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The Nernst equation can be derived from ∆G = ∆G° + RT ln Q by substituting ∆G with -n F E(∆G = - n F E). You then divide both sides by - n F. You can then substitute - ∆G°/nF with E°. This then leaves you with E = E° - (RT/nF) lnQ !
The Nernst equation can be derived using the equation for gibbs free energy. This equation is ∆G = ∆G˚ + RTlnQ. You can then set ∆G equal to -nFEcell and ∆G˚ to -nFE˚cell. Then you can divide both sides by -nF.
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