit and reload) curtipot_i.xls8. When reopen, select Enable Macros

Click on J2 to use these pKas in the pH calculation

EDTA Hydroxide ion Ammonia Carbonic acid

-4 -1 0 -2

0.000 15.745 9.244 6.352

1.500 10.329

2.000

2.680

6.110

10.170

25.0 25.0 25.0 25.0

0.100 0.000 0.000 0.000

How to enable the macro-instructions in Excel


and are fully removed by closing the file.




7. Open (or close and reopen) the CurTiPot file8. When the "Security warning" shows up, click on it to enable content

2. Excel 2007: Click the Office Button (top left corner of screen)3. Click on "Options" (2010; bottom left; 2007: bottom rigth pop-up)


8. Open (or close and reopen) the CurTiPot file9. Click on "Options..." button located by "Security Warning"10. Select "Enable this content" option. 11. Click OK. You'll be trasfered to the form.

To enable macros in MS Excel 97-2003:

7. Load (or exit and reload) curtipot_i.xls

Virtual Titrator – Simulation of curves

Boric acid Acetic acid Ammonia HCl

[B]

[HB]

0.05

0 0.05 0 0 0 0

0 0.15 0 0 0 0

Titrant Strong ACID Strong BASE Carbonic ac.

[B] 0.1 Titrand Water

[HB] Dispensed addedSS 20 0

0 0.1 0 1.00E-01 Titrant max.

0 0 0 0.00E+00 50.00 50

initial "pH" 1.806

Data ID on curves

Copying curves

Resizing axis

Other graphics

Data analysis

Vadd "pH" Vadd "pH" [H] CHtot = Dil. factor

Titrand (sample) and titrant (standard) composition (concentrations in mol/L)

TitrandSpecies

Phosphoric acid

L-Glutamic acid

[H2B]

[H3B]

[H4B]

[H5B]

[H6B]

S[HiB]

S[H]

Volumes of titrand and titrant (in mL)

[H2B]

S[HiB] Nº of titrant additions

S[H]

0.0 10.0 20.0 30.0 40.0 50.0 60.00.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0 Titrations of hydrochloric, phosphoric and glutamic acids (20 mL, 0.05 mol/L, with 0.1 mol/L NaOH)

Volume of titrant (mL)

pH

G1

"Hands on" the "VIRTUAL TITRATOR": - Click on the button "Clear ret(ained) curves" (cell A32) - all but the last simulated curve will disappear; If the button does not work, you must enable macros first, following instructions at cell A22 of molule pH_calc; - click on the button "Titrate with constant volume additions" (A28) - the default tiration of 20 mL of 0.07 mol/L H3PO4 with 0.1 mol/L NaOH will be generated with 50 additions of 1 ml of titrant; - click on "Titrate with constant pH increments" (A24) - notice the difference in data distribution; - click on "Retain curve" (A30); - change the H3PO4 concentration in (C7), press Enter; - titrate again and retain the curve; - change pKa2 (cell M6) from 7.2 to 9.2 (Enter) and titrate; If you haven't learned what acid-base dissociation constants are, or whatfor acids are titrated, perhaps you should go through a simple tutorial first, e.g., a flash animated one: http://www2.wwnorton.com/college/chemistry/gilbert/tutorials/ch16.htm - click on K2 or L2, select another acid; click on J2; ... - observe the effect of CO2 absorption by NaOH solution by writing 0.001 in D16; - add other components to the mixture and titrate; - add random experimental error to the curve fillng values in cells J17 and J18 (e.g., 0.03 and 0.1); - titrate a phosphate buffer of Na2HPO4 + NaH2PO4 with strong base, retain the curve and titrate it with strong acid; - user your creativity... Remark: This version of the CurTiPot's Virtual Titrator calculates "pH" or p[H] (=-log of the concentration of H+) instead of pH (=-log activity of H+), because it does not (yet) correct for the effect of ionic strength, I, on activity coefficients, taken as unity (see cell A20 or the pH_calc module for more information). This does not however change the volume of titrant spent to reach the inflections, nor does it modify the general shape of the curves. Refer to the pH_calc module to calculate the pH of any solution with estimated activity coefficents. Use the apparent pKas for a given I, computed in pH_calc pasted in cells K3 to Q10 of Simulation to obtain titration curves with pH values closer to reality. Copyright: This acid-base titration curve simulator is an expanded Excel version of the original Turbo Basic for DOS program CURTIPOT launched by the Author in 1992. Prof. Dr. Ivano G. R. Gutz www2.iq.usp.br/docente/gutz

A3

Gutz: The titrand is the sample to be evaluated by titration with a strong acid or strong base. Tipically, 5 to 25 mL of titrand (cell F16) are carefully measured and placed in a beaker, a combined glass electrode (connected to a pH meter) and a magnetic stirrer bar are introduced and water is added till the electrode is covered (cell G16). Titration is carried out by adding small aliquots of titrant (usually with a buret or motor driven syringe) and registering the pH afterstabilization of the reading.

B3

Gutz: See comment in cell M1 on how to change acids ans bases.

A4

Gutz: Leave blank/fill out with the concentration (mol/L) of fully deprotonated base (of a conjugated acid) to be considered in the simulation, e.g.: [Na2CO3], [Na3PO4], [NH4OH], [pyridine] or [Na4EDTA]

A5

Gutz: Leave blank/fill out with the concentration (mol/L) of monoprotonated base (or acid, HB) to be considered in the simulation, e.g.: [Acetic acid], [NH4+], [pyridonium], [NaHCO3] or [Na2HPO4]

A6

Gutz: Leave blank/fill out with the concentration (mol/L) of biprotonated base (H2B) to be considered in the simulation, e.g.: [H2CO3], [H2Na2EDTA] or [NaH2PO4]

A7

Gutz:d Leave blank/fill out with the concentration (mol/L) of triprotonated base (H3B) to be considered in the simulation, e.g.: [H3PO4]

A11

Gutz: Sum of concentrations of all forms of base B introduced in the titrand (e.g., [HB] + [H2B] + [H3B])

B11


A12

Gutz: Maximum H+ concentration available from full deprotonation of all forms of HiB used in the formulation of the titrand (e.g., [HB] + 2[H2B] + 3[H3B])

D13

Gutz: CO2 é absorvido por qualquer titulante ou titulado exposto ao ar; em soluções alcalinas, ocorre acumulação na forma de carbonato; daí ser importante simular o efeito da sua interferência, seja no titulante, seja no titulado, ou em ambos.

B14

Gutz: Leave blank - this cell corresponds to the conjugated base of the acid, e.g., Cl- or NO3-.

C14

Gutz: Leave blank/fill with de concentration of strong monoprotonable base used as titrant e.g., NaOH, KOH (or twice the concentration of Ca(OH)2)

D14

Gutz: Leave blank/fill out with de concentration of carbonate used as titrant To simulate the absorption of CO2 in an alkaline titrant, leave blank and fill cell D16

B15

Gutz: Leave blank/fill with de concentration of strong monoprotic acid used as titrant e.g., HCl. For weak or diprotic acids like H2SO4 change charge and pKas first, at cells R4 to R6.

C15

Gutz: Leave blank - as a rule, this cell corresponds to the protonated of OH- , H2O2, handled as solvent. However, if a different acid/base is system is specified in column S, [HB] may be required.

D15

Gutz: Leave blank/fill out with de concentration of bicarbonate, if used as titrant. To simulate the absorption of CO2 from the air by an alkaline titrant, leave blank and fill H2CO3 (cell D16)

B16

Gutz: Leave blank Fill out just in case you have replaced the base, its charge and pKas in cells S4 to S6.

C16

Gutz: Leave blank Fill out just in case you have replaced the base, its charge and pKas in cells S4 to S6.

D16

Gutz: Leave blank/fill out to simulate the absorption of CO2 by an alkaline titrant (effect visible on the curve for 1% or more of [H2CO3] relative to the titrant concentration)

F16

Gutz: Volume of the aliquot of titrand (with the composition given above) to be titrated

G16

Gutz: Water is frequently added to the sample until the glass electrode bulb and reference electrode junction are covered by the solution. The (undesirable) effect of dillution on the simulated curve may be best appreciated by exagerating this volume, retaining the curve and repeating the titration without added water.

A17

Gutz: Sum of concentrations of all forms of base B introduced in the titrand (e.g., [HB] + [H2B] + [H3B])

A18

Gutz: Maximum H+ concentration available from full deprotonation of all forms of HiB used in the formulation of the titrand (e.g., [HB] + 2[H2B] + 3[H3B])

F18

Gutz: Maximum volume of titrant to be added up to the end of the titration (may be less or equal to the capacity of the buret ).

G18

Gutz: Total number of additions of the titrant from the buret (max.: 120; typical: 30 or 50). You can choose constant volume additions (A24) or constant pH increment (A27).

A20

Gutz: Click on button at A22 to calculate the "pH" of the starting solution, before addition of any titrant (but after dillution, if G16 not zero). Refer to the spreadsheet pH_calc to calculate the pH (instead of "pH") of the same solution and for distiction between pH, p[H] and "pH". These values depart increasingly as the electrolyte concentration (more precisely, the ionic strenght) of a solution increases, due to ion-ion interactions. pH = -log aH+ where aH+ is the proton activity (concentration x activity coefficient) This Simulation module calculates p[H], when pK'as (apparent constants at the I of the solution) are provided, or "pH" when thermodynamic constants (from the Database) are used instead. p[H] = -log [H+] , where [H+] is the hydrated proton concentration, in mol/L.

B34

Gutz: Hover the mouse on a curve and point any data point to readout its ID and coordinates. To add labels to your graphics, activate the drawing tools of Excel and insert text boxes.

B35

Gutz: To copy graphics with simulated curves and paste them into other documents (e.g.: Word or Excel without links to the original: - Fill out the header of the figure (optional) - Click in the box of the figure near the margins, to select it - Repeat the last simulation of a curve - Press Ctrl+C and wait for processing - Switch to the Word document - Select Insert/Paste Special/Picture (enhanced metafile)

B36

Gutz: Click twice on the volume or pH scale to redifine it. Use Ctrl+Z (as many times as needed) to undo scale expansion

B37

Gutz: - Use the Graphics spreadsheet to plot derivatives by the DpH/DV aproximation and to overlay curves. - Use Evaluation to generate first and second derivative curves with interpolation and smoothig and to accurately locate inflection points of real and simulated titration curves. - Use Distribution to obtain de fractional composition and the mean protonation level of the bases during the titration as well as in function of pH.

B38

Gutz: - Use Evaluation to accurately evaluate well defined inflection points on real and simulated titration curves, assisted by cubic splines smoothing and interpolation - Use Regression to refine the concentrations of analytes and/or pK values of real or simulated titration curves by nonlinear multiparametric regression and to analyse complex curves, with hidden inflections (some learning required) Data transfer from Simulation to Evaluation or Regression: - Copy data of columns A and B from line 41 on - When evaluating the effect of dispersion (simulation of experimental errors), copy columns A and D instead (select column A, press Ctrl and select column D)

A39

Gutz: Data transfer from Simulation to Evaluation or Regression: - Copy data of columns A and B from line 41 on - When evaluating the effect of dispersion (simulation of experimental errors), copy columns A and D instead (select column A, press Ctrl and select column D) - Paste data in columns A and B of the destination spreadsheet

B39

Gutz: CurTiPot's Virtual Titrator does not (yet) correct for the effect of ionic strength, I, on activity coefficients, taken as unity. Therefore, the "pH" is closer to =-log of the concentration of H+ than to=-log activity of H+. This does not change the volume of the inflections, nor the general shape of the curves although a slight vertical shift of some regions of the curve is expected. The apparent pKas and pKw for a given I can be computed in pH_Calc and pasted here in cells K3 to Q10 of this spreadsheet to correct this limitationand obtain obtain p[H]. Refer to the pH_Calc module to calculate the pH and activity coefficents of any aqueous solution and to Regression to analyse data taking activity coefficients in account.

C39

Gutz: Do NOT use this column for Evaluation or Regression. Values displayed to ilustrate the simulated dispersion in the volume dispensing by the "buret". This column will remain blank when null dispersion is choosen in J17 and J18.

D39

Gutz: These pH values with dispersion will be overlayed in the graphic This column will remain blank when null dispersion is choosen in J17 and J18

E39

Gutz: Free hydrated proton concentration (or activity)

F39

Gutz: Total concentration of H+ required to satisfy all protonation equilibria, using the general equation, the concentration s of line 11 and the pKas given or under refinement.

G39

Gutz: Dilution factor of the titrant when added to the sample (+water). For example, when the added titrant equals the volume of sample (+water), the factor is 0.5

(mL) simulated CHcalc

0.000 1.806 1.563E-02 1.500E-01 1.000E+002.157 2.020 9.540E-03 1.354E-01 9.026E-014.096 2.235 5.822E-03 1.245E-01 8.300E-015.754 2.449 3.553E-03 1.165E-01 7.766E-017.077 2.664 2.168E-03 1.108E-01 7.386E-018.061 2.878 1.323E-03 1.069E-01 7.127E-018.749 3.093 8.073E-04 1.044E-01 6.957E-019.210 3.307 4.927E-04 1.027E-01 6.847E-019.508 3.522 3.006E-04 1.017E-01 6.778E-019.697 3.736 1.835E-04 1.010E-01 6.735E-019.817 3.951 1.120E-04 1.006E-01 6.708E-019.894 4.165 6.832E-05 1.004E-01 6.690E-019.944 4.380 4.169E-05 1.002E-01 6.679E-019.982 4.594 2.544E-05 1.001E-01 6.671E-01

10.014 4.809 1.552E-05 9.995E-02 6.664E-0110.050 5.023 9.474E-06 9.983E-02 6.656E-0110.098 5.238 5.781E-06 9.967E-02 6.645E-0110.170 5.452 3.528E-06 9.944E-02 6.629E-0110.282 5.667 2.153E-06 9.907E-02 6.605E-0110.457 5.881 1.314E-06 9.850E-02 6.567E-0110.730 6.096 8.017E-07 9.763E-02 6.508E-0111.144 6.310 4.892E-07 9.633E-02 6.422E-0111.748 6.525 2.985E-07 9.450E-02 6.300E-0112.577 6.739 1.822E-07 9.209E-02 6.139E-0113.626 6.954 1.112E-07 8.922E-02 5.948E-0114.824 7.168 6.784E-08 8.615E-02 5.743E-0116.044 7.383 4.140E-08 8.323E-02 5.549E-0117.146 7.598 2.526E-08 8.076E-02 5.384E-0118.041 7.812 1.542E-08 7.886E-02 5.258E-0118.706 8.027 9.408E-09 7.751E-02 5.167E-0119.169 8.241 5.741E-09 7.659E-02 5.106E-0119.478 8.456 3.503E-09 7.599E-02 5.066E-0119.677 8.670 2.138E-09 7.561E-02 5.041E-0119.804 8.885 1.305E-09 7.537E-02 5.025E-0119.886 9.099 7.961E-10 7.521E-02 5.014E-0119.941 9.314 4.858E-10 7.511E-02 5.007E-0119.982 9.528 2.965E-10 7.503E-02 5.002E-0120.018 9.743 1.809E-10 7.497E-02 4.998E-0120.059 9.957 1.104E-10 7.489E-02 4.993E-0120.115 10.172 6.737E-11 7.478E-02 4.986E-0120.200 10.386 4.111E-11 7.463E-02 4.975E-0120.333 10.601 2.509E-11 7.438E-02 4.959E-0120.548 10.815 1.531E-11 7.399E-02 4.932E-0120.896 11.030 9.342E-12 7.336E-02 4.890E-0121.459 11.244 5.701E-12 7.236E-02 4.824E-0122.365 11.459 3.479E-12 7.081E-02 4.721E-0123.818 11.673 2.123E-12 6.846E-02 4.564E-0126.155 11.888 1.296E-12 6.500E-02 4.333E-0129.983 12.102 7.906E-13 6.002E-02 4.001E-0136.644 12.317 4.824E-13 5.296E-02 3.531E-0150.000 12.531 2.944E-13 4.286E-02 2.857E-01

with "error" (do not use)

simulated with "error"

Titrand (sample)

<--- read instructions

41 8 98

Acid / Base Boric acid Phosphoric acid L-Glutamic acid

Charge of B -3 -3 -1

9.236 2.148 2.230

12.740 7.199 4.420

13.800 12.350 9.950

SS

0 5.000E-02 pKw 13.997

0 1.500E-01

Remark: curves are simulated considering unit activity coefficients for all species (read remark in A20)

Sum

(initial vol.)

20.00 Titration speed

S pH= 0.000 Slower 0S Vol= 0.000 Faster delay (s)

Dil. Factor h1 h2 h3 h4 h5


Carbonic acid

pKa1

pKa2

pKa3

pKa4

pKa5

pKa6

of titrand and titrant (in mL)

Dispersion simulation

Nº of titrant additions

0.0 10.0 20.0 30.0 40.0 50.0 60.00.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0 Titrations of hydrochloric, phosphoric and glutamic acids (20 mL, 0.05 mol/L, with 0.1 mol/L NaOH)

Volume of titrant (mL)

pH

M1

Gutz: Selecting/editing names, charges ans pKas. Options: a) Write directly in the cells K3 to Q10 and R3 to T6; b) Click on names in line 2, slide along the list, click on another name; finally, click on J2 to load the constants from the Database. Frequently used acids missing in the Database should be added to it.

J4


J5


J6


I11

Gutz: Total concentration of each base (regardless of the protonation level of the added component) in columns B to H; grand total in column I.

J11

Gutz: The ionic dissociation product of water changes with temperature and ionic strength, I. For pure water at 25ºC, the accepted value is 13.997 (or 14.00). Values corrected for I can be calculated with module pH_calc.

I12

Gutz: Maximum concentration of H+ that could possibly be dissociated from all the components added to the solution.

H16

Gutz: Total volume before titration (F16+G16)

J17

Gutz: Optional simulation of random errors in pH measurements, specified as standard deviation of the residues along the complete curve, e.g., 0.03

L17

Gutz: Keep delay = 0 for titration at maximum speed (dictated by the computer performance) Choose delay > 0 to pause between additions of titrant, resembling the time required to wait for pH measurements to sabilize in a real titrations. Press Escape during a titration to ignore the delay, proceeding at max. speed.

J18

Gutz: Optional simulation of random errors in volume measurements (buret meniscus reading), specified as standard deviation of the residues along the complete curve, e.g., 0.05

H39

Gutz: Dilution factor of the sample by optional addition of water (at the beginning) and addition of titrant during the experiment

I39

Gutz: Mean proton number, h, associated with a base B at given pH. Consider HiB as partially dissociated at a given pH; h is the sum of the molar fraction times i of each species.

Boric acid Phosphoric acid L-Glutamic acid Acetic acid Ammonia

0.000E+00 2.68739.735E-02 2.57291.700E-01 2.45012.234E-01 2.33312.614E-01 2.23362.873E-01 2.15683.043E-01 2.10193.153E-01 2.06473.222E-01 2.04033.265E-01 2.02483.292E-01 2.01493.310E-01 2.00863.321E-01 2.00433.329E-01 2.00113.336E-01 1.99813.344E-01 1.99473.355E-01 1.99003.371E-01 1.98293.395E-01 1.97183.433E-01 1.95433.492E-01 1.92703.578E-01 1.88563.700E-01 1.82523.861E-01 1.74234.052E-01 1.63744.257E-01 1.51764.451E-01 1.39564.616E-01 1.28544.742E-01 1.19604.833E-01 1.12954.894E-01 1.08314.934E-01 1.05244.959E-01 1.03254.975E-01 1.01994.986E-01 1.01194.993E-01 1.00674.998E-01 1.00325.002E-01 1.00045.007E-01 0.99775.014E-01 0.99455.025E-01 0.98995.041E-01 0.98295.068E-01 0.97195.110E-01 0.95455.176E-01 0.92745.279E-01 0.88635.436E-01 0.82625.667E-01 0.74365.999E-01 0.63906.469E-01 0.51927.143E-01 0.3973

Titrant (buret)

Click on K2 to Q2; select acids/bases; click on J2; read M1

1 2 6 3

Acetic acid Ammonia HCl Carbonic acid Strong ACID

-1 0 -1 -2 -1

4.757 9.244 -7.000 6.352 -6

10.329

Remark: curves are simulated considering unit activity coefficients for all species (read remark in A20)

Color coding




h6 h7 h1 titrant h2 titrant h3 titrant

R3

Gutz: Strong acids like HCl ou HClO4 have negative pKas, possibly -6 or lower. For a diprotic titrant like H2SO4, use pKa1 = -6 e pKa2 = 1,8. Do not specify systems with more than 2 pKas here.

HCl Carbonic acidStrong ACID Strong BASE Carbonic ac.

1.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99990.99990.99980.99960.9994

Titrant Titrand

Strong BASE Carbonic ac. Acid / Base Boric acid

-1 -2 Charge of B -3 -3 -1

15.745 6.352 6.310E+13 2.239E+12 8.913E+09

10.329 3.467E+26 3.540E+19 2.344E+14

5.970E+35 4.977E+21 3.981E+16

Kw 1.007E-14

Overall protonation constants = bp = SKp (calculated by the program)

Phosphoric acid

L-Glutamic acid

bp1

bp2

bp3

bp4

bp5

bp6

S2

Gutz: The titrant may contain up to three diprotic reagents (other than the default ones). Names and constants must be changed manually.

S3

Gutz: The accepted value of the pKa (=log Kp) of the strong base OH- is 15,745 at 25ºC and infinite dilution. As I increases, the activity coefficient of OH- decreases (as can be checked with module pH_calc), and more specific interaction can occur with cations, so that lower values are sometimes mentioned in the literature (see references in the Database for details). Any other mono or biprotonable acid or base can be used instead of OH-

T3

Gutz: Aqueous solutions exposed to air or stored in (gas permeable) plastic flasks are always contaminated with CO2. Thus, it is advisable to include the carbonic acid system in simulations and regressions. But any othe mono- or biprotic system can be specified here. The pKa1 from the Database for for H2CO3 is apparent. By considering the fraction of dissolved CO2 converted in H2CO3 (most of it remains as CO2(aq)) a "true" pKa1 of 3.58 is found.

