The Ksp of Zn(OH)2 is 1.8 * 10^-14. Find Ecell for the half-reaction: Zn(OH)2(s) + 2 e- ⇌ Zn(s) + 2 OH-(aq)

Verified step by step guidance

1. Identify the half-reaction given: \( \text{Zn(OH)}_2(s) + 2e^- \rightleftharpoons \text{Zn}(s) + 2\text{OH}^-(aq) \).
2. Use the Nernst equation to find the cell potential: \( E_{cell} = E^\circ_{cell} - \frac{RT}{nF} \ln Q \), where \( Q \) is the reaction quotient.
3. Determine \( E^\circ_{cell} \) using the standard reduction potentials. For the reaction \( \text{Zn}^{2+} + 2e^- \rightarrow \text{Zn}(s) \), find \( E^\circ \) from a standard reduction potential table.
4. Calculate the reaction quotient \( Q \) using the expression \( Q = \frac{[\text{OH}^-]^2}{1} \) since \( \text{Zn(OH)}_2 \) and \( \text{Zn} \) are solids and do not appear in the expression.
5. Substitute the values into the Nernst equation to solve for \( E_{cell} \). Remember to use \( n = 2 \) for the number of electrons transferred and the given \( K_{sp} \) to find \( [\text{OH}^-] \).

Key Concepts

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 maximum concentration of ions in a saturated solution at a given temperature. For Zn(OH)2, Ksp indicates the extent to which the compound can dissolve in water, which is crucial for understanding the equilibrium between solid Zn(OH)2 and its ions in solution.

Electrochemical Cell and Ecell

Ecell, or cell potential, is the measure of the voltage produced by an electrochemical cell during a redox reaction. It is determined by the difference in reduction potentials between the two half-reactions involved. In this case, calculating Ecell for the half-reaction involving Zn(OH)2 requires understanding how the solubility of the compound affects the concentration of ions, which in turn influences the cell potential.

Nernst Equation

The Nernst equation relates the cell potential (Ecell) to the concentrations of the reactants and products in an electrochemical reaction. It accounts for non-standard conditions by incorporating the reaction quotient (Q) and temperature. For the half-reaction involving Zn(OH)2, the Nernst equation can be used to calculate Ecell by substituting the concentrations of Zn and OH- ions derived from the Ksp value.