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Chapter 19: Problem 21

Indicate whether each statement is true or false. (a) \(\Delta S\) depends on whether the process is reversible or irreversible. \((\mathbf{b})\) If a system undergoes an irreversible change, the entropy of the universe increases. (c) Only if the change in entropy of the system is exactly matched by an equal and opposite change in the entropy of the surroundings, the system undergoes a reversible process. (d) If the entropy change of the system is zero, the system undergoes a reversible process.

Short Answer

Expert verified
(a) False - \(\Delta S\) is a state function and does not depend on whether the process is reversible or irreversible. (b) True - If a system undergoes an irreversible change, the entropy of the universe will increase. (c) True - A system undergoes a reversible process if the change in entropy of the system is exactly matched by an equal and opposite change in the entropy of the surroundings. (d) False - A zero entropy change of the system does not necessarily imply a reversible process.

Step by step solution

01

Statement a: Is \(\Delta S\) dependant on whether the process is reversible or irreversible?

No, the change in entropy \(\Delta S\) is a state function, meaning it depends only on the initial and final states of the system and not on the path taken between those states. Thus, it doesn't matter if the process is reversible or irreversible. This statement is False.
02

Statement b: If a system undergoes an irreversible change, does the entropy of the universe increase?

Yes, according to the second law of thermodynamics, if a process is irreversible, the total entropy of the universe must increase. This statement is True.
03

Statement c: Is a system undergoing a reversible process only if the change in entropy of the system is exactly matched by an equal and opposite change in the entropy of the surroundings?

Yes, for a reversible process to occur, the entropy change in the system must be equal and opposite to the entropy change in the surroundings, so the total entropy change in the universe is zero. This statement is True.
04

Statement d: If the entropy change of the system is zero, does the system undergo a reversible process?

No, a system having an entropy change of zero does not necessarily guarantee that it has undergone a reversible process. In some cases, the entropy of a system may not change during an irreversible process, such as an adiabatic free expansion of a gas. In this case, the entropy change of the system is zero, but the process is still irreversible. This statement is False.

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Most popular questions from this chapter

Which of the following processes are spontaneous and which are nonspontaneous: (a) mixing of water and ethanol, \((\mathbf{b})\) dissolution of sugar in a cup of hot coffee, (c) formation of oxygen atoms from \(\mathrm{O}_{2}\) molecules at \(\mathrm{STP}\), (d) rusting of iron, (e) formation of glucose from \(\mathrm{CO}_{2}\) and $\mathrm{H}_{2} \mathrm{O}\( at \)\mathrm{STP} ?$

Consider a system consisting of an ice cube. (a) Under what conditions can the ice cube melt reversibly? (b) If the ice cube melts reversibly, is \(\Delta H\) zero for the process?

The \(K_{b}\) for methylamine \(\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)\) at \(25^{\circ} \mathrm{C}\) is given in Appendix \(D\). (a) Write the chemical equation for the equilibrium that corresponds to \(K_{b}\). (b) By using the value of \(K_{b}\), calculate \(\Delta G^{\circ}\) for the equilibrium in part (a). (c) What is the value of \(\Delta G\) at equilibrium? (d) What is the value of \(\Delta G\) when $\left[\mathrm{H}^{+}\right]=6.7 \times 10^{-9} \mathrm{M},\left[\mathrm{CH}_{3} \mathrm{NH}_{3}^{+}\right]=2.4 \times 10^{-3} \mathrm{M}$ and \(\left[\mathrm{CH}_{3} \mathrm{NH}_{2}\right]=0.098 \mathrm{M} ?\)

Which of the following processes are spontaneous: (a) the evaporation of water at \(\$ T P\) to form water vapor of 101.3 kPa pressure; (b) separation of a mixture of water and oil into two separate phases; (c) the souring of milk; (d) the neutralization of hydrochloric acid with sodium hydroxide at \(\mathrm{STP} ;(\mathbf{e})\) the formation of ice from water at \(20^{\circ} \mathrm{C}\) and \(101.3 \mathrm{kPa} ?\)

Most liquids follow Trouton's rule (see Exercise 19.93 ), which states that the molar entropy of vaporization is approximately $88 \pm 5 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$. The normal boiling points and enthalpies of vaporization of several organic liquids are as follows: \begin{tabular}{lcc} \hline & Normal Boiling & \\ Substance & Point \(\left({ }^{\circ} \mathrm{C}\right)\) & $\Delta H_{\text {vap }}(\mathrm{k} / / \mathrm{mol})$ \\ \hline Acetone, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO}\) & 56.1 & 29.1 \\\ Dimethyl ether, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{O}\) & -24.8 & 21.5 \\\ Ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) & 78.4 & 38.6 \\ Octane, \(\mathrm{C}_{\mathrm{s}} \mathrm{H}_{18}\) & 125.6 & 34.4 \\ Pyridine, \(\mathrm{C}_{5} \mathrm{H}_{\mathrm{S}} \mathrm{N}\) & 115.3 & 35.1 \\\ \hline \end{tabular} (a) Calculate \(\Delta S_{\text {vap }}\) for each of the liquids. Do all the liquids obey Trouton's rule? (b) With reference to intermolecular forces (Section 11.2), can you explain any exceptions to the rule? (c) Would you expect water to obey Trouton's rule? By using data in Appendix \(\mathrm{B}\), check the accuracy of your conclusion. (d) Chlorobenzene \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Cl}\right)\) boils at \(131.8^{\circ} \mathrm{C}\). Use Trouton's rule to estimate $\Delta H_{\text {vap }}$ for this substance.
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