U5

Gutz: The betas are cumulative (or global) protonation constants, obtained by multiplying the protonation constants Kp from 1 to i, with i stepping up to n, the maximum number of protons accepted by a (conjugated) base (same as the maximum number os dissociable protons of an acid, but in reversed order). Note that pKa = logKp for a monoprotic acid (because Kp = 1/Kd or pKd = 1/logKd ) and, for multiprotic systems, the first logKp is the last pKa. Protonation constants, Kp, and betas are preferred here in agreement with the most extensive compilations of equilibrium constants, e.g., Critical Stability Constants, Vol. 1–4 (complete references in the Database), and because the equations become unified with those used for metal-ligand-proton equilibria, based on formation (instead of dissociation) constants.

pKa(n) = -log Kd(HB-->B) = log Kp(1)

Titrant

Acetic acid Ammonia HCl Carbonic acid Strong ACID Strong BASE

-1 0 -1 -2 -1 -1

5.715E+04 1.754E+09 1.000E-07 2.133E+10 1.000E-06 5.559E+15

4.797E+16

p = SKp (calculated by the program)

Click on J2 to use these pKas in the Simulation

Carbonic ac. Acid / Base Boric acid Acetic acid

-2 Charge of B -3 -3 -1 -1

2.133E+10 9.236 2.148 2.230 4.757

4.797E+16 12.740 7.199 4.420

13.800 12.350 9.950


Titrand

Phosphoric acid

L-Glutamic acid

pKa1 = logKpn

pKa2 = logKpn-1

pKa3 = logKpn-2

pKa4 = logKpn-3

pKa5 = logKpn-4

pKa6 = logKpn-5

AF2


AF5

Gutz: See U5 to understand why pKa1 = logKpn

Click on J2 to use these pKas in the Simulation

Ammonia HCl Carbonic acid

0 -1 -2

9.244 -7.000 6.352

10.329

Curvas anteriores retidas

Vol

1

03.1648025.5508217.2044498.2847328.9634679.379517

9.63079.7809579.8703479.9233519.9547199.9732629.9842159.9906839.9945019.9967559.998085

9.998879.9993349.9996099.999772

9.999879.99993

9.99997110

10.0000410.0000810.0001510.0002610.0004510.0007610.0012910.0021910.0037110.0062810.0106510.01805

10.030610.0518810.0880210.1494610.25414

10.433210.7415111.2784812.23258

13.989617.44934

25.257550

Curvas anteriores retidas

pH Vol pH Vol pH Vol pH Vol pH

1 2 2 3 3 4 4 5 5

1.30103 0 1.838538 0 1.301031.530077 2.049407 2.050888 3.165531 1.5301371.759125 3.938869 2.263239 5.551868 1.7592451.988172 5.618284 2.475589 7.205499 1.988352

2.21722 7.032329 2.687939 8.285625 2.217462.446267 8.170884 2.900289 8.964158 2.4465672.675315 9.08299 3.112639 9.380021 2.6756752.904362 9.858687 3.32499 9.631052 2.904782

3.13341 10.60375 3.53734 9.781198 3.133893.362457 11.41871 3.74969 9.870507 3.3629973.591505 12.37769 3.96204 9.923457 3.5921053.820552 13.50223 4.174391 9.954788 3.821212

4.0496 14.74101 4.386741 9.973306 4.050324.278647 15.98032 4.599091 9.984243 4.2794274.507695 17.09362 4.811441 9.990701 4.5085354.736742 17.99712 5.023791 9.994512 4.737642

4.96579 18.67074 5.236142 9.996762 4.966755.194837 19.14162 5.448492 9.99809 5.1958575.423885 19.45613 5.660842 9.998873 5.4249655.652932 19.65993 5.873192 9.999336 5.654072

5.88198 19.78955 6.085542 9.99961 5.883186.111027 19.87128 6.297893 9.999772 6.1122876.340075 19.92293 6.510243 9.99987 6.3413956.569122 19.95629 6.722593 9.999931 6.570502

6.79817 19.97918 6.934943 9.999971 6.799617.027217 19.99705 7.147293 10 7.0287177.256265 20.01421 7.359644 10.00004 7.2578257.485312 20.0348 7.571994 10.00008 7.486932

7.71436 20.06374 7.784344 10.00015 7.716047.943407 20.10787 7.996694 10.00026 7.9451478.172455 20.17736 8.209045 10.00045 8.1742558.401502 20.28762 8.421395 10.00076 8.403362

8.63055 20.46167 8.633745 10.00129 8.632478.859597 20.73226 8.846095 10.00218 8.8615779.088645 21.1421 9.058445 10.0037 9.0906859.317692 21.7385 9.270796 10.00627 9.319792

9.54674 22.55746 9.483146 10.01063 9.54899.775787 23.59709 9.695496 10.01802 9.77800710.00483 24.79377 9.907846 10.03054 10.0071110.23388 26.02813 10.1202 10.0518 10.2362210.46293 27.17152 10.33255 10.0879 10.4653310.69198 28.14247 10.5449 10.14927 10.6944410.92102 28.93161 10.75725 10.25386 10.9235411.15007 29.59039 10.9696 10.43277 11.1526511.37912 30.21046 11.18195 10.74088 11.3817611.60817 30.91664 11.3943 11.27756 11.6108711.83721 31.88401 11.60665 12.23125 11.8399712.06626 33.38986 11.819 13.98773 12.0690812.29531 35.93712 12.03135 17.44677 12.2981912.52436 40.57981 12.2437 25.25432 12.5273

12.7534 50 12.45605 50 12.7564

Vol pH Vol pH Vol pH Vol pH Vol

6 6 7 7 8 8 9 9 10

pH Vol pH Vol pH Vol pH

10 11 11 12 12 13 13

Distribution Diagrams, Buffer Capacity and Protonation Curves

Acid/base system Overall protonation constants

8 for the pKas

2.148

of the acid/base system 7.199

Phosphoric acid 12.350

a) as a function of pH and b) overlaid on

1

Buffer Capacity to be plotted for Charge of B -3 Protonations

concentration (mol/L) 1.000000 pKw 13.997

pKa1 = logKpn b1

pKa2 = logKpn-1 b2

pKa3 = logKpn-2 b3

pKa4 = logKpn-3 b4

pKa5 = logKpn-4 b5

pKa6 = logKpn-5 b6

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.00.00

0.20

0.40

0.60

0.80

1.00Distribution of HiB species

pH

ai

<— aHiB aB—>

<— aHiB aB—>

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8Buffer capacity

pH

bu

ffer cap

acity

E2

Gutz: Options for selecting pKas: a) Click on control D3, slide along the list, click on a name; the pKas will be loaded from the Database; finally, click on B3 to plot the curves; b) Write the pKas of any real or hypothetical system in line 10 of the Database (or at the end of the list); return to Distribution and proceed as before (option a). Frequently used systems can be added definitively to the Database and saved as an updated curtipot_.xls file.

E4

Gutz: Do not write here! Click on D3 to select an acid or base. To try other real or hypothetical systems, write their pKas in line 10 of the Database (or at the end of the list); return to Distribution and proceed as before.

F4

Gutz: The betas are cumulative (or global) protonation constants, obtained by multiplying the protonation constants Kp from 1 to i, with i stepping up from 1 to n (the maximum number of protons accepted by a (conjugated) base, same as the maximum number os dissociable protons of an acid, but in reversed order). Note that pKa = logKp for a monoprotic acid (because Kp = 1/Kd or pKd = 1/logKd ) and, for multiprotic systems, the first logKp is the last pKa.

B10

Gutz: Buffer Capacity = Buffer Strength x ln(10) The Buffer Capacity, BC, (or Buffer Index) can be understood as the concentration of strong acid or base that, when added to the solution under consideration, would shift the pH by one unit, in a hypothetical pH region of constant BC. Since the BF changes (sometimes, rapidly) with pH (as shown in Figures 3, 4, 7 and 8), estimates of the resistance against acid or base addition are reasonably accurate only for DpH up to 0.1. See an example of BC in comment of cell N37. Use the pH_calc module to work out more examples (read also cell E27). Detailed explanation and references, see, e.g., the open access article: Understanding, Deriving, and Computing Buffer Capacity, by Edward T. Urbansky and Michael R. Schock, Journal of Chemical Education, 2000, Vol. 77, 1640-44, http://pubs.acs.org/doi/pdf/10.1021/ed077p1640.

D10


0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.00.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5Average protonation (hm) of the base B

pH

av

era

ge

pro

ton

ati

on

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0-8.0

-7.0

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0


pH

log

ai

<— aHiB aB—>

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8Buffer capacity

pH

bu

ffer cap

acity

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

log buffer capacity

pH

lo

g b

uffer cap

acity

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.00.0

0.5

1.0

1.5

2.0

2.5

3.0


pH

av

era

ge

pro

ton

ati

on

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0Mean charge (zm) of species HiB

pH

ch

arg

e

Distribution Diagrams, Buffer Capacity and Protonation Curves <--- read comment

Overall protonation constants Color coding of species in all graphics Warning:

All curves and the isoelectric point

2.239E+12 are estimated disregarding ionic

3.540E+19 strength effects. To refine values,

4.977E+21 point by point, use pH_calc.

Data ID on curves

How to copy/paste a curve

How to change the axis of a curve

3

No Isoelectrc Point in the pH range 0 e 14

bp a B

a HB

a H2B

a H3B

a H4B

a H5B

a H6B

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.00.00

0.20

0.40

0.60

0.80


pH

ai

<— aHiB aB—>

<— aHiB aB—>

0.0 10.0 20.0 30.0 40.0 50.0 60.00.00

0.20

0.40

0.60

0.80

1.00

Distribution of HiB species along a titration

Volume (mL)

ai

pH

7

14

0

<— aHiB aB—>

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8Buffer capacity

pH

bu

ffer cap

acity

0.0 10.0 20.0 30.0 40.0 50.0 60.00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8Buffer capacity alonga a titration

Volume (mL)

bu

ffe

r c

ap

ac

ity

14

0

pH

7

G1

Gutz: This module generates not only Distribution Diagrams, Buffer Capacity (defined in cell B10) and Protonation Curves as a function of pH (as usual) for any acid-base system but also overlays them on titration curves, to unravel the dynamic of species equilibria and their effect along a titration. This is valid for acids and bases effectively present in a titration (real or virtual). It also serves to observe or select indicators by following the transition of differently colored species near a stoichiometric point. Distribution will not run properly until you enable macros, following instructions at cell A22 of module pH_calc. Remark: curves are computed considering unit activity coefficients for all species and disregarding ionic strength effecs, valid only for very diluted solutions (see pH_calc for corrections). The distribution diagrams (or alpha plots) of acids and bases reveal the molar fraction of each species in equilibrium at any pH of the solution. For example, phosphoric acid / phosphate system at pH 7.0: a0 = 0.00 or 0% of phospahte; log a0 = -5.76 a1 = 0.387 or 38.7% of hydrogen phosphate; log a1 = -0,412 a2 = 0.613 or 61.3% of dihydrogen phosphate; log a2 = -0,213 a3 = 0.00 or 0% of phosphoric acid; log a3 = -5.07 Since the index i of ai is the numbe or protons bound to the base, we have H2PO4– as dominant species, with 61.3%, followed by HPO4= with 38.7%, while only 0.0002% of phosphate and 0.0009% of H3PO4 coexist at this pH; the average number of protons bond to each phosphate at this pH is 1.61, as shown in column P. All numerical values of the graphs are available in columns O to BG.

G4


J7

Gutz: Hover the mouse on a curve and point any data point to readout its ID and coordinates.

J8

Gutz: To copy graphics with one or more curves and paste them into other documents (e.g.: Word or Excel) without links to the original: - Fill out the header of the graphic; - Click in the box of the graphic near the margins, to select it; - Repeat the generation of at least one curve; - Press Ctrl+C and wait processing; - Switch to the Word (Excel) document; - Select Insert/Paste Special/Picture (enhanced metafile).

J9

Gutz: Click twice on the volume or pH scale to redifine it. Use Ctrl+Z (as many times as needed) to undo scale expansion.

H11

Gutz: The isoelectric point (pI) corresponds to the pH value where polyfunctional species (zwitterions) like amino acids, in average, present no unbalance of positive and negative charges in the molecules, so that the mean charge, zm = 0. Complete curves of mean charge versus pH or titrant volume are generated at the end of this page using the equation zm = z + hm where z is the charge of the base B (cell E10) and hm is the mean number of protons bound to the base, as shown in figures 9 and 10. For non-switterionic species, the program indicates the pH range where 99,9% or more of a acid / base are in a neutral form, e.g, [OH-] at pH less than 11,6, where H2O largely predominates.

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.00.0

0.5

1.0

1.5

2.0

2.5

3.0


pH

av

era

ge

pro

ton

ati

on

0.0 10.0 20.0 30.0 40.0 50.0 60.00.0

0.5

1.0

1.5

2.0

2.5

3.0Average protonation (hm) of the base along a titration

Volume (mL)

av

era

ge

p

ro

to

na

tio

n

14

0

pH

7

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0-8.0

-7.0

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0


pH

log

ai

<— aHiB aB—>0.0 10.0 20.0 30.0 40.0 50.0 60.0

-8.0

-7.0

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0Distribution of HiB species along a titration

Volume (mL)

lo

g a

i

<— aHiB aB—> 14

0

pH

7

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8Buffer capacity

pH

bu

ffer cap

acity

0.0 10.0 20.0 30.0 40.0 50.0 60.00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7


Volume (mL)

bu

ffe

r c

ap

ac

ity

14

0

pH

7

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

log buffer capacity

pH

lo

g b

uffer cap

acity

0.0 10.0 20.0 30.0 40.0 50.0 60.0-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0log buffer capacity along a titration

Volume (mL)

lo

g b

uffe

r c

ap

ac

ity

14

0

pH

7

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.00.0

0.5

1.0

1.5

2.0

2.5

3.0


pH

av

era

ge

pro

ton

ati

on

0.0 10.0 20.0 30.0 40.0 50.0 60.00.0

0.5

1.0

1.5

2.0

2.5


Volume (mL)

av

era

ge

p

ro

to

na

tio

n

14

0

pH

7

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0Mean charge (zm) of species HiB

pH

ch

arg

e

0.0 10.0 20.0 30.0 40.0 50.0 60.0-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0Mean charge (zm)of species HiB along a titration

Volume (mL)

ch

arg

e

14

0

pH

7

Color coding




Molar fraction of each species as a funciton of pH

pH h0.000 2.9930.200 2.9890.400 2.9820.600 2.9720.800 2.9571.000 2.9341.200 2.8991.400 2.8481.600 2.7791.800 2.6902.000 2.5842.200 2.4702.400 2.3592.600 2.2612.800 2.1823.000 2.1233.200 2.0813.400 2.0533.600 2.0343.800 2.0214.000 2.0134.200 2.0084.400 2.0044.600 2.0014.800 1.9985.000 1.9955.200 1.9915.400 1.9855.600 1.9765.800 1.9626.000 1.9416.200 1.9096.400 1.8636.600 1.7996.800 1.7157.000 1.6137.200 1.4997.400 1.3867.600 1.284

0.0 10.0 20.0 30.0 40.0 50.0 60.00.00

0.20

0.40

0.60

0.80

1.00

Distribution of HiB species along a titration

Volume (mL)

ai

pH

7

14

0

<— aHiB aB—>

0.0 10.0 20.0 30.0 40.0 50.0 60.00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7


Volume (mL)

bu

ffe

r c

ap

ac

ity

14

0

pH

7

N37

Gutz: The Buffer Capacity, BC, (or Buffer Index) estimates the concentration os (strong) acid or sodium hydroxide to be added to a solution for a unit change in pH. The BC estimate is reasonably accurate for a 0.1 DpH or less, with growing errors above. For example, a buffer solution of pH 7.000 prepared with0.0395 mol/L NaH2PO4 and 0.061 mo/L Na2HPO4 presenta BF= 0.055213. i) Addition of a BF/10 concentrarion looking for DpH de 0.1: 0.00552 mol/L HCl addition displaces the computed pH to 6.904, close to the expected 6.900; a similar concentration of NaOH increase the pH to 7.101, practically 7,100. ii) Addition of the BF concentration aiming DpH de 1: For [HCl]=0.0552 mol/L added, pH=5.62 instead of 5.00; [NaOHl]=0.0552 mol/L raises the pH to 10.90. This happens because BF changes with pH (see Distribution) and there is more HPO42- than H2PO4- in the buffer).

7.800 1.2008.000 1.1368.200 1.0918.400 1.0598.600 1.0388.800 1.0249.000 1.0159.200 1.0099.400 1.0059.600 1.0029.800 1.000

10.000 0.99710.200 0.99410.400 0.99010.600 0.98310.800 0.97311.000 0.95711.200 0.93411.400 0.89911.600 0.84911.800 0.78012.000 0.69112.200 0.58612.400 0.47112.600 0.36012.800 0.26213.000 0.18313.200 0.12413.400 0.08213.600 0.05313.800 0.03414.000 0.022

0.0 10.0 20.0 30.0 40.0 50.0 60.00.0

0.5

1.0

1.5

2.0

2.5


Volume (mL)

av

era

ge

p

ro

to

na

tio

n

14

0

pH

7

0.0 10.0 20.0 30.0 40.0 50.0 60.0-8.0

-7.0

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0Distribution of HiB species along a titration

Volume (mL)

lo

g a

i

<— aHiB aB—> 14

0

pH

7

0.0 10.0 20.0 30.0 40.0 50.0 60.00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7


Volume (mL)

bu

ffe

r c

ap

ac

ity

14

0

pH

7

0.0 10.0 20.0 30.0 40.0 50.0 60.0-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0log buffer capacity along a titration

Volume (mL)

lo

g b

uffe

r c

ap

ac

ity

14

0

pH

7

N107

Gutz: hm or h, is the mean number of protons bound with a base B at given pH. For two or more HiB with different number of protons i coexisting at this pH; h is the sum of the molar fraction (cells in lines 44 to 60) times the i of each species.

0.0 10.0 20.0 30.0 40.0 50.0 60.00.0

0.5

1.0

1.5

2.0

2.5


Volume (mL)

av

era

ge

p

ro

to

na

tio

n

14

0

pH

7

0.0 10.0 20.0 30.0 40.0 50.0 60.0-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0Mean charge (zm)of species HiB along a titration

Volume (mL)

ch

arg

e

14

0

pH

7

N132

Gutz: The isoelectric point (Ip) of polyfunctional species (zwitterions) like amino acids is the pH where there is no unbalance of positive and negative charges in the molecules, so that the mean charge, zm = 0. Complete curves of mean charge versus pH or titrant volume are generated using the equation zm = z + hm where Z is the charge of the base B (cell E10) and hm is the mean number of protons bound to the base, as shown in figures 9 and 10. For non-switterionic species, the program indicates the pH range where 99,9% or more of a base is in a neutral form, e.g, [OH-] at pH less than 11,6, where H2O largely predominates.

Do not change or delete

Simulated titration curve

Titration curve under Evaluation

Titration curve under Regression

No titration curve

Molar fraction of each species as a funciton of pH Molar fraction of each species during titration

alpha 0 alpha 1 alpha 2 alpha 3 alpha 4 alpha 5 alpha 6 Buffer

B HB Capacity Vol pH0.000 0.000 0.007 0.993 2.319 0.000 1.8060.000 0.000 0.011 0.989 1.478 2.157 2.0200.000 0.000 0.018 0.982 0.956 4.096 2.2350.000 0.000 0.028 0.972 0.640 5.754 2.4490.000 0.000 0.043 0.957 0.460 7.077 2.6640.000 0.000 0.066 0.934 0.373 8.061 2.8780.000 0.000 0.101 0.899 0.355 8.749 3.0930.000 0.000 0.152 0.848 0.388 9.210 3.3070.000 0.000 0.221 0.779 0.454 9.508 3.5220.000 0.000 0.310 0.690 0.529 9.697 3.7360.000 0.000 0.416 0.584 0.582 9.817 3.9510.000 0.000 0.530 0.470 0.588 9.894 4.1650.000 0.000 0.641 0.359 0.539 9.944 4.3800.000 0.000 0.739 0.261 0.450 9.982 4.5940.000 0.000 0.818 0.182 0.347 10.014 4.8090.000 0.000 0.877 0.123 0.251 10.050 5.0230.000 0.000 0.918 0.081 0.174 10.098 5.2380.000 0.000 0.947 0.053 0.117 10.170 5.4520.000 0.000 0.966 0.034 0.077 10.282 5.6670.000 0.000 0.978 0.022 0.050 10.457 5.8810.000 0.001 0.986 0.014 0.033 10.730 6.0960.000 0.001 0.990 0.009 0.023 11.144 6.3100.000 0.002 0.993 0.006 0.016 11.748 6.5250.000 0.003 0.994 0.004 0.014 12.577 6.7390.000 0.004 0.994 0.002 0.014 13.626 6.9540.000 0.006 0.992 0.001 0.018 14.824 7.1680.000 0.010 0.989 0.001 0.025 16.044 7.3830.000 0.016 0.984 0.001 0.037 17.146 7.5980.000 0.025 0.975 0.000 0.056 18.041 7.8120.000 0.038 0.961 0.000 0.085 18.706 8.0270.000 0.059 0.940 0.000 0.129 19.169 8.2410.000 0.091 0.909 0.000 0.191 19.478 8.4560.000 0.137 0.863 0.000 0.273 19.677 8.6700.000 0.201 0.799 0.000 0.370 19.804 8.8850.000 0.285 0.715 0.000 0.469 19.886 9.0990.000 0.387 0.613 0.000 0.547 19.941 9.3140.000 0.501 0.499 0.000 0.576 19.982 9.5280.000 0.614 0.386 0.000 0.546 20.018 9.7430.000 0.716 0.284 0.000 0.469 20.059 9.957

Options of the A8 slider

H2B H3B H4B H5B H6B

X10

Gutz: The Buffer Capacity, BC, (or Buffer Index) estimates the concentration os (strong) acid or sodium hydroxide to be added to a solution for a unit change in pH. The BC estimate is reasonably accurate for a 0.1 DpH or less, with growing errors above. For example, a buffer solution of pH 7.000 prepared with0.0395 mol/L NaH2PO4 and 0.061 mo/L Na2HPO4 presenta BF= 0.055213. i) Addition of a BF/10 concentrarion looking for DpH de 0.1: 0.00552 mol/L HCl addition displaces the computed pH to 6.904, close to the expected 6.900; a similar concentration of NaOH increase the pH to 7.101, practically 7,100. ii) Addition of the BF concentration aiming DpH de 1: For [HCl]=0.0552 mol/L added, pH=5.62 instead of 5.00; [NaOHl]=0.0552 mol/L raises the pH to 10.90. This happens because BF changes with pH (see Distribution) and there is more HPO42- than H2PO4- in the buffer).

0.000 0.800 0.200 0.000 0.369 20.115 10.1720.000 0.863 0.137 0.000 0.272 20.200 10.3860.000 0.909 0.091 0.000 0.190 20.333 10.6010.000 0.941 0.059 0.000 0.129 20.548 10.8150.000 0.962 0.038 0.000 0.085 20.896 11.0300.000 0.975 0.024 0.000 0.056 21.459 11.2440.000 0.984 0.016 0.000 0.036 22.365 11.4590.001 0.989 0.010 0.000 0.024 23.818 11.6730.001 0.993 0.006 0.000 0.017 26.155 11.8880.002 0.994 0.004 0.000 0.013 29.983 12.1020.003 0.995 0.002 0.000 0.012 36.644 12.3170.004 0.994 0.002 0.000 0.014 50.000 12.5310.007 0.992 0.001 0.000 0.0190.011 0.988 0.001 0.000 0.0270.017 0.982 0.000 0.000 0.0410.027 0.972 0.000 0.000 0.0630.043 0.957 0.000 0.000 0.0970.066 0.934 0.000 0.000 0.1460.101 0.899 0.000 0.000 0.2150.151 0.849 0.000 0.000 0.3040.220 0.780 0.000 0.000 0.4100.309 0.691 0.000 0.000 0.5150.414 0.585 0.000 0.000 0.5960.529 0.471 0.000 0.000 0.6320.640 0.360 0.000 0.000 0.6230.738 0.262 0.000 0.000 0.5910.817 0.183 0.000 0.000 0.5760.876 0.124 0.000 0.000 0.6170.918 0.082 0.000 0.000 0.7550.947 0.053 0.000 0.000 1.0390.966 0.034 0.000 0.000 1.5390.978 0.022 0.000 0.000 2.368

Do not change or delete

Simulated titration curve

Titration curve under Evaluation

Titration curve under Regression

No titration curve

Molar fraction of each species during titration

alpha 0 alpha 1 alpha 2 alpha 3 alpha 4 alpha 5 alpha 6

h B HB2.687 0.000 0.000 0.313 0.6872.573 0.000 0.000 0.427 0.5732.450 0.000 0.000 0.550 0.4502.333 0.000 0.000 0.667 0.3332.234 0.000 0.000 0.766 0.2342.157 0.000 0.000 0.843 0.1572.102 0.000 0.000 0.898 0.1022.065 0.000 0.000 0.935 0.0652.040 0.000 0.000 0.959 0.0412.025 0.000 0.000 0.975 0.0252.015 0.000 0.001 0.984 0.0152.009 0.000 0.001 0.990 0.0102.004 0.000 0.002 0.993 0.0062.001 0.000 0.002 0.994 0.0041.998 0.000 0.004 0.994 0.0021.995 0.000 0.007 0.992 0.0011.990 0.000 0.011 0.988 0.0011.983 0.000 0.018 0.982 0.0001.972 0.000 0.029 0.971 0.0001.954 0.000 0.046 0.954 0.0001.927 0.000 0.073 0.927 0.0001.886 0.000 0.114 0.885 0.0001.825 0.000 0.175 0.825 0.0001.742 0.000 0.258 0.742 0.0001.637 0.000 0.363 0.637 0.0001.518 0.000 0.482 0.518 0.0001.396 0.000 0.604 0.396 0.0001.285 0.000 0.715 0.285 0.0001.196 0.000 0.804 0.196 0.0001.129 0.000 0.870 0.129 0.0001.083 0.000 0.917 0.083 0.0001.052 0.000 0.947 0.052 0.0001.032 0.000 0.967 0.033 0.0001.020 0.000 0.979 0.020 0.0001.012 0.001 0.987 0.012 0.0001.007 0.001 0.991 0.008 0.0001.003 0.001 0.994 0.005 0.0001.000 0.002 0.995 0.003 0.0000.998 0.004 0.994 0.002 0.000

