Question

Why does a mercury cell deliver a constant voltage for its entire life?

Hint:

For weak electrolytes, \(\alpha=\frac{\Lambda_m}{\Lambda_m^\circ}\). Salt bridge prevents charge build-up in half-cells.

Answer 1

Step 1: Cell reactions in a mercury cell.
Anode: $Zn(Hg) + 2OH^- \rightarrow ZnO(s) + H_2O + 2e^-$
Cathode: $HgO(s) + H_2O + 2e^- \rightarrow Hg(l) + 2OH^-$
Step 2: Why voltage is constant.
Both $ZnO$ and $HgO$ are solids; neither dissolves into the electrolyte. Ion concentrations do not change during discharge, keeping the reaction quotient $Q$ constant throughout.
Step 3: Conclusion.
Since $E_{cell} = E^\circ_{cell} - \frac{RT}{nF}\ln Q$ and $Q$ is constant:
\[ \boxed{\text{Constant }Q \Rightarrow \text{constant }E_{cell}\text{ throughout the cell's life.}} \]