Use the table of standard reduction potentials to calculate the equilibrium constant at standard temperature (25 °C) for the reaction: Fe(s) + Ni²⁺(aq) → Fe²⁺(aq) + Ni(s). Which of the following is the correct equilibrium constant (K)?

• A. K = 1.0 x 10^1
• B. K = 1.0 x 10^3
• C. K = 1.0 x 10^2
• D. K = 1.0 x 10^5

Answer: (C)

Verified step by step guidance

1. Identify the half-reactions involved in the given redox reaction. The oxidation half-reaction is Fe(s) → Fe²⁺(aq) + 2e⁻, and the reduction half-reaction is Ni²⁺(aq) + 2e⁻ → Ni(s).
2. Look up the standard reduction potentials (E°) for each half-reaction from the table of standard reduction potentials. The standard reduction potential for Ni²⁺(aq) + 2e⁻ → Ni(s) is typically given, as well as for Fe²⁺(aq) + 2e⁻ → Fe(s).
3. Calculate the standard cell potential (E°cell) using the formula: E°cell = E°(reduction) - E°(oxidation). Substitute the values from the table to find E°cell.
4. Use the Nernst equation to relate the standard cell potential to the equilibrium constant (K). The equation is: ln(K) = (nF * E°cell) / (RT), where n is the number of moles of electrons transferred, F is Faraday's constant (96485 C/mol), R is the universal gas constant (8.314 J/mol·K), and T is the temperature in Kelvin (298 K for standard conditions).
5. Solve for K by rearranging the Nernst equation to K = e^((nF * E°cell) / (RT)). Calculate the exponent using the values for n, F, E°cell, R, and T, and then find K by taking the exponential of the result.