Options of the A8 slider

H2B H3B H4B H5B H6B

0.994 0.007 0.992 0.001 0.0000.990 0.011 0.989 0.001 0.0000.983 0.017 0.982 0.000 0.0000.972 0.028 0.971 0.000 0.0000.955 0.046 0.954 0.000 0.0000.927 0.073 0.927 0.000 0.0000.886 0.114 0.886 0.000 0.0000.826 0.174 0.826 0.000 0.0000.744 0.256 0.744 0.000 0.0000.639 0.361 0.639 0.000 0.0000.519 0.481 0.519 0.000 0.0000.397 0.603 0.397 0.000 0.000

logarithm of molar fraction of each species as a funciton of pH

scaling scaling scaling Buffer log alpha 0 log alpha 1 log alpha 2 log alpha 3

pH/14 n*pH/8 n*pH/6 Capacity pH B HB0.129 0.387 0.103 0.531 0.000 -9.350 -2.151 -0.0030.144 0.433 0.115 0.585 0.200 -8.952 -1.953 -0.0050.160 0.479 0.128 0.583 0.400 -8.555 -1.756 -0.0080.175 0.525 0.140 0.520 0.600 -19.909 -8.159 -1.560 -0.0120.190 0.571 0.152 0.417 0.800 -19.316 -7.766 -1.367 -0.0190.206 0.617 0.164 0.308 1.000 -18.727 -7.377 -1.178 -0.0300.221 0.663 0.177 0.213 1.200 -18.143 -6.993 -0.994 -0.0460.236 0.709 0.189 0.141 1.400 -17.568 -6.618 -0.819 -0.0710.252 0.755 0.201 0.091 1.600 -17.005 -6.255 -0.656 -0.1080.267 0.801 0.214 0.058 1.800 -16.458 -5.908 -0.509 -0.1610.282 0.847 0.226 0.037 2.000 -15.930 -5.580 -0.381 -0.2330.298 0.893 0.238 0.024 2.200 -15.425 -5.275 -0.276 -0.3280.313 0.939 0.250 0.017 2.400 -14.942 -4.992 -0.193 -0.4450.328 0.985 0.263 0.014 2.600 -14.480 -4.730 -0.131 -0.5830.343 1.030 0.275 0.014 2.800 -14.036 -4.486 -0.087 -0.7390.359 1.076 0.287 0.018 3.000 -13.606 -4.256 -0.057 -0.9090.374 1.122 0.299 0.027 3.200 -13.186 -4.036 -0.037 -1.0890.389 1.168 0.312 0.041 3.400 -12.773 -3.823 -0.024 -1.2760.405 1.214 0.324 0.065 3.600 -12.364 -3.614 -0.015 -1.4670.420 1.260 0.336 0.101 3.800 -11.959 -3.409 -0.010 -1.6620.435 1.306 0.348 0.156 4.000 -11.555 -3.205 -0.006 -1.8580.451 1.352 0.361 0.234 4.200 -11.153 -3.003 -0.004 -2.0560.466 1.398 0.373 0.332 4.400 -10.752 -2.802 -0.003 -2.2550.481 1.444 0.385 0.441 4.600 -10.352 -2.602 -0.003 -2.4550.497 1.490 0.397 0.532 4.800 -9.952 -2.402 -0.003 -2.6550.512 1.536 0.410 0.575 5.000 -9.552 -2.202 -0.003 -2.8550.527 1.582 0.422 0.551 5.200 -9.154 -2.004 -0.005 -3.0570.543 1.628 0.434 0.470 5.400 -8.756 -1.806 -0.007 -3.2590.558 1.674 0.446 0.363 5.600 -8.360 -1.610 -0.011 -3.4630.573 1.720 0.459 0.260 5.800 -7.966 -1.416 -0.017 -3.6690.589 1.766 0.471 0.176 6.000 -7.576 -1.226 -0.027 -3.8790.604 1.812 0.483 0.115 6.200 -7.190 -1.041 -0.042 -4.0930.619 1.858 0.495 0.073 6.400 -6.813 -0.863 -0.064 -4.3160.635 1.904 0.508 0.046 6.600 -6.446 -0.697 -0.098 -4.5500.650 1.950 0.520 0.030 6.800 -6.095 -0.545 -0.146 -4.7980.665 1.996 0.532 0.020 7.000 -5.762 -0.412 -0.213 -5.0650.681 2.042 0.544 0.014 7.200 -5.450 -0.301 -0.302 -5.3530.696 2.088 0.557 0.012 7.400 -5.162 -0.212 -0.413 -5.6650.711 2.134 0.569 0.013 7.600 -4.895 -0.145 -0.546 -5.998

H2B H3B

0.727 2.180 0.581 0.018 7.800 -4.647 -0.097 -0.698 -6.3500.742 2.226 0.593 0.027 8.000 -4.414 -0.064 -0.865 -6.7170.757 2.272 0.606 0.041 8.200 -4.191 -0.041 -1.042 -7.0940.773 2.318 0.618 0.065 8.400 -3.977 -0.027 -1.228 -7.4800.788 2.363 0.630 0.103 8.600 -3.767 -0.017 -1.418 -7.8700.803 2.409 0.643 0.159 8.800 -3.561 -0.011 -1.612 -8.2640.818 2.455 0.655 0.239 9.000 -3.357 -0.007 -1.808 -8.6600.834 2.501 0.667 0.342 9.200 -3.155 -0.005 -2.006 -9.0580.849 2.547 0.679 0.457 9.400 -2.953 -0.003 -2.204 -9.4560.864 2.593 0.692 0.561 9.600 -2.752 -0.002 -2.403 -9.8550.880 2.639 0.704 0.623 9.800 -2.552 -0.002 -2.603 -10.2550.895 2.685 0.716 0.630 10.000 -2.353 -0.003 -2.804 -10.656

10.200 -2.153 -0.003 -3.004 -11.05610.400 -1.955 -0.005 -3.206 -11.45810.600 -1.758 -0.008 -3.409 -11.86110.800 -1.562 -0.012 -3.613 -12.26511.000 -1.369 -0.019 -3.820 -12.67211.200 -1.180 -0.030 -4.031 -13.08311.400 -0.996 -0.046 -4.247 -13.49911.600 -0.821 -0.071 -4.472 -13.92411.800 -0.658 -0.108 -4.709 -14.36112.000 -0.510 -0.160 -4.961 -14.81312.200 -0.382 -0.232 -5.233 -15.28512.400 -0.277 -0.327 -5.528 -15.78012.600 -0.194 -0.444 -5.845 -16.29712.800 -0.132 -0.582 -6.183 -16.83513.000 -0.088 -0.738 -6.539 -17.39113.200 -0.057 -0.907 -6.908 -17.96013.400 -0.037 -1.087 -7.288 -18.54013.600 -0.024 -1.274 -7.675 -19.12713.800 -0.015 -1.465 -8.066 -19.71814.000 -0.010 -1.660 -8.461

logarithm of molar fraction of each species as a funciton of pH logarithm of molar fraction of each species during titration

log alpha 4 log alpha 5 log alpha 6 Buffer same same log alpha 0 log alpha 1 log alpha 2

Capacity Vol pH B HB0.365 0.000 0.000 -16.442 -5.898 -0.5050.170 2.157 0.200 -15.878 -5.548 -0.369

-0.019 4.096 0.400 -15.339 -5.224 -0.260-0.194 5.754 0.600 -14.826 -4.925 -0.176-0.338 7.077 0.800 -14.337 -4.651 -0.116-0.428 8.061 1.000 -13.866 -4.395 -0.074-0.450 8.749 1.200 -13.410 -4.153 -0.047-0.411 9.210 1.400 -12.963 -3.921 -0.029-0.343 9.508 1.600 -12.523 -3.695 -0.018-0.277 9.697 1.800 -12.087 -3.474 -0.011-0.235 9.817 2.000 -11.654 -3.255 -0.007-0.231 9.894 2.200 -11.223 -3.038 -0.005-0.268 9.944 2.400 -10.792 -2.822 -0.003-0.347 9.982 2.600 -10.363 -2.607 -0.003-0.460 10.014 2.800 -9.934 -2.393 -0.003-0.600 10.050 3.000 -9.505 -2.179 -0.003-0.759 10.098 3.200 -9.078 -1.966 -0.005-0.932 10.170 3.400 -8.652 -1.754 -0.008-1.113 10.282 3.600 -8.228 -1.545 -0.013-1.298 10.457 3.800 -7.806 -1.338 -0.020-1.479 10.730 4.000 -7.390 -1.136 -0.033-1.647 11.144 4.200 -6.981 -0.941 -0.053-1.783 11.748 4.400 -6.582 -0.757 -0.083-1.857 12.577 4.600 -6.199 -0.589 -0.129-1.846 13.626 4.800 -5.837 -0.441 -0.196-1.754 14.824 5.000 -5.498 -0.317 -0.286-1.608 16.044 5.200 -5.186 -0.219 -0.403-1.435 17.146 5.400 -4.898 -0.146 -0.544-1.252 18.041 5.600 -4.633 -0.095 -0.708-1.068 18.706 5.800 -4.384 -0.060 -0.888-0.889 19.169 6.000 -4.147 -0.038 -1.080-0.719 19.478 6.200 -3.918 -0.023 -1.280-0.565 19.677 6.400 -3.694 -0.015 -1.486-0.432 19.804 6.600 -3.474 -0.009 -1.695-0.328 19.886 6.800 -3.257 -0.006 -1.906-0.262 19.941 7.000 -3.040 -0.004 -2.118-0.240 19.982 7.200 -2.825 -0.003 -2.332-0.263 20.018 7.400 -2.610 -0.002 -2.546-0.329 20.059 7.600 -2.395 -0.003 -2.761

H4B H5B H6B H2B

-0.433 20.115 7.800 -2.182 -0.003 -2.976-0.566 20.200 8.000 -1.969 -0.005 -3.192-0.721 20.333 8.200 -1.757 -0.008 -3.409-0.891 20.548 8.400 -1.548 -0.013 -3.629-1.070 20.896 8.600 -1.341 -0.020 -3.851-1.255 21.459 8.800 -1.139 -0.033 -4.078-1.440 22.365 9.000 -0.944 -0.052 -4.312-1.616 23.818 9.200 -0.760 -0.083 -4.557-1.771 26.155 9.400 -0.591 -0.129 -4.817-1.878 29.983 9.600 -0.442 -0.195 -5.098-1.909 36.644 9.800 -0.318 -0.285 -5.402-1.852 50.000 10.000 -0.220 -0.401 -5.733-1.727 10.200-1.564 10.400-1.383 10.600-1.198 10.800-1.014 11.000-0.835 11.200-0.668 11.400-0.516 11.600-0.388 11.800-0.288 12.000-0.225 12.200-0.199 12.400-0.206 12.600-0.228 12.800-0.240 13.000-0.210 13.200-0.122 13.4000.017 13.6000.187 13.8000.374 14.000

logarithm of molar fraction of each species during titration Mean charge of species HiB

log alpha 3 log alpha 4 log alpha 5 log alpha 6 scaling scaling Buffer vs vs

pH (-8 a 0)pH (-6 a 0) Capacity pH Vol-0.163 -6.968 -5.226 -0.275 0.000 -0.007 1.806-0.242 -6.845 -5.134 -0.233 0.200 -0.011 2.020-0.347 -6.723 -5.042 -0.234 0.400 -0.018 2.235-0.477 -6.600 -4.950 -0.284 0.600 -0.028 2.449-0.632 -6.478 -4.858 -0.380 0.800 -0.043 2.664-0.805 -6.355 -4.766 -0.512 1.000 -0.066 2.878-0.992 -6.233 -4.674 -0.672 1.200 -0.101 3.093-1.189 -6.110 -4.583 -0.851 1.400 -0.152 3.307-1.392 -5.987 -4.491 -1.042 1.600 -0.221 3.522-1.600 -5.865 -4.399 -1.239 1.800 -0.310 3.736-1.810 -5.742 -4.307 -1.435 2.000 -0.416 3.951-2.022 -5.620 -4.215 -1.620 2.200 -0.530 4.165-2.235 -5.497 -4.123 -1.772 2.400 -0.641 4.380-2.449 -5.375 -4.031 -1.856 2.600 -0.739 4.594-2.664 -5.252 -3.939 -1.843 2.800 -0.818 4.809-2.879 -5.129 -3.847 -1.739 3.000 -0.877 5.023-3.095 -5.007 -3.755 -1.576 3.200 -0.919 5.238-3.312 -4.884 -3.663 -1.387 3.400 -0.947 5.452-3.532 -4.762 -3.571 -1.190 3.600 -0.966 5.667-3.754 -4.639 -3.479 -0.994 3.800 -0.979 5.881-3.981 -4.517 -3.387 -0.806 4.000 -0.987 6.096-4.215 -4.394 -3.296 -0.632 4.200 -0.992 6.310-4.460 -4.271 -3.204 -0.479 4.400 -0.996 6.525-4.721 -4.149 -3.112 -0.356 4.600 -0.999 6.739-5.002 -4.026 -3.020 -0.274 4.800 -1.002 6.954-5.307 -3.904 -2.928 -0.240 5.000 -1.005 7.168-5.638 -3.781 -2.836 -0.259 5.200 -1.009 7.383-5.994 -3.659 -2.744 -0.328 5.400 -1.015 7.598-6.372 -3.536 -2.652 -0.440 5.600 -1.024 7.812-6.766 -3.413 -2.560 -0.586 5.800 -1.038 8.027-7.173 -3.291 -2.468 -0.755 6.000 -1.059 8.241-7.587 -3.168 -2.376 -0.940 6.200 -1.091 8.456-8.008 -3.046 -2.284 -1.135 6.400 -1.137 8.670-8.431 -2.923 -2.192 -1.333 6.600 -1.201 8.885-8.857 -2.801 -2.100 -1.529 6.800 -1.285 9.099-9.284 -2.678 -2.008 -1.708 7.000 -1.387 9.314-9.712 -2.555 -1.917 -1.847 7.200 -1.501 9.528

-10.140 -2.433 -1.825 -1.909 7.400 -1.614 9.743-10.570 -2.310 -1.733 -1.871 7.600 -1.716 9.957

H3B H4B H5B H6B zm

BI11

Gutz: Carga média das espécies HiB formadas em cada pH

-10.999 -2.188 -1.641 -1.748 7.800 -1.800 10.172-11.430 -2.065 -1.549 -1.576 8.000 -1.864 10.386-11.862 -1.943 -1.457 -1.383 8.200 -1.909 10.601-12.296 -1.820 -1.365 -1.184 8.400 -1.941 10.815-12.732 -1.697 -1.273 -0.987 8.600 -1.962 11.030-13.174 -1.575 -1.181 -0.797 8.800 -1.976 11.244-13.622 -1.452 -1.089 -0.622 9.000 -1.985 11.459-14.082 -1.330 -0.997 -0.466 9.200 -1.991 11.673-14.557 -1.207 -0.905 -0.340 9.400 -1.995 11.888-15.052 -1.085 -0.813 -0.251 9.600 -1.998 12.102-15.571 -0.962 -0.721 -0.206 9.800 -2.000 12.317-16.116 -0.839 -0.630 -0.201 10.000 -2.003 12.531

10.200 -2.00610.400 -2.01010.600 -2.01710.800 -2.02711.000 -2.04311.200 -2.06611.400 -2.10111.600 -2.15111.800 -2.22012.000 -2.30912.200 -2.41412.400 -2.52912.600 -2.64012.800 -2.73813.000 -2.81713.200 -2.87613.400 -2.91813.600 -2.94713.800 -2.96614.000 -2.978

Mean charge of species HiB

scale

z+N.pH/14-0.313 -2.613-0.427 -2.567-0.550 -2.521-0.667 -2.475-0.766 -2.429-0.843 -2.383-0.898 -2.337-0.935 -2.291-0.960 -2.245-0.975 -2.199-0.985 -2.153-0.991 -2.107-0.996 -2.061-0.999 -2.015-1.002 -1.970-1.005 -1.924-1.010 -1.878-1.017 -1.832-1.028 -1.786-1.046 -1.740-1.073 -1.694-1.114 -1.648-1.175 -1.602-1.258 -1.556-1.363 -1.510-1.482 -1.464-1.604 -1.418-1.715 -1.372-1.804 -1.326-1.871 -1.280-1.917 -1.234-1.948 -1.188-1.968 -1.142-1.980 -1.096-1.988 -1.050-1.993 -1.004-1.997 -0.958-2.000 -0.912-2.002 -0.866

zm

BK11

Gutz: Carga média das espécies HiB formadas em cada pH

-2.006 -0.820-2.010 -0.774-2.017 -0.728-2.028 -0.682-2.045 -0.637-2.073 -0.591-2.114 -0.545-2.174 -0.499-2.256 -0.453-2.361 -0.407-2.481 -0.361-2.603 -0.315

Degree of smoothing

(0 to 100%) 80

Interpolated points 300

Volume pH Fitted pH dpH/dV

0.000 2.265 2.2650 0.0174

2.499 2.386 2.3873 0.1139

4.618 2.664 2.6616 0.0817

6.278 2.784 2.7868 0.1468

7.499 3.059 3.0608 0.2843

8.355 3.302 3.2903 0.2091

8.934 3.437 3.4062 0.2443

9.318 3.552 3.5555 0.6871

9.569 3.823 3.7837 1.2841

9.734 3.891 4.0265 1.8639

9.844 4.301 4.2442 2.2537

9.922 4.118 4.4232 2.4997

9.984 4.422 4.5776 2.5932

10.042 4.841 4.7280 2.5385

10.108 5.186 4.8961 2.3347

10.198 5.192 5.0982 1.9871

10.328 5.380 5.3370 1.5018

10.525 5.567 5.5895 0.9782

10.825 5.768 5.8282 0.6343

11.278 6.083 6.0669 0.3735

11.953 6.222 6.2357 0.2006

12.926 6.444 6.4405 0.1819

14.267 6.617 6.6186 0.1164

16.007 6.828 6.8270 0.1034

18.090 6.995 6.9953 0.0755

20.362 7.224 7.2250 0.1404

22.596 7.537 7.5356 0.0866

24.584 7.631 7.6323 0.0589

26.199 7.783 7.7808 0.1144

27.418 7.983 7.9917 0.2901

28.288 8.285 8.2628 0.2432

28.885 8.406 8.4041 0.3238

29.284 8.629 8.5881 0.689029.547 8.798 8.8196 1.241129.720 9.096 9.0661 1.781829.836 9.085 9.2870 2.223729.918 9.400 9.4741 2.483929.983 9.451 9.6368 2.593030.045 9.812 9.7967 2.5596

Evaluation of Real and Simulated Titration Data by Derivatives with Interpolation

Interpolation and smoothing by cubic splines

0 10 20 30 40 50 60

-3

-2

-1

0

1

2

32nd derivative 1st derivative

Volume (mL)

dp

H/d

V

0 10 20 30 40 50 600

2

4

6

8

10

12

14raw data smoothed data

Volume (mL)

pH

F2

Gutz: Interpolation with smoothing is a valuable tool for automatically and precisely locate well defined inflections on titration curves. This module will not run properly until you enable macros, following instructions at cell A22 of module pH_calc; Multiple inflections, displayed in column P after clicking Process (cell E3), may reflect the stepwise deprotonation of a multiprotic acid like phosphoric or the stepwise protonation of bases like ethylenediamine or EDTA, but they may instead be originated by a mixture of various acids or bases with different pKas contained in a sample. Scattered data can produce false inflections and there are instructions in cell P2 on how to deal with such situation. Up to 300 experimental (or simulated) data pairs can be treated by smoothing with interpolation of up to 1000 points presenting 0 to 15 inflections. To assist the calculations of the sample (titrand) concentration, there is a spreadsheet starting at cell O21. Warning: care should be exercised with unknown samples because there may be hidden/unresolved inflections (e.g., citric acid, see example in Regression). It is advisable to compare the experimental curve with the simulated one based on the supposed interpretation of the results. This can be done superimposing the Simulation and Evaluation data in the Graphs module or, even better for skilled users, analysing the experimental data with the Regression module. Although Regression is far superior for hidden or overlapped inflections, no chemometric tool can extract accurate results from poor data (insufficient measurements, data with high scatter, etc.).

F3

Gutz: Click Clear and paste or fill out with up to 300 data points from a real titration, or Copy previously simulated data using one of the buttons.

H3

Gutz: The smoothing factor is selected empirically, by visual inspection (the correlation coefficient, shown in cell N4, does not help much). Begin, for example, with 80%, process, observe figures 1 and 2, and increase/decrease this value until you reach o compromise of best filtering-out of the data dispersion (scatter) without noticeable distortion (systematic flattening) of the region of the inflection. For curves presenting a sharp and a tiny inflection, select one at a time (selecting the volume range in cells K3 and K4) and adjust the degree of smoothing individually. 0% - minimum filtering, cubic spline curve passes though all points. 100%- maximum filtering; the fitted curve approaches linearity; de correlation coefficient decreases.

C4

Gutz: Click Clear and paste or fill out with up to 300 data points from a real titration, or Copy previously simulated data using one of the buttons.

H4

Gutz: Defines the number of points to be interpolated between the initial (K3) and the final volume (K4). Recommended: 300 (for slow computers: 200 or 100) Maximum: 1000 (Minimum allowed by the algorithm: 4)

A5

Gutz: Delete existing data (or click the Clear button) before you write or paste experimental data, or copy data from Simulation by clicking on the buttons above. Volume values in mL are expected, but mass of titrant or number o coulombs (coulometric titration) can be used instead.

B5

Gutz: Copy or paste pH values, experimental or simulated, with our without dispersion (simulated random errors). Uncalibrated pH electrodes do not impair the determination of concentrations at sharp inflections, but will offset pKa values estimated graphically. Electrode potentials can replace pH values when evaluating data from other ion selective electrodes.

30.116 10.285 9.9775 2.353330.212 10.295 10.1952 1.972230.354 10.522 10.4478 1.419130.570 10.628 10.7013 0.872530.905 10.915 10.9279 0.465231.427 11.085 11.0960 0.211332.239 11.226 11.2276 0.127933.495 11.385 11.3864 0.143335.422 11.677 11.6756 0.112938.365 11.805 11.8057 0.022942.878 12.007 12.0073 0.047450.000 12.224 12.2235 0.0217

Fit quality of the splines to pH

Initial volume 0.000 Fitted pH std. dev. 0.0963 Detector threshold |dpH/dV| >

Final volume 50.000 Correlation coefficient 0.9995 Detected inflection points

step Volume

1 10.01582 30.02923

4

5

6

7

8

9

10

11

12

13

14

15

Volume of titrand (sample pipeted into cell)

Concentration of titrant (in the buret)

step Vol. Inflection

1 10.01582 30.02923

4

5

6

7

8

9

10

Results of the Example: [H3PO4] = 0,0501 mol/L in the 20 mL of sample[NaH2PO4] = [H2PO4- found] - [H3PO4] = 0,1000 - 0,501 = 0,0499 mol/L Remember: half of the determined H2PO4- comes from the H3PO4

How to change the axis of a curveHow to copy/paste a curve

Evaluation of Real and Simulated Titration Data by Derivatives with Interpolation

Fitting range (zoom) Inflection auto-finder - first-derivative-based

0 10 20 30 40 50 60

-3

-2

-1

0

1

2

32nd derivative 1st derivative

Volume (mL)

dp

H/d

V

0 10 20 30 40 50 600

2

4

6

8

10

12

14raw data smoothed data

Volume (mL)

pH

Titration with 0.100 mol/L NaOH of 20 mLof sample containing 0.05 mol/L H3PO4 and 0.05 mol/L NaH2PO4 with simulated dispersion (sVol=0.05 mL and spH=0.05)

J3

Gutz: Starting volume for the smoothing/interpolation/inflection detection process. Zero is the typical value.

P3

Gutz: This is the setting of the minimum peak amplitude to be detected as valid on the 1st derivative curve by the algorithm of the auto-finder. In figure 2, imagine a horizontal line exceeded only by the maxima (or minima) you want to detect, but not by peaks originated from data scatter or other artifacts. Read the corresponding dpH/dV value on the y-axis, type it in cell Q3 and click Process (cell E3) to observe the effect.

J4

Gutz: Upper volume limit for the smoothing /interpolation/ inflection detection process. For curves presenting sharp tiny inflections together, select one at a time (by volume range) and adjust the degree of smoothing.

P6

Gutz: Copy and paste the volumes of the inflections from cells P6, P7, etc. into cells P28, P29, etc., and fill out R24 and 25 to make simple stoichiometric calculations.

