GRATITUDES AND ACKNOWLEDGEMENTS

This work is done on the base of observations of Mr. Eksakustodijan Dobrocvetov, at the time assistent profesor at the Analythical Chemistry of the Faculty of Technology and Metallurgy in Belgrade.

At the same time, I owe gratitude to Mrs McS. Dušanka Vasović, because of her moral support, as well as, because of demonstrated comprenhending for founded solutions, which have been originated after a few years of work.

When the first initial problems arose, related with reactions occuring in circuit current, Mr PhD Popov Konstantin who adviced from electrochemical point of view that work should be countinioued.

Belief in phenomenon, which can be applied in advantageous purposes showed also Mr engineer Borislav Lj. Dragojević, who contributed to successful solution with profesional literature from domain which are close to originated problems.

Also to Mr Ivan Dežarov, whose help in the maintenance of apparatus, was neccessary.

Except profesional help, I've obligation to express respect to Pešić's family, Mrs Milica and Mr Uroš, Because of their wellmeant support, which was needed during the work uncertain outcome.

THE APPLIANCE OF A TEAM OF PAIRS OF INERT ELECTRODES IN ORDER TO DETERMINE

ELECTROLYTE CONCENTRATION

PREFACE

Coincidently with accidental circumstances has been formed a electric circuit, in which there is an ordinary metal wire, which serves as current conductor between two electrolyte solutions.

Instead of standard scheme of the connection between solutions: one solution and two electrodes, which became base for measurement in electrochemistry, there are accepted: two solutions and four electrodes. One of the electrodes from each solution is connected with a source of current. Other two electrodes are mutually connected by metal conductor.

The usual way of binding, when there are two solutions through which follows current, is so-called “electrolytic key”. When, instead of such a mode of connecting through solutions, is being applied electrolytic conductor, current flows through it, but not by the same rules by which it behaves when solutions are electrochemically connected. Through solutions tide on order can, also, flow alternative current. In that case, qualitative variations are not achieved, but, as total concentration in solution does not vary, quantitative issues can be found. Connections between various solutions and various concentrations, which can be realized by metal conductor, can be formed in many different ways. There could be made a net between various electrolytes, various concentrations, more ways of connecting between any of two solutions, and that current flows through each conductor between electrodes of those solutions.

At the beginning, the simplest variant was formed by using only two solutions and four electrodes.

Series of two different solutions are being tested systematically, and all of them behave in the same manner: if one solution has permanent concentration and in the other concentration varies, current strength in circuit, for the constant input tension, depending on variable concentrations. This dependence can be used for determing electrolytes concentration.

ELECTROANALYTIC METHODS

In electroanalytics exist several modes for applying electrochemical variations in analytic purposes. So, there exist: electrogravimetry, electrography, pH-metry, potentiometry, chronoampermetry, polography, chronopotentiometry, colulometry, methods of anode dissolving, dielectrometry, conductometry, stripping methods, etc.

All these methods, because of ionic interaction, realize some lower, so-called “active” concentrations. In order to be found real stochyometric quantity of dissolved substance of electrolyte, we need to know activity factor for defined concentration.

By applying a team of the pairs of inert electrodes, there can be obtained, accordingly to definition, directly measured stochyometric quantities of dissolved substance.

ELECTRODES IN ELECTROANALYTIC CHEMISTRY

Up to date, there have been recognized a great number of electrodes useful in electoranalytical chemistry.

The best known are: Calomel’s, dropping mercury, silver-silver chloride, cuprum-cupro sulfate, bipolar, antimonic, oxygenic, networked – made of platinum, silver-silver oxide, mercury-mercury oxide, mercury-mercury sulfate, hydrogen’s reversible, hydrogen’s irreversible, etc.

In addition to these electrodes, also exist series of ion selective electrodes, one of which is faraway best known and the most frequently used – glass electrode.

Noble metals, like those from platinum group, remain unchanged if they are plunged in majority of electrolyte solutions. Electrodes made of graphite, like electrodes made of platinum group, can be used often the same purpose (as they are of the same characteristics) they are satisfactoy electrochemically and chemically inactive.

CHARACTERISTICS OF ELECTROLYTES

Characteristics of electrolytes are determined by interaction between an ion and ionic atmosphere. The nature of ionic atmosphere is determined by the valence of electrons, electrolytic concentration, temperature and dielectrical constant of solvent.

Differently from an arrangement in metallic lattice, in electrolyte solutions exist an order, but shortly scoped. Arrangement in solutions can be described by presence of ionic atmosphere around each ion. Because of thermal motion in solutions, this relation does not represent a steady state.

While as an electrolyte is not being exposed to action of external electric field, or other forces, which can cause ionic movements relating to solvent, ionic atmosphere is spherically symmetric accordingly to central ion. When, through electrodes in solution, this central ion is exposed to electric tension, ion starts to move, as well as there begin appearances tide, regarding ionic atmosphere.

When, caused by action of imposed tension, ion starts to move, symmetry of ionic atmosphere is being disturbed. Moving, ion permanently crates its atmosphere, while, contemporary, atmosphere is being disturbed after ion’s passing through it.

Considerately to the fact that central ion has a contrary electricity regarding to ionic atmosphere, that electric field strives to move ion in one and ion atmosphere in opposite direction. Because of that, density of ionic atmosphere’s charge will be greater behind ion's moving then density in front of it. As, by sign, ionic atmosphere has electricity inverse comparing with central ion, the ion, while moving within electric field, has to slow.

This effect, which is, otherwise, named «effect of relaxation», or «effect of ionic atmosphere's symmetry», shows that, during flowing of current through electrolyte solutions, there exist «forces of relaxation», which, at the same time, slow ion's moving.

Movement slowing in electrical field also appears because of phenomenon of so-called «effect of electrophorus», which is derived from fact that ion, moving through the solution, does not pass through inertal medium, but constantly collides with particles that are moving in the opposite direction.

When an ion moves through fluid, under influence of constant tension loosing on acceleration because of friction force appears and cited restrainable effects, it reaches on uniformed-constant speed, at which, forces that effect on acceleration, are being in state of balance with forces which restrain the body during its moving.

Generally speaking, structure and dynamics in fluid system are determined by forces that exist between: ions and moleculs, moleculs mutually, and ions mutually. Regarding to these interactions, it is known the division on powers with long and short influence in fluids. Based on simplified models, beside cited relations, there can be described hydrogenic relations between water molecules.

All this shows that, in solutions themselves, there are complicated relations, which become still more cmplicated if they are exposed to electrical field action.

On the contact surface of solid and fluid phase, between electrodes and ions, which react after direct or alternative electric field's influence, exist series of other problems. Inspite of all problems which appear during current flowing in a solution, there can be established extremely simplified relationship, which exist between total concentration in solution and the strength of current in electrical circuit.

DESCRIPTION OF ELECTRIC CIRCUIT

Stable conditions, as much as it was possible, were reached, up to certain degree succesfully, by applying tension stabiliser, which was directly connected with public electric system. Moreover, in he circuit were joined «regulational» variable transformer, as well as ordinar transformer, which has extent up to 3 V.

Regulational and ordinar transformers were used for getting small electric tensions, suitable for measurements, which are requested for electrolytes' concentration determing.

In circuit, through stabilaser and transformers, two electrodes, each one from different solution, are connected with the source of current. Other two electrodes, which are equally distanced from their corresponding electrodes, are connected with source of current, mutually are connected by metal conductor.

Electrodes used for cited measurings are made of graphite, roundly shaped, having diameter 15 mm and, in cited team H2SO4 - H2SO4 , are plunged into solutions up to 100 mm.

In illustration /F.1/ is given the scheme with which can be derived the same way for any combination of two solutions through which current can flow: electrolytic - through solutions, and electronic – through electrotecnic conductors.

Ilustration F.1. Electric cheme used for measuring in these experiments

If in one solution permanent concentration is Cm H2SO4 = 1 mol/dm3 and in the other concentration varies, then can be established the connection between strength of power and concentration, supposing that all other conditions remain unchanged.

The solving for how to determinate solutions’ concentrations was found mathematically. This method simplifies procedure tegarding to methods which use activity factors.

QUANTITATIVE METHOD FOR DETERMING SULPHUR ACID CONCENTRATION BY MEASURING

CURRENT STRENGTH AND TENSION IN CIRCUIT

DETERMING THE CONCENTRATION OF ELECTROLYTHIC SOLUTIONS BY GRAPHIC METOD MEASURING CURRENT STRENGHT

Curves in illustration F.2 (table 1) are related to current strength for six different tensions that are varying from 0.5 to 3V. A changeable concentration is signed as Cm1. Changeable concentration varies from 0 to 1 M, is signed as Cm2. Concentrations are put on abscissa and current, given in mA, on ordinate.

Table 1. Current strength in mA for solutions H2SO4 - H2SO4

for different potentials. Cm1 = 1 mol /dm³

Cm2H2SO4 0.5 V 1.0 V 1.5 V 2.0 V 2.5 V 3.0 V

1.00000 80.0 180.0 280.0 400.0 500.0 600.0 0.50000 75.0 120.0 270.0 380.0 440.0 550.0 0.25000 60.0 110.0 200.0 280.0 400.0 470.0 0.12500 55.0 110.0 180.0 250.0 360.0 380.0 0.06250 40.0 80.0 170.0 240.0 280.0 340.0 0.03125 34.0 65.0 100.0 170.0 240.0 260.0 0.01562 24.0 50.0 90.0 122.0 150.0 180.0 0.00800 14.0 32.0 50.0 80.0 95.0 120.0 0.00400 10.0 23.0 35.0 50.0 60.0 75.0 0.00200 6.0 12.0 18.0 26.0 33.0 39.0 0.00100 3.0 6.0 10.0 14.0 18.0 22.0 0.00050 0.8 3.3 5.2 7.3 9.0 10.7 0.00025 0.5 1.0 2.5 4.0 4.5 5.5

Illustration F.2. Curves of current strenght for different tensions

0

100

200

300

400

500

600

0 0,125 0,25 0,375 0,5 0,625 0,75 0,875 10

100

200

300

400

500

600

0 0,125 0,25 0,375 0,5 0,625 0,75 0,875 10

100

200

300

400

500

600

0 0,125 0,25 0,375 0,5 0,625 0,75 0,875 10

100

200

300

400

500

600

0 0,125 0,25 0,375 0,5 0,625 0,75 0,875 10

100

200

300

400

500

600

0 0,125 0,25 0,375 0,5 0,625 0,75 0,875 10

100

200

300

400

500

600

0 0,125 0,25 0,375 0,5 0,625 0,75 0,875 1

0.5 V

1.0 V1.5 V

2.0 V

2.5 V

3.0 VINPUT TENSIONH2SO4 – H2 SO4

[ ]342

dmmolCm SOH

[ ]mAI

The first step is determing calibration curve, by measuring a number of standard solutions.

When being determined intensity of current in an unknown solution, and, on curve, point that suits

the value, by simple drawing the line vertically from fixed point from curve to abscise, directly can be read unknown Cm2x /F.2/.

In the same way can be formed such electric circuit of any two electrolythic solutions and stated their mutual correlation.

Except solutions H2SO4 - H2SO4, systematically were done researches with various combinations. Determined are: H2SO4 - alkyl chlorides, H2SO4 - Na halogens and H2SO4 - alkaline earth chlorides.

Besides various solutions for the same concentrations under the same conditions, there exist small differences concerning results for current strength, but shape of curve for each combination is simmilar.

STANDARD SOLUTIONS APPLIANCE

A solution concentration dependence of the macro variable in circuit is defined directly as stochyometrically measured substance quantity in that solution.

Each separate dependence can be formulated with the function. If in the circuit were stationary and stable conditions, unknown concentration could be calculated on base of any of macro variably measured dimensions: I, U1, U2, ∆U, or ∆U1. As it is not possible, because technical conditions in circuit, such as it is formed, are, not in slightest ideal, there is resorting to practical solvings, but applying all variables in total function. In this maneer can be carried out the solving based on data measured almost in the same time when determining the unknown solution.

In illustration F.11 graphically are presented relations of functions: Cmx according to searched Cm2 , when Cm2 varies from 0 to 1 M.

In illustration F.12 is separated only a part of line which represents slope Cmx – Cm2, between which should be solution with unknown concentration.

