The Ksp of CuI is 1.1 * 10^-12. Find Ecell for the cell: Cu(s) | CuI(s) | I^-(aq)(1.0 M) || Cu^+(aq)(1.0 M) | Cu(s)

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Identify the half-reactions involved in the cell. The dissolution of CuI involves the equilibrium: CuI(s) ⇌ Cu⁺(aq) + I⁻(aq).

Write the Nernst equation for the cell: E_{cell} = E^0_{cell} - \frac{RT}{nF} \ln Q, where Q is the reaction quotient.

Determine the standard cell potential, E^0_{cell}, using standard reduction potentials: Cu⁺ + e⁻ → Cu(s) and I⁻ → I₂ + 2e⁻.

Calculate the reaction quotient, Q, using the concentrations given: Q = \frac{[Cu^+]}{[I^-]}.

Substitute the values into the Nernst equation to find E_{cell}, considering the temperature is 298 K and n = 1 for the electron transfer.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that applies to the solubility of sparingly soluble ionic compounds. It represents the product of the molar concentrations of the ions, each raised to the power of their coefficients in the balanced equation. For CuI, Ksp = [Cu^+][I^-], indicating how much of the compound can dissolve in water before reaching saturation.

Electrochemical Cell and Ecell

An electrochemical cell consists of two half-cells where oxidation and reduction reactions occur. Ecell, or cell potential, is the measure of the voltage produced by the cell, calculated using the standard reduction potentials of the half-reactions involved. It indicates the driving force for the electrochemical reaction, with positive values suggesting spontaneous reactions.

Nernst Equation

The Nernst equation relates the cell potential (Ecell) to the concentrations of the reactants and products in an electrochemical reaction. It is expressed as Ecell = E°cell - (RT/nF)ln(Q), where E°cell is the standard cell potential, R is the 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. This equation allows for the calculation of Ecell under non-standard conditions.

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The Nernst Equation

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A rechargeable battery is constructed based on a concentration cell constructed of two Ag/Ag⁺ half-cells. The volume of each half-cell is 2.0 L, and the concentrations of Ag⁺ in the half-cells are 1.25 M and 1.0 × 10^–3 M. c. Upon recharging, how long would it take to redissolve 1.00 × 10² g of silver at a charging current of 10.0 amps?

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