NOVEMBER, 1949
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579
LIQUID JUNCTION POTENTIAL CALCULATIONS MEL GORMAN and SISTER MARY CLARE MURPHY, P.B.V.M.1 University of San Francisco, San Francisco, California
CALCULATIONS of liquid junction potentials cannot be performed with strictly thermodynamic accuracy because of the impossibility of determining experimentally the individual activities of the ions of the electrolytes comprising the junction. However, in the case of uni-univalent electrolytes of the same solute at different concentrations, reasonable and satisfactory values of the junction potentials can he obtained from electromotive force measurements of concentration cells, with the aid of certain approximations. MacInnes and his associates2 have shown that this can be done with junctions existing in cells of the type Ag; AgC1, MC1(Cj):MCI(C2),AgCI; Ag
(1)
The liquid junction potential, EL,is related to the measured potential of the whole cell, E, and to the transference number of the cation, t,, by the relation
The derivation of this equation is based on the assumption that the cation transference number is constant Academy of the Pwsentrttion, San Fran1 Present addrpss: cisco, California. 2 MICINNES, D. .4., "Principles of Electrochemistry," Reinhold Publishing Corporation, New York, 1939, p. 222.
between C, and Cz, that the activities of the positive and negative ions are equal to the mean activity of the electrolyte, and that each of the silver chloride electrode potentials depends only on the ionic strength and not upon the nature of the positive ions. Transference numbers determined by LongsworthSn ere used. Also, since C, and Cz did not diffel greatly in concentration, a mean value for t , was used in equation (2). The computed liquid junction potentials as obtained by MacInnes are reproduced in Table 1, column 4. Junction potentials between solutions of different concentrations of the same nni-univalent electrolyte can be calculated from a relation used to derive equation ( 2 ) , namely,=
nhere R is the molar gas constant, T is the absolute temperature, F is the faraday, and as and a2 are the activities of the anion of concentrations C1 and C2, respectively. Equation (3) is an approximation based on the assumptions that t,, is constant and that the individual ionic activities of the positive and negative i m are both equal to the mean ion activity of the elec3 L o ~ c s w o m n ,L. G., J. Am. Chem. Soc. 54, 2741 (1932): 57, 1185 (1935).
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trolyte. Although in precise electrochemical research, It will be observed that the junction potential for junction potentials should be avoided, it is not always pairs of a given electrolyte of the same ratio of concenpossible to do so. In such cases various investigators trations is practically constant. This suggests a have resorted to equation (3), using experimentally method of calculation for the liquid junction potentials determined transference numbers. When the latter between solutions of the same uni-univalent electrolyte. have not been available, rough estimates have been hased on a modification of equation (3), made from similar electrolytes whose transference RT C, EL = (210 - I ) - In r., (4) numbers have been determined. However, transference numbers can be calculated from conductance data by means of an expression based on Onsager's t,reatment where to is the limiting transference numher of the cation, calculated from the limiting ion couductances.~ of conductivity :' In other words, equation (4) gives the limiting value of the liquid junction potential for a given ratio of concentrations. For instance, if the liquid potential between 0.02 molar and 0.01 molar sodium chloride where X+O and XO- are the limiting ionic conductances, (or between any two sodium chloride solutions of the 0 and u are constants whose values in water as a solvent same concentration ratio) is desired, C1/C2 equals 2, and, at 25°C. are 0.2273 and 59.78, respectively, and Cis the wing the limiting ionic conduct,ances, concentration in mols per liter. The reliability of equation (3) can be shown using calculated values of the cation transference numbers for the sdutions listed in Table 1. Mean calculated transference numbers, Substituting these values in equation (4), E, is cal,,L were taken for each pair of solutions because C1 and culated to be -3.69 millivolts; likewise, for concenCz do not differ greatly. Mean ion activities were tration ratios of 8 : l and 3:2, the values are -11.08 obtained from concentrations and activity coefficients.s and -2.16 millivolts. For potassium chloride, the The results are listed in Table 1,column 5. The agree- liquidpotentials calculated for the ratios 2:1, 8:1, and ment with column 4 is ~- o o d . 3 2 are -0.34, -1.00, and-0.20millivolts,res~ectivel~. For hydrochloric acid, the computed potenti& for the ratios 2:1, 8.1, and 3 . 2 are 11.43, 34.28, and6.68milli' MAC~NNES, D. A.. ''Principles of Electrochemistry, Rein- volts, respective~y. ~h~ values for the salt, solutions are hold Publishing Corporation, Kew York, 1939, p. 332. in excellent agreement with columns 4 and 5, differing MACINNEB, D. A_, ibid., pp. 162 and 164. by about 0.01 millivolt. With hydrochloric acid the corresponding average difference is about 0.5 millivolt. TABLE 1 The advantage of equation (4) lies in the fact that Potentials of Liquid Junctions, MC1 (CI):MC~ (CJ it may be used to obtain junction potentials between 4 5 solutions of many uni-univalent strong electrolytes for ./unction poten- Junction potenI 8 , , , . which equations (2) and (3) are not, suitable. For Coneenfralions, Electrouolts from volts from many such electrolytes, equation (2) is not useful bemol./l. lyte equation ( 2 ) elsation($) cause an electrode reversible to the anion is not avail.n.01 0.005 NaCl - 3.68 - 3 . 0 able and thus E cannot be found. Equation (3) is not ICCI - 0.33 - 0.33 always applicable because either transference numbers HCI 11.13 ll.li u.02 0.01 NaCl - 3.69 - 3.73 or act,ivity coefficients, or both, are unknown at the ICCI - 0.34 - 0.33 concentrations of the solutions being used. On the FlCl 11.0i XaCI -11.08 - 111.09 1.28 other hand, limiting conductances for a considerable 0.04 OW5 Pic1 - 1.00 - 1.01 numher of univalent positive and negative ions are HCI :33.22 33.37 available in the literature, enabling the easy calculation NaCl - 2.17 - 2.20 0.03 0.02 KC1 - 0.20 - 0.20 of t 3 for use in equation (4). Even if equations ( 2 ) and 0.04 0.02 XaCI - 3.70 - 3.69 (3) can be used, t,he accuracy of an investigation as R I
