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Chapter 19: Problem 101

For a process to occur spontaneously, (a) the entropy of the system must increase; (b) the entropy of the surroundings must increase; (c) both the entropy of the system and the entropy of the surroundings must increase; (d) the net change in entropy of the system and surroundings considered together must be a positive quantity; (e) the entropy of the universe must remain constant.

Short Answer

Expert verified
For a process to occur spontaneously, the net change in entropy of the system and surroundings considered together must be a positive quantity (option d). Some of the other options (a, b, c) are partially correct, while option e is incorrect.

Step by step solution

01

Understanding the Concept of Spontaneity

A spontaneous process is one which occurs by itself without any continuous external influence. These processes are influenced by changes in the system's entropy, which is a measure of the randomness or disorder of the system.
02

Determining Entropy Changes

The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time, and is constant if and only if all processes are reversible. Isolated systems spontaneously evolve towards thermodynamic equilibrium, the state with maximum entropy.
03

System and Surroundings Entropy

Options (a), (b) and (c) are partially correct. It is true that for a process to be spontaneous, the entropy in the system or/and surroundings should increase. But this is not a complete statement, as it doesn't consider the system and surroundings as a whole.
04

Net Change in Entropy

Option (d) now considers the system and the surroundings as a whole. It states that there should be a positive net change in entropy for a process to be spontaneous. This is a more overall description of the second law of thermodynamics.
05

Entropy of The Universe

Option (e) that 'the entropy of the universe must remain constant' is incorrect. For any spontaneous process, the total entropy (system + surroundings, i.e. the universe) increases.

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Most popular questions from this chapter

If \(\Delta G^{\circ}=0\) for a reaction, it must also be true that (a) \(K=0 ;\) (b) \(K=1 ;\) (c) \(\Delta H^{\circ}=0 ;\) (d) \(\Delta S^{\circ}=0\) (e) the equilibrium activities of the reactants and products do not depend on the initial conditions.

Explain why (a) some exothermic reactions do not occur spontaneously, and (b) some reactions in which the entropy of the system increases do not occur spontaneously.

The following data are given for the two solid forms of \(\mathrm{HgI}_{2}\) at \(298 \mathrm{K}\). $$\begin{array}{llll} \hline & \Delta H_{f}^{\circ} & \Delta G_{f,}^{\circ} & S^{\circ} \\ & \text { kJ mol }^{-1} & \text {kJ mol }^{-1} & \text {J mol }^{-1} \text {K }^{-1} \\ \hline \mathrm{HgI}_{2} \text { (red) } & -105.4 & -101.7 & 180 \\ \mathrm{Hg} \mathrm{I}_{2} \text { (yellow) } & -102.9 & (?) & (?) \\ \hline \end{array}$$ Estimate values for the two missing entries. To do this, assume that for the transition \(\mathrm{HgI}_{2}(\mathrm{red}) \longrightarrow\) \(\mathrm{HgI}_{2}(\text { yellow }),\) the values of \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) at \(25^{\circ} \mathrm{C}\) have the same values that they do at the equilibrium temperature of \(127^{\circ} \mathrm{C}\).

Which of the following changes in a thermodynamic property would you expect to find for the reaction \(\mathrm{Br}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{Br}(\mathrm{g})\) at all temperatures: \((\mathrm{a}) \Delta H<0\) (b) \(\Delta S>0 ;\) (c) \(\Delta G<0 ;\) (d) \(\Delta S<0 ?\) Explain.

For the reaction \(2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{g})\) \(K_{\mathrm{c}}=2.8 \times 10^{2}\) at \(1000 \mathrm{K}\) (a) What is \(\Delta G^{\circ}\) at \(1000 \mathrm{K} ?\left[\text { Hint: What is } \mathrm{K}_{\mathrm{p}} ?\right]\) (b) If \(0.40 \mathrm{mol} \mathrm{SO}_{2}, 0.18 \mathrm{mol} \mathrm{O}_{2},\) and \(0.72 \mathrm{mol} \mathrm{SO}_{3}\) are mixed in a 2.50 L flask at \(1000 \mathrm{K}\), in what direction will a net reaction occur?
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