Consider a galvanic cell that uses the reaction Calculate the potential at 25 °C for a cell that has the following ion concentrations: [Ag+] = 0.010M, [Ni2+] = 0.100M.

Verified step by step guidance

1. Identify the half-reactions involved in the galvanic cell. For the given reaction, the half-reactions are: \( \text{Ag}^+ + e^- \rightarrow \text{Ag} \) and \( \text{Ni}^{2+} + 2e^- \rightarrow \text{Ni} \).
2. Determine the standard electrode potentials (E°) for each half-reaction from a standard reduction potential table. For example, \( E^\circ_{\text{Ag}^+/\text{Ag}} \) and \( E^\circ_{\text{Ni}^{2+}/\text{Ni}} \).
3. Calculate the standard cell potential (E°_cell) using the formula: \( E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} \).
4. Use the Nernst equation to calculate the cell potential (E_cell) at non-standard conditions: \( E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{nF} \ln Q \), where \( Q \) is the reaction quotient.
5. Calculate the reaction quotient \( Q \) using the concentrations given: \( Q = \frac{[\text{Ni}^{2+}]}{[\text{Ag}^+]^2} \). Substitute \( Q \) and other known values into the Nernst equation to find \( E_{\text{cell}} \).

Key Concepts

Galvanic Cell

A galvanic cell is an electrochemical cell that converts chemical energy into electrical energy through spontaneous redox reactions. It consists of two half-cells, each containing an electrode and an electrolyte. The flow of electrons from the anode to the cathode generates an electric current, and the cell potential can be calculated using the Nernst equation.

Nernst Equation

The Nernst equation relates the cell potential to the concentrations of the reactants and products in a redox reaction. It is expressed as E = E° - (RT/nF) ln(Q), where E° 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 cell potential under non-standard conditions.

Reaction Quotient (Q)

The reaction quotient (Q) is a measure of the relative concentrations of reactants and products at any point in a reaction. It is calculated by taking the ratio of the concentrations of the products raised to their stoichiometric coefficients to the concentrations of the reactants raised to their coefficients. In the context of a galvanic cell, Q is used in the Nernst equation to determine how the cell potential changes with varying concentrations.