ARTICLE pubs.acs.org/jchemeduc
The Variation of Electrochemical Cell Potentials with Temperature Gavin D. Peckham*,† and Ian J. McNaught‡ † ‡
Department of Chemistry, University of Zululand, Private Bag X1001, Kwa Dlangezwa, 3886, South Africa Chemistry Department, Petroleum Institute, P.O. Box 2533, Abu Dhabi, United Arab Emirates
bS Supporting Information ABSTRACT: Electrochemical cell potentials have no simple relationship with temperature but depend on the interplay between the sign and magnitude of the isothermal temperature coefficient, dE°/dT, and on the magnitude of the reaction quotient, Q. The variations in possible responses of standard and non-standard cell potentials to changes in the temperature, topics that are not discussed in any current textbook, are described. KEYWORDS: Second-Year Undergraduate, Physical Chemistry, Misconceptions/Discrepant Events, Problem Solving/Decision Making, Electrochemistry, Electrolytic/Galvanic Cells/Potentials temperature. For a given electrode, the “changeover” point between these two responses will occur when
E
lectrochemical cell potential variation with temperature is clear from the Nernst equation, which is routinely included in introductory and physical chemistry textbooks,1 E ¼ E° ðRT=nFÞ ln Q
ðdE°=dTÞ ¼ ðR=nFÞ ln Q
ð1Þ
As an example, consider the following cell SHEðTÞjjI ðaq, a ¼ aðI Þ, TÞjI2 ðsÞ
where E° is the standard electrode potential, R is the gas constant, T is the absolute temperature, n is the amount of electrons, F is the Faraday constant, and Q is the reaction quotient. However, the explicit nature of this variation of cell potential with temperature is not discussed at the introductory level nor in more advanced textbooks of physical chemistry that are in current use. The response of E° to temperature changes is entirely determined by the sign of the temperature coefficient of the electrode, dE°/dT. Within the accuracy of most electrochemical measurements, the variation of E° with temperature2 can be described by E°ðT2 Þ ¼ E°ðT1 Þ þ ðdE°=dTÞðT2 T1 Þ
for which the overall cell reaction may be written as =2 I2 ðsÞ þ 1=2 H2 ðgÞ f I ðaqÞ þ Hþ ðaqÞ
1
where n = 1 and Q = a(I)a(Hþ) = a(I), where a is the activity. By definition, both E°(SHE) and dE°(SHE)/dT are zero at all temperatures, therefore Ecell ¼ E½I ðaq, a ¼ aðI Þ, TÞjI2 ðsÞ ¼ E°½I ðaq, TÞjI2 ðsÞ ðRT=FÞ ln Q
For the I (aq)|I2(s) half cell at 25 °C, it has been established2 that E°[I(aq, T)|I2(s)] = 0.5355 V and dE°[I(aq, T)|I2(s)]/ dT = 0.148 mV/K. Substituting this value of dE°/dT into eq 3 gives Q = 0.180 = a(I). This is the activity at which the cell potential is independent of temperature. For a cell with a(I) > 0.180, the value of [(dE°/dT) (R/F) ln Q] will be negative and Ecell will decrease as temperature rises. Conversely, for a cell with a(I) < 0.180, the value of [(dE°/dT) (R/F) ln Q] will be positive and Ecell will increase as temperature rises, despite the fact that this same temperature rise is simultaneously causing E°cell to decrease. Some numerical results to illustrate these points are given in Table 1. It should be clear from this example and from the foregoing discussion that the variation of a cell potential has no simple and direct relationship with temperature but depends instead on the interaction between the sign and magnitude of the
ð2Þ
However, the response of the actual electrode potential, E, is determined by the interplay between the sign and magnitude of dE°/dT2,3 and the magnitude of Q. This interplay may have various possible outcomes as indicated below. Consider an electrode with a negative temperature coefficient, so that the standard electrode potential, E°, will decrease as the temperature is raised. Depending on the magnitude of Q in the Nernst equation, the electrode potential, E, may either rise or fall as the temperature is increased. More specifically, provided Q is independent of temperature, it can be shown that the temperature dependence of E depends only on the sign of ðdE°=dTÞ ðR=nFÞ ln Q If this expression is positive, E will increase with a rise in temperature, and if the expression is negative, E will decrease with a rise in Copyright r 2011 American Chemical Society and Division of Chemical Education, Inc.
ð3Þ
Published: April 05, 2011 782
dx.doi.org/10.1021/ed100966r | J. Chem. Educ. 2011, 88, 782–783
Journal of Chemical Education
ARTICLE
Table 1. The Variation of E° and E with Concentration and Temperature for the Cell, SHE(T)||I(aq, a = a(I), T)|I2(s) Ecell/V
Ecell/V
Ecell/V
Temperature/°C E°cell/V a(I) = 0.100 a(I) = 0.180 a(I) = 0.300 5 25
0.5385 0.5355
0.5937 0.5947
0.5796 0.5796
0.5674 0.5664
45
0.5325
0.5956
0.5796
0.5655
temperature coefficient, dE°/dT, and the magnitude of the reaction quotient, Q.
’ ASSOCIATED CONTENT
bS
Supporting Information An abridged table of dE°/dT data. This material is available via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT We would like to acknowledge the particularly constructive comments and support of one of the reviewers. ’ REFERENCES (1) Atkins, P.; de Paula, J. Atkins’ Physical Chemistry, 9th ed.; Oxford University Press: Oxford, 2010; p 232. (2) deBethune, A. J.; Licht, T. S.; Swendeman, N. J. Electrochem. Soc. 1959, 106 (7), 616–625. (3) Bratsch, S. G. J. Phys. Chem. Ref. Data 1989, 18 (1), 1–21.
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dx.doi.org/10.1021/ed100966r |J. Chem. Educ. 2011, 88, 782–783
