An electrochemical cell consists of a standard hydrogen...

An electrochemical cell consists of a standard hydrogen electrode and a copper metal electrode. If the copper electrode is placed in a solution of $0.10 \mathrm{M} \mathrm{NaOH}$ that is saturated with $\mathrm{Cu}(\mathrm{OH})_{2}$, what is the cell potential at $25^{\circ} \mathrm{C} ?$ (For $\mathrm{Cu}(\mathrm{OH})_{2}$, $\left.K_{\mathrm{sp}}=1.6 \times 10^{-19} .\right)$

An electrochemical cell consists of a standard hydrogen electrode and a copper metal electrode. If the copper electrode is placed in a solution of $0.10 \mathrm{M} \mathrm{NaOH}$ that is saturated with $\mathrm{Cu}(\mathrm{OH})_{2}$, what is the cell potential at $25^{\circ} \mathrm{C} ?$ (For $\mathrm{Cu}(\mathrm{OH})_{2}$,
$\left.K_{\mathrm{sp}}=1.6 \times 10^{-19} .\right)$

Key Concepts

Electrochemical Cells

This concept involves systems where redox reactions occur between two physically separated electrodes. In an electrochemical cell, one electrode undergoes oxidation while the other undergoes reduction. The overall cell potential is determined by the difference in the electrode potentials of the two half-cells, and it quantifies the driving force for electron flow through the external circuit.

Standard Hydrogen Electrode (SHE)

The SHE serves as the reference electrode in electrochemistry and is assigned a potential of 0.00 V by convention. It involves the half-reaction of hydrogen gas and protons in solution. Using the SHE allows the measurement of other electrode potentials by comparison, forming the basis for defining a standard electrode potential scale.

Redox Reactions and Electrode Potentials

These reactions involve the transfer of electrons between chemical species, with each half-cell in an electrochemical cell representing either oxidation or reduction. The electrode potential is a measure of the tendency of a chemical species to acquire electrons and be reduced, and differences in these potentials between electrodes govern the overall cell voltage.

Nernst Equation

The Nernst equation relates the electrode potential to the standard potential, temperature, and the activities or concentrations of the chemical species involved in the redox reaction. It is particularly useful for calculating the potential of a half-cell under non-standard conditions by accounting for deviations in ion concentration and pressure.

Solubility Product (Ksp) and Precipitation Equilibria

The solubility product, Ksp, is a constant that describes the equilibrium between a sparingly soluble ionic compound and its ions in solution. In the context of an electrode immersed in a solution where a metal hydroxide is saturated, Ksp is used to calculate the concentration of the metal ion limited by the formation of the precipitate. This concentration then influences the electrode potential through the Nernst equation.

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