Two copper concentration cells, X and Y

CHEMISTRY · Multi-part · AP · Chemistry · Thermodynamics and Electrochemistry · Thermodynamics and Electrochemistry

Problem

Two copper concentration cells, X and Y, are operated at 298 K. Both employ copper electrodes and aqueous

\mathrm{Cu^{2+}}

solutions separated by an inert salt bridge. • Cell X:

\mathrm{Cu(s)}\,|\,\mathrm{Cu^{2+}}(1.0\,\text{M})\;||\;\mathrm{Cu^{2+}}(0.020\,\text{M})\,|\,\mathrm{Cu(s)}

• Cell Y:

\mathrm{Cu(s)}\,|\,\mathrm{Cu^{2+}}(1.0\,\text{M})\;||\;\mathrm{Cu^{2+}}(0.00020\,\text{M})\,|\,\mathrm{Cu(s)}

Assume activity coefficients are unity and that temperature remains constant throughout. (a) Write the overall cell reaction that occurs in a generic copper concentration cell of the type shown. (b) Calculate the reaction quotient

Q_{\text{X}}

for Cell X and

Q_{\text{Y}}

for Cell Y using the provided ion concentrations. (c) Determine the cell potential for Cell X and for Cell Y at 298 K. Express each answer in volts with three significant figures. (d) By what numerical factor does the cell potential change when the less-concentrated solution is diluted from

0.020\,\text{M}

0.00020\,\text{M}

? Support your answer with calculations. (e) Explain qualitatively how further dilution of the less-concentrated half-cell would affect both the reaction quotient and the cell potential, and identify the theoretical limit that cannot be exceeded by dilution alone.

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