Chem. 31 – 2/2 Lecture

Announcements• Due Wednesday

– Turn in corrected diagnostic quiz– HW Set 1.1 – just additional problem

• Quiz on Wednesday (covering Ch. 1)• Today’s Lecture

– Stoichiometry– Titrations– Start to Ch. 3

Stoichiometry

• Remember: there are two (common) ways to deliver a known amount (moles) of a reagent:– Mass (using formula weight)– Volume (if molarity is known)

• Titrations = A practical way of using stoichiometry with precise measure of added volume

TitrationsDefinitions

• Titrant:– Reagent solution added

out of buret (concentration usually known)

• Analyte solution:– Solution containing

analyte• Equivalence Point:

– point where ratio of moles of titrant to moles of analyte is equal to the stoichiometric ratio

titrant

analyte solution

for: Al3+ + 3C2O42- → Al(C2O4)3

3- n(Al3+)/n(C2O42-) = 3/1 at equivalence pt.

TitrationsPractical Requirements

• The equilibrium constant must be large– Precision of titration will depend on size

of K and concentration of analyte– Typically K ~ 106 is marginal, K > 1010 is

better• The reaction must be fast• It must be possible to “observe” the

equivalence point– observed equivalence point = end

point

TitrationsOther Definitions

• Standardization vs. Analyte Titrations– To accurately determine an

analyte’s concentration, the titrant concentration must be well known

– This can be done by preparing a primary standard (high purity standard)

– Alternatively, the titrant concentration can be determined in a standardization titration (e.g. vs. a known standard)

• Rationale:– many solutions can not

be prepared accurately from available standards

• Example:– determination of [H2O2]

by titration with MnO4-

– neither compound is very stable so no primary standard

– instead, [MnO4-]

determined by titration with H2C2O4 (made from primary standard) in standardization titration

– then, H2O2 titrated using standardized MnO4

-

TitrationsOther Definitions

• Direct vs. Back Titration– In a direct titration, the titrant added

slowly to the analyte until reaching an end point

– In a back titration, a reagent is added to the analyte in excess, and then the excess reagent (beyond what was needed to react) is titrated to an end point

– Often done to get sharper endpoint

TitrationsBack Titration Example

Titration to determine moles of Na2CO3 in a sample:

First, direct titration: Na2CO3 + 2HCl → H2CO3 + NaCl (we will do following AA lab)

Na2CO3

HCl

Direct Titration Plot

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

0 5 10 15 20 25 30 35 40 45 50

V(HCl)

pH

not that sharp

TitrationsBack Titration Example

Titration to determine moles of Na2CO3 in a sample:

Now, via back titration: excess HCl added to sample

Na2CO3 + HCl → NaCl + H2CO3 +heat → NaCl + H2O + CO2(g)

Excess HCl titrated with NaOH to NaCl + H2O Na2CO3

HCl

After heating only NaCl and excess HCl left

NaOH

Excess HCl

Direct Titration Plot

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30

V(HCl)

pH

Very Sharp

TitrationsWhat Makes a Titration Sharp?

• A sharp titration has a large slope (absolute value)

• Slope at endpoint seen in plot of -log[analyte] vs. V(titrant)

• With a sharp titration, errors or uncertainties in V(equivalence point) are small

V(titrant)

V(titrant)

-Log

[ana

lyte

]-L

og[a

naly

te]

SHARP TITRATION

NON-SHARP TITRATION

[reactant] at eq. point

V(eq. pt.)

uncertainties in log[analyte]

small uncertainty in V results

larger unc. in V

TitrationsSome Questions

1. List two requirements for a titration to be functional.

2. In a back titration, what is actually being titrated? (a) analyte b) reagent added c) excess reagent d) secondary reagent)

3. Why might one want to standardize a prepared solution of 0.1 M NaOH rather than prepare it to exactly 0.100 M? NaOH is a hygroscopic solid that also absorbs CO2.

TitrationsBack Titration Example

Sulfur dioxide (SO2) in air can be analyzed by trapping in excess aqueous NaOH (see 1). With addition of excess H2O2, it is converted to H2SO4 (see 2), using up additional OH- (see 3).

1. SO2 (g) + OH- (aq) → HSO3-

2. HSO3- + H2O2(aq) → HSO4

- + H2O

3. HSO4- + OH- (aq) → SO4

2- + H2O

208 L of air is trapped in 5.00 mL of1.00 M NaOH. After excess H2O2 is added to complete steps 1 to 3 (above), the remaining NaOH requires 21.0 mL of 0.0710 M HCl. What is the SO2 concentration in mmol/L?

Chapter 3 – Error and Uncertainty

• Error is the difference between measured value and true value or error = measured value – true value

• Uncertainty– Less precise definition– The range of possible values that, within

some probability, includes the true value

Measures of Uncertainty

• Explicit Uncertainty: Measurement of CO2 in the air: 399 + 3 ppmvThe + 3 ppm comes from statistics associated with making multiple measurements (Covered in Chapter 4)

• Implicit Uncertainty:Use of significant figures (399 has a

different meaning than 400 and 399.32)

Significant Figures(review of general chem.)

• Two important quantities to know:– Number of significant figures– Place of last significant figureExample: 13.064 significant figures and last place is

hundredths

• Learn significant figures rules regarding zeros

Significant Figures - Review

• Some Examples (give # of digits and place of last significant digit)– 21.0– 0.030– 320– 10.010

Significant Figures in Mathematical Operations

• Addition and Subtraction:– Place of last significant digit is

important (NOT number of significant figures)

– Place of sum or difference is given by least well known place in numbers being added or subtracted

Example: 12.03 + 3Hundredths place ones place

= 15.03

Least well known

= 15

Significant Figures in Mathematical Operations

• Multiplication and Division– Number of sig figs is important– Number of sig figs in Product/quotient is

given by the smallest # of sig figs in numbers being multiplied or divided

Example: 3.2 x 163.02

2 places 5 places

= 521.664

= 520 = 5.2 x 102