P27

Gutz: Fill out with the volumes of the inflections (in mL)

Data ID on curves

Color coding


1 guess value 0.3984808116 F i l l o u t o r c h a n g e

Detected inflection points Interpolated spline smoothed data

pH dpH/dV Interp. Vol. Fitted pH dpH/dV

4.661 2.598996092 -0.022834502 0.0000 2.2650 0.0174 0.0000

9.755 2.602270413 -0.157678286 0.1667 2.2680 0.0178 0.0025

0.3333 2.2710 0.0191 0.0051

0.5000 2.2744 0.0212 0.0076

0.6667 2.2781 0.0241 0.0101

0.8333 2.2824 0.0279 0.0126

1.0000 2.2875 0.0325 0.0152

1.1667 2.2933 0.0380 0.0177

1.3333 2.3002 0.0443 0.0202

1.5000 2.3082 0.0515 0.0227

1.6667 2.3174 0.0595 0.0253

1.8333 2.3280 0.0683 0.0278

2.0000 2.3402 0.0780 0.0303

2.1667 2.3541 0.0885 0.0328

2.3333 2.3698 0.0999 0.0354

Titrand concentration calculator 2.5000 2.3874 0.1121 0.0378

(optional and modifiable) 2.6667 2.4071 0.1235 0.0308

2.8333 2.4285 0.1326 0.0238

Volume of titrand (sample pipeted into cell) 20 mL 3.0000 2.4512 0.1394 0.0168

Concentration of titrant (in the buret) 0.1 mol/L 3.1667 2.4748 0.1439 0.0099

Number of mols of titrant Result (mol/L) 3.3333 2.4990 0.1460 0.0029

total stepwise [species] 3.5000 2.5233 0.1458 -0.0041

0.001001583 0.001001583 0.050079167 3.6667 2.5475 0.1432 -0.0111

0.003002917 0.002001333 0.100066667 3.8333 2.5710 0.1384 -0.0181

4.0000 2.5935 0.1312 -0.0251

4.1667 2.6146 0.1216 -0.0321

4.3333 2.6339 0.1098 -0.0391

4.5000 2.6510 0.0956 -0.0461

4.6667 2.6656 0.0794 -0.0470

4.8333 2.6777 0.0660 -0.0332

5.0000 2.6879 0.0572 -0.0194

5.1667 2.6970 0.0531 -0.0057

5.3333 2.7058 0.0535 0.0081[H3PO4] = 0,0501 mol/L in the 20 mL of sample 5.5000 2.7151 0.0585 0.0219[NaH2PO4] = [H2PO4- found] - [H3PO4] = 0,1000 - 0,501 = 0,0499 mol/L 5.6667 2.7255 0.0681 0.0356Remember: half of the determined H2PO4- comes from the H3PO4 5.8333 2.7380 0.0822 0.0494

6.0000 2.7532 0.1010 0.0632How to change the axis of a curve 6.1667 2.7719 0.1244 0.0769How to copy/paste a curve 6.3333 2.7949 0.1519 0.0836

Inflection auto-finder - first-derivative-based

d2pH/dV2 d2pH/dV2

R4

Gutz: Stoichiometric points (or "end points") of potentiometric acid-base titrations correspond to the volumes where the pH vs. Vol curves present inflections, easily located by looking for maxima in the first derivative curves (or a minima, when a base is titrated with an acid) as well as detecting zero crossing points in the second derivative curves. Once the degree of smoothing (cell I3) of the spline interpolation is tuned to the data set and the peak amplitude filter (cell Q3) is set to discard false peaks in the derivative curve (caused by scattered/noisy data), the auto-finder interpolates the inflections in the pH vs Vol. curve automatically and with improved accuracy in comparison with the direct dpH/dV calculation suggested in textbooks or linearization methods, like Gran I and II. Of course, plentiful accurate measurements near the inflections are decisive. Oversmoothing of (scatered) data is to be avoided. To exclude outliers from a set, simply delete the data pair and shift the remaining data one row up to exclude the empty cells. The (more complex) Regression module may provide superior results, due to fitting to a general equation describing the entire curve instead of empirical splines fitted with an arbitrary smoothing factor (that influences the result for poor data or undefined inflections).

R5

Gutz: Maximum value of the first derivative of the curve at the inflection volume, as calculated from the fitted cubic spline. Precision is higher than for the conventional dpH/dV calculation suggested in textbooks. The Regression module may provide even better results in the hand of skilled users, since a general equation describing the theoretical curve is fitted to data, instead of empirical splines. Of course, good data near the inflections is decisive for all approaches.

S5

Gutz: Second derivatives estimated from the splines fitted with smoothing to the original data. Inflections correspond to zero crossing 2nd derivative. Therefore, low values are expected.

T5

Gutz: The number of interpolated points can be chosen from 4 to 1000 in cell I4.

R22

Gutz: This spreadshhet assists trivial stoichiometric calculations, like the concentration of acids/bases in the titrand or sample. Click Copy volumes or copy the volumes of inflections from P6, P7, etc. and paste them in P27, P28, etc. Fill out the blanks in R24 and R25.

Q27

Gutz: Cumulative number of mols of titrant added from the begining of the titration up to a given inflection.

R27

Gutz: Number of mols of titrant added from the previous inflection to the current one.

S27

Gutz: Concentration (in mol/L) of a titrand (titrated specie) in the sample pipeted into the titration cell (subsequent addition of water, to immerge the sensor does not matter), obtainded by dividing the number of mols of titrant consumed to reach an inflection by the volume of sample. Sucessive inflections may correspond to the stepwise deprotonation of a multiprotic acid like phosphoric (or stepwise protonation of bases like ethylenediamine or EDTA), but they may result as well from a mixture of acids or bases of different strengths. Warning: care should be exercised with unknown samples because there may be hidden/unresolved inflections (e.g., citric acid, see example in Regression). It is advisable to compare the experimental curve with the simulated one based on the supposed interpretation of the results. This can be done superimposing the Simulation and Evaluation data in the Graphs module or, even better for skilled users, analysing the experimental data with the Regression module.

R43

Gutz: Click twice on the dpH/dV or pH scale to redifine it. Use Ctrl+Z (as many times as needed) to undo scale expansion

R44

Gutz: To copy graphics with one or more curves and paste them into other documents (e.g.: Word o Excel) without links to the original: - Fill out the header of the graphic (optional) - Click in the box of the graphic near the margins, to select it - Repeat generation of at least one curve - Press Ctrl+C and wait processing - Switch to the Word document - Select Insert/Paste Special/Picture (enhanced metafile)

Data ID on curves 6.5000 2.8225 0.1785 0.07586.6667 2.8542 0.2024 0.06796.8333 2.8898 0.2238 0.06017.0000 2.9287 0.2425 0.05237.1667 2.9705 0.2586 0.04457.3333 3.0147 0.2722 0.03677.5000 3.0610 0.2831 0.02887.6667 3.1088 0.2882 0.00187.8333 3.1566 0.2843 -0.02518.0000 3.2030 0.2714 -0.05218.1667 3.2466 0.2496 -0.07908.3333 3.2857 0.2187 -0.10598.5000 3.3196 0.1917 -0.04538.6667 3.3510 0.1888 0.02828.8333 3.3839 0.2105 0.10169.0000 3.4226 0.2634 0.27739.1667 3.4773 0.4111 0.60859.3333 3.5658 0.6691 0.93719.5000 3.7061 1.0322 1.24119.6667 3.9160 1.5153 1.73699.8333 4.2204 2.1334 1.7011

10.0000 4.6198 2.5937 0.351310.1667 5.0311 2.2100 -1.931810.3333 5.3451 1.5698 -1.780710.5000 5.5633 1.0827 -1.143010.6667 5.7169 0.7861 -0.660110.8333 5.8338 0.6418 -0.230311.0000 5.9340 0.5585 -0.269911.1667 6.0192 0.4619 -0.309611.3333 6.0873 0.3545 -0.304511.5000 6.1388 0.2690 -0.208611.6667 6.1788 0.2155 -0.112711.8333 6.2124 0.1939 -0.016812.0000 6.2451 0.2028 0.046212.1667 6.2800 0.2148 0.026112.3333 6.3164 0.2202 0.006112.5000 6.3531 0.2188 -0.014012.6667 6.3890 0.2108 -0.034112.8333 6.4230 0.1961 -0.054213.0000 6.4540 0.1757 -0.060913.1667 6.4816 0.1570 -0.051113.3333 6.5065 0.1416 -0.041313.5000 6.5290 0.1294 -0.031513.6667 6.5498 0.1206 -0.021713.8333 6.5694 0.1150 -0.011914.0000 6.5883 0.1126 -0.002114.1667 6.6071 0.1136 0.007714.3333 6.6263 0.1174 0.012314.5000 6.6462 0.1210 0.009114.6667 6.6666 0.1235 0.005914.8333 6.6873 0.1249 0.002615.0000 6.7082 0.1252 -0.000615.1667 6.7290 0.1245 -0.003815.3333 6.7496 0.1227 -0.0070

R45

Gutz: Hover the mouse on a curve and point any data point to readout its ID and coordinates.

15.5000 6.7698 0.1198 -0.010315.6667 6.7895 0.1158 -0.013515.8333 6.8084 0.1108 -0.016716.0000 6.8264 0.1047 -0.020016.1667 6.8433 0.0983 -0.018116.3333 6.8592 0.0926 -0.016016.5000 6.8742 0.0877 -0.013916.6667 6.8884 0.0834 -0.011816.8333 6.9020 0.0798 -0.009717.0000 6.9151 0.0769 -0.007617.1667 6.9277 0.0747 -0.005517.3333 6.9400 0.0732 -0.003417.5000 6.9521 0.0724 -0.001317.6667 6.9642 0.0723 0.000717.8333 6.9763 0.0729 0.002818.0000 6.9885 0.0742 0.004918.1667 7.0010 0.0762 0.006618.3333 7.0139 0.0786 0.007818.5000 7.0273 0.0814 0.009018.6667 7.0411 0.0845 0.010118.8333 7.0555 0.0881 0.011319.0000 7.0705 0.0921 0.012519.1667 7.0862 0.0965 0.013719.3333 7.1026 0.1012 0.014919.5000 7.1199 0.1064 0.016119.6667 7.1381 0.1119 0.017219.8333 7.1573 0.1179 0.018420.0000 7.1774 0.1242 0.019620.1667 7.1987 0.1310 0.020820.3333 7.2211 0.1381 0.022020.5000 7.2447 0.1449 0.018020.6667 7.2693 0.1501 0.013020.8333 7.2946 0.1536 0.008021.0000 7.3204 0.1554 0.003021.1667 7.3464 0.1556 -0.002021.3333 7.3722 0.1541 -0.006921.5000 7.3976 0.1510 -0.011921.6667 7.4224 0.1462 -0.016921.8333 7.4463 0.1397 -0.021922.0000 7.4689 0.1315 -0.026922.1667 7.4900 0.1217 -0.031922.3333 7.5094 0.1103 -0.036922.5000 7.5267 0.0971 -0.041922.6667 7.5417 0.0826 -0.042222.8333 7.5543 0.0696 -0.036023.0000 7.5650 0.0586 -0.029823.1667 7.5740 0.0497 -0.023623.3333 7.5817 0.0429 -0.017423.5000 7.5884 0.0381 -0.011223.6667 7.5945 0.0354 -0.005023.8333 7.6003 0.0348 0.001224.0000 7.6062 0.0362 0.007324.1667 7.6125 0.0397 0.013524.3333 7.6196 0.0452 0.0197

24.5000 7.6277 0.0528 0.025924.6667 7.6373 0.0622 0.027824.8333 7.6484 0.0710 0.025525.0000 7.6609 0.0791 0.023125.1667 7.6747 0.0864 0.020725.3333 7.6897 0.0929 0.018325.5000 7.7057 0.0987 0.015925.6667 7.7225 0.1036 0.013625.8333 7.7401 0.1077 0.011226.0000 7.7584 0.1110 0.008826.1667 7.7771 0.1136 0.006426.3333 7.7963 0.1175 0.020026.5000 7.8166 0.1270 0.037426.6667 7.8389 0.1424 0.054826.8333 7.8644 0.1636 0.072227.0000 7.8938 0.1906 0.089627.1667 7.9282 0.2233 0.107027.3333 7.9686 0.2619 0.124427.5000 8.0157 0.3033 0.104727.6667 8.0687 0.3285 0.046527.8333 8.1241 0.3342 -0.011728.0000 8.1790 0.3206 -0.070028.1667 8.2299 0.2876 -0.128228.3333 8.2738 0.2373 -0.137728.5000 8.3107 0.2119 -0.015028.6667 8.3467 0.2273 0.107728.8333 8.3887 0.2837 0.230429.0000 8.4436 0.3822 0.364129.1667 8.5187 0.5268 0.502929.3333 8.6218 0.7225 0.742029.5000 8.7672 1.0500 1.222529.6667 8.9800 1.5221 1.573029.8333 9.2808 2.1152 2.039330.0000 9.6796 2.5903 0.493330.1667 10.0958 2.2589 -1.920630.3333 10.4163 1.5887 -1.937530.5000 10.6330 1.0561 -1.193230.6667 10.7824 0.7606 -0.728230.8333 10.8909 0.5531 -0.516631.0000 10.9706 0.4105 -0.364931.1667 11.0298 0.3067 -0.258131.3333 11.0748 0.2385 -0.151331.5000 11.1113 0.2029 -0.084631.6667 11.1429 0.1773 -0.069131.8333 11.1707 0.1569 -0.053632.0000 11.1955 0.1416 -0.038132.1667 11.2182 0.1315 -0.022632.3333 11.2396 0.1260 -0.012732.5000 11.2603 0.1227 -0.007132.6667 11.2806 0.1213 -0.001532.8333 11.3008 0.1217 0.004233.0000 11.3213 0.1241 0.009833.1667 11.3423 0.1283 0.015433.3333 11.3641 0.1344 0.0211

33.5000 11.3872 0.1423 0.026333.6667 11.4116 0.1501 0.020533.8333 11.4371 0.1560 0.014734.0000 11.4635 0.1600 0.008934.1667 11.4903 0.1620 0.003134.3333 11.5174 0.1620 -0.002734.5000 11.5442 0.1602 -0.008534.6667 11.5706 0.1564 -0.014334.8333 11.5962 0.1506 -0.020135.0000 11.6207 0.1430 -0.025935.1667 11.6438 0.1334 -0.031735.3333 11.6651 0.1218 -0.037535.5000 11.6843 0.1087 -0.039335.6667 11.7014 0.0960 -0.036535.8333 11.7164 0.0843 -0.033736.0000 11.7295 0.0736 -0.030836.1667 11.7410 0.0638 -0.028036.3333 11.7508 0.0549 -0.025236.5000 11.7593 0.0470 -0.022436.6667 11.7666 0.0400 -0.019636.8333 11.7727 0.0340 -0.016737.0000 11.7779 0.0288 -0.013937.1667 11.7824 0.0247 -0.011137.3333 11.7862 0.0215 -0.008337.5000 11.7896 0.0192 -0.005437.6667 11.7926 0.0178 -0.002637.8333 11.7956 0.0174 0.000238.0000 11.7985 0.0180 0.003038.1667 11.8016 0.0194 0.005838.3333 11.8050 0.0219 0.008738.5000 11.8089 0.0249 0.008838.6667 11.8133 0.0277 0.008438.8333 11.8182 0.0304 0.007939.0000 11.8234 0.0330 0.007439.1667 11.8291 0.0354 0.006939.3333 11.8352 0.0376 0.006539.5000 11.8417 0.0397 0.006039.6667 11.8484 0.0416 0.005539.8333 11.8555 0.0433 0.005040.0000 11.8629 0.0449 0.004640.1667 11.8705 0.0464 0.004140.3333 11.8783 0.0476 0.003640.5000 11.8863 0.0488 0.003140.6667 11.8946 0.0497 0.002740.8333 11.9029 0.0505 0.002241.0000 11.9114 0.0512 0.001741.1667 11.9200 0.0517 0.001241.3333 11.9286 0.0520 0.000841.5000 11.9373 0.0522 0.000341.6667 11.9460 0.0522 -0.000241.8333 11.9547 0.0521 -0.000742.0000 11.9634 0.0518 -0.001142.1667 11.9719 0.0513 -0.001642.3333 11.9805 0.0507 -0.0021

42.5000 11.9888 0.0499 -0.002642.6667 11.9971 0.0490 -0.003042.8333 12.0052 0.0479 -0.003543.0000 12.0131 0.0467 -0.003643.1667 12.0207 0.0455 -0.003543.3333 12.0282 0.0444 -0.003443.5000 12.0355 0.0433 -0.003343.6667 12.0427 0.0422 -0.003243.8333 12.0496 0.0411 -0.003144.0000 12.0564 0.0401 -0.003144.1667 12.0630 0.0391 -0.003044.3333 12.0694 0.0381 -0.002944.5000 12.0757 0.0372 -0.002844.6667 12.0818 0.0362 -0.002744.8333 12.0878 0.0353 -0.002645.0000 12.0936 0.0345 -0.002545.1667 12.0993 0.0337 -0.002545.3333 12.1048 0.0328 -0.002445.5000 12.1102 0.0321 -0.002345.6667 12.1155 0.0313 -0.002245.8333 12.1206 0.0306 -0.002146.0000 12.1257 0.0299 -0.002046.1667 12.1306 0.0292 -0.002046.3333 12.1354 0.0286 -0.001946.5000 12.1401 0.0280 -0.001846.6667 12.1448 0.0274 -0.001746.8333 12.1493 0.0269 -0.001647.0000 12.1537 0.0263 -0.001547.1667 12.1581 0.0258 -0.001447.3333 12.1623 0.0254 -0.001447.5000 12.1665 0.0249 -0.001347.6667 12.1706 0.0245 -0.001247.8333 12.1747 0.0241 -0.001148.0000 12.1787 0.0238 -0.001048.1667 12.1826 0.0235 -0.000948.3333 12.1865 0.0232 -0.000848.5000 12.1904 0.0229 -0.000848.6667 12.1941 0.0227 -0.000748.8333 12.1979 0.0224 -0.000649.0000 12.2016 0.0223 -0.000549.1667 12.2053 0.0221 -0.000449.3333 12.2090 0.0220 -0.000349.5000 12.2127 0.0219 -0.000349.6667 12.2163 0.0218 -0.000249.8333 12.2199 0.0218 -0.000150.0000 12.2235 0.0217 0.0000

Titration Data Analysis - Multiple Regression

Citric acid Hydroxide ion Ascorbic acid EDTA

[B] 1.25748925E-09 0 1.41193601E-13 0

[HB] 1.63936634E-05 0 0.000456023002 0

0.004952765301 0 0.030071734878 0

0.034835294195 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0.03980445442 0 0.03052775788 0

0.11442780685 0 0.060599492758 0

max. free H 0.004985556401 0 0.000456023003 0

Titrant Strong ACID Strong BASE Carbonic ac.

[B] 0.1 Sample

[HB] 20

SS

S[HiB] 0 0.1 0 0.1

0 0 0 0

Concentrations (in mol/L) – known or to fit (in blue) – and equilibrium conc. of titrant at initial pH

Titrand Species

[H2B]

[H3B]

[H4B]

[H5B]

[H6B]

S[HiB]

S[H] bound

[H2B]

S[H]

0.0 10.0 20.0 30.0 40.0 50.0 60.00.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0 Titration with 0.100 mol/L NaOH of 20.0 mLof a mixture of 0.040 mol/L citric acid

+ 0.030 mol/L ascorbic acid(sVol=0.02; spH=0.02)

Titrant volume (mL)

pH

B3

Gutz: Do not write here. See comment in cell M1 on how to change acids and bases.

A4

Gutz: Fitted equilibrium concentration of the deprotonated (conjugated) base at the initial pH (J15); The fitted global concentration of all forms of the acid-base system, [B]+[HB]+[H2B]+... appears in line 11

B4


A5

Gutz: Fitted equilibrium concentration of the monoprotonated (conjugated) base at the initial pH (J15); The global concentration [B]+[HB]+[H2B]+... appears in line 11

A11

Gutz: Total concentration of the acid or base identified in line 3, obtained by summing up the contributions of all forms in equilibrium: [B]+[HB]+[H2B]+... This concentration is a parameter fitted by regression with help of the Solver. The more the pKas of a system depart from the pH region explored in the titration, the more inaccurate the fitted concentration. Strong acids pose the worst condition; their concentration cannot be fitted directly, but is obtained from the excess of H+ (cell I14). Convergence is accelarated with good initial guesses but, in general, zero is an acceptable starting value for the concentrations to fit.

B11

Gutz: You may write 0 (zero) as starting value in all cells of line 11 (B11 to H11). During regression, the values of the cells specified by you in the Solver setup will be adjusted accordingly. For complicated systems an initial guess, based on graphical evaluatian, will help and speed up Solver's convergence.

A12

Gutz: Dissociable H+ concentration still bound to each (conjugated) base at the initial pH.

A13

Gutz: Free H+ originated from each acid or (conjugated) base at the initial pH, supposing that it was added to the sample protonated to neutrality, and not as a salt (e.g., H3PO4 but not H2NaPO4). As this is frequently not the case, the value can be zero or negative. E.g., dissolved NH3 (same as NH4OH) dissociates no protons; it will remove protons from acids with lower pKa (weaker bases) if available, or from water, in small extent). The undissociated H+ at the initial pH is not include here; it appears in line 12.

D14

Gutz: Aqueous solutions exposed to air or stored in (gas permeable) plastic flasks are always contaminated with CO2. Thus, it is advisable to include the carbonic acid system in simulations and regressions. But any other mono- or biprotic system can be specified in T3.

C15

Gutz: Leave blank/fill with de concentration of strong monoprotonable base used as titrant e.g., NaOH, KOH (or twice the concentration of Ca(OH)2). For diprotic systems see cell S3.

B16

Gutz: Leave blank/fill with the concentration of strong monoprotic acid used as titrant e.g., HCl. For a diprotic acid like H2SO4 see comment at cell R3.

E16

Gutz: Volume of the aliquot of titrand (sample)

D17

Gutz: Leave blank/fill out with the concentration of CO2 that may have been absorbed by the the titrant. CO2 absorption is most relevant for dilluted alkaline titrants. It is advisable to titrate the dilluted base against a strong standardized acid to determine this concentration of bicarbonate/carbonate with help of Regression before using the base as a titrant for the titration of unknown samples.

Vad simulated or [H] dpH/dV

(mL) from regression mol/L

0.000 2.2808 2.2699 5.24E-03 2.12E-010.897 2.4714 2.4715 3.38E-03 2.05E-011.864 2.6625 2.6733 2.18E-03 1.89E-012.961 2.8606 2.8750 1.38E-03 1.85E-014.198 3.0950 3.0766 8.04E-04 1.60E-015.548 3.2735 3.2779 5.33E-04 1.40E-016.970 3.4831 3.4790 3.29E-04 1.39E-018.440 3.6744 3.6798 2.12E-04 1.32E-019.958 3.8778 3.8803 1.32E-04 1.34E-01

11.528 4.0878 4.0807 8.17E-05 1.20E-0113.142 4.2595 4.2811 5.50E-05 1.22E-0114.769 4.4838 4.4816 3.28E-05 1.32E-0116.357 4.6824 4.6823 2.08E-05 1.32E-0117.845 4.8894 4.8829 1.29E-05 1.46E-0119.182 5.0960 5.0835 8.02E-06 1.62E-0120.352 5.2953 5.2841 5.07E-06 1.84E-0121.384 5.5012 5.4851 3.15E-06 1.97E-0122.343 5.6876 5.6867 2.05E-06 1.97E-0123.297 5.8781 5.8889 1.32E-06 2.08E-0124.292 6.0934 6.0913 8.06E-07 2.11E-0125.326 6.3069 6.2936 4.93E-07 1.93E-0126.348 6.4902 6.4957 3.23E-07 2.00E-0127.280 6.6985 6.6975 2.00E-07 2.34E-0128.063 6.8921 6.8993 1.28E-07 2.79E-0128.670 7.0866 7.1010 8.19E-08 3.91E-0129.112 7.3027 7.3027 4.98E-08 5.76E-0129.419 7.5183 7.5045 3.03E-08 7.81E-0129.625 7.7039 7.7066 1.98E-08 1.14E+0029.761 7.9083 7.9090 1.24E-08 1.84E+0029.849 8.1150 8.1121 7.67E-09 2.36E+0029.906 8.2506 8.3161 5.62E-09 4.84E+0029.944 8.5723 8.5212 2.68E-09 6.74E+0029.969 8.6735 8.7271 2.12E-09 8.55E+0029.988 8.9492 8.9322 1.12E-09 1.47E+0130.004 9.1846 9.1337 6.54E-10 7.63E+0030.021 9.2019 9.3312 6.28E-10 9.60E+0030.043 9.5546 9.5273 2.79E-10 1.03E+0130.073 9.7397 9.7241 1.82E-10 4.75E+0030.120 9.9213 9.9221 1.20E-10 3.19E+0030.192 10.1181 10.1213 7.62E-11 2.27E+0030.304 10.3403 10.3212 4.57E-11 1.42E+0030.479 10.5265 10.5216 2.97E-11 8.46E-0130.749 10.7167 10.7223 1.92E-11 5.80E-0131.161 10.9218 10.9232 1.20E-11 3.96E-0131.777 11.1236 11.1243 7.52E-12 2.72E-0132.681 11.3351 11.3254 4.62E-12 1.78E-0133.983 11.5157 11.5268 3.05E-12 1.29E-0135.846 11.7421 11.7283 1.81E-12 8.80E-02

calculated pH

measured pH

0.0 10.0 20.0 30.0 40.0 50.0 60.00.0

2.0

4.0

6.0

8.0

10.0

12.0



Titrant volume (mL)p

H

A39

Gutz: Click on the Clear data button and then: a) Type or paste experimental pH vs. Volume data from real titrations or b) Click on one of the Simulation buttons in line 38 to copy previously simulated curves (with or without random errors).

