Calculate the standard cell potential (E°cell) for the reaction X(s) + Y⁺(aq) ⇌ X⁺(aq) + Y(s) if the equilibrium constant (K) is 7.12×10⁻³. Answer: E°cell = ________ V

• A. 0.25 V
• B. 0.75 V
• C. 0.12 V
• D. 0.50 V

Answer: (A)

Verified step by step guidance

1. Understand that the standard cell potential (E°cell) can be calculated using the Nernst equation, which relates the equilibrium constant (K) to E°cell.
2. Recall the Nernst equation for the relationship between E°cell and K: $E_{°}\mathrm{cell}=\frac{\mathrm{RT}}{\mathrm{nF}}\cdot \ln \left(K\right)$, where R is the gas constant (8.314 J/mol·K), T is the temperature in Kelvin, n is the number of moles of electrons transferred, and F is Faraday's constant (96485 C/mol).
3. Assume standard conditions, which means the temperature (T) is 298 K. Substitute the values for R, T, and F into the equation: $E_{°}\mathrm{cell}=\frac{8.314\cdot 298}{n\cdot 96485}\cdot \ln (7.12\times {10}^{-})$.
4. Determine the number of electrons transferred (n) in the balanced redox reaction. For the reaction X(s) + Y⁺(aq) ⇌ X⁺(aq) + Y(s), identify the oxidation and reduction half-reactions to find n.
5. Calculate the natural logarithm of the equilibrium constant (K) and substitute all known values into the Nernst equation to solve for E°cell.