Based on previously known data for series of standard solutions, repeatly are to be determined data for two standard solutions, among which should be solution with unknown concentration.

Data given in tables 1 to 5 were all obtained for entrance tensions Uo = 0.5 V.

Latter measuring were carried out with input tensions Uo = 0.3 V. Calculal example, cited as illustration, is also calculated for entrance tension Uo = 0.3 V . Distance between electrodes into both solutions for 35 mm, diameter of each electrode is 15 mm, electrodes were plunged into unchangeable solution for 50 mm., and, in solution with unknown concentration – 25 mm.

CONCLUSIONS

1. If two electrolyte solutions, through pairs of plunged electrodes are mutually connected by metal conductor, in series of current circuit /F.2/, through metal conductor is flowing current.

2. The strength of current in circuit is proportional to electrolyte concentration. The greater concentration of sollutions, the more intense current will be in the circuit, for the same input tension U o .

3. When one solution has constant concentration, and in the other solution concentration varies, current strength varies, current strength rises if concentration, in solution of variable concentration, also rises. In such a maneer, if on diagram are being put, carefully, values for Cm2 – varying concentration, also as data for current strength for corresponding concentrations, will be obtained calibration diagram, basing on which can be graphically determined unknown concentration, of course all under condition that Uo (entrance tension) is constant.

4. Tension variations in circuit, for the same input tension Uo, varies in contrary of variation of current values. If concentration rises, total tension drop of U also falls. This tension is equal to the sum of all tension fallings in solution with permanent concentration also as in solution where concentration varies:

U = U1 + U2

5. Tensions drop in solution where concentration Cm1 – is constant, varies proportionally to

concentration variation, Cm2 in the other solution. If concentration Cm2 rises, also rises U1 – total tension dropping between electrodes in solution with constant concentration.

6. Tension dropping U2, in solution in which concentration varies, behaves in the same manner as total tension drop U. If concentration rises, U2 falls.

7. The difference between tension Uo and total tension drop in circuit U:

∆ U = Uo - U rises with concentration Cm2.

8. ∆ U1 = U2 – U1 : Tension difference falls when concentration Cm2 rises. U2 is tension in solution of variable concentration and U1 in solution where concentration is permanent.

9. When variable dimensions are being formulated as variations ∆U and ∆U1, as well as current strength I and then are put in equation

( )( )21

2121

UUIKCmx ∆

∆⋅=

is gained dependence for expression Cmx from variable concentration Cm2,  which, possibly, could be rectilinear, under a suitable angle for each electrolyte separately, if in circuit should

be stationary conditions. As in circuit conditions are never ideal, neither line Cmx is under the same slope Cm2,  but is , therefore, in some determined limits, which depend of realized technical conditions in circuit.

10. The purpose of measuring – calculating the unknown concentration, can be achieved if, for series of solutions with known concentration, data are being determined for the same entrance tension Uo: I, U, U1, U2, ∆ U, ∆ U1 and, basing on equation No. 6., function Cmx. Already measured values for solution with unknown concentration, should be compared with previously known data for known concentrations, and there should be selected two solutions, one of which should have smaller and the other with greater concentration than the one in unknown solution. Basing on calculated angle, which is determined by slope of data for two solutions, can be obtained:

12

12

22 CmCmCmCm

tg xx

−

−=α

Concentration for unknown solution can be calculated:

αtgCmCm

CmCm xyx

x

1

122

−+=

Or , with the same results:

αtgCmCm

CmCm x

x

yx −−= 2

222

11. According to second procedure for calculating the unknown concentration can be also used

total slope of the line, when aplied Cmx towards Cm2.

xCmCmK 2= or

xCmCmctg 2=α

K is number which with is multiplying calculated value Cmx in order to be obtained concentration of unknown solution. Constant K is not the real constant, because it permanently varies in a range determined with technical conditions Because of that for each

standard separately are being determined K1 and K2. When the medial result of slope is being multiply by CmYx, which can be obtained by measuring

unknown concentration, result is xymed CmK ⋅x

Cm =2 more exactly, demanded concentration.

221 KKKmed

+=

All curves of current strength – concentration, were systematically measured for alkyl and alkaline earth metals chlorides, as well as Na – halogens. Another solution was usually sulphuric acid with constant concentration. In fact, practical appliance should be in determing unknown

solution concentration in function of changeable macro variables in current circuit, which are depending of solution concentration.

In that purpose are used solutions of sulphuric acid, with intension that, later, the same method can be applied concerning other electrolytes.

Electric circuit and electrodes are described in the first part of this paper. For quantitative researches, was available an unlimited choice of potentials. For first quantitative measuring is accepted the smallest potential of 0.5V, which was applied at the very beginning. Next measurings do not refer only to current strength in circuit, but, also, to potentials, which, equally vary dependently of concentration changes (table 2), illustration F.3.

Table 2. Current strength and potential in a circuit for solutions H2SO4 – H2SO4, according to variation of a solution concentration – Cm2. Entrance potential 500 mV. Concentration of one solution Cm1 = 1.0 mol/dm3. Both pair of graphite electrodes plunged in solutions up to 100 mm. Distance between electrodes 35 mm. Diameter of each electrode 15 mm.

Cm2 I mA U mV U2 mV U1 mV

1.0000 80.0 100 50 50.0 0.5000 75.0 120 50 40.0 0.2500 60.0 130 90 40.0 0.1250 55.0 170 130 15.0 0.0625 40.0 250 210 10.0 0.0312 34.0 300 290 5.0 0.0156 24.0 370 350 1.0 0.0078 14.0 425 410 0.5 0.0040 10.0 440 410 0.0 0.0020 6.0 475 470 0.0 0.0010 3.0 490 490 0.0 0.0005 0.8 500 500 0.0

0

50

100

0 0,125 0,25 0,375 0,5 0,625 0,75 0,875 13

42dmmolCm SOH

mAI

Illustrartion F.3. Current strength according to variation of a solution concentration.

For any input potential Uo, potential between electrodes in solution with known concentration Cm H2S04 = 1.0 mol/dm3 is signed as U1.

Potential between electrodes in solution which concentration Cm2 varies, is signed as U2.

U = U1 + U2 is total potential in circuit.

When all current strength and potentials are being compared with changes of solution concentration, result are curves, which show scattered dependences I, U, U1 and U2 of Cm2.

As it is already known, if in one solution concentration is constant, and in the other it rises, also rises current strength in circuit (Illustration F.3).

Potential U2, between electrodes in solution with varying concentration, falls if concentration rises (Illustration F.4).

0

50

100

150

200

250

300

350

400

450

500

0 0,25 0,5 0,75 1

mVU

342

dmmolCm SOH3

42dmmolCm SOH

mVU2

0

50

100

150

200

250

300

350

400

450

500

0 0,25 0,5 0,75 1

Illustration F.4. Potential in sollution with rising concerntration.

Illustration F.5. Total potential in sollution with rising concerntration

.

U = U1 + U2 : total potential in circuit falls when Cm2 rises (Illustration F.5).

U1 - potential between electrodes in solution in with concentration is constant, rises until rises concentration in another solution (Illustration F.6).

Illustration F.6. Potential in solution with nocstant concentration

For all these dependences which can be measured in a circuit could be formulated extra function. Also it can be made a function which has all variables at the same time, and a restriction which appears because of determined input potential Uo.

If, because of choosing Uo accordingly to needs and conditions, correlations are being presented in another way, like differences between input potential Uo and U – total potential drop in circuit, then will be: ∆U = Uo – U, and potential variation between both solutions : ∆ U1 = U2 – U1. So, presented relationships, which include restricrionc because of determined input potential, are presented in table 3.

Table 3. Comparative results from data, tension difference from table 4.

Cm2 ∆U mV ∆U1 mV1.0000 400 00.5000 380 100.2500 370 500.1250 330 1150.0625 250 2000.0312 200 2850.0156 130 3490.0080 75 4100.0040 60 4100.0020 25 4700.0010 10 490

When rises concentration Cm2 also rises ∆U – potential differences between input (imposed) potential and total potential dropping in circuit, in a way presented in Illustration F.7.

If Cm2 rises, potential difference ∆ U1 reduces in a way presented in Illustration F.8.

0

50

100

150

200

250

300

350

400

450

500

0 0,25 0,5 0,75 13

42dmmolCm SOH

mVU1∆

0

50

100

150

200

250

300

350

400

450

500

0 0,25 0,5 0,75 13

42dmmolCm SOH

mVU∆

Illustration F.7. Total potential difference change in

solution with rising concentration. Illustration F.8. Potential difference change in solution with rising concentration

Now, to form mathematical correlations, problem can be posed like this: Cm2 - rises - rises cuttent strength Cm2 - rises - rises ∆ U , and Cm2 - rises - ∆ U1 falls.

ONE WAY OF DETERMING UNKNOWN CONCENTRATION

Dependance I of Cm2 can be formulated as the simplest linear function:

IkCm ⋅=2 ..................... /1/ (F.3)

By same equation can be presented dependence ∆ U of Cm2 :

UkCm ∆⋅=2 ..................... /2 / (F.7)

The third macrovariable value ∆ U1 of Cm2 can be obtained by comparing curves from illustrations F.9 and F.10.

0

500

1000

0 0,25 0,50,0

0,5

1,0

0 100 200 300 400 500

mVU1∆

Y

X

1UfCm ∆= 2

1X

Y =

⎥⎦⎤

⎢⎣⎡

3dmmolCm

Illustration F.9. Concentration as function of potential difference

Illustration F.10. Theoretical .function Y=X-2

In illustration F.9 is drawn curve ( )12 UfCm ∆=

Mathematical function 21

xY = is presented in illustration F.10

Basing on similarity of these two curves, equation can be written as:

( )22 UkCm ∆⋅= ............../3/

When equations 1 and 2 are being multiplied, the result is :

( ) UIkCm ⋅∆⋅=22 .................. /4/

and, from it can be derived:

( ) 222

11

UIkCm ∆⋅⋅= ......................./5/

Influence of all three macro variables : I, ∆ U, and ∆ U1 on Cm2 can be formulated by one equation:

( )( )21

2

21

21

UUIKCm

∆∆⋅

= ............................. /6/

Part of that function ( )( )21

21

21

UUI

∆∆⋅ is signed Cmx.

Values for Cmx are calculated basing on equation No.6, with data from table 4, for two solutions H2SO4 – H2SO4, according to already known concentration for solution Cm2, enumerated in table 5 and graphically shown in illustration F.11.

Table 4. Comparative results of changes of all macrosizes in circuit, from tables 2 and 3.

Cm2 I mA U1 mv U2 mv ∆U mV ∆U1 mV

0.010004 3,2 7 281 12 274 0.020008 4,8 9 271 20 262 0.030012 6.0 10 261 29 251 0.040016 7.0 12 252 36 240 0.050020 7,7 13 248 39 235 0.060024 8,6 14 241 45 227 0.080032 9,5 17 230 53 213 0.100040 10.7 18 220 62 202 0.120048 11,1 19 211 70 192

Table 5. Functions Cmx and K out of data from table 2. Cm2 mol/dm3 Cmx A1/2V-3/2 K mol V3/2 A-1/2 dm-3

0.010004 0.082543 0.121200 0.020008 0.145680 0.137343 0.030012 0.209376 0.143340 0.040016 0.275599 0.145200 0.050020 0.314808 0.158890 0.060024 0.381986 0.157136 0.800320 0.494584 0.161866 0.100040 0.632697 0.158116 0.120048 0.756149 0.158762

Illustration F.11. Calculated values for Cmx to already known concentration for solution Cm2

In the same table, comparatively are also enumerated values for K. Supposing that K is constant (at least in one volume of concentration), it should be the number with which would be multiplied in order to obtain real concentration of Cmx – which is being looked for.

Dimensions for K can be obtained from equation:

[ ] ( )( ) ⎥

⎦

⎤⎢⎣

⎡ ⋅∆∆⋅

= 221

32

21

21

21

21

VVA

UUIKdmmolCm

where K has dimensions : V³/² x mol/dm ³ x A¯¹/² . For part of function Cmx dimensions should be:

A1/2 x V¯³/²

If values for accounting Cmx and K are expressed for current strength in amperes and for

potentials in volts. Such mode of concentration determing could be applied in large volume if conditions in current circuit would vary as needed.

