At 298 K a cell reaction has a standard cell potential of +0.17 V. The equilibrium constant for the reaction is 5.5 × 10⁵. What is the value of n for the reaction?

Verified step by step guidance

1. Identify the relationship between the standard cell potential (E°), the equilibrium constant (K), and the number of moles of electrons transferred (n) using the Nernst equation at equilibrium: E° = (RT/nF)ln(K).
2. Since the temperature is 298 K, use the simplified form of the Nernst equation: E° = (0.0257 V/n)ln(K).
3. Substitute the given values into the equation: 0.17 V = (0.0257 V/n)ln(5.5 × 10^5).
4. Solve for n by isolating it on one side of the equation: n = (0.0257 V/0.17 V)ln(5.5 × 10^5).
5. Calculate the natural logarithm of the equilibrium constant and then solve for n.

Key Concepts

Nernst Equation

The Nernst Equation relates the cell potential of an electrochemical reaction to the concentrations of the reactants and products. It is expressed as E = E° - (RT/nF)ln(Q), where E is the cell potential, E° is the standard cell potential, R is the universal gas constant, T is the temperature in Kelvin, n is the number of moles of electrons transferred, F is Faraday's constant, and Q is the reaction quotient.

Standard Cell Potential (E°)

The standard cell potential (E°) is the voltage measured under standard conditions (1 M concentration, 1 atm pressure, and 25°C) for a galvanic cell. It indicates the tendency of a chemical reaction to occur spontaneously; a positive E° suggests a spontaneous reaction, while a negative E° indicates non-spontaneity.

Equilibrium Constant (K)

The equilibrium constant (K) quantifies the ratio of the concentrations of products to reactants at equilibrium for a reversible reaction. It is related to the standard cell potential through the equation ΔG° = -nFE°, where ΔG° is the change in Gibbs free energy. A larger K value indicates a greater tendency for the reaction to favor products at equilibrium.