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Chapter 11: Problem 1

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

Short Answer

Expert verified
The correct answer is option (a) \((d G)_{T . P} \geq 0\) , as it is not the criterion for spontaneity of a process.

Step by step solution

01

Identifying the Criteria for Spontaneity

Using the rules from thermodynamics regarding the spontaneity of processes, we know that for a process to be spontaneous at constant temperature and pressure, Gibbs free energy must decrease or stay the same, i.e. \((d G)_{T . P} \leq 0\) . Likewise, for a process to be spontaneous at constant temperature and volume, Helmholtz free energy must decrease or stay the same, i.e. \((d A)_{T, V} \leq 0\) . Additionally, for entropy, the change should be \((d S)_{U, V} \geq 0\)
02

Evaluate Each Option

Now, let's evaluate each of the given options. (a) \((d G)_{T . P} \geq 0\) contradicts our criteria, hence it could be a potential candidate for the non-spontaneous process. Let's check the remaining options too. Option (b) \((d A)_{T, y} \leq 0\) follows the criteria, hence it is not the answer. Also, option (c) \((d G)_{T . P} \leq 0\) agrees with our criteria so it is not the correct answer. Lastly, option (d) \((d S)_{U, y} \geq 0\) is also in accordance with our stipulated criteria, hence this is also not the answer.
03

Final Assessment

Only option (a) \((d G)_{T . P} \geq 0\) contradicts the criteria for spontaneity. Therefore, it represents a condition that does not fulfill the criteria for a process to be spontaneous at constant temperature and pressure.

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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

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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