Illustration F.11. Calculated values for Cmx to already known concentration for solution Cm2

CALCULAL EXAMPLE

Input potential: Uo = 300 mV Unknown concentration: Cm2x = 0.03501 mol/dm³

Momental measuring results: I = 6,30 mA U = 272 mV U2 = 259 mV ∆ U = 28 mV U1 = 13 mV ∆ U1 = 246 mV

( )( )

23

21

21

21947.01046.2

1080.21030.621

23−

=⋅

⋅⋅⋅=

−

−−

VACmx

According to previously measured values of current strength for standard solutions, unknown concentration should be between :

3

1030010.02 dm

molCm = and 32

040010.02 dmmolCm =

(table 4 and 5).

Measuring again values of current strength and potentials, for two mentioned standard solutions, new data can be used for next calculations:

a./ 3

1030010.02 dm

molCm = I = 5,70 mA U = 275 mV ∆ U = 25 mV U2 = 261 mV ∆ U1 = 247 mV U1 = 14 mV

( )( )

23

21

21

119566.0

1047.21050.21070.521

23−

=⋅

⋅⋅⋅=

−

−−

VACmx

b./ 2Cm 32

040010.0 dmmol=

I = 6,60 mA U = 270 mV ∆ U = 30 mV U2 = 255 mV ∆ U1 = 240 mV U1 = 15 mV

( )( )

23

21

21

124429.0

1040.2100.31060.621

23−

=⋅

⋅⋅⋅=

−

−−

VACmx

Slope of the graph, which was obtained by incleaning Cmx towards Cm2 only for two standard solutions, between whom should be unknown concentration, can be obtained from relation: /F.12/

8630.401000.0

019566.024429.0

12

12

22

=−

=−−

=CmCmCmCm

tg xxα

Dimensions for such defined tangens are: A1/2 V-3/2 mol-1 dm3

Unknown concentration can be calculated

322 03490.0

8630.419566.021947.003001.01

1dmmol

tgCmCm

CmCm xxx

=−

+=−

+=α

/ relative error -0.30% / or:

322 03490.0

8630.421947.024429.004001.02

2dmmol

tgCmCm

CmCm xxx

=−

−=−

−=α

Another way which can be used for calculation of unknown resultsalso uses the slope of the rectilinear, where are again data Cmx towards Cm2, but using all data for several standards (Illustration F.11) and also using equation:

xCmCmK 2=

where K is cottanges of total angle of function-line Cmx towards Cm2, but not only between two values. For first solution Cm21 :

15338.019566.003001.01 ==K

For second solution Cm22:

16374.024429.004001.02 ==K Medial value:

321 23

2115859.0

216378.015338.0

2dmmolVAKKKm

−=

+=

+=

Unknown concentration can be obtained in the next way:

03480.015859.021947.02 =⋅=⋅= xm CmKCmx

/ relative error 0.60% /

TEMPERATURE INFLOWING

Coefficient of the temperature is not determined, although should be logical to establish of dependence on temperature, while establishing other dependences. As technical conditions in circuit are far from stable and ideal, but they are the result of possibly attainable apparatuses, by appliance of standards, error, that could appear because of temperature differences, should be avoided.

Basing on numerous measuring, already known about has been only confirmed, more exactly the fact that comparatively with temperature rising rises current strength. Also increases dissociation in solutions and greater number of ions emerge, which have an effect on changing the current intensity.

While measuring, temperatures are not precisely determined, except data that complete series of researches were done in range of temperatures between 15oC and 30oC.

DETERMINING THE QUANTITATIVE COMPONENTS OF THE MIXTURE COMPOSED OF TWO ELECTROLYTES BY

MEASURING THE ELECTROTECHNICAL DATA

PREFACE

There is a great amount of data concerning the characteristics of ions in liquid solutions under the influence of electric field. The most of those specific characteristics has been developed under the direct current.

As it was already emphasized in the first part of the preface of the paper “The Appliance of a team of pairs of inert electrodes in order to determine electrolyte concentration”, the first electro-technical connection between the two solutions of electrolytes was set up by mr. A. Dobrocvetov.

The appliance of the phenomenon of current flow between two solutions in analythical purposes is only a small part of possible problems, as in electric circuit with two solutions and four electrodes as well as in all other possible combinations with more solutions and with different connections between them.

When determining the two-component solution, besides the concentration (that is, the number of ions) the specific characteristics of each ion are taken under consideration.

After a number of experiments, under different conditions, under which the mixtures of alkaline chlorides were comparably measured as well as the hydrochloric acids with some of the alkaline chlorides, an HCl - NaCl mixture has been adopted as the quantitative solution.

The way of measuring and calculating the quantitative composition applied to this system can be employed on a number of other twofold systems.

If the quantitative composition is known, the fastest and the most simple way is to apply the graphical solution for determining the total concentration, as it is done with single-component solutions.

0

1

2

3

0 0.5

ImA

Cm2X Cm = Cm + Cm2 a b Picture 2.

THE MIXTURE OF SOLUTION NaCl - KCl

For preliminary measurements the mixture of solution has been chosen in which NaCl and KCl are present. This choice has been made due to the realization that sodium and potassium ions have very similar characteristics. The assumption was that if one could, with this combination, obtain results which determined the quantitative composition, every other two-component solution could be determined thus as well.

First data shows that there are differences between some single-component solutions, even with their mixtures, but they are not sensitive enough.

In table 1 to 16, the data for solutions NaCl and KCl and their mixtures with equal concentration when they are present in the solution in equal amounts is listed.

The concentration of solution can be determined graphically as well as mathematically:

Cm2 = Cma + Cmb

The quantitative relation of two components can be defined by the ratio:

X = Cma / Cmb

By using these two simple relations one can determine individual amounts: Input tension between electrodes in the sulphuric acid solution is U1. In solutions NaCl – KCl, the tension is U2. The intensity of current for the measuring in these tables is changed minimally. (Tables 1 to 16).

The distance between two electrodes in solutions is 2.50 cm. The contact surface between the liquid and solid phase in the sulphuric acid solution for each electrode is around 6 cm2. In solutions NaCl and KCl, as well as in their mixtures the contact surface is 10.00 cm2 each.

• Cm1 is the concentration of sulphuric acid.

• Cm2 is the concentration of the examined solution.

• X is the quantitative ratio of two electrolytes.

• U0 is the input tension. (Diagrams 3,4 and 5)

Graphic illustrations are made for the results in table 14. As in other tables in this line only three points are defined.

The results are related to concentrations 0.125 M, 0.50 M and 1 M, solutions in relation with different concentrations of sulphuric acid. Three input tensions are applied: 100. 200 and 300 mV.

The electric circuit is not in that amount stable so that reproductive results can be obtained, but after multiple repetitions tables 1 to 16 can be firmly presented. No matter how slight the differences among the results are, for relations NaCl and KCl, they exist in certain amount in order to establish the direction of variations, while the relations in the examined solution is being changed.

Table 1. Cm1 = 0.10 M Cm2 = 0.125 M

U0 = 100 mV Solutions I mA U1 mV U2 mV (U2 – U1) mV

NaCl 0.12 26.00 49.00 23.00 X = 1 0.20 30.00 45.00 15.00 KCl 0.20 31.50 46.00 14.00

U0 = 200 mV

NaCl 0.37 57.00 95.00 32.00 X = 1 0.39 64.00 90.00 26.00 KCl 0.39 69.00 90.00 21.00

U0 = 300 mV

NaCl 0.62 85.00 146.00 61.00 X = 1 0.62 97.00 146.00 49.00 KCl 0.64 100.00 146.00 46.00

. Table 2.

Cm1 = 0.05 M Cm2 = 0.125 M U0 = 200 mV

Solutions I mA U1 mV U2 mV (U2 – U1) mV NaCl 0.36 110.00 45.00 65.00 X = 1 0.37 119.00 40.00 79.00 KCl 0.37 120.00 35.00 85.00

Uo = 300 mV

NaCl 0.60 165.00 65.00 100.00 X = 1 0.61 172.00 54.00 118.00 KCl 0.60 175.00 61.00 114.00

Table 3.

Cm1 = 0.02 M Cm2 = 0.125 M U0 = 100 mV

Solutions I mA U1 mV U2 mV (U2 – U1) mV NaCl 0.10 49.00 10.00 39.00 X = 1 0.12 51.00 9.00 42.00 KCl 0.12 51.00 10.00 41.00

U0 = 200 mV

NaCl 0.32 90.00 40.00 50.00 X = 1 0.34 100.00 38.00 62.00 KCl 0.35 100.00 40.00 60.00

U0 = 300 mV

NaCl 0.52 140.00 61.00 79.00 X = 1 0.54 150.00 57.00 93.00 KCl 0.55 150.00 62.00 88.00

Table 4.

Cm1 = 0.01 M Cm2 = 0.125 M U0 = 200 mV

Solutions I mA U1 mV U2 mV (U2 – U1) mV NaCl 0.32 110.00 24.00 86.00 X = 1 0.33 102.00 28.00 74.00 KCl 0.32 104.00 18.00 96.00

Uo = 300 mV

NaCl 0.50 158.00 40.00 118.00 X = 1 0.48 160.00 45.00 115.00 KCl 0.50 167.00 40.00 127.00

Uo = 500 mV

NaCl 0.85 257.00 71.00 186.00 X = 1 0.85 268.00 70.00 198.00 KCl 0.85 270.00 52.00 218.00

SOLUTIONS NaCl – KCl 0.50 M

Table 5. Cm1 = 2 M Cm2 = 0.50 M

U0 = 100 mV Solutions I mA U1 mV U2 mV (U2 – U1) mV

NaCl 0.19 12.00 60.00 48.00 X = 1 0.20 15.00 51.00 36.00 KCl 0.21 25.00 53.00 28.00

Uo = 200 mV

NaCl 0.45 56.00 109.00 53.00 X = 1 0.45 51.00 110.00 59.00 KCl 0.42 60.00 98.00 38.00

Uo = 300 mV

NaCl 0.72 69.00 189.00 20.00 X = 1 0.72 88.00 152.00 64.00 KCl 0.73 91.00 149.00 58.00

Table 6.

Cm1 = 1 M Cm2 = 0.50 M U0 = 100 mV

Solutions I mA U1 mV U2 mV (U2 – U1) mV NaCl 0.20 20.00 52.00 32.00 X = 1 0.20 25.00 50.00 25.00 KCl 0.20 29.00 45.00 6.00

U0 = 200 mV

NaCl 0.45 58.00 106.00 48.00 X = 1 0.41 61.00 100.00 39.00 KCl 0.42 70.00 87.00 17.00

Table 7.

Cm1 = 0.50 M Cm2 = 0.50 M U0 = 100 mV

Solutions I mA U1 mV U2 mV (U2 – U1) mV NaCl 0.17 37.00 45.00 8.00 X = 1 0.17 40.00 43.00 3.00 KCl 0.18 41.00 41.00 0.00

Uo = 200 mV

NaCl 0.47 74.00 79.00 5.00 X = 1 0.44 79.00 78.00 -1.00 KCl 0.45 85.00 80.00 -5.00

Uo = 300 mV

NaCl 0.70 111.00 130.00 19.00 X = 1 0.70 120.00 130.00 10.00 KCl 0.71 123.00 123.00 0.00

Table 8.

Cm1 = 0.20 M Cm2 = 0.50 M U0 = 100 mV

Solutions I mA U1 mV U2 mV (U2 – U1) mV NaCl 0.17 50.00 25.00 25.00 X = 1 0.19 51.00 24.00 27.00 KCl 0.17 56.00 21.00 35.00

U0 = 200 mV

NaCl 0.42 97.00 68.00 29.00 X = 1 0.42 101.00 66.00 35.00 KCl 0.47 110.00 68.00 42.00

Uo = 300 mV

NaCl 0.68 146.00 103.00 43.00 X = 1 0.62 152.00 92.00 60.00 KCl 0.65 168.00 88.00 80.00

Table 9.

