Dependence of cell potential on concentration (Nernst equation)

The standard cell potential tells us whether or not the reactants in their standard states form the products in their standard states spontaneously. To predict the spontaneity of reactions for anything other than standard concentration conditions, we need to know how the voltage of a galvanic cell varies with concentration.

The dependence of cell voltage on concentrations is given by the Nernst equation. For any general reaction

the cell voltage is given by

where $n$ = moles of electrons used in the reaction, $F$ = Faraday = 96500 C, $T$ = temperature in kelvin, and $R$ = gas constant = $8.314\ \mathrm{J\,K^{-1}\,mol^{-1}}$. At $25\,^0\mathrm{C}$, $\dfrac{2.303\,RT}{F} = 0.0592$ V. Therefore at $25\,^0\mathrm{C}$ the equation becomes

Eq. (5.25) or Eq. (5.26) is the Nernst equation. The first term on the right hand side represents standard-state electrochemical conditions; the second term is the correction for non-standard-state conditions. The cell potential equals the standard potential if the concentrations of reactants and products are 1 M each: if $[\mathrm{A}] = [\mathrm{B}] = [\mathrm{C}] = [\mathrm{D}] = 1\mathrm{M}$, then $E_{cell} = E^0_{cell}$. If a gaseous substance is present in the cell reaction, its concentration term is replaced by the partial pressure of the gas.

The Nernst equation can be used to calculate cell potential and electrode potential.

i. Calculation of cell potential : Consider the cell $\mathrm{Cd\,(s)\ \vert\ Cd^{2+}\,(aq)\ \Vert\ Cu^{2+}\,(aq)\ \vert\ Cu}$. Let us first write the cell reaction:

Here $n = 2$. The potential of the cell is given by the Nernst equation as

$E_{cell} = E^0_{cell} - \frac{0.0592}{2}\,\log_{10}\frac{[\mathrm{Cd^{2+}}]}{[\mathrm{Cu^{2+}}]} \;\;\text{at } 25\,^0\mathrm{C}$ …