## The Nernst Equation

$E_{cell} = E_{cell}^{\circ}-\frac{RT}{nF}\ln Q$

Ardo 2K
Posts: 31
Joined: Fri Sep 29, 2017 7:05 am

### The Nernst Equation

Can someone please derive the Nernst equation the way we did it in class one more time? Thank you

Kathleen Vidanes 1E
Posts: 62
Joined: Fri Sep 29, 2017 7:07 am

### Re: The Nernst Equation

In class, to derive the Nernst Equation, we began with E= E° - (RT/nF) x ln Q.
That equation can be rewritten in terms of logbase10 as E = E° - (2.303RT/nF) x logbase10 Q.
At standard temperature (T=25°C or 298K), 2.303RT/F = 0.0592V, since R and F are both given constants.
As a result, the Nernst Equation can finally be written as E = E° - (0.0592V/n) x logbase10 Q.

Kathleen Vidanes 1E
Posts: 62
Joined: Fri Sep 29, 2017 7:07 am

### Re: The Nernst Equation

I just looked over my notes again and realized that if you wanted to go back even further with the derivation, you would have to know that deltaG = deltaG ° + RT ln ([P]/[R]) and deltaG = /nFE.
From there, you can combine the two equations so that -nFE = deltaG ° + RT ln ([P]/[R]).
Solving for E, you would obtain E = (-deltaG ° / nF) + (-RT/nF) ln ([P]/[R]).
Since -deltaG ° /nF = E ° , then E = E ° - RT/nF ln ([P]/[R]).

As a result, the Nernst Equation would be written as: E = E ° - RT/nF lnQ

Return to “Appications of the Nernst Equation (e.g., Concentration Cells, Non-Standard Cell Potentials, Calculating Equilibrium Constants and pH)”

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