Cm1 = 0.10 M Cm2 = 0.50 M U0 = 100 mV

Solutions I mA U1 mV U2 mV (U2 – U1) mV NaCl 0.15 59.00 16.00 43.00 X = 1 0.16 60.00 14.00 46.00 KCl 0.17 64.00 13.00 51.00

Uo = 200 mV

NaCl 0.41 119.00 50.00 69.00 X = 1 0.42 120.00 48.00 75.00 KCl 0.44 122.00 45.00 77.00

Uo = 300 mV

NaCl 0.69 180.00 70.00 110.00 X = 1 0.68 183.00 67.00 116.00 KCl 0.68 188.00 67.00 121.00

Table 10.

Cm1 = 0.01 M Cm2 = 0.50 M U0 = 200 mV

Solutions I mA U1 mV U2 mV (U2 – U1) mV NaCl 0.28 149.00 1.00 148.00 X = 1 0.29 158.00 0.50 157.00 KCl 0.30 160.00 0.10 159.00

U0 = 300 mV

NaCl 0.45 222.00 11.00 211.00 X = 1 0.46 237.00 5.00 232.00 KCl 0.50 240.00 5.00 235.00

SOLUTIONS NaCl – KCl 1 M

Table 11. Cm1 = 2 M Cm2 =1 M

U0 = 100 mV Solutions I mA U1 mV U2 mV (U2 – U1) mV

NaCl 0.20 28.00 44.00 16.00 X = 1 0.21 30.00 43.00 13.00 KCl 0.20 32.00 40.00 8.00

Uo = 200 mV

NaCl 0.46 23.00 40.00 17.00 X = 1 0.46 48.00 60.00 12.00 KCl 0.46 72.00 80.00 8.00

Uo = 300 mV

NaCl 0.68 91.00 140.00 49.00 X = 1 0.73 100.00 130.00 30.00 KCl 0.74 110.00 180.00 8.00

Table 12.

Cm1 = 1 M Cm2 = 1 M U0 = 100 mV

Solutions I mA U1 mV U2 mV (U2 – U1) mV NaCl 0.18 27.00 50.00 23.00 X = 1 0.18 30.00 44.00 14.00 KCl 0.19 35.00 40.00 5.00

U0 = 200 mV

NaCl 0.44 61.00 100.00 39.00 X = 1 0.45 68.00 90.00 22.00 KCl 0.45 75.00 79.00 4.00

Uo = 300 mV

NaCl 0.70 97.00 145.00 48.00 X = 1 0.71 100.00 148.00 48.00 KCl 0.72 114.00 122.00 8.00

Table 13.

Cm1 = 0.50 M Cm2 =1 M U0 = 100 mV

Solutions I mA U1 mV U2 mV (U2 – U1) mV NaCl 0.18 44.00 30.00 14.00 X = 1 0.18 49.00 25.00 24.00 KCl 0.19 49.00 22.00 27.00

Uo = 200 mV

NaCl 0.45 90.00 75.00 15.00 X = 1 0.45 93.00 66.00 27.00 KCl 0.45 97.00 64.00 33.00

Uo = 300 mV

NaCl 0.71 137.00 110.00 27.00 X = 1 0.71 140.00 98.00 42.00 KCl 0.71 146.00 99.00 47.00

Table 14.

Cm1 = 0.25 M Cm2 = 1 M U0 = 100 mV

Solutions I mA U1 mV U2 mV (U2 – U1) mV NaCl 0.18 53.00 15.00 38.00 X = 1 0.19 58.00 12.00 46.00 KCl 0.19 60.00 10.00 50.00

U0 = 200 mV

NaCl 0.48 110.00 56.00 54.00 X = 1 0.48 113.00 52.00 61.00 KCl 0.48 122.00 44.00 78.00

Uo = 300 mV

NaCl 0.70 161.00 82.00 79.00 X = 1 0.71 173.00 79.00 94.00 KCl 0.71 186.00 64.00 122.00

Table 15.

Cm1 = 0.20 M Cm2 =1 M U0 = 100 mV

Solutions I mA U1 mV U2 mV (U2 – U1) mV NaCl 0.18 61.00 16.00 46.00 X = 1 0.18 61.00 15.00 46.00 KCl 0.18 61.00 10.00 50.00

Uo = 200 mV

NaCl 0.44 120.00 49.00 71.00 X = 1 0.44 121.00 45.00 76.00 KCl 0.44 124.00 42.00 82.00

Uo = 300 mV

NaCl 0.70 180.00 83.00 97.00 X = 1 0.70 188.00 73.00 115.00 KCl 0.70 188.00 65.00 123.00

Table 16.

Cm1 = 0.10 M Cm2 = 1 M U0 = 100 mV

Solutions I mA U1 mV U2 mV (U2 – U1) mV NaCl 0.17 67.00 ≈ 7.00 60.00 X = 1 0.17 70.00 ≈ 5.00 65.00 KCl 0.17 71.00 ≈ 4.00 67.00

U0 = 200 mV

NaCl 0.42 130.00 38.00 92.00 X = 1 0.42 133.00 25.00 108.00 KCl 0.43 140.00 25.00 115.00

Uo = 300 mV

NaCl 0.68 199.00 58.00 141.00 X = 1 0.68 209.00 50.00 159.00 KCl 0.68 212.00 48.00 164.00

50

100

150

200

0 1 2

0

60

120

0 1 2

0

30

60

0 1 2

U = 100 mV0

U = 300 mV0

U = 200 mV0

mV

mV

mV

U1

U2

U1

U2

U1

U2

NaCl X = 1 KCl

NaCl X = 1 KCl

NaCl X = 1 KCl

Picture 3.

75

85

95

105

115

125

0 1 2

75

85

95

105

115

125

0 1 2

75

85

95

105

115

125

0 1 2

U = 100 mV0

U = 300 mV0

U = 200 mV0

U 1

U 2

NaCl X = 1 KCl

NaCl X = 1 KCl

NaCl X = 1 KCl

(U -

U) m

V1

2(U

- U

) mV

12

(U -

U) m

V1

2

Picture 4.

Picture 5.

3

5

7

9

0 1 2NaCl X = 1 KCl

U = 200 mV0

f =

(U

/ U

)X

12

2

10

20

30

40

0 1 2NaCl X = 1 KCl

U = 100 mV0

f =

(U /

U)

X1

22

3

5

7

9

0 1 2NaCl X = 1 KCl

U = 300 mV0

f =

(U /

U)

X1

22

FUNCTION fX

Based on the measuring of only three solutions, it can be concluded that while the amount of KCl increases in the solution, and the concentration of NaCl decreases, the tension U1 increases while U2 decreases.

The intensity of current, under given conditions, shows slight growth, starting from single-component solution, through the ratio X = 1, to the pure solution KCl.

The difference in tensions (U1 - U2) grows, that is, changes in greater amount than each individual tension does.

All these changes are not prominent enough in order to be used in obtaining the exact results. If the solution is of consistent total concentration, and only the ratio of electrolytes in the mixture varies, the changes measured are slight.

More noticeable change, that is, the greater slope of a function, can be obtained when the ratio of tensions is set in a different way.

If only KCl is observed, in tables 2 to 16, it can clearly be seen that while the amount of KCl increases, U1 increases as well, while the U2 decreases.

CmKCl = k . U1 / U2 ..................... /1/

For component NaCl, a reverse relation is set up

CmNaCl = k . U2 / U1 ..................... /2/

The ratio of quantitative amounts is

X = CmKCl / CmNaCl ..................... /3/

The function of relation of two components can then be represented as:

fX = K . U1 . U2

. U2 . U1 and the final version is:

fX = K . (U1 / U2)2 ..................... /4/

where K = kKCl . kNaCl ..................... /5/

The next variable which can be related to the state of solution is the intensity of current. In tables the intensity of currents shows a very slight changes, but there is a tendency for a growth in the intensity of current when there is increase in concentration of KCl and decrease in amounts of NaCl.

The intensity of current increases if the concentration of the solution examined increases. When two electrolytes are in question, a small amount of the intensity of current changes due to the change in quantitative composition of the mixture, besides the concentration:

I = f (Cm2 and X) ..................... /6/

When the concentration is constant, and only the quantitative relation changes in the mixture the ratio becomes more simple:

I = k . X ..................... /7/

According to the function fX, the greatest differences between certain compositions can be formulated.

Table 17. fX = (U1 / U2)2

U0 100 mV 200 mV 300 mV NaCl 12.50 3.86 3.85 X = 1 23.40 4.70 4.80 KCl 36.00 7.70 8.44

Data from the table 14, picture 5.

Function fX offers a possibility to establish the differences between certain quantitative compositions with greater certainty.

The intensity of current, which changes just slightly, still shows a tendency to grow if the amount of KCl increases and the concentration of NaCl decreases. The tension U1 and the difference between the tensions (U1 - U2) as well as fX act in the same way.

Tables 18, 19 and 20 consist all the variables including the function fX.

In order for the differences which exist between different solutions to be increased, the contact surfaces of liquid and solid phases in the solution of unknown composition have been increased. Moreover, the electrodes in that solution have been placed closer than in other measurements.

The distance between two electrodes in the examined solution is 1cm. the contact surface for each electrode specifically is 19.0 cm2.

The sulphuric acid solution remains the same, as well as the conditions which exist in the tables 1 to 17.

As can be seen in the examples in tables 18, 19 and 20 the intensity of current still shows no changes, according to which the rules in relation between NaCl and KCl can be established.

That is why different combinations of two-component solutions have been examined , in which two ions in the same mixture differ in greater amount, than it is the case with the sodium and potassium salts.

Table 18. Cm1 = 1 M Cm2 = 0.25 M

U0 = 100 mV Solutions I mA U1 mV U2 mV (U2 – U1) mV fX

NaCl 0.17 43.0 40.0 3.0 1.14 X = 1 0.17 44.0 35.0 9.5 1.64 KCl 0.18 48.0 17.0 30.5 7.52

Cm1 = 0.50 M Cm2 = 0.25 M

Solutions I mA U1 mV U2 mV (U2 – U1) mV fXNaCl 0.17 53.0 17.0 36.0 9.72 X = 1 0.17 54.0 15.0 39.0 13.00 KCl 0.18 57.0 14.0 43.0 15.00

Table 19.

Cm1 = 1 M Cm2 = 0.50 M U0 = 100 mV

Solutions I mA U1 mV U2 mV (U2 – U1) mV fXNaCl 0.19 48.0 25.0 23.0 3.70 X = 1 0.19 50.0 18.0 32.0 7.70 KCl 0.19 54.0 15.0 39.0 13.00

Cm1 = 0.50 M Cm2 = 0.50 M

Solutions I mA U1 mV U2 mV (U2 – U1) mV fXNaCl 0.16 56.0 15.0 41.0 13.9 X = 1 0.15 57.0 12.5 44.5 20.80 KCl 0.16 58.0 11.0 47.0 27.80

Table 20.

Cm1 = 2 M Cm2 = 1 M U0 = 100 mV

Solutions I mA U1 mV U2 mV (U2 – U1) mV fXNaCl 0.17 42.0 14.0 28.0 9.00 X = 1 0.18 50.0 14.0 36.0 13.00 KCl 0.18 50.0 7.0 43.0 51.00

Cm1 = 1 M Cm2 = 1 M

Solutions I mA U1 mV U2 mV (U2 – U1) mV fXNaCl 0.19 52.0 12.5 39.5 17.30 X = 1 0.19 54.0 12.5 41.5 18.70 KCl 0.19 57.0 11.0 46.0 26.85

Cm1 = 0.50 M Cm2 = 1 M

Solutions I mA U1 mV U2 mV (U2 – U1) mV fXNaCl 0.18 62.0 ≈ 5.0 57.0 154.00 X = 1 0.19 64.0 ≈ 3.0 61.0 455.10 KCl 0.19 64.0 ≈ 2.0 62.0 1024.00

0

10

20

30

40

0 1 20

10

20

30

40

0 1 2NaCl X = 1 KCl

(U -

U) m

V1

2Cm = 0.25 M2 Cm = 0.5 M1

Cm = 1 M1

0

5

10

15

0 1 20

5

10

15

0 1 2NaCl X = 1 KCl

Cm = 0.25 M2Cm = 0.5 M1

Cm = 1 M1

fX

Picture 6.

22

30

38

46

0 1 222

30

38

46

0 1 2NaCl X = 1 KCl

(U -

U) m

V1

2

Cm = 0.5 M2 Cm = 0.5 M1

Cm = 1 M1

0

10

20

30

0 1 20

10

20

30

0 1 2NaCl X = 1 KCl

Cm = 0.5 M2

Cm = 0.5 M1

Cm = 1 M1

fX

Picture 7.

