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Chapter 19: Problem 34

(a) In a chemical reaction, two gases combine to form a solid. What do you expect for the sign of \(\Delta S ?\) (b) How does the entropy of the system change in the processes described in Exercise 19.12\(?\)

Short Answer

Expert verified
(a) In a chemical reaction where two gases combine to form a solid, the sign of \(\Delta S\) is expected to be negative, as the disorder decreases. (b) For both processes described in Exercise 19.12, the entropy of the system increases, and the sign of \(\Delta S\) is expected to be positive.

Step by step solution

01

(a) Identify the initial and final states of the system

In this scenario, the initial state of the system consists of two gases, while the final state is a solid. Consider that gases have more disorder compared to solids.
02

(a) Determine the change in entropy for the reaction

As the system goes from two gases to a solid, there is a decrease in the disorder as the molecules become more organized in the solid state. Therefore, we expect the entropy change, \(\Delta S\), to be negative.
03

(a) Final conclusion for part (a)

In a chemical reaction where two gases combine to form a solid, the sign of \(\Delta S\) is expected to be negative, as the disorder decreases.
04

(b) Review Exercise 19.12

In Exercise 19.12, the properties and processes of a system are described. For this part, we need to analyze how the entropy of the system changes in the processes mentioned in Exercise 19.12. Exercise 19.12 description: (i) A perfect gas expands in volume (reversibly) without any change in temperature. (ii) A perfect gas expands within a container due to a temperature increase.
05

(b) Analyze process (i)

In this process, a perfect gas expands in volume (reversibly) without any change in temperature. As the gas expands, the molecules are more spread out and occupy a larger volume, which leads to an increase in disorder. Hence, the entropy change, \(\Delta S\), should be positive.
06

(b) Analyze process (ii)

In this process, a perfect gas expands within a container due to a temperature increase. The expansion of the gas and the increase in temperature both contribute to an increase in disorder. Thus, the entropy change, \(\Delta S\), should be positive in this case as well.
07

(b) Final conclusion for part (b)

For both processes described in Exercise 19.12, the entropy of the system increases, and the sign of \(\Delta S\) is expected to be positive.

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Most popular questions from this chapter

(a) For a process that occurs at constant temperature, does the change in Gibbs free energy depend on changes in the enthalpy and entropy of the system? (b) For a certain process that occurs at constant \(T\) and \(P\) , the value of \(\Delta G\) is positive. Is the process spontaneous? (c) If \(\Delta G\) for a process is large, is the rate at which it occurs fast?

Consider the vaporization of liquid water to steam at a pressure of 1 atm. (a) Is this process endothermic or exothermic? (b) In what temperature range is it a spontaneous process? (c) In what temperature range is it a nonspontaneous process? (d) At what temperature are the two phases in equilibrium?

(a) What sign for \(\Delta S\) do you expect when the pressure on 0.600 mol of an ideal gas at 350 \(\mathrm{K}\) is increased isothermally from an initial pressure of 0.750 atm? (b) If the final pressure on the gas is 1.20 atm, calculate the entropy change for the process. (c) Do you need to specify the temperature to calculate the entropy change?

Classify each of the following reactions as one of the four possible types summarized in Table \(19.3 :\) (i) spontanous at all temperatures; (ii) not spontaneous at any temperature; (iii) spontaneous at low \(T\) but not spontaneous at high \(T ;\) (iv) spontaneous at high T but not spontaneous at low \(T .\) $$ \begin{array}{c}{\text { (a) } \mathrm{N}_{2}(g)+3 \mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{NF}_{3}(g)} \\ {\Delta H^{\circ}=-249 \mathrm{kJ} ; \Delta S^{\circ}=-278 \mathrm{J} / \mathrm{K}}\\\\{\text { (b) } \mathrm{N}_{2}(g)+3 \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NCl}_{3}(g)} \\\ {\Delta H^{\circ}=460 \mathrm{kJ} ; \Delta S^{\circ}=-275 \mathrm{J} / \mathrm{K}} \\ {\text { (c) } \mathrm{N}_{2} \mathrm{F}_{4}(g) \longrightarrow 2 \mathrm{NF}_{2}(g)} \\ {\Delta H^{\circ}=85 \mathrm{kJ} ; \Delta S^{\circ}=198 \mathrm{J} / \mathrm{K}}\end{array} $$

A standard air conditioner involves a refrigerant that is typically now a fluorinated hydrocarbon, such as \(\mathrm{CH}_{2} \mathrm{F}_{2} .\) An air- conditioner refrigerant has the property that it readily vaporizes at atmospheric pressure and is easily compressed to its liquid phase under increased pressure. The operation of an air conditioner can be thought of as a closed system made up of the refrigerant going through the two stages shown here (the air circulation is not shown in this diagram). During expansion, the liquid refrigerant is released into an expansion chamber at low pressure, where it vaporizes. The vapor then undergoes compression at high pressure back to its liquid phase in a compression chamber. (a) What is the sign of \(q\) for the expansion? (b) What is the sign of q for the compression? (c) In a central air-conditioning system, one chamber is inside the home and the other is outside. Which chamber is where, and why? (d) Imagine that a sample of liquid refrigerant undergoes expansion followed by compression, so that it is back to its original state. Would you expect that to be a reversible process? (e) Suppose that a house and its exterior are both initially at \(31^{\circ} \mathrm{C}\) . Some time after the air conditioner is turned on, the house is cooled to \(24^{\circ} \mathrm{C}\) . Is this process spontaneous or nonspontaneous?
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