POTENTIALS O F CELLS INVOLVING MOVING BOUNDARIES’ F. D. MARTIN
AND
R. F . NEWTON
Department of Chemistry, Purdue University, W e s t LaFayette, I n d i a n a Received July $3, 1934
The thermodynamic treatment of a cell involving a liquid junction between two electrolytes having a common ion would be greatly simplified if the boundary between the two solutions could be regarded as a moving boundary such as is used in the determination of transference numbers (7), for under these conditions the potential of the cell becomes a simple function of the activity of the water in the two different solutions. Referring to figure 1, consider, for example, the case of a cell involving a moving boundary, 01-02,between solution I, C1normal with respect to lithium chloride, and solution 11, Cz normal with respect to potassium chloride. Using electrodes reversible to chloride ions, let 1 faraday of negative electricity pass through the cell from right to left, causing the boundary to sweep through V liters of solution to the new position 03-& Letting TLi and TK be the transference numbers of the cations in solutions I and 11, respectively, it is apparent that TLi equivalents of lithium cross 0 1 - 0 2 into V , while TK equivalents of potassium cross O3-O4 out of V . If it is assumed that the boundary is to be maintained without mixing the two solutions or changing their concentrations, the following relations must hold :
On dividing equation 1 by equation 2 there results the familiar “regulating” equation, first derived in a more general form by Kohlrausch (3):
When C1and C2 are chosen so as to satisfy the above equations, the net transfer of chloride ion can be calculated as follows: 1 This article is based upon a thesis submitted by F. D. Martin to the Faculty of Purdue University i n partial fulfillment of the requirements for the degree of Doctor of Philosophy, June, 1931.
485
486
F. D. MARTIN AND R. F. NEWTON
QAIN OR LOSS IN W.UIVALENTS PIR FARADAY PROCESS
Electrode reactions .... . . . . . . . Movement of the boundary.. . Transference across Os-04 . . . Net effect. .... .
.. ... . . . . . ,
Solution I
Solution I1
Loses one equivalent Gains VC, equivalents Gains (1 - T K )equivalents Gains
Gains one equivalent Loses VC, equivalents Loses (1 - TK)equivalents Loses
VCa
+ (1 - T K ) - 1 = 0 vc,~f (1 - T K ) - 1 = 0
Since the concentrations are adjusted so that no mixing or transfer of the cations will occur, there is no net transfer of any of the three ions. The transfer of water remains to be considered. I t has been shown by MacInnes and Dole (6) that transference numbers calculated from experi-
c
-I
J FIG. 1
c
ments with moving boundaries are identical with Hittorf transference numbers, hence the transfer of water by the ions themselves need not be taken into account. There is, however, a transfer of water from solution I1 to solution I as a result of the movement of the boundary; the water originally present in V liters of I1 becomes a part of I as the boundary moves from 01-02 to 0 3 - 0 4 . Let M , be the number of moles of water thus transferred, and let al and a2 be the activities of the water in solutions I and 11, respectively. The free energy change, A F , of the transfer will be: AF =
M , RT In
az
(4)
Taking T as 298°K. and noting that M , represents the number of moles transferred per faraday, the potential, E , of the cell represented in figure 1 becomes
POTENTIALS OF CELLS INVOLVING MOVING BOUNDARIES
487
a2 E = 0.05915 M w loglo -
(5)
a1
Equation 5 provides a means for calculating the exact potential of such a cell, using data which is readily available. It is valid, however, only in case the passage of electricity through the cell brings about the movement of the boundary. Dole (1) has derived an equation similar to equation 5 to account for the deviations of the glass electrode in acid and in nonaqueousrsolutions.
C
R'
FIG.2 EXPERIMENTAL
In an effort to test equation 5 , a modification of the moving boundary apparatus developed by Brighton (4)was set up. As shown in figure 2, in addition to the compartments AA, containing the working electrodes €or carrying the current used to establish the moving boundary, the compartments BB, were added, containing the potential electrodes for measuring the potential of the cell. The tubes CC furnished a means for renewing the electrolyte around the potential electrodes and for adjusting the surfaces of the two solutions before establishing contact. The boundaries were of the descending type and were made visible by an illuminated screen with a black horizon as recommended by MacInnes and Smith (8). Thermostat. All runs were made in an oil thermostat at a temperature of 25.0"C.