25

35

45

55

65

0 1 225

35

45

55

65

0 1 225

35

45

55

65

0 1 2NaCl X = 1 KCl

(U -

U) m

V1

2

Cm = 1 M2 Cm = 0.5 M1

Cm = 1 M1

Cm = 2 M1

15

20

25

30

0 1 2NaCl X = 1 KCl

Cm = 1 M2

Cm = 1 M1

fX

Picture 8.

SOLUTIONS LiCl - NaCl

Table 21. Cm1 = 1 M Cm2 = 0.25 M

U0 = 100 mV Solutions I mA U1 mV U2 mV (U2 – U1) mV fX

LiCl 0.18 33.0 39.0 - 6.0 0.72 X = 1 0.19 38.0 30.0 8.0 1.60 NaCl 0.19 39.0 30.0 9.0 1.70

Cm1 = 0.50 M Cm2 = 0.25 M

U0 = 100 mV Solutions I mA U1 mV U2 mV (U2 – U1) mV fX

LiCl 0.16 42.0 28.5 13.5 2.17 X = 1 0.17 48.0 26.5 21.5 3.28 NaCl 0.17 48.0 26.5 21.5 3.28

This combination of two solutions does not give better results as well. As in NaCl - KCl, the changes are very slight, especially when the intensity of current is in question.

Table 22. Cm1 = 1 M Cm2 = 0.50 M

U0 = 100 mV Solutions I mA U1 mV U2 mV (U2 – U1) mV fX

LiCl 0.18 42.0 28.0 14.0 2.25 X = 1 0.19 44.0 24.0 20.0 3.36 NaCl 0.19 50.0 21.0 29.0 5.70

Cm1 = 0.50 M Cm2 = 0.50 M

Solutions I mA U1 mV U2 mV (U2 – U1) mV fXLiCl 0.18 50.0 17.5 32.5 8.16 X = 1 0.18 56.0 16.0 40.0 12.25 NaCl 0.18 57.0 16.0 42.0 14.44

Cm1 = 0.20 M Cm2 = 0.50 M

Solutions I mA U1 mV U2 mV (U2 – U1) mV fXLiCl 0.15 52.0 ≈ 7.0 45.5 56.25 X = 1 0.16 65.0 ≈ 5.0 60.0 169.00 NaCl 0.15 62.5 ≈ 5.0 57.0 156.25

The ratio of concentrations when the measured values are out of the measure range of the instrument, under which the defined results are obtained, cannot be taken into account.

0

5

10

15

0 1 20

5

10

15

0 1 213

23

33

43

0 1 213

23

33

43

0 1 2LiCl X = 1 NaCl

(U -

U) m

V1

2

Cm = 0.5 M2 Cm = 0.5 M1

Cm = 1 M1

LiCl X = 1 NaCl

Cm = 0.5 M2 Cm = 0.5 M1

Cm = 1 M1

fX

Picture 10.

0

1

2

3

4

0 1 20

1

2

3

4

0 1 2-10

0

10

20

0 1 2-10

0

10

20

0 1 2LiCl X = 1 NaCl

(U -

U) m

V1

2

Cm = 0.25 M2Cm = 0.5 M1

Cm = 1 M1

LiCl X = 1 NaCl

Cm = 0.25 M2

Cm = 0.5 M1

Cm = 1 M1

fX

Picture 9. a)b)

a)b)

SOLUTIONS LiCl – KCl (Measurements are done under the same conditions as for

NaCl – KCl and LiCl – NaCl)

Table 23. Cm1 = 1 M Cm2 = 0.25 M

U0 = 100 mV Solutions I mA U1 mV U2 mV (U2 – U1) mV fX

LiCl 0.17 30.0 39.0 - 9.0 0.60 X = 1 0.17 36.0 30.0 6.0 1.44 KCl 0.17 42.0 26.0 15.5 7.34

Cm1 = 0.50 M Cm2 = 0.25 M

U0 = 100 mV Solutions I mA U1 mV U2 mV (U2 – U1) mV fX

LiCl 0.17 47.0 26.0 21.0 3.30 X = 1 0.17 50.0 19.0 31.0 6.60 KCl 0.18 52.0 14.0 38.0 13.80

Table 24.

Cm1 = 1 M Cm2 = 0.5 M U0 = 100 mV

Solutions I mA U1 mV U2 mV (U2 – U1) mV fXLiCl 0.18 42.0 30.5 11.5 1.90 X = 1 0.19 48.0 24.0 24.0 4.00 KCl 0.19 50.0 17.0 33.0 8.65

Cm1 = 0.50 M Cm2 = 0.5 M

U0 = 100 mV Solutions I mA U1 mV U2 mV (U2 – U1) mV fX

LiCl 0.16 50.0 18.0 32.0 7.72 X = 1 0.16 54.0 10.0 44.0 29.20 KCl 0.16 66.0 10.0 56.0 43.56

10

20

30

40

50

60

0 1 210

20

30

40

50

60

0 1 20

10

20

30

40

0 1 20

10

20

30

40

0 1 2

0

5

10

15

0 1 20

5

10

15

0 1 2-10

0

10

20

30

40

0 1 2-10

0

10

20

30

40

0 1 2LiCl X = 1 KCl

(U -

U) m

V1

2

Cm = 0.25 M2 Cm = 0.5 M1

Cm = 1 M1

Cm = 0.5 M1

LiCl X = 1 KCl

Cm = 0.25 M2

Cm = 1 M1

fX

Picture 11.

LiCl X = 1 KCl

(U -

U) m

V1

2

Cm = 0.5 M2 Cm = 0.5 M1

Cm = 1 M1

Cm = 0.5 M1

LiCl X = 1 KCl

Cm = 0.5 M2

Cm = 1 M1

fX

Picture 12.

a)b)

a)b)

THE COMPARISON OF DUAL SYSTEMS NaCl - KCl, LiCl - NaCl AND LiCl - KCl

In spite of coarse work conditions, it’s evident that the intensity of current depends both on concentration as well as the quantitative composition of the mixture.

When single component solutions of alkaline chlorides are compared the intensity of current increases slightly but steadily for the series LiCl, NaCl and KCl.

If in the examined solution the concentration is not changed, just the quantitative composition, the number of one ion is replaced by the other in the same amount. The change of the results then derives only from the different characteristics of ions.

Electro-chemical values which are defined for the behavior of the ions in the direct current conditions, can only be approximately compared with the data obtained in the alternating current circuit. Conductivity, mobility, and the transmission numbers which are related to the ions in the solution, are compared to the data acquired by measuring electrotechnical variables for the series LiCl, NaCl and KCl and their mixtures when X = 1.

Hydration numbers are also listed. They are involved in regulation of the movement of ions through the solution, as well as in the reactions of the electrodes and ions on the contact surface.

The cause of all the changes in the circuit is due to the change in concentration and quantitative compositions of the solution which is being determined. In that solution what changes is the tension U2 – the tension between the electrodes. Simultaneously, the tension U1 – the one in the sulphuric acid solution, changes as well.

As it has already been established, when U2 decreases, U1 increases and vice versa.

Although the values for the same solutions in tables up to 25th are not equal, and sometimes even very different, the direction in which the changes move always remains the same.

For the current circuit which is not stable enough, in which the tensions lower then 20 mV are already not accurate, it is not possible to obtain precise results. Only the functional relations between I, U1, U2, (U1-U2) and fX of Cm2 and X are defined.

In table 25 the data for single-component solutions of alkaline chlorides and their two-component variants of quantitative composition X = 1 are compared.

Table 25. Cm1 = 1 M Cm2 = 0.5 M

U0 = 100 mV Solutions (U1 – U2) mV fX

LiCl 32.5 8.16 LiCl 32.0 7.72 NaCl 41.0 13.90 NaCl 42.0 14.44 KCl 47.0 27.80 KCl 58.0 43.56

LiCl - NaCl 40.0 12.25 NaCl - KCl 44.5 20.30 LiCl - KCl 44.0 29.20

3 0

4 0

5 0

6 0

0 1 23 0

4 0

5 0

6 0

0 1 23 0

4 0

5 0

6 0

0 1 2X = 1

(U -

U) m

V1

2

Picture 13.

a)Cm = 0.5 M1 Cm = 2

fX

5

15

25

35

45

0 1 25

15

25

35

45

0 1 25

15

25

35

45

0 1 2X = 1

Cm = 0.5 M1 Cm = 2

b)LiCl - KCL

NaCl - KCl

LiCl - NaCl

LiCl - KCL

NaCl - KClLiCl - NaCl

MIXTURES OF SOLUTIONS OF ALKALINE CHLORIDE WITH HYDROCHLORIC ACID

The changes which occur between the dual systems of the three mentioned alkaline chlorides, are not distanced enough from one another, for the composition X to be precisely defined, under the given conditions. Moreover, the results are not always reproductive.

Considerable differences between the results for individual quantitative compositions, which can be determined more precisely, are obtained when two cations present in the mixture differ more by other chemical, electrochemical and physicochemical characteristics.

Dual systems in which HCl is one component, while the other is some alkaline chloride , has greater differences in results for some compositions, then when the mixture comprises of two alkaline chlorides.

Table 26. X = CmHCl / Cmalkaline chloride

Cm1 = 0.50 M Cm2 = 0.25 M U0 = 100 mV

Solutions I mA U1 mV U2 mV (U2 – U1) mV fXLiCl 0.17 39.0 39.0 0.0 1.00 X = 1 0.18 53.0 12.0 41.0 19.00 HCl 0.17 60.0 5.0 55.0 144.00 NaCl 0.18 40.0 25.0 15.0 2.56 X = 1 0.18 53.0 12.0 41.0 19.00 KCl 0.19 50.0 20.0 30.0 6.25

X = 1 0.18 53.0 12.0 41.0 19.50

Picture 14.a)

0

50

100

150

0 1 20

50

100

150

0 1 20

50

100

150

0 1 2X = 1

Cm = 0.25 M2

Cm = 0.50 M1fX

KCl - HClNaCl - HClLiCl - HCl

0

20

40

60

0 1 20

20

40

60

0 1 20

20

40

60

0 1 2X = 1

(U -

U) m

V1

2

Cm = 0.25 M2

Cm = 0.50 M1

b)

KCl

NaCl

LiCl

There is the possibility of dual mixtures of alkaline chlorides can be determined thus as well. Obviously, the current circuit has to be formed in such a maneer that stable conditions and reproductive results of measurement are insured.

The use of a more sensitive amperemeter has contributed to the recording of each change of Cm2 and X, in the area in which the experiments have been conducted.

High values for the HCl solution in relation to the alkaline chlorides solution, occur as a consequence to great differences between other electrochemical characteristics of hydrogen ion regarding to the ions of alkaline cations. (table 26, picture 14, a and b).

By comparing all the functions fX for alkaline chlorides, including the RbCl, CsCl as well as HCl solutions, of the same concentration (picture 27) not only the changes but also the regular arrangement become obvious.

Function fX for the single-component solutions of alkaline chlorides and chloric acid.

Table 27.

Cm1 = 0.50 M Cm2 = 0.25 M U0 = 100 mV

Solutions fX

LiCl 1.00

NaCl 2.56

KCl 6.25

RbCl 10.68

CsCl 13.36

HCl 144.00

The characteristics of ions in aqueous solutions, under the influence of electric field can be compared with the functions listed in table 27, although the functions fX are related to the alternating current circuit, and the values from the area of classic electrochemistry to the direct current.

The tables for ionic radii as well as the hydration numbers for the series of alkaline cations and hydrogen ion are given, without going into a detailed analysis of the cause and result of the occurrences in the solution and on the contact of the liquid and solid phase during the flow of current.

Table 28. Cm1 = 0.50 M Cm2 = 0.125 M

U0 = 100 mV Solutions I mA U1 mV U2 mV (U2 – U1) mV fX

LiCl 2.40 36.0 39.0 - 3.0 0.85 NaCl 2.70 42.0 29.0 13.0 2.10 KCl 2.75 48.0 26.5 21.5 3.28 HCl 3.25 57.0 14.0 43.0 16.60

Table 29.

