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Chapter 19: Problem 37

Does the entropy of the system increase, decrease, or stay the same when (a) a solid melts, (b) a gas liquefies, (c) a solid sublimes?

Short Answer

Expert verified
When a solid melts, the entropy of the system increases. When a gas liquefies, the entropy of the system decreases. When a solid sublimes, the entropy of the system increases.

Step by step solution

01

Understand the process of melting

In the process of melting, a solid becomes a liquid. The particles in a solid are tightly packed and have a well-defined structure, while the particles in a liquid have more freedom to move around and are less structured.
02

Analyze the change in entropy

Since the particles in a liquid have more freedom to move around and are less structured, there is an increase in the number of possible energy states. This means that the entropy of the system increases.
03

Answer: Entropy increases during melting

When a solid melts, the entropy of the system increases. (B) A gas liquefies:
04

Understand the process of liquefaction

In the process of liquefaction, a gas becomes a liquid. The particles in a gas are far apart and have a lot of freedom to move around, while the particles in a liquid are relatively closer and have less freedom to move around.
05

Analyze the change in entropy

Since the particles in a liquid have less freedom to move around than in a gas, there is a decrease in the number of possible energy states. This implies that the entropy of the system decreases.
06

Answer: Entropy decreases during liquefaction

When a gas liquefies, the entropy of the system decreases. (C) A solid sublimes:
07

Understand the process of sublimation

In the process of sublimation, a solid becomes a gas without going through the liquid phase. The particles in a solid are tightly packed and have a well-defined structure, while the particles in a gas are far apart and have a lot of freedom to move around.
08

Analyze the change in entropy

Since the particles in a gas have more freedom to move around than in a solid, there is an increase in the number of possible energy states. This results in an increase in the entropy of the system.
09

Answer: Entropy increases during sublimation

When a solid sublimes, the entropy of the system increases.

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Most popular questions from this chapter

Which of the following processes are spontaneous: (a) the melting of ice cubes at \(-10^{\circ} \mathrm{C}\) and 1 atm pressure; (b) separating a mixture of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) into two separate samples, one that is pure \(\mathrm{N}_{2}\) and one that is pure \(\mathrm{O}_{2}\) (c) alignment of iron filings in a magnetic field; (d) the reaction of hydrogen gas with exygen gas to form water vapor at room temperature; (e) the dissolution of HCl(g) in water to form concentrated hydrochloric acid?

(a) For each of the following reactions, predict the sign of \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) without doing any calculations. (b) Based on your general chemical knowledge, predict which of these reactions will have \(K>1\). (c) In each case indicate whether \(K\) should increase or decrease with increasing temperature. (i) \(2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{MgO}(s)\) (ii) \(2 \mathrm{KI}(s) \rightleftharpoons 2 \mathrm{~K}(g)+\mathrm{I}_{2}(g)\) (iii) \(\mathrm{Na}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{Na}(\mathrm{g})\) (iv) \(2 \mathrm{~V}_{2} \mathrm{O}_{5}(s) \rightleftharpoons 4 \mathrm{~V}(\mathrm{~s})+5 \mathrm{O}_{2}(\mathrm{~g})\)

About \(86 \%\) of the world's electrical energy is produced by using steam turbines, a form of heat engine. In his analysis of an ideal heat engine, Sadi Carnot concluded that the maximum possible efficiency is defined by the total work that could be done by the engine, divided by the quantity of heat available to do the work (for example, from hot steam produced by combustion of a fuel such as coal or methane). This efficiency is given by the ratio \(\left(T_{\text {hyda }}-T_{\text {low }}\right) / T_{\text {high }}\). where \(T_{\text {bigh }}\) is the temperature of the heat going into the engine and \(T_{\text {low }}\) is that of the heat leaving the engine, (a) What is the maximum possible efficiency of a heat engine operating between an input temperature of \(700 \mathrm{~K}\) and an exit temperature of \(288 \mathrm{~K}\) ? (b) Why is it important that electrical power plants be located near bodies of relatively cool water? (c) Under what conditions could a heat engine operate at or near \(100 \%\) efflciency? (d) It is often said that if the energy of combustion of a fuel such as methane were captured in an electrical fuel cell instead of by burning the fuel in a heat engine, a greater fraction of the energy could be put to useful work. Make a qualitative drawing like that in Figure \(5.10\) (p. 175) that illustrates the fact that in principle the fuel cell route will produce more useful work than the heat engine route from combustion of methane.

The normal boiling point of \(\mathrm{Br}_{2}(l)\) is \(58.8^{\circ} \mathrm{C}\), and its molar enthalpy of vaporization is \(\Delta H_{\text {vap }}=29.6 \mathrm{kl} / \mathrm{mol}\). (a) When \(\mathrm{Br}_{2}(l)\) boils at its normal boiling point, does its entropy increase or decrease? (b) Calculate the value of \(\Delta S\) when \(1.00\) mol of \(\mathrm{Br}_{2}(l)\) is vaporized at \(58.8^{\circ} \mathrm{C}\)

Using data from Appendix \(C\), calculate \(\Delta G^{\circ}\) for the following reactions. Indicate whether each reaction is spontaneous at \(298 \mathrm{~K}\) under standard conditions. (a) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) (b) \(\mathrm{NO}_{2}(g)+\mathrm{N}_{2} \mathrm{O}(\mathrm{g}) \longrightarrow 3 \mathrm{NO}(g)\) (c) \(6 \mathrm{Cl}_{2}(g)+2 \mathrm{Fe}_{2} \mathrm{O}_{3}(s) \longrightarrow 4 \mathrm{FeCl}_{3}(s)+3 \mathrm{O}_{2}(g)\) (d) \(\mathrm{SO}_{2}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{S}(s)+2 \mathrm{H}_{2} \mathrm{O}(g)\)
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