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F. D. MARTIN A N D R. F. NlWTON
Potentiometer and electrical system. A diagram of the electrical connections is shown in figure 3. The current used to establish the boundary could be regulated by the rheostats t o any desired value, as read on the milliammeter, A. When a reading of the potential of the cell was being taken this current was shut off by switch SI, while contact with the potential electrodes was established by means of switch Sz. A Leeds and Northrup Type K potentiometer was used. Electrodes and solutions. Both the working and the potential electrodes were of the silver-silver chloride type. The former were made by silver plating cylindrical electrodes of platinum foil, then chloridizing the electrode which was to serve as cathode. The electrodes used for measuring the potential were made by filling platinum spirals, about 1 cm. long, with a paste of pure silver oxide, decomposing the oxide in an electric furnace, then chloridizing the resulting spongy silver in a dilute solution of hydrochloric acid for one to two hours. The electrodes were then thqroughly washed and stored in the solution in which they were to be used. Solutions of the chlorides of sodium, potassium, and lithium were used, solu-
L
=
FIQ.3. ELECTRICAL CIRCUIT 110 volts; W. E., t o working electrodes; P. E., to potential electrodes
tions of the first two being prepared by direct weighing of the dry, recrystallized salts into calibrated volumetric flasks, while the lithium chloride solutions were prepared by weighing out the calculated amount of one of three different stock solutions, then diluting as before. Procedure. In the first series of experiments, readings of the potential were taken about one second after the interruption of the current used to establish the boundary. Several different combinations of the three chlorides were used, the concentrations in each case conforming to the requirements of equation 3, as calculated from data in the International Critical Tables. Table 1 gives the results of this series of measurements, as compared with the values calculated from equation 5. In view of the discrepancy between the observed and the predicted values of the potentials, the first series of runs was discontinued and a search begun for possible causes of the lack of agreement. The results of this investigation may be summarized as follows : 1. There appeared to be no serious error in the data used for calculating the potentials according to equation 5. The ratios of a2/a,were calculated
POTENTIALS
OF CELLS INVOLVING MOVING BOUNDARIES
489
from the vapor pressure lowerings of the various solutions as recorded in the International Critical Tables. Each value of M , was calculated by three different methods with concordant results. 2. The experimental error was insufficient to account for differences amounting to several millivolts. 3. There remained to be considered the behavior of the boundary after the working current had been interrupted. In the derivation of equation 5 it was assumed that the boundary was maintaiqed during the measurement of the potential of the cell. The experiments of MacInnes and Cowperthwaite ( 5 ) showed that the boundary faded slowly when the current was shut off and regained its original sharpness shortly after the current was turned on again. These observations were repeated and confirmed in this laboratory. In order to study further the effect of the interruption of the working current upon the potential of the cell, a second series of measTBBLE 1 Potentials of cells w i t h liquid junction established b y a moving boundary T = 25°C. SOLUTION
1
0.594 N LiCl 0.303 N LiCl 0.064 N LiCl 0.77 N N a C l 0.40 N N a C l 0.303 N LiCl
BOLETION
11
1.00 N KCl 0.50 N KCl 0.10 N KC1 1.00NKC1 0 . 5 0 NKC1 0 . 4 0 N NaCl
AVERAQE POTENTIAL OF CELL
POTENTIAL CALCULATDD FROM EQUATION 6
volts per cm.
millivolts
millivolts
2.3-2.7 2.6 2.4-2.8 2.7 2.6-3.0 2.5-3.0
-17.9 -17.9 -18.1 -11.0 -10.5 -7.1
-8.4 -8.4 -8.33 -4.9 -4.15 -4.27
POTENTIAL DROP IN 11
-
The sign on the potential corresponds to the flow of negative electricity through the cell from solution I1 to solution I.
urements was undertaken. In this series the working current was shut off after the boundary had been established, then readings of the potential were taken a t short intervals until no further significant change was noted. The influence of other factors, such as the potential drop used to form the boundary and the concentration of the indicator solution, was also studied. As the result of nearly one hundred runs using various concentrations of lithium chloride solutions against 0.10 N solutions of potassium chloride and sodium chloride, also different concentrations of sodium chloride solutions against 0.10 N potassium chloride solution, the following conclusions were drawn: 1. The “instantaneous” potential of a cell involving a moving boundary, taken within a fraction of fc second after the interruption of the current used to establish the boundary, is not a constant but varies with the potential gradient used to form the boundary. As shown in figure 4, an
.
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F. D. MARTIN AND R. F. NEWTON
increase in the potential gradient causes a rise in the observed “instantaneous” potential of the cell.
Potential Gradient in Lower Solution,‘hlts/cm FIQ. 4. EFFECTOF POTENTIAL GRADIENT UPON INSTANTANEOUS POTENTIAL I, 0.1 N sodium chloride, using 0.050 N lithium chloride as indicator solution; 11, 0.1 N sodium chloride, using 0.064 N lithium chloride as indicator solution; 111, 0.1 N sodium chloride, using 0.0822 N lithium chloride as indicator solution; IV, 0.1N sodium chloride, using 0.1000 N lithium chloride as indicator solution. TABLE 2 Potential of the cell Ag, AgCl, 0.064 N LiCl, junction formed by moving boundary, 0.10N KCl, AgCl, Ag
T TIME INTBRVAL B E T W E E N INTERRUPTION OF CURRENT A N D MEASUREMBNT OF CELL POTENTIAL
minutes
0.0 0.25 0.50 1.0 2.0 5.0 10.0 15.0
POTENTIAL DROP IN
4.43
I
= 25°C.