Ionic Radii

Cation Ionic Radius

Li+ 0.068

Na+ 0.098

K+ 0.133

H+ 0.208 *see literature 10, page 547

Table 30. Hydration Numbers

Li+ Na+ K+ Cs+ H+ 14.0 8.4 5.4 4.7 1.0

*see literature 1, page 707

-5

5

15

25

35

45

0.5 1.5 2.50

5

10

15

20

0 5 10 15

Pict ure 16.

fX

(U -

U)

mV

12

Cm = 0.125 M2

Cm = 0.50 M1

hydration numbe r (h)

HCl

KClNaCl

LiCl

U = 100 mV0

Picture 15.

Cm = 0.125 M2

Cm = 0.50 M1

H+

K +

Na+

Li+

U = 100 m V0

nm

0

Transmission numbers in aqueous solutions, 25 oC

Table 31. LiCl NaCl KCl HCl

0.3289 0.3918 0.4902 0.8521 *see literature 2, page 380

Picture 17.

H+

K+Na+

Li+

0

5

10

15

0.5 1. 5 2.50

5

10

15

0.5 1.5 2. 5

fX

f=

(U/ U

)X

1

22

h

hydr

atio

n nu

mbe

rs

ionic radii

0

5

10

15

0. 5 1.5 2. 50

0.5

1

0.5 1 1.5 2 2.5

Cm = 0.125 M2

Cm = 0.50 M1

U = 100 mV0

H+

K+

Na+

Li+

fX

fX

Picture 18.

ionic radi i

tran

smis

sion

num

bers

transmission numbers

0

5

10

15

0.5 1.5 2.5

Cm = 0.125 M2

Cm = 0.50 M1

U = 100 mV0

H +

K+

Na+

Li+

fX

fX

Picture 19.

ionic radii

mobi lit

y (10

-4)

mob

ility

(10

)-4

(cm

cec

vol

t)

2-1

-1

0

10

20

30

40

0.5 1 1.5 2 2.5

Picture 20.

0

5

10

15

0. 5 1.5 2. 5

Cm = 0.125 M2

Cm = 0.50 M1

U = 100 mV0

H+

K+

Na+

Li+

fX

fX

ionic radii

0

50

100

150

200

250

300

350

0.5 1 1.5 2 2.5

Λ0

Λ0 -

equ

ival

ent c

ondu

ctiv

ity

Mobility of ions in aqueous solutions, 25 oC

Table 32. cm2sec-1volt-1

Cation Ionic Radius

Li+ 4.01 . 10-4

Na+ 5.19 . 10-4

K+ 7.62 . 10-4

H+ 36.30 . 10-4 *see literature 2, page 381

Equivalent ionic conductivities for endless dilution, 25 oC

Table 33. Cation Conductivity

Li+ 38.69

Na+ 50.11

K+ 73.52

H+ 349.82 *see literature 2, page 380

fX FUNCTIONS COMPARED TO STANDARD ELECTROCHEMICAL DATA

fX functions which that are calculated based on electrotechnical data in the current circuit in which only the conditions in one solution are changed, have been compared to the characteristics of ions defined in the area of electrochemistry, by the sizes of ionic radiuses.

In tables 29 to 33, data for three alkaline cations and hydrogen ion are listed: hydration number, mobility, transmission numbers, conductivity, as well as ionic radiuses.

Except from hydration number and ionic radiuses, other characteristics listed are related to the conditions when the direct current flows through the circuit.

Mobility and conductivity are defined for the endless dilutions. The transmission numbers are related to 0.01 M of concentration.

The solutions whose functions are listed in tables have 0.125 M of concentration.

By comparing the function with other data, in spite of different conditions of measurement regularity in relations is shown. (Pictures 15 to 20)

Tension differences (U1 - U2) are changed similarly as fX, when they are placed towards the ionic radiuses. (Picture 14, a and b)

Ionic radiuses are applied, as the common comparison base.

Judging by all the results, it appears that, during the changes in the quantitative relations in the mixture, the ion which has grater conductivity, greater transmission number, greater mobility, and smaller hydration number, influences the results in such maneer that the intensity if current in the circuit increases, the tension U2 decreases and U1 increases. Cation which has greater hydration number, and lesser conductivity, mobility and transmission numbers makes the intensity of current to decrease and tension U2 increase, and thus decreases U1.

Besides some defined relations in the solutions, such as activities, ionic strengths, thickness of ionic atmosphere, energy of electrostatic interrelations, thermal movement of the ions and the mechanisms of reactions on the electrodes, only the three other macro values are measured: the intensity of current in the circuit, and two tensions U1 and U2.

Based on these results the concentration and the quantitative composition in an unknown solution can be determined.

THE INTENSITY OF CURRENT

The intensity of current in the circuit is proportional to the concentration of solution, if all the other conditions remain the same.

Nevertheless, in dual systems the intensity of current depends not only from the concentration, but also partly from the quantitative composition.

From the data gathered so far it is obvious that the influence of quantitative composition on the intensity of current is very mild.

Larger contact surface between the liquid and solid phase in the solution examined makes the influence of each change in that solution on the U2 tension greater.

The range between the results for the similar quantitative compositions is expanded by greater differences between the characteristics of two ions in a mixture.

THE INFLUENCE OF TEMPERATURE

Except for the unstable circuit where the measurements are not reproductive, there is also the influence of temperature.

It has been known for a long time that temperature is one of the causes for the change in the electrotechnical data.

In the case of equivalent conductivity for each degree of raise in temperature, conductivity increases for approximately 2 %. That percentage increases in such a maneer that, when the temperature reaches around 40 °C, there occurs an increase in conductivity for 3 % for each degree of raise. (see literature No 9, page 23)

In the following section the experiments have been conducted on the mixture HCl - NaCl, with a remark that other alkaline chlorides in the solution with the chloric acid behave in the same way.

PART II

THE MIXTURE OF SOLUTIONS HCl - NaCl

According to the data from the first section, some regularities can be seen, during the change in the solutions which consist of two electrolytes.

For more detailed examinations the HCl - NaCl combination has been chosen.

The mixture of any two alkaline chlorides requires better technical conditions and more sensitive measuring instruments. The characteristics of alkaline cations are, as it is known, more similar between themselves, than any of them with regard to hydrogen ion.

In order for the quantitative composition to be determined the main intention is to get as greater the difference between the results of measurement and their functions as possible, for similar quantitative compositions.

Quantitative composition X, is defined as the ratio X = CmHCl / CmNaCl, for all following results in the tables to the end of the paper.

According to this definition, for the solution NaCl, X = 0. for the sollution of HCl, X = ∞.

In previous tables the results from broader framework of concentrations for both solutions, are listed.

Following measurements are related to the solutions whose concentrations are determined: sulphuric acid has the adopted concentration of 0.50 M, and the solution HCl - NaCl whose quantitative composition changes 0.125 M.

In the table 1, the solution which contains 75% NaCl and 25% HCl, is compared to single-component solution of NaCl.

The change in results for two different quantitative compositions is the change of one amount of one ion with the other. In this case 0.03125 mols of NaCl has been replaced by the same amount of mols of HCl. (table 1)

In the sulphuric acid solution electrodes are placed at 2.5 cm distance, and the contact surface between the electrodes and the solution is 6.0 cm2, for each individual electrode.

Table 1. Cm1 = 1 M Cm2 = 0.125 M

U0 = 100 mV X I mA U1 mV U2 mV (U2 – U1) mV fX

0 (NaCl) 2.20 35.0 35.0 0.0 1.0 0.3333 2.40 48.0 20.0 28.0 5.76

Table 2.

Cm1 = 0.50 M Cm2 = 0.125 M U0 = 100 mV

X I mA U1 mV U2 mV (U2 – U1) mV fX0.1111 2.30 45.0 30.0 15.0 2.25

1 2.40 52.0 15.0 37.0 12.00 9 2.60 60.0 ≈ 10.0 50.0 36.00

∞ (HCl) 2.80 50.0 ≈ 8.0 42.0 39.00

In HCl - NaCl solution, the distance between the electrodes is 1 cm, and the contact surface of each individual electrode is 19.00 cm2. (picture 1)

In table 1, data from the measurements of two quantitative compositions HCl - NaCl, with concentration 0.125 M is listed. (pictures 2a and 2b)

Greater amount of data is listed in table 2. (pictures 3a and 3b)

These results have been established by repeating the experiments under same conditions. The medial values of similar data are listed.

Tensions U1 and U2 are not always reproductive, but they and their functions fX and (U1 - U2) always have the same direction of changes.

If the results were reproductive, the values in question could be found according to the graphic relations fX - X, (U1 - U2) - X, and I - X. The functions of these relations can also be formulated, but only for the known concentrations.

The intensity of current, although slightly changing, usually has reproductive results, but what is needed is for the concentration of the solution to be known.

0

10

20

30

40

0 1 20

10

20

30

40

50

0 1 20

10

20

30

40

50

0 1 2

Picture 3b.

a)

fX

X = 1

(U -

U) m

V1

2

b)

0

3

6

0 1 2X = 1

(U -

U) m

V1

2

Picture 2a.

X = 0.330

15

30

0 1

fX

2X = 1X = 0.33

Picture 13.

Cm = 0.125 M2

Cm = 0.50 M1

X = Cm / CmHC l NaCl

f = (U / U2)X 12

(NaCl)0.11

0.33 89

Picture 3a.

X = 1(NaCl)0.11

0.33 89(HCl) (HCl)

THE INTERRELATIONS OF ALL THE VARIABLES

Simultaneous determining of all the variables in one circuit establishes functional dependence between the unknown Cm2 and X, and the measured data which change according to the wanted unknown walues.

When the input tension U0 and Cm1 as well as the technical details in the circuit are constant, the intensity of current I, and two tensions in the solutions U1 and U2 can be measured. Each change in these three values depends on the change in the unknown solution.

Functions fX and (U1 - U2) can be used as better solution if the solutions determined have similar values.

According to a number of measurements under same conditions for same solutions in the range of 0.025 M to 0.10 M whose quantitative compositions are known, data has been gathered and listed in table 3.

The solutions chosen are single-component HCl, NaCl and the solution of quantitative composition X=1, when both components in the mixture are present in equal amounts.

Conditions in the circuit and solutions are the same as the data listed in tables 1 and 2.

Table 3. Solution HCl (X = ∞)

Cm2 I mA U1 mV U2 mV (U2 – U1) mV fX0.10 2.80 63.0 15.5 47.5 16.52 0.05 2.50 54.0 30.0 24.0 3.24 0.025 2.30 47.0 46.0 1.0 1.04

Solution HCl – NaCl (X = 1)

0.10 2.55 50.0 15.0 35.0 11.11 0.05 2.20 43.0 33.5 9.5 1.65 0.025 1.75 26.5 48.5 - 22.0 0.30

Solution NaCl (X = 0)

0.10 2.40 42.0 44.5 - 2.5 0.89 0.05 1.60 20.0 50.0 - 30.0 0.16 0.025 1.15 ≈ 6.0 64.0 - 58.0 0.09

Graphic representation of the relation from the table 3, for all changes, is shown on their diagrams(pictures 4 to 11).

0

1

2

3

0 0.025 0.05 0. 075 0. 10

1

2

3

0 0.025 0.05 0 .075 0.10

1

2

3

0 0.025 0.05 0 .075 0.1

Picture 4.X = (HCl)8

X = 1X = 0 (NaCl)

I mA

M-60

-10

40

0 0.025 0. 05 0.075 0. 1-60

-10

40

0 0.025 0 .05 0.075 0.1-60

-10

40

0 0.025 0 .05 0.075 0.1

Picture 5.

(U -

U) m

V1

2

X = (HCl)

8X = 1

X = 0 (NaCl)

M

0

5

10

15

0 0.025 0.05 0.075 0.10

5

10

15

0 0.025 0.05 0 .075 0.10

5

10

15

0 0.025 0.05 0 .075 0.1

fX

P icture 6.fX

X = (HCl)8

X = 1

X = 0 (NaCl)

M0

1

2

3

0 1 20

1

2

3

0 1 20

1

2

3

0 1 2

Picture 7

I mA

8

(NaCl) (HCl)

Cm = 0.10 M2

Cm = 0.05 M2

Cm = 0.025 M2

X

-60

-10

40

0 1 2

Cm = 0.10 M2

Cm = 0.05 M2

Cm = 0.025 M2

- 60

- 10

40

0 1 2-60

-10

40

0 1 2

8

X

(NaCl) (HCl)

(U -

U) m

V1

2

P icture 8.

