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Chapter 11: Problem 2

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

Short Answer

Expert verified
The change in work function is equal to the change in Gibbs free energy when there is no change in temperature.

Step by step solution

01

Analyze the given options

It's understood that the work function and the Gibbs free energy are related, and when conditions change they equal. Let's analyze each of the conditions provided to determine if they maintain the equilibrium.
02

Evaluate Option (a)

When \(\Delta V = 0\), it means that there is no change in volume. However, Gibbs free energy (\(G\)), according to its formula \(G = H - TS\), is not directly correlated with volume. Therefore, a change in Gibbs free energy does not necessarily imply a change in the work function under this condition. So, option (a) is not correct.
03

Evaluate Option (b)

When \(\Delta H = 0\), it means that there is no change in enthalpy. However, enthalpy (\(H\)) is a part of the Gibbs free energy, but it's not the sole variable. So, the enthalpy change being zero doesn't mean \(\Delta A = \Delta G\), as the entropy and temperature could still cause changes. Therefore, option (b) is not correct.
04

Evaluate Option (c)

When there is no change in temperature, \(\delta Q = \Delta U + P \Delta V\), where \(\delta Q\) denotes heat transfer, \(\Delta U\) change in internal energy and \(P \Delta V\) work done by the system. If the temperature is constant, then all changes are due to work done by the system. This means that \(\Delta A = \Delta G\). Therefore, option (c) is correct.
05

Evaluate Option (d)

When there is no change in pressure, the Gibbs free energy does not necessarily remain constant since it is also dependent on entropy and temperature. So, even if the pressure is constant, other contributing factors may still cause a change in Gibbs free energy that does not equal a change in the work function. Therefore, option (d) is not correct.

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Most popular questions from this chapter

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) \((d S)_{U, y} \geq 0\)

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) \(\Delta G=-n R T \ln E_{\text {cell }}\)
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