B39

Gutz: Copy "pH" data from the simulation (click on button at cell B38 for "clean" data or D38 for data with dispersion ) or type or paste real pH data.

C39

Gutz: Click on button at cell D20 to calculate the pH with the fitted parameters and to overlay the fitted curve on the raw data graph.

D39

Gutz: Free hydrated proton concentration (or activity if not corrected by clicking on button at cell C20 )

C41

Gutz: Do NOT write in this colored region! You will corrupt the equations.

D41

Gutz: Do NOT write in this colored region! You will corrupt the equations.

38.567 11.9191 11.9302 1.20E-12 5.66E-0242.781 12.1346 12.1324 7.34E-13 3.59E-0250.000 12.3300 12.3347 4.68E-13 2.71E-02

Titration Data Analysis - Multiple Regression <--- read important remarks and instructions

Phosphoric acid Carbonic acid HCl Acid / Base

0 0 0 Charge of B

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0 SS

0 0 0 7.033E-02

0 0 0 1.750E-01

0 0 0 5.442E-03

Vol. Titrand (mL) 5.027E-05

Water Total 5.238E-03 2.281

0 20.00 [OH]=Kw/[H] 1.922E-12 11.716

Initial CHcalc 1.803E-01

SS[HiB] 1.805E-01

12.775 1.293E-06 <--- Minimize with Solver

exponent a 2.000 exponent b

– and equilibrium conc. of titrant at initial pH

pKa1

pKa2

pKa3

pKa4

pKa5

pKa6

SS[bases]

SS[H] bound

SS[H] max.free H+ (negative results are possible)

if >0, [ H+] non-fitted (strong acid); if <0, -[anions] to balance with cations

[H]=10-p[H]

Initial CHReg <---Fit with Solver: CHReg and concentrations (line 11, in blue)

SS [H] pH S|CHR-CHcalc|aWb

0.0 10.0 20.0 30.0 40.0 50.0 60.00.0

2.0

4.0

6.0

8.0

10.0

12.0



Titrant volume (mL)

pH

0.0 10.0 20.0 30.0 40.0 50.0 60.0-6.0E-04

-4.0E-04

-2.0E-04

0.0E+00

2.0E-04

4.0E-04

6.0E-04 Residues (CH,Reg - CH,calc)

Titrant volume (mL)

CH

Re

g-C

Hc

alc

0.0 10.0 20.0 30.0 40.0 50.0 60.0-1.5E-01

-1.0E-01

-5.0E-02

0.0E+00

5.0E-02

1.0E-01 Residues (pH - pHRNL) To update click Overlay curve (B20)

Titrant volume (mL)

pH

Re

g-p

H

F1

Gutz: Gutz: This module employs nonlinear regression (NLR) to assist you in fitting the concentrations of acidic and basic components to pH data of volumetric acid-base titrations; optionally, pKa values and some other parameters can be determined or refined. The supplement Solver of the software Excel MUST be previously installed. See instructions in comment I19. This module, like all others, will not run properly until you enable macros, following instructions at cell A22 of module pH_calc; NLR is a powerful alternative to the graphical evaluation of titration data, being faster and, in general, more accurate. It is the method of choice for: - complex mixtures or overlapped pKas; - very diluted samples; - detect (and, possibly, quantify) CO2 absorption and other minor components that may have been overlooked in the graphical evaluation; - detect curve distortions caused by malfunctioning or calibration problems of the sensor; The Regression module is not as simple and intuitive to use as the Evaluation module and beginners unfamiliar with MPNLR are directed to the "red dot" comments and instructions in the spreadsheet to learn and find answers to many but not all questions. Like the pH_calc module, the Regression module (from CurTiPot version 3.4 up) also estimates the ionic strength I of the medium and its effects on acid-base equilibria. The thermodynamic constants from the Database (valid strictly at I=0) may not generate the best possible fit to experimental curves. More coincident curves will be obtained by refining the pKas after a first fit of the concentrations (viable when their values fall within the pH region explored during the titration). In this module pH is taken as minus the logarithm of the hydrated hydrogen ion activity (see definition, http://www.iupac.org/goldbook/P04524.pdf) as measured with a calibrated pH meter connected to a combined glass electrode. Information about the differences and interconversion of pH, p[H] and "pH" is available in the pH_calc module. Inaccurate calibration of the sensor (unreliable buffer solutions, temperature different from specified) and deviation from Nersntian reponse and/or alkaline error of the glass electrode are also sources of deviation that can, sometimes, be compensated by inclusion of N12 and N13 as variable cells in the Solver, at a refinement stage of the fitting. Warning: no chemometric tool can extract accurate results from poor data (insufficient measurements, data with high scatter, systematic errors, etc.). Before you analyze difficult titration data with Regression, collect the best data you can in the laboratory, after careful planning (assisted by Simulation) and well executed experiments with calibrated instrumentation and high purity well standardized reagents. The program fits the user-selected parameters by minimizing the squares of the difference of calculated and fitted total dissociable H+ concentrations (or the non-squared residue, a user's choice, I20). To force fitting to the inflections, extra weight can be given to data in these regions by entering K20 > 0).

J4


J5


J6


H11

Gutz: Do not fit the concentration of HCl or any other strong acid by regression. Meaningless results will result due to lack of titration data in the required pH region of 0 to -7 (minus seven), out of reach in aqueous medium. The summation of concentrations of non-fitted strong acids is, however, equivalent to the concentration determined in cell I14 by regression. You may write this result in cell H11 and the excess of H+ in cell I14 will fall to zero.

I12

Gutz: Summation of the undissociated H+ at the initial pH for all bases

I13

Gutz: Summation of the maximum H+ that could dissociate from the bases, supposing that each reactant was added to the solution protonated to neutrality, and not as a salt (e.g., H3PO4 or NH3, instead of H2NaPO4 or NH4Cl). This is frequently not the case, therefore the value can be zero or negative (e.g., NH3 or NH4OH has no protons to dissociate and will extract them from acids with lower pKa, or even from water). The H+ undissociated at the initial pH does not appear in this cell but in I12.

I14

Gutz: Positive value: There is more H+ available than required by the equilibria of the regression-fitted bases (at the titrand pH), originated from the dissociation of strong acids. The conjugated base concentration of low pKa acids cannot be fitted correctly, but their stoichiometric concentration is inferred from I14. To check results, e.g., for HCl, write the I14 value in cell G11 (not to be fitted) to see if a null value (within experimental data uncertainty) appears in I14. Negative value: The titrated sample is dominated by negatively charged (conjugated) bases like SO3-2, PO43- or H2PO4- at the initial pH value and a stoichiometric concentration of dissociated cations like Na+ is probably balancing the value displayed in I14. Remark: acid-base titrations curves of different samples may be undistinguishable For example, when titrated with NaOH, the curves of the following solutions will differ by no more than a slight vertical displacement in the alkaline region caused by differences in ionic strength: a) 0.1 mol/L H3PO4; b) 0.1 mol/L HCl + 0.1 mol/L NaH2PO4; c) 0.2 mol/L HCl + 0.1 mol/L Na2HPO4. Extra determination of the concentration of Cl- or Na+ (e.g., by ion chromatography) or conductance measurement (if there is no other electrolyte in the sample) will be conclusive in this case.

F16

Gutz: Water (or electrolyte solution) is frequently added to the sample until the glass electrode bulb and reference electrode junction are immersed in the solution.

G16

Gutz: Total volume before titration

H16

Gutz: Calculated for I given in cell M16. To change I read comment in cell L16.

I17

Gutz: CH calculated for the titrand based on the initial pH (before addition of tittrant), based on concentrations (and pKas) fitted by the Solver.

I18

Gutz: Read comment in cell I19 on how to open the Solver and define the destination cell. In the field for variable cells of the Solver, write: I18 for a sample containing solely strong acid(s), what means, with pKa values lower than the region of pH covered by the titration. and the index of cells of the concentrations of acids/bases in the sample to be fitted (B11-H11, in blue). I18; B11; ... cell(s) of line 11 corresponding to the acids/bases with pKas in the explored pH region (or near it) and supposed to be present (at any protonation level). Due to data scatter, the Solver may return a message that no solution was found (to the stringent convergence criteria); despite of this, usually the fitted values are OK (fitting can be repeated for possible improvement). Refinement of some pKa values that are within the explored pH region can be considered in a second fitting, to adjust them to the real conditions (temperature and ionic strength) of the titration. In special cases, the concentration of components of the titrant may be also refined, e.g., the contamination with carbon dioxide. In case of convergence problems, start again including the smallest possible number of most relevant components and providing reasonable initial estimates of the concentrations and pKas. Convergence criteria can be changed in the Solver setup. 100 iteractions and 30 seconds is a good default.

G19

Gutz This pH value is NOT updated automatically. Click on "Find titrant pH" or "Calculate / Update I" after any change in the titrant composition (acids, bases or electrolytes, including cells T12 and T13), in order to have a better estimate I.

I19

Gutz: This blue cell I19 is the Destination cell of the Solver, with the residuals of the fitting, to be minimized. To open the Solver: (Office 2007) Data / Analysis / ? (Solver) (older Office) Tools/Solver Configure the second line of the setup box: Equal to: Value: 0 (zero). Destination cell (to be minimized): I19 Variable cells: I18 and cells of line 11 corresponding to acids/bases supposedly present in the sample, separated by a semicolon (you can also hold down Ctrl and click on all cells to be fitted); pKas can also be fitted, but see comments at I18 and F1. At the first regression, enter the Solver Options and check the box ordering the program to fit only positive values. Adjust other options, if required or to see if there is any improvement in the regression. If the Solver is not listed in Tools (Excel 2003) or Data / Analysis (Excel 2007), proceed as follows: (Excel 97-2003) - Close CurTiPot - Open a blank form - Click Tools/Supplements - Mark the Solver box and install it - If the file is not on the hard disk, locate it on the Office installation CD - Once Solver appears on the Tools list, load Curtipot again This procedure is required only once on a computer. (Excel 2007) - Click on the Windows button (upper left corner) - Click on the Excel options at the last line - Look for suplements and load the Solver like described above.

I20

Gutz: 2 (two) is the normal exponent. 1 (one) may be tried to reduce effect of outliers in the data. With b=1 the Solver will minimize the |CHReg-CHcalc| residues (instead of their squares). Examination of the residues plot is recommended to decide about the value of a and/or rejection of outlliers from the data set.

Ready for 100 real or simulated data points; to expand range to 160, copy all columns, from line 141 down to 200

weighted CHcalc

residue mol/L mol/L mol/L

6.440E-08 2.538E-04 1.81E-01 1.80E-018.885E-12 -2.981E-06 1.73E-01 1.73E-016.589E-08 -2.567E-04 1.65E-01 1.65E-011.352E-07 -3.677E-04 1.57E-01 1.58E-012.472E-07 4.972E-04 1.49E-01 1.49E-011.431E-08 -1.196E-04 1.41E-01 1.41E-011.222E-08 1.105E-04 1.34E-01 1.34E-011.968E-08 -1.403E-04 1.27E-01 1.27E-013.935E-09 -6.273E-05 1.21E-01 1.21E-013.272E-08 1.809E-04 1.15E-01 1.14E-012.799E-07 -5.291E-04 1.09E-01 1.09E-012.585E-09 5.084E-05 1.04E-01 1.04E-011.102E-11 3.319E-06 9.93E-02 9.93E-021.456E-08 1.207E-04 9.54E-02 9.53E-023.942E-08 1.985E-04 9.21E-02 9.19E-022.260E-08 1.503E-04 8.95E-02 8.93E-023.569E-08 1.889E-04 8.72E-02 8.71E-029.438E-11 9.715E-06 8.53E-02 8.53E-021.420E-08 -1.191E-04 8.34E-02 8.35E-025.686E-10 2.385E-05 8.15E-02 8.15E-022.263E-08 1.504E-04 7.97E-02 7.95E-023.408E-09 -5.838E-05 7.79E-02 7.80E-027.277E-11 8.530E-06 7.64E-02 7.64E-022.662E-09 -5.160E-05 7.51E-02 7.52E-025.963E-09 -7.722E-05 7.42E-02 7.43E-025.640E-15 7.510E-08 7.35E-02 7.35E-021.175E-09 3.428E-05 7.31E-02 7.30E-022.058E-11 -4.537E-06 7.28E-02 7.28E-026.090E-13 -7.804E-07 7.26E-02 7.26E-023.970E-12 1.992E-06 7.24E-02 7.24E-029.866E-10 -3.141E-05 7.23E-02 7.24E-022.069E-10 1.438E-05 7.23E-02 7.23E-021.335E-10 -1.155E-05 7.23E-02 7.23E-027.869E-12 2.805E-06 7.22E-02 7.22E-026.829E-11 8.263E-06 7.22E-02 7.22E-025.219E-10 -2.285E-05 7.22E-02 7.22E-025.161E-11 7.184E-06 7.21E-02 7.21E-023.582E-11 5.985E-06 7.21E-02 7.21E-022.200E-13 -4.691E-07 7.20E-02 7.20E-027.931E-12 -2.816E-06 7.19E-02 7.19E-027.237E-10 2.690E-05 7.18E-02 7.17E-021.117E-10 1.057E-05 7.15E-02 7.15E-023.220E-10 -1.794E-05 7.11E-02 7.12E-024.864E-11 -6.975E-06 7.06E-02 7.06E-021.929E-11 -4.392E-06 6.97E-02 6.97E-029.528E-09 9.761E-05 6.85E-02 6.84E-022.291E-08 -1.514E-04 6.69E-02 6.70E-026.786E-08 2.605E-04 6.46E-02 6.44E-02

CHReg-CHcalc CHReg

0.0 10.0 20.0 30.0 40.0 50.0 60.00.0

2.0

4.0

6.0

8.0

10.0

12.0



Titrant volume (mL)

pH

0.0 10.0 20.0 30.0 40.0 50.0 60.0-1.5E-01

-1.0E-01

-5.0E-02

0.0E+00

5.0E-02


Titrant volume (mL)

pH

Re

g-p

H

F39

Gutz: Usually, squared value of the residues given in column H, minimized by the Solver by fitting the selected parameters. See I20 and K20 comments for optional weighting sechemes.

G39

Gutz: unused column.

H39

Gutz: Residue (difference) of the total H+ concentration fitted with the Solver (column H) and the calculated one by the general equation (column I).

I39

Gutz: Value of the H+ concentration fitted by the Solver by minimization of the squares of the residues (column F) (or other weighting secheme, , see I20 and K20), taking dilution in account.

J39

Gutz: Total concentration of H+ required to satisfy all protonation equilibria, using the general equation, the concentrations of line 11 and the pKas given or under refinement.

7.917E-08 -2.814E-04 6.16E-02 6.19E-026.367E-09 7.979E-05 5.75E-02 5.74E-026.234E-08 -2.497E-04 5.16E-02 5.18E-02

Click on K2 to Q2; select acids/bases; click on J2; other options, read M1

62 7 31 5 8

Citric acid Hydroxide ion Ascorbic acid EDTA Phosphoric acid

-3 -1 -2 -4 -3

3.128 15.745 4.100 0.000 2.148

4.761 11.790 1.500 7.199

6.396 2.000 12.350

2.680

6.110

10.170

Correction of the pH sensor calibration

Intersection pH (may be fitted)

Slope (may be fitted, read comment)

Davies equation parameters

initial pH for activity coefficient estimation

0.000000 A

b

<--- Minimize with Solver

0.000

]


[H] max.free H+ (negative results are possible)

if >0, [ H+] non-fitted (strong acid); if <0, -[anions] to balance with cations

initial pOH for a ionic strength, I

<---Fit with Solver: CHReg and concentrations (line 11, in blue)

and (optionally) pKas

Wb=|dpH/dVol|b

0.0 10.0 20.0 30.0 40.0 50.0 60.0-6.0E-04

-4.0E-04

-2.0E-04

0.0E+00

2.0E-04

4.0E-04

6.0E-04 Residues (CH,Reg - CH,calc)

Titrant volume (mL)

CH

Re

g-C

Hc

alc

0.0 10.0 20.0 30.0 40.0 50.0 60.0-1.5E-01

-1.0E-01

-5.0E-02

0.0E+00

5.0E-02


Titrant volume (mL)

pH

Re

g-p

H

M1

Gutz: Options for selecting/editing names, charges and pKas: a) Write directly in the cells K3 to Q10 and R3 to T6 (ignoring line 2 settings); b) Click on names in line 2, slide along the list, click on another name (or a blank line); finally, click on J2 to load the constants from the Database; c) When applicable (see comments F1 and I18) , refine the pKas loaded by options a or b, by including them in the regression. Frequently used acids missing in the Database should be added to it.

N11

Gutz: Systematic departure of fitted curves from the experimental ones may have various (combined) causes, and N12 and N13 fitting should be attempted only when inaccurate calibration of the sensor is the most likey one (unreliable buffer solutions, temperature different from specified, deffective/drifting sensor), especially when the titrant and titrand composition is known and I was already estimated. Examples of other causes of misfitting: i) Incorrect use of the Regression module by beginners; ii) Deviation of the sensor response from the theoretical (Nersntian) one due to uncorrected acid or alkalyne error or uncorrected junction (diffusion) potential; these errors become more significant ant extreme pHs; iii) Standardization errors of the titrant or decomposition/contamination (CO2 absorption, etc.); Some improvement may be reached by the fitting CO2 contamination in the titrant; iv) Missing or undercorrection of the effect of ionic strength and temperature on activity coefficients and pKas; Regression assumes that the pKa values (from the database or other source) are for I=0 and same temperature as the titration. This may not be the case (the database contains some pKas for I>0 or t not 25oC; pKa values can be refined by MPNLR if all other parameters are accurately known.

L16

Gutz: To set I=0, click on "Set I=0 and gH+=1" at cell A20; To enter concentrations of electrolytes, fill cells S12 to T13; To calculate I and recalculate it after each regression, click on "Calculate / Update I" at cells C20 or Q25 .

O16

Gutz: Default value is 0.509. A and b are parameters of the Davies equation, used for activity coefficient estimation. They depend on temperature, dielectric constant, electrolyte, etc. The recommended values for water at 25ºC are: A=0.509; b=0.300. The Davies eq. does not require the size of different hydrated ions but, to some degree, the A and b parameters may be empirically adjusted to more closely describe a given electrolyte. For example: For NaCl + HCl solutions, A=0.43 and b=0.49 conducts to gH+ values in excellent agreement with those provided (up to 0.5 mol/kg) in http://www.iupac.org/projects/2000/Aq_Solutions.zip on base of more complete equations fitted to experimental data. For phosphate solutions, A=0.51 and b=0.20 seems appropriate at pHs above neutrality.

O17

Gutz: Default value is 0.300. Read comment in cell J6 (above) and K15.

K20

Gutz: Default value of this exponent is 0 (zero), corresponding to unitary weight for all data (W0=1). A higher exponent (1 or more) increses the relative weight of pH data near inflections (higher |dpH/dVol|), resulting in a better fit in comparison with buffered regions, w hen the parameters of the chosen model cannot precisely describe the full data set.

Ready for 100 real or simulated data points; to expand range to 160, copy all columns, from line 141 down to 200

Dill. Titrant Dil Titrand den1 den2 den3

Citric acid Hydroxide ion Ascorbic acid

0.0000 1.0000 3.165E+07 2.912E+13 2.162E+110.0429 0.9571 9.072E+06 1.878E+13 9.063E+100.0853 0.9147 2.669E+06 1.209E+13 3.808E+100.1289 0.8711 7.812E+05 7.663E+12 1.560E+100.1735 0.8265 1.947E+05 4.467E+12 5.508E+090.2172 0.7828 7.119E+04 2.961E+12 2.531E+090.2584 0.7416 2.318E+04 1.828E+12 1.042E+090.2968 0.7032 8.784E+03 1.176E+12 4.782E+080.3324 0.6676 3.298E+03 7.365E+11 2.179E+080.3656 0.6344 1.267E+03 4.541E+11 1.022E+080.3965 0.6035 6.045E+02 3.058E+11 5.742E+070.4248 0.5752 2.442E+02 1.825E+11 2.860E+070.4499 0.5501 1.164E+02 1.155E+11 1.616E+070.4715 0.5285 5.742E+01 7.172E+10 9.247E+060.4896 0.5104 3.028E+01 4.456E+10 5.442E+060.5044 0.4956 1.732E+01 2.816E+10 3.323E+060.5167 0.4833 1.028E+01 1.753E+10 2.022E+060.5277 0.4723 6.717E+00 1.141E+10 1.299E+060.5381 0.4619 4.547E+00 7.360E+09 8.299E+050.5485 0.4515 3.101E+00 4.483E+09 5.023E+050.5588 0.4412 2.263E+00 2.742E+09 3.061E+050.5685 0.4315 1.820E+00 1.798E+09 2.003E+050.5770 0.4230 1.504E+00 1.113E+09 1.238E+050.5839 0.4161 1.321E+00 7.127E+08 7.917E+040.5891 0.4109 1.205E+00 4.554E+08 5.057E+040.5928 0.4072 1.124E+00 2.769E+08 3.073E+040.5953 0.4047 1.076E+00 1.685E+08 1.870E+040.5970 0.4030 1.049E+00 1.099E+08 1.220E+040.5981 0.4019 1.031E+00 6.866E+07 7.617E+030.5988 0.4012 1.019E+00 4.266E+07 4.733E+030.5992 0.4008 1.014E+00 3.122E+07 3.464E+030.5995 0.4005 1.007E+00 1.488E+07 1.652E+030.5998 0.4002 1.005E+00 1.179E+07 1.309E+030.5999 0.4001 1.003E+00 6.248E+06 6.941E+020.6000 0.4000 1.002E+00 3.634E+06 4.041E+020.6002 0.3998 1.002E+00 3.492E+06 3.883E+020.6003 0.3997 1.001E+00 1.550E+06 1.730E+020.6006 0.3994 1.000E+00 1.012E+06 1.133E+020.6010 0.3990 1.000E+00 6.663E+05 7.490E+010.6015 0.3985 1.000E+00 4.236E+05 4.798E+010.6024 0.3976 1.000E+00 2.539E+05 2.917E+010.6038 0.3962 1.000E+00 1.654E+05 1.934E+010.6059 0.3941 1.000E+00 1.067E+05 1.284E+010.6091 0.3909 1.000E+00 6.656E+04 8.383E+000.6137 0.3863 1.000E+00 4.182E+04 5.638E+000.6204 0.3796 1.000E+00 2.570E+04 3.850E+000.6295 0.3705 1.000E+00 1.696E+04 2.881E+000.6419 0.3581 1.000E+00 1.007E+04 2.117E+00

0.0 10.0 20.0 30.0 40.0 50.0 60.0-1.5E-01

-1.0E-01

-5.0E-02

0.0E+00

5.0E-02


Titrant volume (mL)

pH

Re

g-p

H

K39

Gutz: Dilution factor of the titrant when added to the sample (+water). For example, when the added titrant equals the volume ofthe sample (+water), the factor is 0.5

L39

Gutz: Dilution factor of the sample (plus dillution water, if any) that results from the addition of titrant at each point of the titration.

M39

Gutz: Sbpi [H]i, the denominator of h, average protonation numbers and of the species distribution coefficients.

