A Calomel Cell and the Fugacity of Hydrogen

Abstract

By use of recent data for hydrogen as a real gas, it has been shown that there is no need to introduce changes in the activities of condensed phases to explain the electromotive forces measured when the partial pressure of hydrogen in a calomel cell (0.1N HC1 as electrolyte) is increased up to 1035 atm at 25%In a classic investigation (1, 2) it was found at 25 ~ that the emf, e, of the cell 1-12 (g) Pt]HC1 (0.1N) [Hg2Cl2 (s) ]Hg (1) increased more rapidly than required by the Nernst equation when the partial pressure p of hydrogen, varied up to 1035 atm, was used in the calculation. The departure of hydrogen from ideal behavior was of course mainly responsible, and all but 2.3 mV of the difference at 1000 arm was accounted for by using a simple equation of state for this gas in a treatment based on the volume change attending the cell reaction. The residual difference was attributed in the main to an effect of hydrogen dissolved at high pressure on the partial mo~al volume of hydrochloric acid. Calculations reported here, which are based on recent data (3-6), show that this assumption is no longer necessary. Extensive preliminary calculations indicated the results of Michels et al. (5, 6) to be best for our purposes.Two sets of final calculations were made. In the first, the increment • resulting from an increase of p above 1 arm (101325 N/m 2) was obtained for each such increase from the familiar equation z~e _--(0.029580V)log fp/fl [1] which contains the fugacity quotient for the two partial pressures in question. The fugacities were obtained from In ~/p = (14.38P)/RT 4-(O.O06671P2)/2RT [2]where P is the pressure in atmospheres for a hydrogen Pv isotherm experiment; R has the value 82.056 cm 3 9 atm/kmol, and T is the temperature in Kelvins. The calculation assumes that P may be substituted for p, the partial pressure of hydrogen in the cell, when the two pressures are equaI. This assumption is tantamount to saying that the water vapor present does not change the fugacity of hydrogen. The first virial coefficient is the value of B for 25 ~ in Ref. (6); the second is that of (C --B2)/RT for the same temperature. In addition, a differential calculation was needed. This is based on three thermodynamic relations d In ~ = (pv/RT) d In p(v ----molar volume of He)[3]