What is Ecell at 25°C of the spontaneous cell made from the Zn²⁺/Zn (0.76 V) and Br₂(l)/Br- (1.07 V) half cells if [Zn²⁺] = 10^-² and [Br-] = 10^-4?

Question

Quizplus · Accepted Answer

The equation for the spontaneous cell reaction is: Zn²⁺ + Br₂(l) → Zn²⁺ + Br- The standard reduction potentials are: E°(Zn²⁺/Zn) = -0.76 V E°(Br₂(l)/Br-) = 1.07 V The overall cell potential, Ecell, can be calculated using the formula: Ecell = E°(reduction at cathode) - E°(reduction at anode) Ecell = E°(Br₂(l)/Br-) - E°(Zn²⁺/Zn) Ecell = 1.07 V - (-0.76 V) Ecell = 1.83 V However, this is the cell potential under standard conditions (1 M solutions and 1 atm pressure). To calculate the cell potential under non-standard conditions, we need to use the Nernst equation: Ecell = E° - (RT/nF) ln(Q) where R = gas constant = 8.31 J/mol•K T = temperature in K = 25°C + 273 = 298 K n = number of electrons transferred = 2 (from the half-reactions) F = Faraday constant = 96485 C/mol Q = reaction quotient = [products]/[reactants] For this cell, the reaction quotient is: Q = [Br-]^1/[Zn²⁺]^1 = [Br-]/[Zn²⁺] Substituting the given concentrations and constants into the Nernst equation gives: Ecell = 1.07 V - (8.31 J/mol•K × 298 K / (2 × 96485 C/mol)) ln ([Br-]/[Zn²⁺]) Ecell = 1.07 V - (0.0256 V) ln (10^-4 / 10^-) Ecell = 0.608 V Therefore, the answer is (C) 0.61 V.

What Is Ecell at 25°C of the Spontaneous Cell Made