0.6585 0.3415 1.000E+00 6.698E+03 1.743E+000.6814 0.3186 1.000E+00 4.079E+03 1.452E+000.7143 0.2857 1.000E+00 2.601E+03 1.288E+00

Click on K2 to Q2; select acids/bases; click on J2; other options, read M1

3 6 Titrant

Carbonic acid HCl Strong ACID Strong BASE Carbonic ac.

-2 -1 -1 -1 -2

6.352 -7.000 -7 15.745 6.352

10.329 10.329

pKw

13.9970

Correction of the pH sensor calibration Titrand ions Titrant ions

7.0000 Other ions 0.000000 0.000000

100.00% mol/L 0.000000 0.000000

Davies equation parameters (z = ion charge) 0.000000 0.000000

for activity coefficient estimation Minimum 0.000204 0.100029

0.509 of counter-ions 0.000102 0.050014

0.300 for acids/bases Counterion charge 1 1

Acid/base ions -0.005442 -0.040064

at given pH 0.002737 0.039990

0.005458 0.119986

0.000000 0.000000

Activity coeff. 1.000 1.000

5.2381E-03 1.6792E-13

1.9223E-12 5.9964E-02

pH

"p[H]" 2.281 12.775

Color coding




Ionic Strength, I (initial)

SCk(z=1)

SCk(z=2)

1/2.SCkzk2 = Ik

SzjCj

1/2.SCjzj2 = Ij

SziCi

1/2.SCizi2 = Ii

Total I I = Ii+Ij+Ik+IH

I applied I applied

g H+

[H+]

[OH-]

S2

Gutz: The titrant may contain up to three diprotic reagents (other than the default ones). Names and constants must be changed manually (load pKas from the database as a titrand and copy them to the titrant cells)

R3

Gutz: Strong acids like HCl ou HClO4 have negative pKas, possibly -6 or lower. For a diprotic titrant like H2SO4, use pKa1 = -6 and pKa2 = 1,8. You can specify any system with no more than 2 pKas as titrant (can be expanded by the author).

S3

Gutz: The accepted value of the pKa (=log Kp) of the strong base OH- is 15,745 at 25ºC and infinite dilution. The activity coefficient of OH- (and other ions) decreases as I grows up to 0,5 mol/L and more specific interactions with other cations becomo relevant at high I , so that lower pKa values are sometimes mentioned in the literature (see references in the Database for details). Any other mono or biprotonable acid or base can be used instead of OH-to compose the titrant.

T3

Gutz: Aqueous solutions exposed to air or stored in (gas permeable) plastic flasks are always contaminated with CO2. Thus, it is advisable to include the carbonic acid system in simulations and regressions. But any other mono- or biprotic system can be specified here. The pKa1 from the Database for for H2CO3 is the apparent one. By considering the fraction of dissolved CO2 converted in H2CO3 (most of it remains as CO2(aq)) a "true" pKa1 of 3.58 is reported.

R8

Gutz: The ionic dissociation product of water changes with temperature and ionic strength, I. For pure water at 25ºC, the accepted value is 13.997 (or 14.00). Values corrected for I can be calculated in module pH_calc.

S11

Gutz: Calculations in this column depend of the concentrations of acids and bases fitted by regression and of the update of I (click on button at Q25 or C20, "Calculate / Update I". Unknown concentrations of strong electrolytes in the sample (cells S12 and S13) will augment the uncertainty of the activity coefficient estimation.

T11

Gutz: Calculations in this column are made by clicking on G17 "Find titrant pH" and depend of the known or fitted concentrations of acids, bases and electrolytes in the titrant.

P12

Gutz: Default value is 7.000, meaning that the calibration is accurate for pH=7.000

R12

Gutz: Summation of monovalent ion concentrations. Example: for 0.1 mol/L NaCl, write 0.2 because you have 0.1 Na+ + 0.1 Cl-. This parameter may be fitted by regression to estimate the ammount of background electrolyte in the titrant or titrand, but uncertainty is high and results can be wrong, because activity coefficients present a minimum in function of concentration (around 0.4 mol/L) so that there are two concentrations with the same g.

P13

Gutz: Default value is 1.000, meaning that the slope of the sensor response is accurately calibrated (even if different from 100% or the theoretical one) and the operation temperature is the same of the calibration one (or compensated correctly by the pH meter).

R13

Gutz: Summation of bivalent ion concentrations. Example: for 0.1 mol/L Ca(NO3)2, write 0.1 in this line and 0.2 in the upper line.

P15

Gutz: CurTiPot recalculates apparent equilibrium constants at the ionic strength, I, of the solution from thermodynamic constants (I=0) by estimating activity coefficients with help of the Davies equation. The accuracy is good for I<0.05, acceptable for I<0.2 and poor for higher values of I. There is no rigorous means to calculate activity coefficients of individual ions, although there are many equations pursuing the reduction of the uncertainty of the estimates by taking in accountt individual effective ion size parameters and specific ion-ion interactions and/or introducing empirical coefficients fitted to real data. Such parameters are readily available only for the most common inorganic and organic ions, limiting their application range in comparision with the simple and general Davies eq. A compilation of over twenty equations with references to original work is available in the file Ionic St_effects.pdf contained in the package http://www.iupac.org/projects/2000/Aq_Solutions.zip For calculations involving seawater (e.g. ionic strength at different salinities), see: http://ioc.unesco.org/oceanteacher/oceanteacher2/02_InfTchSciCmm/01_CmpTch/05_ocsoft/01_toolbox/OcCalc/OcCalc.htm

Q15

Gutz: Minimum concentration of cations or anions to satisfy charge balance, after taking in account the H+ and OH- concentrations.

S18

Gutz: Includes H+ and OH- from water dissoc.

T18

Gutz: Includes H+ and OH- from water dissoc.

R22

Gutz: All activity coefficientes are estimated with the Davies equation. Read more in cells O15, N16 and N17.

R26

Gutz: "p[H]" is the value found in calculations where concentrations are used in the law of mass action expressions supplied with thermodynamic equilibrium constants – as usual in high school or introductory general chemistry classes and textbooks. Comparison with pH reveals that errors are small only for diluted solutions, where ion-ion interactions are less significant and activities depart less from concentrations (see comments in cells O15, N16 and N17).

den4 den5 den6 den7 den1 titrant

EDTA Phosphoric acid Carbonic acid HCl Strong ACID

2.635E+12 1.687E+15 1.316E+12 1.000E+00 1.000E+007.001E+11 5.956E+14 5.473E+11 1.000E+00 1.000E+002.059E+11 2.188E+14 2.271E+11 1.000E+00 1.000E+006.356E+10 8.031E+13 9.119E+10 1.000E+00 1.000E+001.744E+10 2.544E+13 3.099E+10 1.000E+00 1.000E+006.868E+09 1.080E+13 1.362E+10 1.000E+00 1.000E+002.399E+09 4.004E+12 5.192E+09 1.000E+00 1.000E+009.448E+08 1.633E+12 2.153E+09 1.000E+00 1.000E+003.579E+08 6.332E+11 8.448E+08 1.000E+00 1.000E+001.334E+08 2.391E+11 3.219E+08 1.000E+00 1.000E+006.002E+07 1.081E+11 1.464E+08 1.000E+00 1.000E+002.134E+07 3.839E+10 5.238E+07 1.000E+00 1.000E+008.615E+06 1.537E+10 2.115E+07 1.000E+00 1.000E+003.382E+06 5.932E+09 8.260E+06 1.000E+00 1.000E+001.348E+06 2.296E+09 3.254E+06 1.000E+00 1.000E+005.652E+05 9.205E+08 1.339E+06 1.000E+00 1.000E+002.365E+05 3.593E+08 5.445E+05 1.000E+00 1.000E+001.108E+05 1.539E+08 2.460E+05 1.000E+00 1.000E+005.300E+04 6.502E+07 1.123E+05 1.000E+00 1.000E+002.433E+04 2.483E+07 4.841E+04 1.000E+00 1.000E+001.194E+04 9.720E+06 2.220E+04 1.000E+00 1.000E+006.780E+03 4.429E+06 1.192E+04 1.000E+00 1.000E+003.727E+03 1.867E+06 6.195E+03 1.000E+00 1.000E+002.210E+03 8.688E+05 3.524E+03 1.000E+00 1.000E+001.341E+03 4.210E+05 2.070E+03 1.000E+00 1.000E+007.850E+02 1.993E+05 1.182E+03 1.000E+00 1.000E+004.669E+02 1.004E+05 6.917E+02 1.000E+00 1.000E+003.010E+02 5.812E+04 4.416E+02 1.000E+00 1.000E+001.866E+02 3.305E+04 2.718E+02 1.000E+00 1.000E+001.156E+02 1.927E+04 1.675E+02 1.000E+00 1.000E+008.466E+01 1.369E+04 1.223E+02 1.000E+00 1.000E+004.074E+01 6.249E+03 5.845E+01 1.000E+00 1.000E+003.245E+01 4.908E+03 4.645E+01 1.000E+00 1.000E+001.765E+01 2.562E+03 2.504E+01 1.000E+00 1.000E+001.068E+01 1.480E+03 1.497E+01 1.000E+00 1.000E+001.030E+01 1.421E+03 1.442E+01 1.000E+00 1.000E+005.126E+00 6.281E+02 6.952E+00 1.000E+00 1.000E+003.694E+00 4.098E+02 4.886E+00 1.000E+00 1.000E+002.773E+00 2.698E+02 3.557E+00 1.000E+00 1.000E+002.127E+00 1.718E+02 2.625E+00 1.000E+00 1.000E+001.676E+00 1.033E+02 1.974E+00 1.000E+00 1.000E+001.440E+00 6.763E+01 1.635E+00 1.000E+00 1.000E+001.284E+00 4.399E+01 1.410E+00 1.000E+00 1.000E+001.177E+00 2.781E+01 1.255E+00 1.000E+00 1.000E+001.111E+00 1.784E+01 1.160E+00 1.000E+00 1.000E+001.068E+00 1.135E+01 1.099E+00 1.000E+00 1.000E+001.045E+00 7.829E+00 1.065E+00 1.000E+00 1.000E+001.027E+00 5.054E+00 1.039E+00 1.000E+00 1.000E+00

1.018E+00 3.697E+00 1.026E+00 1.000E+00 1.000E+001.011E+00 2.642E+00 1.016E+00 1.000E+00 1.000E+001.007E+00 2.047E+00 1.010E+00 1.000E+00 1.000E+00

Titrand

Acid / Base Citric acid Hydroxide ion Ascorbic acid EDTA

Charge of B -3 -1 -2 -4 -3

2.489E+06 5.559E+15 6.166E+11 1.479E+10 2.239E+12

1.435E+11 10E-10 7.762E+15 1.905E+16 3.540E+19

1.928E+14 1E-10 1E-10 9.120E+18 4.977E+21

1E-10 1E-10 1E-10 9.120E+20 1E-10

1E-10 1E-10 1E-10 2.884E+22 1E-10

1E-10 1E-10 1E-10 2.884E+22 1E-10

0.000000

2.49E+06 5.56E+15 6.17E+11 1.48E+10 2.24E+12

1.44E+11 7.76E+15 1.91E+16 3.54E+19

1.93E+14 9.12E+18 4.98E+21

9.12E+20

2.88E+22

2.88E+22

-0.004986 0.000000 -0.000456 0.000000 0.000000

0.005018 0.000000 0.000456 0.000000 0.000000

Overall protonation constants = bp = PKp (calculated by the program)

Phosphoric acid

bp1

bp2

bp3

bp4

bp5

bp6

Overall apparent constants recalculated for applied intial I =bp1

bp2

bp3

bp4

bp5

bp6

SziCi

Szi2Ci

U5

Gutz: Blank cells were filled with a neglectable constant ,10-10, for calculation convenience. The betas are cumulative (or global) protonation constants, obtained by the product of the protonation constants Kp from 1 to i, with i stepping up to n (the maximum number of protons accepted by a base, same as the maximum number os dissociable protons of an acid, but in reversed order). Note that pKa = logKp for a monoprotic acid (because Kp = 1/Kd or pKd = 1/logKd ) and, for multiprotic systems, the first logKp is the last pKa. Protonation constants, Kp, and betas are preferred here in agreement with the most extensive compilations of equilibrium constants, e.g., Critical Stability Constants, Vol. 1–4 (complete reference in the Database), and because the equations become unified with those used for metal-ligand-proton equilibria, based on formation (instead of dissociation) constants.

U12

Gutz: Blank cells were filled with an insignificant dummy constant 10-10 for calculation convenience. The betas are cumulative (or global) protonation constants, obtained by multiplying the protonation constants Kp from 1 to i, with i stepping up to n, the maximum number of protons accepted by a (conjugated) base (same as the maximum number os dissociable protons of an acid, but in reversed order). Note that pKa = logKp for a monoprotic acid (because Kp = 1/Kd or pKd = 1/logKd ) and, for multiprotic systems, the first logKp is the last pKa. Protonation constants, Kp, and betas are preferred here in agreement with the most extensive compilations of equilibrium constants, e.g., Critical Stability Constants, Vol. 1–4 (complete references in the Database), and because the equations become unified with those used for metal-ligand-proton equilibria, based on formation (instead of dissociation) constants.

U18


den2 titrant den3 titrant h1 h2 h3 h4

Strong BASE Carbonic ac. Citric acid Hydroxide ion Ascorbic acid EDTA

2.912E+13 1.316E+12 2.875 1.000 1.985 3.1491.878E+13 5.473E+11 2.818 1.000 1.977 2.8951.209E+13 2.271E+11 2.741 1.000 1.965 2.6757.663E+12 9.119E+10 2.642 1.000 1.946 2.4864.467E+12 3.099E+10 2.503 1.000 1.910 2.3162.961E+12 1.362E+10 2.391 1.000 1.870 2.2211.828E+12 5.192E+09 2.260 1.000 1.805 2.1421.176E+12 2.153E+09 2.148 1.000 1.727 2.0927.365E+11 8.448E+08 2.035 1.000 1.625 2.0554.541E+11 3.219E+08 1.921 1.000 1.507 2.0293.058E+11 1.464E+08 1.823 1.000 1.409 2.0121.825E+11 5.238E+07 1.685 1.000 1.292 1.9921.155E+11 2.115E+07 1.553 1.000 1.207 1.9747.172E+10 8.260E+06 1.413 1.000 1.140 1.9494.456E+10 3.254E+06 1.278 1.000 1.092 1.9162.816E+10 1.339E+06 1.158 1.000 1.060 1.8701.753E+10 5.445E+05 1.043 1.000 1.038 1.8041.141E+10 2.460E+05 0.942 1.000 1.025 1.7277.360E+09 1.123E+05 0.836 1.000 1.016 1.6314.483E+09 4.841E+04 0.708 1.000 1.010 1.5102.742E+09 2.220E+04 0.574 1.000 1.006 1.3891.798E+09 1.192E+04 0.459 1.000 1.004 1.2941.113E+09 6.195E+03 0.339 1.000 1.003 1.2057.127E+08 3.524E+03 0.245 1.000 1.002 1.1414.554E+08 2.070E+03 0.171 1.000 1.001 1.0952.769E+08 1.182E+03 0.111 1.000 1.001 1.0591.685E+08 6.917E+02 0.070 1.000 1.000 1.0351.099E+08 4.416E+02 0.047 1.000 1.000 1.0216.866E+07 2.718E+02 0.030 1.000 1.000 1.0104.266E+07 1.675E+02 0.019 1.000 1.000 1.0013.122E+07 1.223E+02 0.014 1.000 1.000 0.9951.488E+07 5.845E+01 0.007 1.000 0.999 0.9791.179E+07 4.645E+01 0.005 1.000 0.999 0.9726.248E+06 2.504E+01 0.003 1.000 0.999 0.9453.634E+06 1.497E+01 0.002 1.000 0.998 0.9073.492E+06 1.442E+01 0.002 1.000 0.997 0.9041.550E+06 6.952E+00 0.001 1.000 0.994 0.8051.012E+06 4.886E+00 0.000 1.000 0.991 0.7296.663E+05 3.557E+00 0.000 1.000 0.987 0.6394.236E+05 2.625E+00 0.000 1.000 0.979 0.5302.539E+05 1.974E+00 0.000 1.000 0.966 0.4031.654E+05 1.635E+00 0.000 1.000 0.948 0.3061.067E+05 1.410E+00 0.000 1.000 0.922 0.2216.656E+04 1.255E+00 0.000 1.000 0.881 0.1504.182E+04 1.160E+00 0.000 1.000 0.823 0.1002.570E+04 1.099E+00 0.000 1.000 0.740 0.0641.696E+04 1.065E+00 0.000 1.000 0.653 0.0431.007E+04 1.039E+00 0.000 1.000 0.528 0.026

W39

Gutz: Mean proton number, h, associated with a base B at given pH. Consider HiB as partially dissociated at a given pH; h is the sum of the molar fraction times i of each species.

6.698E+03 1.026E+00 0.000 1.000 0.426 0.0184.079E+03 1.016E+00 0.000 1.000 0.311 0.0112.601E+03 1.010E+00 0.000 1.000 0.224 0.007

Titrant

Carbonic acid HCl Strong ACID Strong BASE Carbonic ac. Acid / Base

-2 -1 -1 -1 -2 Charge of B

2.133E+10 1.000E-07 1.000E-07 5.559E+15 2.133E+10

4.797E+16 1E-10 1E-10 1E-10 4.797E+16

1E-10 1E-10

1E-10 1E-10 Kw

1E-10 1E-10 1.007E-14

1E-10 1E-10

1.000 1.000

2.13E+10 1.00E-07 1.00E-07 5.56E+15 2.13E+10

4.80E+16 4.80E+16

0.000000 0.000000 0.000000 -0.000107 -0.039957

0.000000 0.000000 0.000000 0.000107 0.079872

Kw Kw

1.007E-14 1.007E-14


pKa1 = logKpn

pKa2 = logKpn-1

pKa3 = logKpn-2

pKa4 = logKpn-3

pKa5 = logKpn-4

pKa6 = logKpn-5

and g H+= recalc for g H+=

AF2


AF5

Gutz: See U5 to understand why pKa1 = logKpn

h5 h6 h7 h1 titrant h2 titrant h3 titrant

Carbonic acid HCl Strong ACID Strong BASE Carbonic ac.

2.424 2.000 0.000 0.000 1.000 2.0002.322 2.000 0.000 0.000 1.000 2.0002.234 2.000 0.000 0.000 1.000 2.0002.162 2.000 0.000 0.000 1.000 2.0002.101 1.999 0.000 0.000 1.000 1.9992.070 1.999 0.000 0.000 1.000 1.9992.044 1.999 0.000 0.000 1.000 1.9992.029 1.998 0.000 0.000 1.000 1.9982.018 1.997 0.000 0.000 1.000 1.9972.011 1.995 0.000 0.000 1.000 1.9952.007 1.992 0.000 0.000 1.000 1.9922.003 1.987 0.000 0.000 1.000 1.9872.000 1.979 0.000 0.000 1.000 1.9791.997 1.967 0.000 0.000 1.000 1.9671.993 1.947 0.000 0.000 1.000 1.9471.988 1.919 0.000 0.000 1.000 1.9191.981 1.876 0.000 0.000 1.000 1.8761.970 1.822 0.000 0.000 1.000 1.8221.955 1.749 0.000 0.000 1.000 1.7491.927 1.645 0.000 0.000 1.000 1.6451.886 1.526 0.000 0.000 1.000 1.5261.837 1.421 0.000 0.000 1.000 1.4211.760 1.310 0.000 0.000 1.000 1.3101.670 1.223 0.000 0.000 1.000 1.2231.564 1.155 0.000 0.000 1.000 1.1551.441 1.100 0.000 0.000 1.000 1.1001.324 1.062 0.000 0.000 1.000 1.0621.238 1.040 0.000 0.000 1.000 1.0401.163 1.023 0.000 0.000 1.000 1.0231.108 1.011 0.000 0.000 1.000 1.0111.081 1.004 0.000 0.000 1.000 1.0041.040 0.989 0.000 0.000 1.000 0.9891.032 0.983 0.000 0.000 1.000 0.9831.017 0.962 0.000 0.000 1.000 0.9621.010 0.935 0.000 0.000 1.000 0.9351.009 0.932 0.000 0.000 1.000 0.9321.003 0.857 0.000 0.000 1.000 0.8571.000 0.796 0.000 0.000 1.000 0.7960.998 0.719 0.000 0.000 1.000 0.7190.995 0.619 0.000 0.000 1.000 0.6190.991 0.494 0.000 0.000 1.000 0.4940.986 0.388 0.000 0.000 1.000 0.3880.978 0.291 0.000 0.000 1.000 0.2910.964 0.203 0.000 0.000 1.000 0.2030.944 0.138 0.000 0.000 1.000 0.1380.912 0.090 0.000 0.000 1.000 0.0900.872 0.061 0.000 0.000 1.000 0.0610.802 0.037 0.000 0.000 1.000 0.037

Phosphoric acid

0.730 0.025 0.000 0.000 1.000 0.0250.622 0.015 0.000 0.000 1.000 0.0150.512 0.010 0.000 0.000 1.000 0.010

Click on J2 to use these pKas in the Regression

Citric acid Hydroxide ion Ascorbic acid EDTA Carbonic acid

-3 -1 -2 -4 -3 -2

3.128 15.745 4.100 0.000 2.148 6.352

4.761 11.790 1.500 7.199 10.329

6.396 2.000 12.350

2.680

6.110

10.170

s loaded from the Database

Titrand

Phosphoric acid

Citric acid Hydroxide ion Ascorbic acid EDTA Carbonic acid

2.509E-03 2.280E-043.509E-03 3.357E-044.781E-03 4.919E-046.359E-03 7.244E-048.508E-03 1.135E-031.008E-02 1.551E-031.197E-02 2.203E-031.362E-02 2.929E-031.550E-02 3.820E-031.773E-02 4.774E-031.969E-02 5.442E-032.300E-02 6.213E-032.613E-02 6.656E-032.955E-02 6.939E-033.289E-02 7.077E-033.595E-02 7.112E-033.912E-02 7.095E-034.205E-02 7.028E-034.535E-02 6.935E-034.963E-02 6.823E-035.412E-02 6.694E-035.773E-02 6.560E-036.157E-02 6.441E-036.442E-02 6.342E-036.663E-02 6.266E-036.846E-02 6.213E-036.966E-02 6.176E-037.030E-02 6.152E-037.080E-02 6.136E-037.112E-02 6.127E-037.123E-02 6.122E-037.146E-02 6.123E-037.148E-02 6.123E-037.155E-02 6.133E-037.158E-02 6.150E-037.156E-02 6.150E-037.156E-02 6.206E-037.153E-02 6.258E-037.146E-02 6.335E-037.137E-02 6.463E-037.121E-02 6.693E-037.097E-02 6.986E-037.059E-02 7.421E-037.002E-02 8.102E-036.919E-02 9.033E-036.800E-02 1.031E-026.636E-02 1.154E-026.415E-02 1.321E-02

I1 I2 I3 I4 I5 I6

Phosphoric acid

6.117E-02 1.418E-025.706E-02 1.491E-025.118E-02 1.452E-02

HCl

-1

-7.000

I Ac./Base I total

HCl

0.000E+00 5.356E-03 5.458E-03 0.000000 0.0000001.143E-16 5.533E-03 7.777E-03 0.000000 0.0000003.525E-16 6.361E-03 1.072E-02 0.000000 0.0000008.413E-16 7.772E-03 1.431E-02 0.000000 0.0000001.942E-15 1.004E-02 1.881E-02 0.000000 0.0000003.667E-15 1.189E-02 2.283E-02 0.000000 0.0000007.071E-15 1.433E-02 2.733E-02 0.000000 0.0000001.261E-14 1.665E-02 3.156E-02 0.000000 0.0000002.257E-14 1.938E-02 3.608E-02 0.000000 0.0000004.026E-14 2.255E-02 4.090E-02 0.000000 0.0000006.483E-14 2.516E-02 4.506E-02 0.000000 0.0000001.164E-13 2.922E-02 5.053E-02 0.000000 0.0000001.948E-13 3.279E-02 5.535E-02 0.000000 0.0000003.287E-13 3.650E-02 6.014E-02 0.000000 0.0000005.493E-13 3.997E-02 6.451E-02 0.000000 0.0000008.954E-13 4.307E-02 6.834E-02 0.000000 0.0000001.474E-12 4.622E-02 7.211E-02 0.000000 0.0000002.312E-12 4.908E-02 7.552E-02 0.000000 0.0000003.656E-12 5.229E-02 7.925E-02 0.000000 0.0000006.117E-12 5.645E-02 8.393E-02 0.000000 0.0000001.019E-11 6.082E-02 8.881E-02 0.000000 0.0000001.581E-11 6.429E-02 9.277E-02 0.000000 0.0000002.592E-11 6.801E-02 9.691E-02 0.000000 0.0000004.096E-11 7.076E-02 1.000E-01 0.000000 0.0000006.467E-11 7.290E-02 1.024E-01 0.000000 0.0000001.070E-10 7.467E-02 1.044E-01 0.000000 0.0000001.766E-10 7.583E-02 1.056E-01 0.000000 0.0000002.715E-10 7.646E-02 1.064E-01 0.000000 0.0000004.356E-10 7.693E-02 1.069E-01 0.000000 0.0000007.018E-10 7.724E-02 1.072E-01 0.000000 0.0000009.599E-10 7.736E-02 1.074E-01 0.000000 0.0000002.014E-09 7.759E-02 1.076E-01 0.000000 0.0000002.544E-09 7.761E-02 1.076E-01 0.000000 0.0000004.800E-09 7.769E-02 1.077E-01 0.000000 0.0000008.255E-09 7.774E-02 1.078E-01 0.000000 0.0000008.593E-09 7.771E-02 1.078E-01 0.000000 0.0000001.936E-08 7.778E-02 1.079E-01 0.000000 0.0000002.967E-08 7.781E-02 1.079E-01 0.000000 0.0000004.510E-08 7.784E-02 1.079E-01 0.000000 0.0000007.101E-08 7.790E-02 1.080E-01 0.000000 0.0000001.186E-07 7.801E-02 1.082E-01 0.000000 0.0000001.825E-07 7.812E-02 1.084E-01 0.000000 0.0000002.838E-07 7.827E-02 1.086E-01 0.000000 0.0000004.575E-07 7.854E-02 1.090E-01 0.000000 0.0000007.338E-07 7.889E-02 1.096E-01 0.000000 0.0000001.207E-06 7.940E-02 1.105E-01 0.000000 0.0000001.856E-06 7.956E-02 1.111E-01 0.000000 0.0000003.188E-06 8.015E-02 1.123E-01 0.000000 0.000000

I7 I1 titrant I2 titrant I3 titrant IA/B/CI IA/B/CI

Strong ACID

Strong BASE

Carbonic ac.

calculated mol/L

calculated mol/L

applied mol/L

applied mol/L

AQ39

Gutz: Calculated at every iteraction, but applied manually between regressions. Considers I resulting from species of all protonation equilibria, including H+ and OH- but excluding counter-ions like Na+, Cl-, etc.

