Use the tabulated half-cell potentials to calculate the equilibrium constant (K)for the following balanced redox reaction at 25°C. 3 I₂(s)+ 2 Fe(s)→ 2 Fe³⁺(aq)+ 6 I⁻(aq) A) 3.5 × 10^-59 B) 1.1 × 10¹⁷ C) 2.4 × 10⁵⁸ D) 8.9 × 10^-18 E) 1.7 × 10²⁹

Question

Quizplus · Accepted Answer

1. Write the expression for the equilibrium constant:

K = [(FeS)/(I⁶)][(Fe²⁺)/(S²⁻)³]

2. Use the half-cell potentials to calculate the standard electrode potential (E°) for each half-reaction:

Fe²⁺ + 2e⁻ → Fe(s)      E° = -0.44 V
S²⁻ → ½S₂⁻ + 2e⁻       E° = -0.69 V
I⁻ → ½I₂ + e⁻         E° = +0.54 V

3. Calculate the cell potential (E°cell) using the Nernst equation:

E°cell = E°reduction + E°oxidation
E°cell = E°Fe²⁺/Fe + E°S²⁻/S - E°I⁻/I
E°cell = (-0.44 V) + (-0.69 V) - (+0.54 V)
E°cell = -1.67 V

4. Calculate K using the relationship between E°cell and K:

E°cell = -RT/nF ln K
K = e^(-nF(E°cell)/RT)

where:
n = number of electrons transferred = 2 (from the balanced equation)
F = Faraday's constant = 96485 C/mol
R = gas constant = 8.31 J/mol·K
T = temperature = 25°C = 298 K

K = e^(-2(96485 C/mol)(-1.67 V)/(8.31 J/mol·K)(298 K))
K = 2.4 × 10^158

Therefore, the best choice is C.

Use the Tabulated Half-Cell Potentials to Calculate the Equilibrium Constant