X0

5

10

15

0 1 20

5

10

15

0 1 20

5

10

15

0 1 2

Picture 9.

fX

Cm = 0.10 M2

Cm = 0.05 M2

Cm = 0.025 M2

8

(NaCl) (HCl)X

Table 4 Data from table 3.

Intensity of current in mA Solutions Cm2 0.025 0.05 0.10

HCl 2.30 2.50 2.80 X = 1 1.75 2.20 2.55 NaCl 1.15 1.60 2.40

Function fX

HCl 1.04 3.24 16.52 X = 1 0.30 1.65 11.11 NaCl 0.09 0.16 0.89

(U1 – U2) mV

HCl 1.0 24.0 47.5 X = 1 - 22.0 9.5 35.0 NaCl - 58.0 - 30.0 - 2.5

0

1

2

3

4

1.5 2 2.5

X = 0 - 1 - 8

Picture 10c.

0

0.5

1

1.5

1 1.5 2 2.50

5

10

15

2 2.5 3

X = 0 - 1 - 8

X = 0 - 1 - 8

Picture 10a.

Picture 10b.

I mA I mA

I mA

fX fX

fX

Cm = 0.05 M

2

Cm =

0.1

M2

Cm = 0.

025 M

2

0

5

10

1.5 2 2.5

0

0.5

1

1 1.5 2 2.5

0

5

10

15

2 2.5 3

Cm = 0.025 - 0.05 - 0.10 M 2

Picture 11c.

Cm = 0.025 - 0.05 - 0.10 M2

Cm = 0.025 - 0.05 - 0.10 M2

Picture 11a.

Picture 11b.

I mA I mA

I mA

fX fX

fX

X = 0

X = 1X =

8

The following measurements are related to just two solutions, that is two concentrations and three quantitative compositions.

All conditions are the same as for previous results

Table 5. Solution HCl (X = ∞)

Cm2 I mA U1 mV U2 mV (U2 – U1) mV fX0.05 2.40 50.0 25.0 25.0 4.00 0.025 2.00 40.0 38.0 2.0 1.11

Solution HCl – NaCl (X = 1)

0.05 2.20 42.0 36.0 6.0 1.36 0.025 1.80 25.0 45.0 - 20.0 0.31

Solution NaCl (X = 0)

0.05 1.80 20.0 50.0 -30.0 0.16 0.025 1.20 6.0 60.0 - 54.0 0.01

Picture 13b.

1

1.5

2

2.5

0 1 21

1.5

2

2.5

0 1 2

0

2

4

0 0.025 0.050

2

4

0 0.025 0.050

2

4

0 0.025 0.05

1

1.5

2

2.5

0 0.025 0.051

1.5

2

2.5

0 0.025 0.051

1.5

2

2.5

0 0.025 0.05

-60

-30

0

30

0 0.025 0.05-60

-30

0

30

0 0.025 0.05-60

-30

0

30

0 0.025 0.05

0

2

4

0 1 20

2

4

0 1 2

-60

-30

0

30

0 1 2-60

-30

0

30

0 1 2

Picture 12c.

Picture 12b.

Picture 12a.

fXfX

X = 1

X = 1

X = 1

(U -

U) m

V1

2

(U -

U) m

V1

2

Picture 13c.

Picture 13a

I mA I mA

X = 1

X = 1

X = 1

X = 0

X = 0

X = 0

X =

8

X =

8

X =

8

Cm = 0.05 M2

Cm = 0.05 M2

Cm = 0.05 M2

Cm = 0.025 M2

Cm = 0.025 M2

Cm = 0.025 M2

0 (NaCl)

0 (NaCl)

0 (NaCl) 8 (HCl)

8 (HCl)

8 (HCl)

M

M

MCm2

Cm2

Cm2

0

2

4

1 1.5 2 2.50

2

4

1 1.5 2 2.50

2

4

1 1.5 2 2.

Picture 14

50

2

4

1 1.5 2 2.5I mA

fX

0,05 M; X =

0.025 M; X =

8

80.025 M; X = 1

0.05 M; X = 1

0.05 M; X = 00.025 M; X = 0

-60

-30

0

30

1 1.5 2 2.5-60

-30

0

30

1 1.5 2 2.5-60

-30

0

30

1 1.5 2 2.5

(U -

U) m

V1

2

-60

-30

0

30

1 1.5 2 2.5I mA

Picture 15.

X = 0

X = 0

X = 1

X = 1

X = 8

X = 8

Cm = 0.025 M

2

Cm =

0.05 M

2

Table 6. Comparison of the data from table 5.

Intensity of current in mA Solutions

Cm2 0.025 0.05 HCl (X = ∞) 2.00 2.40

X = 1 1.80 2.20 NaCl (X = 0) 1.20 1.80

Function fX

HCl (X = ∞) 1.11 4.00 X = 1 0.31 1.36

NaCl (X = 0) 0.01 0.16

(U1 – U2) mV HCl (X = ∞) 2.00 25.0

X = 1 - 20.00 6.0 NaCl (X = 0) - 54.00 - 30.0

After the relationships between all the variables in the circuit and the required unknowns Cm2

and X have been established, some results can be formed.

The intensity of current, although, the least sensitive to the changes in the solution examined, is at the same time the most reliable criterion, since the results are usually reproductive. Function fX, although neither stable nor reproductive enough, differs in greatest amount for different X compositions.

The dependency Cm2 - I and Cm2 - fX are defined for certain compositions as X, while the relations X - I and X - fX are for certain concentrations Cm2.

Obviously, the intensity of current and the function fX increase, if the concentration of composition of solution Cm2 rises and quantitative composition X defined as CmHCl / CmNaCl increases as well. (pictures 12 a, b, c and 13 a, b, c)

The difference of tensions (U1- U2) in relation to Cm2 and X behaves in the same way - it increases when Cm2 and X increase. The defect is that measurements of tensions U1 and U2 are not accurate enough, and thus, their difference is not useable enough.

The only thing that can be concluded with precision is that there is a regularity in relations between the changes in the solution examined and electro-technical data measured in the circuit.

Pictures 14 and 15 contain graphic representations of the relations between function fX and the intensity of current I, as well as the difference of the tensions (U1- U2).

All the data in table 6 is connected by straight lines.

Bordered surfaces represent surface functions. Mathematically, according to the measurements, the relations could be defined according to which the functions can lead to correct results for Cm2 and X.

The relation fX - (U1 - U2) is not set up clearly enough. In a stable circuit the relation of these functions could be securely determined.

In this example data is determined for the range of concentrations from 0.025 M to 0.05 M, and X from 0 to 1. During the measurement, if any tension, U1 or U2, is measured inaccurately for just 1 mV, the result will differ from the correct value for 4 to 6 %.

All the changes mentioned and the relations between the sought unknowns and measured data, have brought to one manner of dealing with the dual solutions and determining their quantitative composition.

ONE WAY OF DETERMINING THE QUANTITATIVE COMPOSITION OF THE SOLUTIONS WHICH CONTAIN TWO ELECTROLYTES

In picture 1, the circuit of current is shown in which two solutions are tied lineary as resistors, with their electrodes. In one solution there are two electrolytes whose quantitative composition is not known.

If the quantitative composition is changed, the intensity of current I and tensions between two electrodes in solutions U1 and U2 change as well.

Series of solutions of alkaline chlorides and their mixtures have been examined, both between themselves and in combinations with HCl. Only the mixture HCl - NaCl has been examined in detail.

The changes in the intensity of current I, tensions U1 and U2, as well as their functions fX and (U1 - U2) have been measured.

The sum concentration equals

Cm2 = CmHCl + CmNaCl

The way of determining the concentration is shown in the paper: “The Appliance of a team of pairs of inert electrodes in order to determine electrolyte concentration”

The procedure applied on determining the single-component solutions can be applied to the solutions which consist of two or more electrolytes, as well, if the quantitative composition is known.

The quantitative relation of dual mixture is defined by

X = CmHCl / CmNaCl

Concentration Cm2 can not be determined until the quantitative composition is known.

Without the formed functions between the known and sought unknowns, there is a possibility of finding the unknowns individually.

If neither Cm2 nor X are known, quantitative composition X can first be determined, and later the concentration as well, by using the already known way as for the single-component solutions.

In tables 7 and 8 all data relating to the range of concentration from 0.025 M to 0.05 M and of quantitative composition from X = 0 to X = 1 have been compared. All the values in the tables are the results of many repetitions - average values of similar results are listed.

Conditions in the circuit are the same as in the tables 1 to 6.

As in all the previous measurements, the intensity of current has the most reproductive results, while the tensions U1 and U2, although more sensitive, are less reproductive. For each change in the solution of dual mixture, the greatest changes are noticed for function fX.

Table 7. Solution (X = 1)

Cm2 I mA U1 mV U2 mV (U2 – U1) mV fX0.05 2.00 48.0 25.0 23.0 3.70 0.025 1.40 24.0 42.0 - 18.0 0.33

Solution NaCl (X = 0)

0.05 1.80 34.0 48.0 - 14.0 0.50 0.025 1.00 16.0 52.0 - 36.0 0.10

Table 8.

Cm2 0.025 0.05 Intensity of current in mA

X = 1 1.40 2.00 X = 0 1.00 1.80

Function fX

X = 1 0.33 3.70 X = 0 0.1 0.50

(U1 – U2) mV

X = 1 - 18.0 23.0 X = 0 - 36.0 - 14.0

25

35

45

55

0 125

35

45

55

0 125

35

45

55

0 125

35

45

55

0 1

Picture 18a. Picture 18b.

X = 1

X = 0

Cm = 0.05 M2

Cm = 0.025 M2

0.025 0.050Cm2

UmV

2UmV

2

1

2

0 11

2

0 11

2

0 11

2

0 1

10

20

30

40

50

0 110

20

30

40

50

0 110

20

30

40

50

0 110

20

30

40

50

0 1

Picture 17b.Picture 17a.

Picture 16a.

UmV

1UmV

1

Picture 16b

I mA I mA

X = 1

X = 1

X = 0

X = 0

Cm = 0.05 M2

Cm = 0.05 M2

Cm = 0.025 M2

Cm = 0.025 M2

0.025 0.050Cm2

0.025 0.050Cm2

X

X

X

0

2

4

0 10

2

4

0 10

2

4

0 10

2

4

0 1

Picture 20b.Picture 20a.

fXfX X = 1

X = 0

Cm = 0.05 M2

Cm = 0.025 M2

0.025 0.050Cm2

-40

-20

0

20

0 1-40

-20

0

20

0 1-40

-20

0

20

0 1-40

-20

0

20

0 1

Picture 19a. Picture 19b

(U -

U) m

V1

2

(U -

U) m

V1

2

X = 1

X = 0

Cm = 0.05 M2

Cm = 0.025 M2

0.025 0.050Cm2X

X

-40

-20

0

0 1

-25

0

25

0 1 2 3 4

(U -

U) m

V1

2

(U -

U) m

V1

2

X = 1

∆Cm = 0.05 - 0.0252

∆Cm = 0.05 - 0.0252

fX

fX

Picture 25a.

Picture 15b.

X = 0

-40

-20

0

20

1 2-40

-20

0

20

1 2

Picture 24.

I mA

(U -

U) m

V1

2

0

2

4

0 10

2

4

0 1

Picture 23.∆Cm = 0.05 - 0.0252

∆Cm = 0.05 - 0.0252

fX

I mA1 2

X = 0

X = !X = 1

X = 0

The surface bordered by connecting the values determined for two concentrations and three quantitative compositions, is marked by two lines. (Pictures 21 and 22)

It is possible that the defined surface is not exactly of that shape. Stable circuit, exact measurements and reproductive results can perhaps change the shapes formed by the relations fX – I and (U1- U2) – I.

Individual influences of Cm2 and X, on the measured values are graphically shown on pictures 16 to 20.

Cm2 – I and X – I

Cm2 – U1 and X – U1

Cm2 – U2 and X – U2

Cm2 – (U1 – U2) and X – (U1 – U2)

Since there is already a way of determining the concentration of single-component electrolytes, the same way can be applied to the mixture of solutions, under the condition that the quantitative composition of the mixture is known.

