# Why does temperature affect cell potential?

The Nernst equation describes the relationship between cell potential and temperature. But why does temperature affect cell potential?

My understanding is that the collision model of kinetics is not relevant to electrochemical cells, plus an increase in temperature decreases cell potential. So why does the potential change?

Depending on how you write the Nernst equation the temperature might increase or decrease the potential of the cell. This depends more on the reaction quotient than on anything else.

The temperature comes in to the equation as a scaling factor where RT/nF has units Volt. This essentially defines how much the voltage changes per a decade change in the reaction quotient.

The temperature dependence here is just a matter of the scaling factor.

Going back to the collision model, that is more about kinetics than thermodynamics and it is not at play for the Nernst equation.

Nernst equation describes the thermodynamics of the electrochemical system.

The temperature dependence can be explained by the temperature dependence of work-functions.

Any electrochemical reaction by definition is an electron transfer. The electron goes from the highest occupied MO of one species to the lowest unoccupied MO of the other. Both these levels are temperature dependent.

• Thank you. Could you please expand on the role of the work function? Is it analogous to the first ionization energy? – Tim Feb 20 '15 at 11:37
• I did add a couple lines on that. It is essentially the interplay between first ionization energy and the electron affinity. – Burak Ulgut Feb 20 '15 at 15:26

$$\Delta G^\circ = -nF\Delta E^\circ$$ $$\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$$ $$\Delta E^\circ = \left(\frac{\Delta S^\circ}{nF}\right)T + \frac{\Delta H^\circ}{nF}$$

This is where the temperature dependence comes from. Of course, a requirement is that the the reaction quotient remains at 1, because as soon as it differs, the $$\Delta E^\circ$$ no longer represents the standard electrical potential of the directly cell, and so it must be adjusted for using the Nernst equation.