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Chapter 19: Problem 33

How does the entropy of the system change when (a) a solid melts, (b) a gas liquefies, (c) a solid sublimes?

Short Answer

Expert verified
The entropy change during different phase transitions can be summarized as follows: (a) When a solid melts, the entropy of the system increases (螖S > 0) because particles gain kinetic energy and freedom of movement, resulting in higher randomness. (b) When a gas liquefies, the entropy of the system decreases (螖S < 0) because particles lose energy and become more organized and less random. (c) When a solid sublimes, the entropy of the system increases (螖S > 0) as particles gain freedom and randomness by directly transitioning from the solid to the gaseous state.

Step by step solution

01

(a) Entropy Change when a Solid Melts

When a solid melts, its particles gain kinetic energy and freedom of movement, allowing them to move more randomly and freely than before. As a result, the entropy (S) of the system will increase during the process. Therefore, we can say that the change in entropy 螖S > 0 for the melting process.
02

(b) Entropy Change when a Gas Liquefies

In the process of gas liquefaction, gas particles lose energy and come closer to each other. This results in a more organized and less random arrangement of the particles as compared to when they were in the gaseous state. Therefore, the entropy of the system will decrease during the liquefaction process. Consequently, we can conclude that the change in entropy 螖S < 0 for the gas liquefaction process.
03

(c) Entropy Change when a Solid Sublimes

When a solid sublimes, it directly transforms from the solid to the gaseous state, skipping the liquid phase. This transition provides the particles with a higher degree of freedom and randomness as they move from the highly-ordered solid structure to the more disordered gaseous state. As a result, the entropy of the system will increase during the sublimation process. Thus, the change in entropy 螖S > 0 for the solid sublimation process.

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Most popular questions from this chapter

Using data in Appendix C, calculate \(\Delta H^{\circ}, \Delta S^{\circ}\), and \(\Delta G^{\circ}\) at \(298 \mathrm{~K}\) for each of the following reactions. In each case show that \(\Delta G^{\circ}=\Delta H^{\circ}-T \Delta S^{\circ}\). (a) \(\mathrm{H}_{2}(g)+\mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{HF}(g)\) (b) \(\mathrm{C}(s\), graphite \()+2 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CCl}_{4}(g)\) (c) \(2 \mathrm{PCl}_{3}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{POCl}_{3}(g)\) (d) \(2 \mathrm{CH}_{3} \mathrm{OH}(g)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\)

A particular reaction is spontaneous at \(450 \mathrm{~K}\). The enthalpy change for the reaction is \(+34.5 \mathrm{~kJ} .\) What can you conclude about the sign and magnitude of \(\Delta S\) for the reaction?

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 \(K_{b r}\) 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 \(\left[\mathrm{CH}_{3} \mathrm{NH}_{3}+\right]=\left[\mathrm{H}^{+}\right]=1.5 \times 10^{-8} \mathrm{M}\) \(\left[\mathrm{CH}_{3} \mathrm{NH}_{3}{ }^{+}\right]=5.5 \times 10^{-4} \mathrm{M}\), and \(\left[\mathrm{CH}_{3} \mathrm{NH}_{2}\right]=0.120 \mathrm{M} ?\)

The element cesium (Cs) freezes at \(28.4^{\circ} \mathrm{C}\), and its molar enthalpy of fusion is \(\Delta H_{\text {fus }}=2.09 \mathrm{~kJ} / \mathrm{mol}\). (a) When molten cesium solidifies to \(\mathrm{Cs}(\mathrm{s})\) at its normal melting point, is \(\Delta S\) positive or negative? (b) Calculate the value of \(\Delta S\) when \(15.0 \mathrm{~g}\) of \(\mathrm{Cs}(l)\) solidifies at \(28.4^{\circ} \mathrm{C}\).

(a) What is the meaning of the standard free-energy change, \(\Delta G^{\circ}\), as compared with \(\Delta G ?\) (b) For any process that occurs at constant temperature and pressure, what is the significance of \(\Delta G=0 ?(c)\) For a certain process, \(\Delta G\) is large and negative. Does this mean that the process necessarily occurs rapidly?
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