Question

If the temperature of an electrochemical cell increases, what specific change occurs to the theoretical cell potential according to the Nernst equation, assuming the reaction quotient remains constant?

Accepted Answer

The theoretical cell potential changes based on the sign of the standard entropy change of the reaction. The Nernst equation is E = E-nought minus (RT/nF) times the natural logarithm of Q, where E is the cell potential, E-nought is the standard cell potential, R is the ideal gas constant, T is the absolute temperature in Kelvin, n is the number of moles of electrons transferred, F is the Faraday constant, and Q is the reaction quotient. Because the Gibbs free energy change is defined as delta G = delta H minus T times delta S, where delta H is the enthalpy change and delta S is the entropy change, and because delta G is also equal to negative n times F times E, the potential can be expressed as E = (T times delta S / nF) minus (delta H / nF) minus (RT/nF) times the natural logarithm of Q. When the reaction quotient Q is held constant, the change in potential with respect to temperature is determined by the term (delta S / nF). If the entropy of the reaction is positive, meaning the system becomes more disordered, an increase in temperature will increase the cell potential. If the entropy of the reaction is negative, meaning the system becomes more ordered, an increase in temperature will decrease the cell potential. Therefore, the direction of the change depends entirely on whether the chemical reaction results in a net increase or decrease in entropy.

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If the temperature of an electrochemical cell increases, what specific change occurs to the theoretical cell potential according to the Nernst equation, assuming the reaction quotient remains constant?

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