Question

Set up Nernst equation for the standard dry cell. Using this equation
show that the voltage of a dry cell has to decrease with use

Answer 1

Dear Student,

Dry Cell or Leclanche Cell:
It consists of an anode which is a zinc container and the cathode is a carbon rod surrounded by powdered manganese dioxide and carbon. The space between the two electrodes (anode and cathode) is filled with a paste of ammonium chloride (NH₄Cl) and zinc chloride (ZnCl₂).

Electrode reactions:

$$\begin{gathered} AtAnode:Zn\to Z{n}^{2+}+2e^{-} \\ AtCathode:Mn{O}_2+2N{H_4}^{+}+2e^{-}\to M{n}_2{O}_3+2N{H}_3+H_{2}O \end{gathered}$$

Hence the Nernst equation for the above cell can be described as:

$$\begin{gathered} E_{cell}=E_{(M{n}^{4+}/M{n}^{3+})}-E_{(Z{n}^{2+}/Zn)} \\ {E}_{cell}=E_{cell}^0-\frac{0.059}{2}\log \frac{\left[Z{n}^{2+}\right]\left[N{H}_3{]}^2\right[H_{2}O]}{[N{H}_4^{+}{]}^2} \end{gathered}$$



So, as you can see here, E_cell increases with increase in concentration of [NH₄⁺] and decreases with increase in concentration of [Zn²⁺] and [NH₃]. Hence, with use more and more ​[Zn²⁺] and [NH₃] will form which will decrease the voltage of a dry cell.

Best Wishes !