AR39

Gutz: Same as the column on the left plus counter-ions like Na+, Cl-, etc.

AS39

Gutz: Updated from the collumn on left by clicking on the button "Update I"

AT39

Gutz: Same as the column on the left plus background electrolyte (other completely dissociated ions not consideed yet). May be fitted by regression (cells S12 to T14)

4.916E-06 7.954E-02 1.125E-01 0.000000 0.0000008.353E-06 7.884E-02 1.130E-01 0.000000 0.0000001.373E-05 7.647E-02 1.122E-01 0.000000 0.000000

6.13E+01

1.0000 0.01091.0000 -0.00011.0000 -0.01081.0000 -0.01441.0000 0.01841.0000 -0.00441.0000 0.00411.0000 -0.00541.0000 -0.00241.0000 0.00721.0000 -0.02161.0000 0.00221.0000 0.00011.0000 0.00651.0000 0.01251.0000 0.01121.0000 0.01601.0000 0.00091.0000 -0.01081.0000 0.00211.0000 0.01331.0000 -0.00551.0000 0.00091.0000 -0.00721.0000 -0.01441.0000 0.00001.0000 0.01381.0000 -0.00271.0000 -0.00071.0000 0.00291.0000 -0.06541.0000 0.05111.0000 -0.05361.0000 0.01711.0000 0.05091.0000 -0.12931.0000 0.02731.0000 0.01561.0000 -0.00081.0000 -0.00321.0000 0.01911.0000 0.00491.0000 -0.00561.0000 -0.00141.0000 -0.00061.0000 0.00971.0000 -0.01111.0000 0.0138

g H+ pH - pHRNL

1.0000 -0.01111.0000 0.00221.0000 -0.0047

Titration curves and first derivatives overlay

Source of data to plot/overlay

1 0 0 0

0 0 1 1

1 0 0 0

0.0 10.0 20.0 30.0 40.0 50.0 60.00

2

4

6

8

10

12

14Titration curve(s) and/or derivative(s)

Titrant Volume (mL)

pH

DpH

/DV

Simulation dpH/dV Simulation with dispersion dpH/dV

Evaluation

Regression

dpH/dV Evaluation with smoothingAnalise I c/alisamentodpH/dV

dpH/dV Regression fitted curve dpH/dV

Titration curves and first derivatives overlay

Enable macros first; instructions at cell A22 of module calc_pH

How to change the axis of a curve Data ID on curves

How to copy/paste a curve

Update curve(s) after any change in Simulation, Evaluation or Regression

0.0 10.0 20.0 30.0 40.0 50.0 60.00

2

4

6

8

10

12

14Titration curve(s) and/or derivative(s)

Titrant Volume (mL)

pH

DpH

/DV

O3

Gutz: Uncheck and check a curve again to update it.

L4

Gutz: Click twice on the volume or pH scale to redifine it. Use Ctrl+Z (as many times as needed) to undo scale expansion

O4

Gutz: Click once on the graphic area, hover the mouse on any data point to readout its ID and coordinates.

L5

Gutz: To copy graphics with one or more curves and paste them into other documents (e.g.: Word or Excel) without links to the original: - Fill out the header of the graphic; - Click in the box of the graphic near the margins, to select it; - Replot at least one curve (uncheck / check again); - Press Ctrl+C and wait processing; - Switch to the Word (Excel) document; - Select Insert/Paste Special/Picture (enhanced metafile).

Simulation Simulation with dispersion (random errors)Vol pH Vol dpH/dVol Vol pH Vol dpH/dVol

0 1.80593272.1570917 2.02043534.0960384 2.23493795.7539624 2.4494405

7.077085 2.66394328.0608041 2.87844588.7492476 3.09294849.2095434 3.3074519.5078177 3.52195369.6974923 3.73645629.8172889 3.95095889.8936795 4.1654614

9.944385 4.37996419.9815251 4.594466710.014129 4.808969310.050161 5.023471910.098345 5.237974510.170081 5.452477110.281694 5.666979710.457025 5.881482310.729794 6.09598511.143875 6.3104876

11.74754 6.524990212.576545 6.739492813.625773 6.953995414.824492 7.16849816.043755 7.383000617.145787 7.597503218.040535 7.812005918.705899 8.0265085

19.16921 8.241011119.477513 8.4555137

19.676958 8.6700163

19.804374 8.884518919.886334 9.099021519.941236 9.313524119.981976 9.528026820.018398 9.742529420.059441 9.95703220.115237 10.17153520.199536 10.386037

20.332999 10.6005420.548016 10.81504220.896024 11.02954521.458622 11.24404822.364653 11.4585523.818284 11.67305326.154666 11.88755529.983217 12.10205836.643807 12.316561

50 12.531063

Evaluation Evaluation with smoothing/interpolationVol pH Vol dpH/dVol Vol pH Vol dpH/dVol Vol

0 2.265042 00.166667 2.267962 0.083333 0.017521 0.8968890.333333 2.271022 0.25 0.018363 1.864139

0.5 2.274363 0.416667 0.020047 2.960580.666667 2.278125 0.583333 0.022572 4.1980950.833333 2.282449 0.75 0.025939 5.548356

1 2.287474 0.916667 0.030149 6.9703871.166667 2.29334 1.083333 0.0352 8.4402231.333333 2.300189 1.25 0.041093 9.957523

1.5 2.30816 1.416667 0.047828 11.527831.666667 2.317394 1.583333 0.055404 13.142041.833333 2.328031 1.75 0.063823 14.76872

2 2.340212 1.916667 0.073083 16.356732.166667 2.354076 2.083333 0.083185 17.844782.333333 2.369764 2.25 0.094129 19.18178

2.5 2.387417 2.416667 0.105915 20.351672.666667 2.407084 2.583333 0.118003 21.384162.833333 2.428464 2.75 0.128279 22.34269

3 2.451168 2.916667 0.136225 23.2973.166667 2.474808 3.083333 0.14184 24.292353.333333 2.498996 3.25 0.145125 25.32645

3.5 2.523342 3.416667 0.14608 26.347643.666667 2.54746 3.583333 0.144705 27.280333.833333 2.57096 3.75 0.140999 28.06266

4 2.593454 3.916667 0.134963 28.669754.166667 2.614553 4.083333 0.126597 29.111924.333333 2.63387 4.25 0.1159 29.41908

4.5 2.651015 4.416667 0.102873 29.625484.666667 2.665606 4.583333 0.087545 29.761184.833333 2.677656 4.75 0.0723 29.84931

5 2.687862 4.916667 0.061238 29.906395.166667 2.69699 5.083333 0.054764 29.94375

5.333333 2.705803 5.25 0.05288 29.96912

5.5 2.715067 5.416667 0.055583 29.987865.666667 2.725546 5.583333 0.062876 30.003985.833333 2.738006 5.75 0.074757 30.02098

6 2.75321 5.916667 0.091227 30.042536.166667 2.771925 6.083333 0.112285 30.073286.333333 2.794906 6.25 0.13789 30.11979

6.5 2.822471 6.416667 0.16539 30.191836.666667 2.854245 6.583333 0.190645 30.30418

6.833333 2.889794 6.75 0.213293 30.479037 2.928683 6.916667 0.233335 30.74903

7.166667 2.970478 7.083333 0.250771 31.160637.333333 3.014745 7.25 0.2656 31.77711

7.5 3.061049 7.416667 0.277823 32.681427.666667 3.108776 7.583333 0.286363 33.983397.833333 3.156604 7.75 0.286969 35.84641

8 3.203037 7.916667 0.278596 38.567448.166667 3.246577 8.083333 0.261243 42.780718.333333 3.285729 8.25 0.234909 50

8.5 3.319613 8.416667 0.2033038.666667 3.350983 8.583333 0.1882228.833333 3.383918 8.75 0.197608

9 3.422646 8.916667 0.232379.166667 3.477306 9.083333 0.3279589.333333 3.565772 9.25 0.530796

9.5 3.706113 9.416667 0.8420489.666667 3.91601 9.583333 1.2593839.833333 4.220426 9.75 1.826496

10 4.619836 9.916667 2.39646210.16667 5.031093 10.08333 2.46754210.33333 5.345139 10.25 1.884272

10.5 5.56327 10.41667 1.30878610.66667 5.716865 10.58333 0.92157310.83333 5.833781 10.75 0.701497

11 5.933998 10.91667 0.60130111.16667 6.019219 11.08333 0.51132611.33333 6.087287 11.25 0.408411

11.5 6.138817 11.41667 0.30917611.66667 6.178756 11.58333 0.23963711.83333 6.212433 11.75 0.20206

12 6.24515 11.91667 0.196312.16667 6.280039 12.08333 0.20933612.33333 6.316381 12.25 0.218051

12.5 6.353059 12.41667 0.22006912.66667 6.388957 12.58333 0.21538912.83333 6.422959 12.75 0.204013

13 6.453974 12.91667 0.18608713.16667 6.481649 13.08333 0.16605213.33333 6.506484 13.25 0.149005

13.5 6.529022 13.41667 0.13522813.66667 6.549808 13.58333 0.1247213.83333 6.569388 13.75 0.117482

14 6.588307 13.91667 0.11351314.16667 6.607109 14.08333 0.11281314.33333 6.626332 14.25 0.115337

14.5 6.646214 14.41667 0.11928814.66667 6.6666 14.58333 0.12232114.83333 6.687313 14.75 0.124277

15 6.708173 14.91667 0.12515715.16667 6.729 15.08333 0.12496115.33333 6.749614 15.25 0.123688

15.5 6.769838 15.41667 0.12133915.66667 6.78949 15.58333 0.117914

15.83333 6.808392 15.75 0.11341316 6.826365 15.91667 0.107835

16.16667 6.843272 16.08333 0.10144316.33333 6.859175 16.25 0.095417

16.5 6.874189 16.41667 0.09008816.66667 6.888432 16.58333 0.08545616.83333 6.902019 16.75 0.081521

17 6.915066 16.91667 0.07828317.16667 6.92769 17.08333 0.07574217.33333 6.940006 17.25 0.073899

17.5 6.952132 17.41667 0.07275317.66667 6.964182 17.58333 0.07230317.83333 6.976274 17.75 0.072551

18 6.988523 17.91667 0.07349618.16667 7.001046 18.08333 0.07513418.33333 7.013933 18.25 0.077326

18.5 7.027253 18.41667 0.07992118.66667 7.041072 18.58333 0.0829118.83333 7.055454 18.75 0.086293

19 7.070466 18.91667 0.0900719.16667 7.086173 19.08333 0.09424219.33333 7.10264 19.25 0.098807

19.5 7.119935 19.41667 0.10376719.66667 7.138122 19.58333 0.10912119.83333 7.157267 19.75 0.114869

20 7.177435 19.91667 0.12101220.16667 7.198693 20.08333 0.12754820.33333 7.221107 20.25 0.134479

20.5 7.244708 20.41667 0.14160820.66667 7.269311 20.58333 0.14761720.83333 7.294638 20.75 0.151962

21 7.320411 20.91667 0.15464221.16667 7.346354 21.08333 0.15565621.33333 7.372188 21.25 0.155006

21.5 7.397637 21.41667 0.15269121.66667 7.422422 21.58333 0.1487121.83333 7.446266 21.75 0.143064

22 7.468892 21.91667 0.13575422.16667 7.490021 22.08333 0.12677822.33333 7.509377 22.25 0.116137

22.5 7.526682 22.41667 0.10383122.66667 7.541667 22.58333 0.08990622.83333 7.554327 22.75 0.075964

23 7.564988 22.91667 0.06396623.16667 7.573994 23.08333 0.05403223.33333 7.581687 23.25 0.046162

23.5 7.588413 23.41667 0.04035523.66667 7.594515 23.58333 0.03661323.83333 7.600337 23.75 0.034934

24 7.606224 23.91667 0.03531924.16667 7.612519 24.08333 0.03776824.33333 7.619565 24.25 0.042281

24.5 7.627708 24.41667 0.04885824.66667 7.637282 24.58333 0.05744

24.83333 7.648392 24.75 0.06666225 7.660917 24.91667 0.075152

25.16667 7.674725 25.08333 0.08284825.33333 7.689684 25.25 0.089751

25.5 7.70566 25.41667 0.0958625.66667 7.722523 25.58333 0.10117625.83333 7.740139 25.75 0.105698

26 7.758377 25.91667 0.10942826.16667 7.777105 26.08333 0.11236326.33333 7.796285 26.25 0.115082

26.5 7.816578 26.41667 0.12175726.66667 7.838949 26.58333 0.13422726.83333 7.864365 26.75 0.152498

27 7.893794 26.91667 0.17657227.16667 7.928202 27.08333 0.20644827.33333 7.968556 27.25 0.242126

27.5 8.015741 27.41667 0.28310927.66667 8.068651 27.58333 0.31746227.83333 8.124144 27.75 0.332958

28 8.178984 27.91667 0.32904128.16667 8.229936 28.08333 0.30571228.33333 8.273798 28.25 0.263168

28.5 8.310661 28.41667 0.22117828.66667 8.346689 28.58333 0.2161728.83333 8.3887 28.75 0.252067

29 8.44356 28.91667 0.32915929.16667 8.518654 29.08333 0.45056729.33333 8.621767 29.25 0.618678

29.5 8.767218 29.41667 0.87270429.66667 8.979965 29.58333 1.27648329.83333 9.280774 29.75 1.804852

30 9.679624 29.91667 2.39310230.16667 10.09585 30.08333 2.49733630.33333 10.41627 30.25 1.922549

30.5 10.63304 30.41667 1.30060930.66667 10.78242 30.58333 0.89625430.83333 10.89093 30.75 0.651075

31 10.97056 30.91667 0.47780231.16667 11.02985 31.08333 0.35571931.33333 11.0748 31.25 0.269684

31.5 11.11126 31.41667 0.21881331.66667 11.14288 31.58333 0.18972531.83333 11.17067 31.75 0.166698

32 11.19547 31.91667 0.14883232.16667 11.21816 32.08333 0.13612832.33333 11.23958 32.25 0.128487

32.5 11.26028 32.41667 0.12420332.66667 11.28058 32.58333 0.12184132.83333 11.30081 32.75 0.121357

33 11.32127 32.91667 0.1227533.16667 11.34227 33.08333 0.12602133.33333 11.36413 33.25 0.13117

33.5 11.38717 33.41667 0.13819633.66667 11.41157 33.58333 0.146401

33.83333 11.43711 33.75 0.15324734 11.46347 33.91667 0.158157

34.16667 11.49032 34.08333 0.16113234.33333 11.51735 34.25 0.162171

34.5 11.54423 34.41667 0.16127634.66667 11.57064 34.58333 0.15844434.83333 11.59625 34.75 0.153678

35 11.62075 34.91667 0.14697635.16667 11.6438 35.08333 0.13833835.33333 11.6651 35.25 0.127765

35.5 11.68431 35.41667 0.11530635.66667 11.70136 35.58333 0.10227635.83333 11.71638 35.75 0.090115

36 11.72953 35.91667 0.07889436.16667 11.74096 36.08333 0.06861436.33333 11.75084 36.25 0.059274

36.5 11.75932 36.41667 0.05087536.66667 11.76656 36.58333 0.04341736.83333 11.77271 36.75 0.036899

37 11.77793 36.91667 0.03132137.16667 11.78238 37.08333 0.02668537.33333 11.78621 37.25 0.022989

37.5 11.78958 37.41667 0.02023337.66667 11.79265 37.58333 0.01841837.83333 11.79557 37.75 0.017544

38 11.79851 37.91667 0.0176138.16667 11.80161 38.08333 0.01861738.33333 11.80504 38.25 0.020565

38.5 11.80893 38.41667 0.02335638.66667 11.81331 38.58333 0.02629638.83333 11.81816 38.75 0.02908

39 11.82344 38.91667 0.03170539.16667 11.82914 39.08333 0.03417339.33333 11.83522 39.25 0.036482

39.5 11.84166 39.41667 0.03863339.66667 11.84843 39.58333 0.04062639.83333 11.85551 39.75 0.042462

40 11.86286 39.91667 0.04413940.16667 11.87047 40.08333 0.04565840.33333 11.87831 40.25 0.047019

40.5 11.88635 40.41667 0.04822240.66667 11.89456 40.58333 0.04926740.83333 11.90292 40.75 0.050154

41 11.9114 40.91667 0.05088341.16667 11.91997 41.08333 0.05145341.33333 11.92862 41.25 0.051866

41.5 11.9373 41.41667 0.05212141.66667 11.94601 41.58333 0.05221741.83333 11.9547 41.75 0.052156

42 11.96336 41.91667 0.05193742.16667 11.97195 42.08333 0.05155942.33333 11.98045 42.25 0.051024

42.5 11.98884 42.41667 0.0503342.66667 11.99709 42.58333 0.049478

42.83333 12.00517 42.75 0.04846943 12.01305 42.91667 0.047313

43.16667 12.02074 43.08333 0.04612543.33333 12.02823 43.25 0.044964

43.5 12.03554 43.41667 0.04383243.66667 12.04266 43.58333 0.04272843.83333 12.0496 43.75 0.041653

44 12.05637 43.91667 0.04060544.16667 12.06297 44.08333 0.03958644.33333 12.0694 44.25 0.038596

44.5 12.07567 44.41667 0.03763344.66667 12.08179 44.58333 0.03669944.83333 12.08775 44.75 0.035794

45 12.09357 44.91667 0.03491645.16667 12.09925 45.08333 0.03406745.33333 12.10479 45.25 0.033246

45.5 12.1102 45.41667 0.03245445.66667 12.11548 45.58333 0.03168945.83333 12.12064 45.75 0.030953

46 12.12568 45.91667 0.03024646.16667 12.13061 46.08333 0.02956646.33333 12.13543 46.25 0.028915

46.5 12.14014 46.41667 0.02829346.66667 12.14476 46.58333 0.02769846.83333 12.14928 46.75 0.027132

47 12.15372 46.91667 0.02659447.16667 12.15806 47.08333 0.02608547.33333 12.16233 47.25 0.025604

47.5 12.16652 47.41667 0.02515147.66667 12.17064 47.58333 0.02472647.83333 12.1747 47.75 0.02433

48 12.17869 47.91667 0.02396248.16667 12.18263 48.08333 0.02362248.33333 12.18651 48.25 0.023311

48.5 12.19035 48.41667 0.02302848.66667 12.19415 48.58333 0.02277348.83333 12.19791 48.75 0.022547

49 12.20163 48.91667 0.02234949.16667 12.20533 49.08333 0.02217949.33333 12.209 49.25 0.022037

49.5 12.21265 49.41667 0.02192449.66667 12.21629 49.58333 0.02183949.83333 12.21992 49.75 0.021783

50 12.22355 49.91667 0.021754

Regression raw data Regression fitted curvepH Vol dpH/dVol Vol pH Vol dpH/dVol

2.2808282.4714172.6624662.8605853.0949883.2735313.4831263.6744163.8778454.0878324.2595044.4838214.6824084.8893595.0960085.2953255.5011585.6875895.8781366.0934066.3068686.4901536.6984796.8921227.0865817.3027167.5183357.7038727.9083238.1149918.2506368.572292

8.673532

8.9492349.1845859.2019199.5545949.7397159.92132810.1180910.34027

10.5265110.7167110.9217711.1236411.3351311.5156611.7421211.9191312.1345812.32998

Database of dissociation constants of acids / protonation constants of bases

More systems, e.g., from the sources given next, can be added: a) at the end of the list; b) in alphabetic order by inserting line(s) and redoing the sequential numbering (column B).

Larger compilations of equilibrium constants and examples of on-line literature on acid-base equilibrium

Martell, A. E., Smith, R. M., Critical Stability Constants, Vol. 1–4. Plenum Press: New York, 1976.

Perrin, D. D., Dissociation Constants of Organic Bases in Aqueous Solution, Butterworths, London, 1965; Supplement, 1972.

Serjeant, E. P., and Dempsey, B., Ionization Constants of Organic Acids in Aqueous Solution, Pergamon, Oxford, 1979.

Albert, A., "Ionization Constants of Heterocyclic Substances", in Physical Methods in Heterocyclic Chemistry, Katritzky, A. R., Ed., Academic Press, New York, 1963.

Perrin, D. D., Dempsey, B., and Serjeant, E. P., pKa Prediction for Organic Acids and Bases, Chapman & Hall, London, 1981.

Dawson, R. M. C., Elliot, D. C., Elliot, W. H., and Jones, K. M., Data for Biochemical Research, Oxford Science Publications, Oxford, 1986.

Dissociation constants of inorganic and organic compounds (compliation with 33 pages)

Dissociation constants of organic compounds (~600 compounds)

Visual Indicators for acid-base titrations

Activity coefficient estimation:an appreciation of 20 equations: Ionic St_effects.pdf in the package: http://www.iupac.org/projects/2000/Aq_Solutions.zip

Ácid or Base Charge, fully

deprotonated

F R E Q U E N T L Y U S E D 1 Acetic acid -1 4.7572 Ammonia 0 9.2443 Carbonic acid -2 6.352 10.3294 Citric acid -3 3.128 4.761 6.3965 EDTA -4 0 1.5 26 HCl -1 -77 Hydroxide ion -1 15.7458 Phosphoric acid -3 2.148 7.199 12.359 0 0

10 0 011 A L P H A B E T I C O R D E R Insert new lines anywere to add more systems; renumber column B12 Acetamide 0 0.6313 Acetic acid -1 4.75714 Acetoacetic acid -1 3.5815 Acrylic acid -1 4.2516 Adipic acid -2 4.43 5.4117 Alanine -1 2.348 9.86718 Aminobenzene = aniline 0 4.619 2-Aminobenzoic acid -1 2.108 4.94620 4-Animobenzoic acid -1 2.501 4.87421 2-Aminobutanoic acid -1 2.29 9.8322 6-Aminohexanoic acid -1 4.373 10.80423 5-Aminopentanoic acid -1 4.27 10.76624 2-Aminophenol -1 4.78 9.9725 -1 3.55 10.2426 Ammonia 0 9.24427 Aniline 0 4.63

Most constants given in this compilation of ~250 systems – but not all – were obtained at 25º C and are thermodynamic ones ( I=0), as required by the pH_calc and Regression modules.

