Write the given standard reduction potentials

$\mathrm{Ag}^+ + e^- \rightarrow \mathrm{Ag}, \qquad E^\circ = x$ $\mathrm{Cu}^{2+} + 2e^- \rightarrow \mathrm{Cu}, \qquad E^\circ = y$

Decide which electrode is cathode and which is anode

In the cell, the half-cell with higher reduction potential acts as the cathode and the other acts as the anode.

For the expression of cell emf, we use:

$E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}$

Identify the overall cell reaction

Since the copper half-reaction is written as reduction with potential $y$, and silver half-reaction as reduction with potential $x$, the cell emf becomes:

$E^\circ_{\text{cell}} = y - x$

Important: Standard electrode potentials are intensive properties, so multiplying a half-reaction to balance electrons does not multiply its electrode potential.

Check options

• A: $x + 2y$ ❌
• B: $2x + y$ ❌
• C: $y - x$ ✅
• D: $y - 2x$ ❌

Final answer

$\boxed{E^\circ_{\text{cell}} = y - x}$