A galvanic cell using Mg / Mg^2+ and Cu / Cu^2+ half-cells...

A galvanic cell using $\mathrm{Mg} / \mathrm{Mg}^{2+}$ and $\mathrm{Cu} / \mathrm{Cu}^{2+}$ half-cells operates under standard-state conditions at $25^{\circ} \mathrm{C},$ and each compartment has a volume of $218 \mathrm{mL}$. The cell delivers $0.22 \mathrm{A}$ for $31.6 \mathrm{h}$. (a) How many grams of Cu are deposited? (b) What is the $\left[\mathrm{Cu}^{2+}\right]$ remaining?

Key Concepts

Galvanic Cells

A galvanic cell is an electrochemical device that generates electrical energy from spontaneous redox reactions occurring in two separate half-cells. Each half-cell contains an electrode and an electrolyte, and the flow of electrons from the oxidation site to the reduction site through an external circuit produces current.

Faraday's Law of Electrolysis

Faraday's Law of Electrolysis states that the amount of chemical change—such as the deposition or dissolution of a substance at an electrode—is directly proportional to the total electric charge passed through the cell. This relationship allows calculation of the mass of material deposited using current, time, and the Faraday constant.

Redox Reaction Stoichiometry

Redox reaction stoichiometry involves balancing the electron transfer between oxidized and reduced species to ensure conservation of charge. It is used to relate the number of electrons transferred during the electrochemical process to the moles of reactants consumed or products formed.

Standard-State Conditions and Concentration Calculations

Standard-state conditions, typically defined at 1 M concentration, 1 atm pressure, and 25°C, provide a basis for comparing electrochemical reactions and determining electrode potentials. Determining the remaining concentration of a species after an electrochemical reaction involves relating the amount of reactant consumed (calculated via stoichiometry and Faraday's law) to the initial moles present in a known volume.

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