Individual influences of Cm2 and X show only slight changes on the diagrams.

In order for the first approximate values in the area of concentration where the unknown solution is found to be determined, one proceeds from the previous data, which are known.

In a limited area of concentration the unknown solution should be found.

In this case the concentration goes from 0.05 to 0.025 M.

Quantitative composition does not exceed X = 1..

Data in table 10 is related to the familiar solutions. The account is, nevertheless, derived as if it was one of the unknowns.

Let the standard solution be of concentration 0.05 and quantitative composition X = 1.

According to the relation fX – I, as in the picture 23, the tangens of the angle of this solution is derived:

tg α1 = ∆fX / ∆ I for X = 1

This relation is derived by diluting the solution of concentration from 0.05 to 0.025 M.

The unknown solution has, by diluting, been brought to the moment when the intensity of current does not exceed, for that mixture intensity of current, which is also present in the standard solution in its greatest value.

The angle tangent of the unknown solution is thus determined as well:

tg αX = ∆fX / ∆ I for X = x

Now, relation can be set as:

1 tg α1

X tg αX

X = tg αX / α1

CALCULAL EXAMPLES

The concentration of the unknown solution can be determined as it has already been mentioned, by using two standard solutions. When mixture is in question, in order for the standards to be prepared, the quantitative composition has to be known first.

In tables 10. 11, and 12, the results of measurements of one amount of solutions are listed, and the obtained results are compared with foreknown quantitative compositions.

Exceptions and mistakes occur, more or less, because of the circuit of current which is not stable enough.

The calculal examples which will be presented here, are neither the best nor the worst in the series of measurements. They just prove the possibilities which exist.

The range of concentrations from 0.05 to 0.025 M has been adopted according to the range in which the data can be easily read on the measuring instrument, for the given conditions in the circuit.

The assumption is that between two values on the graphical representation of the relation fX – I, there is a straight line.

The relation tg α – ∆fX / ∆I is thus established with quantitative composition of the mixture X.

Other variants for relations ∆ I – ∆(U1 – U2) and ∆fX – ∆(U1 – U2) can probably be used in the same way, only when the reproductive measurement of the tension is enabled.

Table 9. X = 0

Cm2 I mA U1 mV U2 mV fX0.05 1.50 48.0 28.0 2.940 0.025 1.00 28.0 38.0 0.543

tg α0 = 4.794 X = 1

0.05 1.60 50.0 14.0 12.755 0.025 1.35 45.0 18.0 2.58

tg α1 = 40.70 X = 2

0.05 1.70 60.0 14.0 18.36 0.025 1.50 48.0 28.0 2.94

tg α2 = 77.10

Now, relation can be set as: 1 40.7

X 77.1

X α2 = 77.10 / 40.7 = 1.895

It should be obtained X = 2.00 (in this particular case, cumulative error is – 5.0 %)

1

1.5

2

0 1 21

1.5

2

0 1 2

10

30

50

0 1 210

30

50

0 1 2

10

20

30

40

50

60

0 1 210

20

30

40

50

60

0 1 2

Picture 27a.

X

X

X

Picture 27b.

Picture 26

I mA

Cm = 0.05 M2

Cm = 0.05 M2

Cm = 0.025 M2

Cm = 0.025 M2

mV

mV U1

U1

U2

U2

Table 10.

X = 0 Cm2 I mA U1 mV U2 mV fX0.05 2.0 18.0 28.0 0.4185 0.025 1.7 28.0 60.0 0.217

tg α0 = 0.662 X = 0.25

0.05 2.1 25.0 28.0 0.797 0.025 1.5 20.0 64.0 0.0976

tg α1 = 1.16 X = 1

0.05 2.4 42.0 28.0 2.25 0.025 2.0 30.0 46.0 0.425

tg α0.25 = 4.56

If for X = 1 tg α1 = 4.56 and for X = 0.23 tg α0.25 = 1.16 then X α0.25 = 1.16 / 4.56 = 0.25438 (error 1.75 %)

0

0.5

1

1.5

2

2.5

1 .5 2 2.50

0.5

1

1.5

2

2.5

1 .5 2 2.50

10

20

0 1 20

10

20

0 1 2

Picture 28.

X

Cm = 0.05 M2

Cm = 0.025 M2

fX

I mA

fX

0.025 M

Picture 29.

0.05 M

1. 5

2

2. 5

0 0.25 0.5 0.75 1

∆Cm = 0.05 - 0.0252

Picture 30.

0

40

80

0 1 2X

tg α

Cm = 0.052

Cm = 0.0252

Picture 31.

ImA

X

1.5

2

2.5

0 0.25 0.5 0.75 1

Table 11.

NaCl Cm2 I mA U1 mV U2 mV fX0.05 2.0 18.0 28.0 0.4185 0.025 1.7 28.0 60.0 0.2170

tg αNaCl = 0.663 KCl

0.05 1.65 30.0 30.0 1.000 0.025 1.40 22.0 57.0 0.152

tg αKCl = 3.39 HCl

0.05 2.5 60.0 17.0 12.456 0.025 2.1 50.0 35.0 2.041

tg αHCl = 26.0

0

1

2

3

2 2.25 2.50

0.25

0.5

1.5 1.75 2

0

2.5

5

0 0.25 0.5 0.75 1

Picture 34..

X

Picture 33b.Picture 33a.

I mAI mA

0

1

2

3

0 0.25 0.5 0.75 10

1

2

3

0 0.25 0.5 0.75 1X

Picture 32.

Cm = 0.05 M2

Cm = 0.025 M2

fX

fX fX

tg α

tg = f / Iα ∆ ∆X

0.025 M

0.05 M

The calculal examples from the tables 9 and 10 are listed although they are not completely accurate. In a number of cases results obtained can move in the range of ± 2 %.

In the same way results according to the relation ∆(U1 – U2) - ∆I can be obtained. This way applied to the same solutions has a lesser percentage of accurate results. The differences in tensions can vary within certain ranges and results are thus uneven. It still comes down to the relation between the tangent of the angle according to the quantitative composition.

tg α = ∆(U1 – U2) / ∆I

Table 11 contains three examples of single-component solutions. Except from the change of tangent of angles which depend on the quantitative composition of the mixture, it can be presupposed that each electrolyte can have its own slope.

Pictures 30 and 34 represent the relation of the slope of angles and quantitative compositions. According to the data presented so far, this relation should be rectilinear.

It is highly possible that the combination of the function fX and the difference between the tensions (U1- U2) can establish rectilinear relation between themselves. That would require the circuit of current in which the tensions can be measured in such a way that they can always be reproductive.

CONCLUSIONS

1. When an electrotechnical connection is put between two electrolytic solutions (a common wire) and the current starts flowing, the metal conductor between the solutions carries electricity (Picture 1).

2. The intensity of current in the circuit is proportional to the concentration of electrolytes in the solutions (Picture 2).

3. If one solution is of stable concentration and the other has a changeable one, a relation between the intensity of current in the circuit and the concentration of solution can be established. The condition that has to be met is that the initial tension has to be stable.

4. The fastest and the most simple way of determining the concentration of the unknown solution would be the graphical one (picture 2).

5. If in the examined solution there are two electrolytes present, the intensity of current depends not only on the concentration, but also on the quantitative composition.

6. Tensions U1 and U2, which exist between the electrodes in the solutions also depend on the quantitative composition, as well as on the concentration.

7. Under condition that the input tension U0. the concentration of sulphuric acid Cm1 and the concentration of the dual solution Cm2, have constant values, the measured data I, U1 and U2 depend only on the quantitative composition of the mixture.

8. The quantitative composition is defined by the relation X = Cma / Cmb

9. The data were compared for the dual mixtures LiCl - NaCl, LiCl - KCl and NaCl - KCl. Although there are differences between certain mixtures the results between themselves are not different enough.

10. The mixtures of each of these three chlorides with HCl already have visibly greater differences for certain quantitative compositions.

11. The common conclusion defines the relation between two ions in a mixture: if the solution contains the ions which already differ between themselves, by comparing the other already known electro chemical characteristics, the measured electrotechnical data for different quantitative compositions differ in greater extent between themselves.

12. Greater differences for some quantitative compositions can be achieved by using the greater contact surface between the solid and liquid phase in the solution examined.

13. Tension U1 in the sulphuric acid solution changes as a consequence of the changes that occur in the mixture whose tension is U2.

14. The differences of tensions (U1- U2) or (U2 - U1) have even greater differences between themselves, than each tension U1 or U2 individually for the same mixtures.

15. The square relation of two tensions is represented by the function fx = /U1/ U2/2 or U2/ U1/2 makes the greatest difference in results between any two quantitative compositions.

16. All changes that occur in the circuit- two sought unknowns Cm2 and X, as well as the three measured variables I, U1 and U2 are compared simultaneously. In a stable circuit of current in which reproductive results can be obtained, there is a possibility of defining the equations in which the relation between all the variables is established.

17. In the circuit which has been applied here, ways have been established, by which the sought unknowns are determined individually.

18. Hydration numbers are compared to the functions fx for single-component systems. It was shown that there is a regularity for a series of alkaline chlorides: LiCl, NaCl, KCl as well as HCl. It was concluded that the higher the hydration numbers, the lower the intensity of current in the circuit. At the same time, the tension U2 increases and U1 decreases.

19. The conductivity for the same cations in comparison to the corresponding functions works in the opposite direction in relation to the hydration number. If the conductivity of ions in the solution is greater, the intensity of current increases, tension U2 decreases and tension U1 increases. Data concerning conductivity relates to the conditions of direct current.

20. Mobility works in the same way, although they, as well, are determined in direct current conditions.

21. Transmission numbers influence the measured variables as well as the conductivity and mobility, although they too are related to direct current, while the functions fx with whom they are compared are related to alternating current.

22. Quantitative composition X can be determined according to the relation between function fX and the intensity of current I. The slope of this relation depends on the concentration and quantitative composition of X. By diluting the solution with quantitatively determined amount of the solvent, the concentration changes but not the ratio of the two ions in the mixture. Thus, the tangent of the slope of the angle which is presented on the graphic fX – I can be determined, and it depends only on the quantitative composition of X. In order for the exact result to be determined it is essential that one standard solution be used whose composition is known and whose angle slope is determined under the same conditions as in the unknown solution.

23. When the quantitative composition of the mixture is already known, the concentration of the solution can be determined in the manner which has been applied with the single-component solutions.

LITERATURE

1) Dr. S.Gleston, Udžbenik fizičke hemije, Naučna knjiga, Beograd, 1967.

2) W.J.Moore, Fizička hemija, Naučna knjiga, Beograd, 1962.

3) Peter Kruus, Liquids and Solutions, Structure and Dynamics, Marcel Dekker, inc New York, 1980.

4) J.O’M.Bockris; E.Conway and Yeager, Comreehensive Treatise of Electrochemistry, Plenum Press, New York, 1980.

5) Albery, Electrode Kinetics, Clarendon Press, Oxford, 1975.

6) Vojin Dajović, Analiza i numerička analiza, Naučna knjiga, Beograd, 1980.

7) Slobodan M. Popović, Elektrotehnička merenja, Zavod za udžbenike i nastavna sredstva, Beograd, 1983.

8) Milutin Petković, Elektronika, Zavod za udžbenike i nastavna sredstva, Beograd, 1982.

9) P.Nikolić, Č.Petrović i D.Raković, Elektrotehnički materijali, Zavod za udžbenike i nastavna sredstva, Beograd, 1980.

10) Ivan Filipović, Stjepan Lipanović, Opća i anorganska kemija, Školska knjiga, Zagreb, 1982.

11) Dr. S.Mladenović, Tehnička elektrohemija, Tehnološko-metalurški fakultet, Beograd, 1987.

12) Dr. M.S.Jovanović, Kvalitativna hemijska analiza, Naučna knjiga, Beograd, 1982.

13) Dr. M.S.Jovanović, Elektroanalitička hemija, Tehnološko-metalurški fakultet, Beograd, 1978.

14) E.C.Potter, Elektrokemije, Školska knjiga, Zagreb, 1968.

15) F.Taylor, Inorganic and Theoretical Chemistry, William Heineman Ltd. London, 1948.

16) R.H.Stokes and R.A.Robinson, J. Am. Chem. Soc. 70. 1948, 1870.