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Chapter 11: Problem 5

The relationship between decrease in Gibbs free energy and electrical energy is (a) \(-\Delta \mathrm{G}=n F E_{\text {cell }}\) (b) \(\Delta \mathrm{G}=n R T \ln E_{\text {cell }}\) (c) \(-\Delta G=-n F E_{\text {cell }}\) (d) \(\Delta G=-n R T \ln E_{\text {cell }}\)

Short Answer

Expert verified
Statement (a) is the correct relationship between decrease in Gibbs free energy and cell potential.

Step by step solution

01

Evalutate Statement (a)

The statement \(-\Delta \mathrm{G}=n F E_{\text {cell }}\) is the correct relationship of a cell operating in spontaneous conditions. Here, \(-\Delta \mathrm{G}\) represents decrease in Gibbs free energy, \(n\) is the number of moles of electrons, \(F\) is the Faraday's constant and \(E_{\text {cell }}\) is the cell potential.
02

Evaluate Statement (b)

This expression \(\Delta \mathrm{G}=n R T \ln E_{\text {cell }}\) is incorrect. The Relationship between Gibbs free energy change and cell potential is not logarithmical. This modifies the Nernst equation's structure, which measures Gibbs free energy change through equilibrium.
03

Evaluate Statement (c)

This statement \(-\Delta G=-n F E_{\text {cell }}\) has a double negative on both sides of the equation and thus is wrong. This means it is describing a situation where an increase in Gibbs free energy corresponds to a decrease in cell potential, which isn't accurate as per the fundamentals of electrochemistry.
04

Evaluate Statement (d)

This statement \(\Delta G=-n R T \ln E_{\text {cell }}\) is also incorrect, for the same reason as explained in Statement (b). It is not giving a correct relationship between Gibbs free energy and cell potential.

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Most popular questions from this chapter

Under what conditions is change in work function equal to change in Gibbs free energy, i.e. \(\Delta \mathrm{A}=\Delta G\) (a) When there is no change in volume, i.e. \(\Delta V=0\) (b) When there is no change in enthalpy, i.e. \(\Delta H=0\) (c) When there is no change in temperature (d) When there is no change in pressure

Which of the following is not the criterion for spontaneity of a process? (a) \((d G)_{T . P} \geq 0\) (b) \((d A)_{T, y} \leq 0\) (c) \((d G)_{T . P} \leq 0\) (d) \((d S)_{U, y} \geq 0\)
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