Electrochemistry: Step-by-Step Worked Examples (6)

Question

Calculate the EMF of the cell: Zn | Zn$^{2+}$ ($0.1$ M) || Cu$^{2+}$ ($0.01$ M) | Cu at $25°$C. Given $E°_{\text{Zn}^{2+}/\text{Zn}} = -0.76$ V and $E°_{\text{Cu}^{2+}/\text{Cu}} = +0.34$ V.

Solution — Step by Step

Final Answer: $E_{\text{cell}} \approx 1.07$ V.

Why This Works

The Nernst equation adjusts the standard EMF for non-standard concentrations. The reaction quotient $Q = [\text{Zn}^{2+}]/[\text{Cu}^{2+}]$ shows up because solid metals have activity $1$ — only the dissolved ions appear in $Q$.

Since $Q > 1$, the system is “more product-rich than standard”, so the EMF is less than $E°$. That’s why we got $1.07 < 1.10$ V. Quick directional check passes.

Alternative Method

Apply the Nernst equation separately to each half-cell, then subtract. Useful when the question asks for individual electrode potentials. For total cell EMF, the combined-cell approach above is faster.