No guarantee is given that the compiled pKas or the calculations made with CurTiPot are correct or accurate. CurTiPot takes in account only protonation equilibria and other chemical reactions can occur for many combinations of two or more of the listed systems.

The modules pH_calc and Regression estimate gi by the Davies equation:

pKa1 pKa2 pKa3

b-Alanine

A3

Gutz: Gray or red numbers denote knowingly uncertain pKas; the number os decimal places is indicative of precision, but values may be wrong or innacurate; for many systems, the "constants" vary from author to author or depend of the experimental technique used to study the equilibria. For other systems, no reliable determination is available.

A5

Gutz: Attention: some extensive compilations of equilibrium constants present protonation constants (or their logarithms) instead of dissociation constants. The conversion is straightforward as shown in cells M12-M18.

D19

Gutz: Charge of the most deprotonated (dissociated) form of the (conjugated) base considered in the equilibria of an acid-base system for the constants given.

E20

Gutz: Uncertain pKa values are displayed in gray; very uncertain values, in red.

C24

Gutz: Aqueous solutions exposed to air or stored in (gas permeable) plastic flasks are always contaminated with CO2. Thus, it is advisable to include the carbonic acid system in simulations and regressions. The pKa1 for H2CO3 is apparent. By considering the fraction of dissolved CO2 converted in H2CO3 (most of it remains as CO2(aq)) a "true" pKa of 3.58 is found.

E24

Gutz: This is the aparent pKa. By considering that only a part of the dissolved CO2 is converted in H2CO3 and part remains as CO2(aq), the "true" pKa would be 3.58

E27

Gutz: Very uncertain pKa value, but still so low that it does not impair tha accuracy of calculations in the usual pH range.

B28

Gutz: Aqueous solutions exposed to air or stored in (gas permeable) plastic flasks are always contaminated with CO2. Thus, it is advisable to include the carbonic acid system in simulations and regressions. The pKa1 for H2CO3 is apparent. By considering the fraction of dissolved CO2 converted in H2CO3 (most of it remains as CO2(aq)) a "true" pKa of 3.58 is found.

28 Arginine -1 1.823 8.991 12.4829 Arsenic acid -3 2.24 6.96 11.530 Arsenous acid -1 9.2231 Ascorbic acid -2 4.1 11.7932 Asparagine -1 2.14 8.7233 Aspartic acid -2 1.99 3.9 10.00234 Barbital 0 7.4335 Barbituric acid -1 4.0136 Benzenesulfonic acid -1 0.737 Benzoic acid -1 4.1938 Benzylamine 0 9.3339 2-Benzylpyridine 0 5.1340 Betaine -1 1.8341 Boric acid -3 9.236 12.74 13.842 Butanoic acid -1 4.8343 3-Butenoic acid -1 4.3444 Butylamine 0 10.7745 sec-Butylamine 0 10.5646 tert-Butylamine 0 10.6847 Cadaverine 0 10.05 10.9348 Carbonic acid -2 6.352 10.32949 Catechol -2 9.4 12.850 Chloroacetic acid -1 2.86551 2-Chloroaniline 0 2.6552 3-Chloroaniline 0 3.4653 4-Chloroaniline 0 4.1554 2-Chlorobenzoic acid -1 2.9255 3-Chlorobenzoic acid -1 3.8256 4-Chlorobenzoic acid -1 3.9857 3-Chlorophenol -1 8.8558 4-Chlorophenol -1 9.1859 2-Chlorophenol -1 8.4960 Choline 0 13.961 Chromic acid -2 –0,2 6.5162 Citric acid -3 3.128 4.761 6.39663 Codeine 0 8.2164 Creatinine 0 4.83 9.265 m-Cresol -1 10.0166 O-Cresol -1 10.267 p-Cresol -1 10.1768 Cupferron -1 4.1669 Cyanic acid -1 3.4670 Cysteine -2 1.71 8.36 10.7771 Decylamine 0 10.6472 2,4-Diaminobutanoic acid -1 1.85 8.24 10.4473 Dichloroacetic acid -1 1.374 2,3-Dichlorophenol -1 7.4675 Diethylamine 0 10.93376 Diisopropylamine 0 11.0577 Dimethylamine 0 10.77478 Dimethylglyoxime -2 10.66 12.079 2,3-Dimethylpyridine 0 6.5880 2,4-Dimethylpyridine 0 6.9981 2,5-Dmethylpyridine 0 6.4

E69

Gutz: The pKa1 for H2CO3 is apparent. By considering the fraction of dissolved CO2 converted in H2CO3 (most of it remains as CO2(aq)) a "true" pKa of 3.58 is found.

82 2,6-Dimethylpyridine 0 6.6583 3,4-Dimethylpyridine 0 6.4684 3.5-Dimethylpyridine 0 6.1585 Dinicotinic acid -1 2.886 Diphenylamine 0 0.7987 Dipicolinic acid -2 2.16 4.7688 Dopamine -1 8.9 10.689 d-Ephedrine 0 10.13990 Ethanolamine 0 9.591 Ethylamine 0 10.63692 Ethylenediamine 0 6.848 9.92893 Ethylenediaminetetraacet -4 0 1.5 294 Ethyleneimine 0 8.0195 2-Ethylpyridine 0 5.8996 Formic acid -1 3.74597 Fumaric acid -2 3.053 4.49498 L-Glutamic acid -1 2.23 4.42 9.9599 L-Glutamine -1 2.17 9.13

100 L-Glutathione -2 2.12 3.59 8.75101 Glyceric acid -1 3.52102 Glycerol -1 14.15103 Glycine -2 2.35 9.778104 Glycolic acid -1 3.831105 Glyoxylic acid -1 3.18106 Heptanedioic acid -1 4.71107 Heptanoic acid -1 4.89108 Heptylamine 0 10.67109 Hexamethylenediamine 0 10.762 11.857110 Hexanoic acid -1 4.85111 Hexylamine 0 10.56112 Histamine 0 6.04 9.75113 Histidine -1 1.7 6.02 9.08114 Hydrazine 0 8.07115 Hydroazoic -1 4.72116 Hydrogen bromide -1 -9117 Hydrogen chloride -1 -7118 Hydrogen chromate ion -1 6.52119 Hydrogen cyanide -1 9.21120 Hydrogen fluoride -1 3.17121 Hydrogen peroxide -1 11.65

122 Hydrogen selenate ion -1 1.66123 Hydrogen sulfide -2 7.02 13.9124 Hydrogen thiocyanate -1 0.9125 Hydroquinone 0 10.35126 Hydroxylamine 0 5.96127 m-Hydroxybenzoic acid -2 4.06 9.92128 p-Hydroxybenzoic acid -2 4.48 9.32129 3-Hydroxypropanoic acid -1 4.51130 8-Hydroxyquinoline -1 4.91 9.81131 Hypobromous -1 8.63132 Hypochlorous -1 7.53133 Hypoiodous -1 10.64134 Imidazole 0 6.953135 Iodic acid -1 0.77

E137


E138


136 Isocitric acid -3 3.29 4.71 6.4137 Isoleucine -1 2.319 9.754138 Lactic acid -1 3.86139 l-Ephedrine 0 9.958140 l-Leucine -1 2.328 9.744141 Lysine -1 2.04 9.08 10.69142 Maleic acid -2 1.91 6.332143 Malic acid -2 3.459 5.097144 Malonic acid -2 2.847 5.696145 Melamine = 1,3,5-triazine- 0 5146 Methionine = (S)-2-amino- -1 2.13 9.27147 Methylamine 0 10.63148 2-Methylaniline = o-toui 0 4.447149 4-Methylaniline = p-tolui 0 5.084150 2-Methylbenzimidazole 0 6.19151 2-Methylbutanoic acid -1 4.8152 3-Methylbutanoic acid -1 4.77153 Methylmalonic acid -2 3.07 5.76154 Methyl-1-naphthylamine 0 3.67155 4-Methylpentanoic acid -1 4.84156 1-Methylpiperidine 0 10.08157 2-Methylphenol = o-creso -1 10.28158 4-Methylphenol = p-creso -1 10.26159 2-Methylpyridine 0 5.97160 3-Methylpyridine 0 5.68161 4-Methylpyridine 0 6.02162 Morphine 0 8.21163 Morpholine 0 8.33164 1-Naphthol -1 9.34165 2-Naphthol -1 9.51166 Nicotine 0 3.12 8.02167 Nitrilotriacetic acid -3 1.1 1.65 2.94168 2-Nitroaniline 0 -0.26169 3-Nitroaniline 0 2.466170 4-Nitroaniline 0 1171 2-Nitrobenzoic acid -1 2.179172 2-Nitrophenol -1 7.21173 3-Nitrophenol -1 8.39174 4-Nitrophenol -1 7.15175 3-Nitrobenzoic acid -1 3.449176 4-Nitrobenzoic acid -1 3.442177 Nitrous acid -1 3.15178 Noradrenaline -1 8.64 9.7179 Octadecylamine 0 10.6180 Octanedioic acid -1 4.52181 Octanoic acid -1 4.89182 Oxalic acid -2 1.252 4.266183 Oxaloacetic acid -2 2.22 3.89 13.03184 Papaverine 0 6.4185 Pentanoic acid -1 4.84186 Perchloric acid -1 -10187 p-Periodic acid -2 1.55 8.28188 1,10-Phenanthroline 0 4.84189 m-Phenetidine 0 4.18

E207


190 o-Phenetidine 0 4.43191 Phenol -1 9.98192 Phenylacetic acid -1 4.28193 Phenylalanine -1 2.2 9.31194 Phenylethylamine 0 9.84195 Phenylglycine -1 1.83 4.39196 Phosphoric acid -3 2.148 7.199 12.35197 m-Phthalic acid -2 3.54 4.6198 o-Phthalic acid -2 2.95 5.408199 p-Phthalic acid -2 3.51 4.82200 Picolinic acid -2 1.07 5.25201 Picric acid -1 0.38202 Pilocarpine 0 6.87203 Piperazine 0 5.56 9.83204 Piperidine 0 7.53 11.123205 p-Phenetidine 0 5.2206 Proline -1 1.952 10.64207 Propanoic acid -1 4.874208 Propylamine 0 10.566209 Purine 0 2.3 8.96210 Pyridine 0 5.229211 3-Pyridinecarboxylic acid -1 4.85212 4-Pyridinecarboxylic acid -1 4.96213 Pyrimidine 0 6.35214 Pyrocatechol -2 9.4 12.8215 Pyrophosphoric -4 1.52 2.36 6.6216 Pyrrolidine 0 11.27217 Pyruvic acid -1 2.39218 Quinine 0 4.13 8.52219 Quinoline 0 4.9220 Resorcinol -2 9.3 11.06221 Saccharin -1 11.68222 Salicylic acid -2 2.97 13.74223 Selenic acid -1 1.92224 Selenous acid -2 2.64 8.28225 Serine -1 2.19 9.05226 o-Silicic acid -2 9.66 11.7227 m-Silicic acid -2 9.7 12228 Strychnine 0 8.26229 Succinic acid -2 4.207 5.636230 Sulfuric acid -2 -3 1.99231 Sulfurous acid -2 1.91 7.18232 d-Tartaric acid -2 3.036 4.366233 meso-Tartaric acid -2 3.22 4.82234 Terephthalic acid -1 3.51235 Thiazole 0 2.44236 Thioacetic acid -1 3.33237 Thiosulfuric acid -2 0.6 1.63238 Threonine -1 2.088 9.1239 m-Toluic acid -1 4.27240 o-Toluic acid -1 3.91241 p-Toluic acid -1 4.36242 Trichloroacetic acid -1 0.66243 Triethanolamine 0 7.762244 Triethylamine 0 10.715

245 Trimethylacetic acid -1 5.03246 Trimethylamine 0 9.8247 Tris(hydroxymethyl)- amin 0 8.075248 Tryptophan -1 2.35 9.33249 Tyramine 0 9.74 10.52250 Tyrosine -1 2.17 9.19 10.47251 Urea 0 0.1252 Uric acid -1 3.89253 Valine -1 2.286 9.718254255256257258259260261262263264265266267268269270271272273274275276277278279280

Database of dissociation constants of acids / protonation constants of bases

More systems, e.g., from the sources given next, can be added: a) at the end of the list; b) in alphabetic order by inserting line(s) and redoing the sequential numbering (column B).

Larger compilations of equilibrium constants and examples of on-line literature on acid-base equilibrium

Martell, A. E., Smith, R. M., Critical Stability Constants, Vol. 1–4. Plenum Press: New York, 1976. Tutorial on acids and bases

Perrin, D. D., Dissociation Constants of Organic Bases in Aqueous Solution, Butterworths, London, 1965; Supplement, 1972. Properties of acids and bases

Serjeant, E. P., and Dempsey, B., Ionization Constants of Organic Acids in Aqueous Solution, Pergamon, Oxford, 1979. Measurement of pH. Definitions, Standards and Procedures (IUPAC - 2002)

Albert, A., "Ionization Constants of Heterocyclic Substances", in Physical Methods in Heterocyclic Chemistry, Katritzky, A. R., Ed., Academic Press, New York, 1963. Temperature dependence of potassium hydrogen phtalate 0.05 mol/kg buffer

Perrin, D. D., Dempsey, B., and Serjeant, E. P., pKa Prediction for Organic Acids and Bases, Chapman & Hall, London, 1981. Primiary standard buffer solutions pH at various temperatures

Dawson, R. M. C., Elliot, D. C., Elliot, W. H., and Jones, K. M., Data for Biochemical Research, Oxford Science Publications, Oxford, 1986.

Conversion of dissociation constants of acids in protonation constants of their conjugated bases

Activity coefficient estimation:an appreciation of 20 equations: Ionic St_effects.pdf in the package: http://www.iupac.org/projects/2000/Aq_Solutions.zip

Temperat. Ionic

ºC strength Formula

25 0 CH3COOH25 0 NH325 0 H2CO325 0 H3C6H5O7

2.68 6.11 10.17 25 0.1 C10H16N2O825 0 HCl25 0 NaOH25 0 H3PO4

Insert new lines anywere to add more systems; renumber column B Find more values in the references and links25 0 C2H5NO 25 0 CH3COOH18 0 C4H6O3 25 0 C3H4O2 25 0 C6H10O4 25 0 C3H7NO225 0 C6H7N25 0 C7H7NO2 25 0 C7H7NO2 25 0 C4H9NO2 25 0 C6H13NO2 25 0 C5H11NO2 20 0 C6H7NO25 0 C3H7NO2 25 0 NH325 0 C6H7N

Most constants given in this compilation of ~250 systems – but not all – were obtained at 25º C and are thermodynamic ones ( I=0), as required by the pH_calc and Regression modules.

is given that the compiled pKas or the calculations made with CurTiPot are correct or accurate. CurTiPot takes in account only protonation equilibria and other chemical reactions can occur for many combinations of two or more of the listed systems.

http://research.chem.psu.edu/brpgroup/pKa_compilation.pdf

http://www.zirchrom.com/organic.htm pKa1 = logKpn

http://www.beloit.edu/~chem/Chem220/indicator/ pKa2 = logKpn-1

pKa3 = logKpn-2

where I, the ionic stregth is: pKa4 = logKpn-3

pKa5 = logKpn-4

pKa6 = logKpn-5

pKa4 pKa5 pKa6

http://research.chem.psu.edu/brpgroup/pKa_compilation.pdf

http://www.zirchrom.com/organic.htm

http://www.beloit.edu/~chem/Chem220/indicator/

L12

Gutz: Protonation constants, Kp, (or global protonation constants, bp) are preferred in the most extensive compilations of equilibrium constants, e.g., Critical Stability Constants, Vol. 1–4 because the equations become unified with those used for metal-ligand-proton equilibria, based on formation (instead of dissociation) constants. Note that pKa = logKp for a monoprotic acid (because Kp = 1/Kd or pKd = 1/logKd ) and, for multiprotic systems, the first logKp is the last pKa. The index n inKpn is the maximum number protons accepted by the most deprotonated form of a (conjugated) base.

M20

Gutz: The structural formula of most of the acids and bases listed here can be found in the Wikipedia, en.wikipedia.org

25 0 C6H14N4O2 25 0 H3AsO4

0 H3AsO3 24 0 C6H8O6 25 0.1 C4H8N2O3 25 0 C4H7NO4 25 0 C8H12N2O3 25 0 C4H4N2O3 25 0 C6H6O3S 25 0 C7H6O2 25 0 C7H9N 25 0 C12H11N 0 0 C5H11NO2

20 0 H3BO325 0 C4H8O2 25 0 C4H6O2 20 0 C4H11N 25 0 C4H11N 25 0 C4H11N 25 0 C5H14N2 25 0 H2CO325 0 C6H4(OH)225 0 ClCH2COOH25 0 C6H6CIN 25 0 C6H6CIN 25 0 C6H6CIN 25 0 C7H5CIO2 25 0 C7H5CIO2 25 0 C7H5CIO2 25 0 C6H5CIO 25 0 C6H5CIO 25 0 C6H5CIO 25 0 C5H14NO 20 0 H2CrO425 0 H3C6H5O7 25 0 C18H21NO3 25 0 C4H7N3O 25 0 C7H8O 25 0 C7H8O 25 0 C7H8O 25 0.1 C6H6N2O

HCNO 25 0 C3H7NO2S 25 0 C10H23N 25 0 C4H10N2O2 25 0 Cl2CHCOOH25 0 C6H4Cl2O 25 0 (CH3CH2)2NH25 0 C6H15N 25 0 (CH3)2NH25 0 C4H12O2N225 0 C7H9N 25 0 C7H9N 25 0 C7H9N

25 0 C7H9N 25 0 C7H9N 25 0 C7H9N 25 0 C7H5NO4 25 0 C12H11N 25 0 C7H5NO4 25 0 C8H11NO2 10 0 C10H15NO 25 0 C2H7NO 25 0 CH3CH2NH225 0 H2NCH2CH2NH2

2.68 6.11 10.17 25 0.1 C10H16N2O825 0 C2H5N 25 0 C7H9N 20 0 HCOOH25 0 C4H4O4 25 0 C5H9NO4 25 0 C5H10N2O3

9.65 25 0 C10H17N3O6S 25 0 C3H6O4 25 0 C3H8O3 25 0 H2NCH2COOH25 0 HOCH2COOH25 0 C2H2O3 25 0 C7H12O4 25 0 C7H14O2 25 0 C7H17N 0 0 C6H16N2

25 0 C6H12O2 25 0 C6H15N 25 0 C5H9N3 25 0.1 C6H9N3O2 30 N2H4

HN3 25 0 HI25 0 HCl

25 0 HCN25 0 HF25 0 H2O2

25 0 H2S25 0 HSCN20 C6H6O2 25 0 NH2OH19 0 C7H6O3 19 0 C7H6O3 25 0 C3H6O3 25 025 0 HOBr25 0 HOCl25 0 HOI25 0 C3H4N2 25 0 HIO3

HCrO4-

HSeO4-

25 0 C6H8O7 25 0 C6H13NO2

HC3H5O3 10 0 C10H15NO 25 0 C6H13NO2 25 0.1 C6H14N2O2 25 0 C4H4O4 25 0 C4H6O5 25 0 HOOCCH2COOH25 0 C3H6N6 25 0 C5H11NO2S 25 0 CH5N 25 0 C7H9N25 0 C7H9N25 0 C8H8N2 25 0 C5H10O2 25 0 C5H10O2 25 0 C4H6O4 27 0 C11H11N 18 0 C6H12O2 25 0 C6H13N 25 0 C7H8O 25 0 C7H8O 20 0 C6H7N 20 0 C6H7N 20 0 C6H7N 25 0 C17H19NO3 25 0 C4H9NO 25 0 C10H8O 25 0 C10H8O 25 0 C10H14N2

10.334 20 025 0 C6H6N2O2 25 0 C6H6N2O2 25 0 C6H6N2O2 25 0 C7H5NO4 25 0 C6H5NO3 25 0 C6H5NO3 25 0 C6H5NO3 25 0 C7H5NO4 25 0 C7H5NO4 25 0 HNO225 0 C8H11NO3 25 0 C18H39N 25 0 C8H14O4 25 0 C8H16O2 25 0 C2H2O4 25 0 C4H4O5 25 0 C20H21NO4 25 0 C5H10O2 25 0 HClO4

H5IO6 25 0 C12H8N2 25 0 C8H11NO

28 0 C8H11NO 25 0 HC6H5O 18 0 C8H8O2 25 0 C9H11NO2 25 0 C8H11N 25 0 C8H9NO2 25 0 H3PO425 0 C8H6O4 25 0 C8H6O4 25 0 C8H6O4 25 0 C6H5NO2

C6H3N3O7 30 0 C11H16N2O2 23 0 C4H10N2 25 0 C5H11N28 0 C8H11NO 25 0 C5H9NO225 0 CH3CH2COOH25 0 CH3CH2CH2NH220 0 C5H4N4 25 0 C5H5N25 0 C6H5NO2 25 0 C6H5NO2 20 0 C11H8N2 20 0 C6H6O2

9.25 H4P2O7 25 0 C4H9N 25 0 C3H4O3 25 0 C20H24N2O2 20 0 C9H7N 25 0 C6H6O2 18 0 C7H5NO3S 25 0 C7H6O3 25 0 H2SeO4

0 H2SeO3 25 0 C3H7NO3

H4SiO4H2SiO3

25 0 C21H22N2O2

25 0 H2SO4 25 0 H2SO325 0 C4H6O6 25 0 C4H6O6 25 0 C8H6O4 20 0 C3H3NS 25 0 C2H4OS 25 0 H2S2O325 0 C4H9NO325 0 C8H8O2 25 0 C8H8O2 25 0 C8H8O2 25 0.1 Cl3CCOOH25 025 0 (CH3CH2)3NH

HOOCCH2CH2COOH

(HOCH2CH2)3N

25 0 C5H10O2 25 0 (CH3)3NH25 0 (HOCH2)3CNH325 0.1 C11H12N2O2 25 0 C8H11NO 25 0 C9H11NO3 21 0 CH4N2O 12 0 C5H4N4O3 25 0 C5H11NO2

Tutorial on acids and bases http://achpc50.chemie.uni-karlsruhe.de/Cours%20de%20Chris%20Anson/OHP8acids.doc

Properties of acids and bases http://ptcl.chem.ox.ac.uk/MSDS/msds-searcher.html

Measurement of pH. Definitions, Standards and Procedures (IUPAC - 2002) http://www.iupac.org/publications/pac/2002/pdf/7411x2169.pdf

Temperature dependence of potassium hydrogen phtalate 0.05 mol/kg buffer http://nvl.nist.gov/pub/nistpubs/jres/081/1/V81.N01.A03.pdf

Primiary standard buffer solutions pH at various temperatures http://nvl.nist.gov/pub/nistpubs/jres/066/2/V66.N02.A06.pdf

Conversion of dissociation constants of acids in protonation constants of their conjugated bases

Molar mass

g/mol

60.05217.026

192.027

292.09

97.976

59.06760.052

102.08972.063

146.14389.094

93.13137.138137.138

17.026

=0), as required by the pH_calc and Regression modules.

is given that the compiled pKas or the calculations made with CurTiPot are correct or accurate. CurTiPot takes in account only protonation equilibria and other chemical reactions can occur for many combinations of two or more of the listed systems.

Overall protonation constants = bp = SKp

N19

Gutz: Molecular weight calculator Java Applet: http://www.ch.cam.ac.uk/magnus/MolWeight.html

184.19128.09

110.1

153.18165.23

116.07147.13146.15

75.07

68.08

131.18

165.23

31.1107.17107.17

108.14108.14

180.3

166.14166.14

208.259

85.15

115.13

120.1179.1

110.1177.98

88.06324.42129.16

110.1

138.12

105.09

334.41118.09

98.0882.07

150.09150.09

119.12

http://achpc50.chemie.uni-karlsruhe.de/Cours%20de%20Chris%20Anson/OHP8acids.doc

http://ptcl.chem.ox.ac.uk/MSDS/msds-searcher.html

http://www.iupac.org/publications/pac/2002/pdf/7411x2169.pdf

http://nvl.nist.gov/pub/nistpubs/jres/081/1/V81.N01.A03.pdf

http://nvl.nist.gov/pub/nistpubs/jres/066/2/V66.N02.A06.pdf

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