KC1 SOLUTION I N 3.31
VOLTS PER CENTIMETER
I
1.65
I
(5.7 MM.
TUBE)
0.55
Potential of the cell mv
I
-17.9 -16.5 -16.5 -16.4 -16.4 -16.4 -16.4
mv
.
-17.5 -16.6 -16.5 -16.4 -16.4 -16.3 -16.3
mu.
mo.
-17.1 -16.6 -16.6 -16.6 -16.5 -16.4 -16.4
-16.7 -16.5 -16.4 -16.4 -16.4 -16.4 I
Negative current flowed from right to left through the cell. Similar results were obtained for other pairs of solutions.
2. After the current used to form the boundary has been cut off, the potential of the cell diminishes with time, approaching a constant value. Although, as stated above, the instantaneous values of the potential of the
POTENTIALS OF CELLS INVOLVING
MOVING BOUNDARIES
491
cell vary with potential gradient used to form the boundary, the final or equilibrium value, obtained after the lapse of several minutes, is constant and reproducible, depending only on the concentration and the composition of the solutions used. The data in table 2 furnish a typical illustration of this effect.
Conc e n t TCIt i on of Indi cat o r Solu t ion FIG. 5. EQUILIBRIUM POTENTIALS OF CELLSAFTER ESTABLISHING A LIQUIDJUNCTION BY MEANSOF A MOVING BOUNDARY I, 0.10 N potassium chloride, using lithium chloride as an indicator solution; 11, 0.10 N potassium chloride, using sodium chloride as an indicator solution; 111, 0.10 N sodium chloride, using lithium chloride as an indicator solution. TABLE 3 Comparison of observed and calculated values of the liquid junction potentials LIQUID JUNCTION POTENTIAL JUNCTION
Observed by moving boundary method mu
0.1 N KCl, 0.1 N LiCl 0.1 N KCl, 0.1 N NaCl 0 . 1 N NaCl, 0.1 N LiCl
Sargent formula
I
8.0 4.88 2.5
7.4 4.9 2.5
3. These equilibrium values of the potential vary in a regular manner with the concentration of the indicator solution. This is clearly shown in figure 5, where these equilibrium potentials are plotted against the concentrations of the various indicator solutions. Since there is no abrupt
492
F. D. MARTIN AND R . F. NEWTON
change in the regions in which the concentrations of the indicator solutions are close to the “adjusted” values required by equation 3, there is no reason for believing that lack of agreement with equation 5 was due to any error in selecting an indicator solution, of exactly the right concentration. It may be of interest to point out that these equilibrium potentials for the 0.1 N solutions agree fairly well with the potentials calculated from the Lewis and Sargent formula (9). Table 3 gives a comparison of the observed and calculated values. 4. A possible explanation for the high potentials obtained experimentally, as compared with the values predicted from equation 5, may lie, in a peculiar lag effect now being investigated in this laboratory. A preliminary report on this effect by Hunt and Chittum (2) showed that when a direct current is passed through an electrolyte and the fall in potential over a section of the solution measured by means of a set-up similar to that used for measuring the potentials in the present investigation, a distinct lag occurs when the current is interrupted, that is, the potential between the two electrodes dipping in the same solution does not instantly fall to zero when the current is shut off. Further investigation is necessary before deciding whether this lag effect will account for the observed deviations from the values predicted by equation 5. SUMMARY
1. An equation has been derived for the potential of a cell involving a moving boundary between two electrolytes having a common ion. 2. Potentials of such cells were measured immediately after the interruption of the current used to establish the boundary. The experimental results were not in agreement with the equation. 3. Possible reasons for this disagreement were investigated without revealing the exact cause of the deviation. I t is suggested that a lag effect now being studied in this laboratory may be involved. REFERENCES
(1) DOLE:J. Am. Chem. SOC.64, 2120, 3100 (1932). (2) HUNT AND CHITTUM: Unpublished paper presented before the Division of Physical and Inorganic Chemistry, at the Eighty-seventh Meeting of the American Chemical Society, held a t St. Petersburg, Florida, April, 1934. 13) KOHLRAUSCH: Ann. Physik 62, 209 (1897) (4) MACINNEB AND BRIQHTON: J. Am. Chem. SOC.47, 994 (1925). (5) MACINNEB AND COWPERTHWAITE: Proc. Nat. Acad. Sei. 16, 18 (1929). (6) MACINNESAND DOLE:J. Am. Chem. SOC.63, 1357 (1931). (7) MACINNES AND LONOSWORTH: Chem. Rev. 11, 171 (1932). (8) MACINNES AND SMITH: J. Am. Chem. SOC.46, 2249 (1923). (9) MACINNES AND YEH: J. Am. Chem. SOC.43, 2563 (1921).
