Nernst Equation

The Nernst equation relates a cell's potential to the actual concentrations of the species taking part in its electrochemical reaction, rather than assuming they sit fixed at their standard 1 M states. For a general electrochemical cell reaction $xA + yB \rightarrow lC + mD$, the reaction quotient Q is

Recall from thermodynamics that the actual Gibbs free energy change relates to the standard one and the reaction quotient as $\Delta G = \Delta G^{o} + RT\ln Q$. Substituting the electrochemical relationships $\Delta G = -nFE_{cell}$ and $\Delta G^{o} = -nFE^{o}_{cell}$ from the previous section turns this into

Dividing throughout by $-nF$ gives the Nernst equation in its natural-log form, and converting to base-10 logarithms gives the more commonly used form:

At 25°C (298 K), substituting $R = 8.314\ \text{J K}^{-1}\text{mol}^{-1}$, $T = 298$ K and $F = 96500\ \text{C mol}^{-1}$ collapses the constant $2.303RT/F$ down to a single practical number, giving the equation its most-used form:

$E_{cell} = E^{o}_{cell} - \dfrac{0.0591}{n}\log Q$ …