What is the standard cell potential (E°cell) in volts for a redox reaction where one electron is transferred and the equilibrium constant (K) is 7.23 × 10^8?

• A. 0.75 V
• B. 0.50 V
• C. 1.10 V
• D. 0.95 V

Answer: (D)

Verified step by step guidance

1. Understand that the relationship between the standard cell potential (E°cell) and the equilibrium constant (K) is given by the Nernst equation. For standard conditions, this is simplified to: $E_{°}\mathrm{cell}=\frac{\mathrm{RT}}{\mathrm{nF}}\cdot \ln K$.
2. Identify the constants and variables in the equation: R is the universal gas constant (8.314 J/mol·K), T is the temperature in Kelvin (standard conditions are 298 K), n is the number of moles of electrons transferred (given as 1), and F is Faraday's constant (96485 C/mol).
3. Substitute the known values into the equation: $E_{°}\mathrm{cell}=\frac{(8.314\cdot 298)}{(1\cdot 96485)}\cdot \ln (7.23\cdot {10}^8$.
4. Calculate the natural logarithm of the equilibrium constant: $\ln (7.23\cdot {10}^8$. This will be used in the equation to find E°cell.
5. Perform the multiplication and division to solve for E°cell. This involves calculating the product of R, T, and ln(K), then dividing by the product of n and F. This will yield the standard cell potential in volts.