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Ch.20 - Electrochemistry
All textbooksBrown 14th EditionCh.20 - ElectrochemistryProblem 8c
Chapter 20, Problem 8c

Consider the following voltaic cell:
Diagram of a voltaic cell showing Cd and Cu electrodes, voltmeter, and salt bridge.
(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?

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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).
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.
Determine the standard cell potential (E°_cell) using standard reduction potentials: E°_cell = E°_cathode - E°_anode.
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⁺]).
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.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.
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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.
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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.
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Related Practice
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