Question

Standard cell voltage for the cell \[ \text{Pb} | \text{Pb}^{2+} | \text{Sn}^{2+} | \text{Sn} \] is \( -0.01 \, \text{V} \). If the cell is to exhibit \( E_{\text{cell}} = 0 \), the value of \( [\text{Sn}^{2+}] / [\text{Pb}^{2+}] \) should be:

• A. \( 10^{-1} \)
• B. \( 10^2 \)
• C. \( 10^3 \)
• D. \( 10^4 \)

Hint:

The Nernst equation can be used to calculate the concentrations of ions in a cell at equilibrium.

Answer 1

The Correct Option is A

Step 1: The Nernst equation for this system is: \[ E = E^\circ - \dfrac{0.0592}{n} \log \left( \dfrac{[\text{Sn}^{2+}]}{[\text{Pb}^{2+}]} \right). \] Step 2: Setting \( E = 0 \) and solving for the ratio, we find that \( [\text{Sn}^{2+}] / [\text{Pb}^{2+}] = 10^{-1} \).

Final Answer: \[ \boxed{10^{-1}} \]