## Derivation of Formula

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

TanveerDhaliwal3G
Posts: 105
Joined: Fri Aug 30, 2019 12:17 am

### Derivation of Formula

From what is the Nernst Equation derived from?

AKatukota
Posts: 100
Joined: Thu Jul 25, 2019 12:18 am

### Re: Derivation of Formula

As reactants are consumed in a working electrochemical cell, the cell potential will also decrease until it reaches zero. The Nernst equation is used to establish the relationship between how cell potential depends on concentration

Julie Park 1G
Posts: 100
Joined: Thu Jul 25, 2019 12:15 am

### Re: Derivation of Formula

You can take these two equations that we already know:
$\Delta G = \Delta G^{\circ} + RTln\frac{[P]}{[R]}$ and $\Delta G=-nFE$
and combine them to get
$-nFE = \Delta G^{\circ} + RTln\frac{[P]}{[R]}$

when you solve for E, you will get
$E=-\frac{\Delta G^{\circ}}{nF} - \frac{RT}{nF}ln\frac{[P]}{[R]}$

Since $-\frac{\Delta G^{\circ}}{nF}=E^{\circ}$

You can get
$E = E^{\circ} - \frac{RT}{nF}lnQ$ (Nernst equation)

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

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