Consider the following voltaic cell:

(c) What is the change in the cell voltage when the ion concentrations in the cathode half-cell are increased by a factor of 10?

Verified step by step guidance

1. Identify the half-reactions for the voltaic cell. For the Cd/Cu cell, the half-reactions are: Cd(s) → Cd²⁺(aq) + 2e⁻ (anode) and Cu²⁺(aq) + 2e⁻ → Cu(s) (cathode).
2. Write the Nernst equation for the cell: E_cell = 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 the Faraday constant, and Q is the reaction quotient.
3. Determine the standard cell potential (E°_cell) using standard reduction potentials: E°_cell = E°_cathode - E°_anode.
4. Calculate the reaction quotient (Q) for the cell. Initially, Q = [Cd²⁺]/[Cu²⁺]. When the ion concentration in the cathode half-cell is increased by a factor of 10, Q becomes [Cd²⁺]/(10*[Cu²⁺]).
5. Substitute the new value of Q into the Nernst equation to find the new cell potential. Compare the new cell potential with the original cell potential to determine the change in cell voltage.

Key Concepts

Voltaic Cell

A voltaic cell, also known as 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, connected by a salt bridge. The flow of electrons from the anode to the cathode generates a voltage, which can be measured using a voltmeter.

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 us to calculate how changes in concentration affect the cell voltage.

Reaction Quotient (Q)

The reaction quotient (Q) is a measure of the relative concentrations of products and reactants in a chemical reaction at a given moment. For a redox reaction, Q is calculated using the concentrations of the ions involved. In the context of a voltaic cell, increasing the concentration of ions in the cathode half-cell will affect Q, thereby influencing the cell voltage according to the Nernst equation.