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David C. Silverman |
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Isothermal and Thermal Liquid Junction Potentials - Calculation As mentioned in the section entitled Isothermal and Thermal Liquid Junction Potentials - Theory, calculation of isothermal liquid junction potentials and thermal liquid junction potentials from first principles is difficult if even possible. They often have to be measured. But, under certain circumstances, estimation of their effect on the overall potential difference between working and reference electrodes is possible. Such is the case for the cell shown in this figure) .
Enough data either could be obtained by measurement or was available in the
literature from which the liquid junction potentials between a calomel reference
electrode and a silver-silver chloride reference electrode and the thermal
liquid junction potential in the capillary separating the two could be estimated.
The example is somewhat simple but illustrates the thinking and methodology that
should be used.
The example contains two cases, one in which the electrodes are at the same
temperature and the other in which the electrodes are at different temperatures
(25°C and 95°C)
The response of the cell in this figure
was broken into the following steps shown in this table. Note that the 4 molar
KCl was dictated by the electrode used.
E1 E1 is the standard electrode potential of the mercury-mercurous chloride electrode in saturated KCl. Its value is -0.2415V relative to the standard hydrogen electrode. E2 E2 has two contributions, the free energy change between saturated KCl and 4 molar KCl and the isothermal liquid junction potential across the junction separating the two compartments in that portion of the capillary immersed in saturated KCl. The voltage equivalent to the free energy change caused by the concentration difference is given by 
(18)where ΔG is the free energy change, F is the Faraday constant, R is the gas constant, T is the absolute temperature, and a is the activity. The activities of chloride ion in 4 molar KCl and at saturation differ by about 5%. Equation (18) makes little contribution to E2. Had either capillary held either a much lower concentration of KCl or a different ion, equation (18) could have had a larger impact on the potential. The isothermal liquid junction potential is estimated from equation 7 in the section Isothermal and Thermal Liquid Junction Potentials - Theory by assuming that the transference numbers are constant across the junction. The resulting equation is 
(19)where t is the transference number of each ion. Again, the activities in the two solutions are similar. Also, the transference number of potassium and chloride are very similar. Equation (19) makes little contribution. For this case, E2 is approximately 0 (<0.001 V). Again, a greater contribution might have been expected had a different salt been used with larger differences in transference numbers and activities between the compartments. E3 E3 is the thermal liquid junction potential created by the temperature gradient along the capillary for the non-isothermal case. This liquid junction potential was estimated in the literature and correlated to temperature (D. D. Macdonald, A. D. Scott, and P. Wentreck, J. Electrochem. Soc., Vol. 126, p. 1618, 1979). A weak dependence on concentration was found. Their data were correlated again to remove the concentration dependence. The thermal liquid junction potential for this case was estimated to be approximately 0.018V for the 70°C temperature difference. E4, E5, E6 E4 + E5 + E6 is the potential of the Ag/AgCl electrode exposed to 4 molar KCl at 95oC. Since the standard potential is for unit activity at 25oC, the correction has to be made for both elevated temperature and elevated concentration. Equation (18) could be used with the appropriate concentrations for chloride inserted. Activity coefficients were estimated using correlations in the literature (C. L. Kusik and H. P. Meissner, in "Fundamental Aspects of Hydrometallurgical Processing", AIChE Symposium Series, No. 173, 1978). The correction was also made for the free energy change between 25oC and 95oC using thermodynamic properties from the literature with all components in their standard states . The results of the calculation for the cell shown in this figure
are given in the following table along with the measurement. A calculation
for the case in which both electrodes are at the same temperature is included.
The thermal liquid junction potential was allowed to establish itself over 24
hours in for the measurement.
Note that the agreement is partly a function of the simplicity of the cell. Chloride concentrations were fairly similar and the salt in the cell was chosen to be the same as those in the electrode compartments. The similarity in transport numbers for potassium and chloride also decrease the potentials. Such good agreement should not be expected in more complex systems. Previous Page: Isothermal and Thermal Liquid Junction Potentials - Theory |
David C. Silverman, Ph.D. - Primary Consultant |