Question
A voltaic cell consists of A/A⁺ and B/B⁺ half-cells, where A and B are metals and the A electrode is negative. The initial [A⁺]/[B⁺] is such tha21.53 A voltaic cell consists of A/A⁺ and B/B⁺ half-cells, where A and B are metals and the A electrode is negative. The initial [A⁺]/[B⁺] is such that Ecell > E°cell.(c) What is [A⁺]y[B⁺] when Ecell = E°cell ? Explain.
Answer
[A⁺] = 1/[B⁺], where A and B are the metals in the A/A⁺ and B/B⁺ half-cells of the voltaic cell, respectively.
- Q: What is the equation for calculating Ecell? A: Ecell = E°cell - (RT/nF)ln(Q) where R, T, n, and F are constants, and Q is the reaction quotient.
- Q: What is the equation for the reaction quotient, Q? A: Q = [A⁺]^x[B⁺]^y, where x and y are the stoichiometric coefficients of A⁺ and B⁺ in the balanced equation.
- Q: What is the relationship between Ecell and E°cell? A: If Ecell is greater than E°cell, the reaction is spontaneous and Q is less than 1. If Ecell equals E°cell, the reaction is at equilibrium and Q equals 1.
- Q: What is the equation for calculating [A⁺]y[B⁺] at equilibrium? A: At equilibrium, Ecell = E°cell, so Q = 1. Substituting Q = 1 into the equation for Q gives [A⁺]^x[B⁺]^y = 1. Since the A electrode is negative, the reduction half-reaction is B⁺ + e⁻ → B, so x = 1 and y = 1. Therefore, [A⁺][B⁺] = 1, or [A⁺] = 1/[B⁺].
- Q: What is the final answer? A: [A⁺] = 1/[B⁺], where A and B are the metals in the A/A⁺ and B/B⁺ half-cells of the voltaic cell, respectively.