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Chapter 19: Problem 44

Predict the sign of \(\Delta S_{\text {sys }}\) for each of the following processes: (a) Molten gold solidifies. (b) Gaseous \(\mathrm{Cl}_{2}\) dissociates in the stratosphere to form gaseous \(\mathrm{Cl}\) atoms. (c) Gaseous CO reacts with gaseous \(\mathrm{H}_{2}\) to form liquid methanol, \(\mathrm{CH}_{3} \mathrm{OH}\). (d) Calcium phosphate precipitates upon mixing \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}(a q)\) and \(\left(\mathrm{NH}_{4}\right)_{3} \mathrm{PO}_{4}(a q)\)

Short Answer

Expert verified
(a) ΔS_sys < 0 (negative) since molten gold solidifies and becomes more ordered. (b) ΔS_sys > 0 (positive) due to the increase in the number of gas particles, increasing disorder. (c) ΔS_sys < 0 (negative) as the gaseous reactants combine to form a liquid, decreasing disorder. (d) ΔS_sys < 0 (negative) because precipitate formation causes the system to become more ordered.

Step by step solution

01

(a) Molten gold solidifies

In this process, molten gold (which is a liquid) is transformed into solid gold. The liquid state of matter has more disorder than the solid state since the particles in a liquid have more kinetic energy and a higher degree of freedom. Therefore, as the gold solidifies, the disorder of the system is decreasing. Consequently, the entropy change for this process, ΔS_sys, is expected to be negative.
02

(b) Gaseous Cl2 dissociates in the stratosphere to form gaseous Cl atoms.

For this process, one mole of gaseous Cl2 molecules dissociate into two moles of gaseous Cl atoms. The increase in the number of gas particles results in an increase in disorder of the system. The entropy change ΔS_sys is therefore positive.
03

(c) Gaseous CO reacts with gaseous H2 to form liquid methanol, CH3OH.

Through this reaction, one mole of gaseous CO and two moles of gaseous H₂ combine to form one mole of liquid methanol. This results in a decrease in the number of gas particles and a change in state from gas to liquid, accompanied by a decrease in disorder. Consequently, the entropy change ΔS_sys for this process is negative.
04

(d) Calcium phosphate precipitates upon mixing Ca(NO3)2(aq) and (NH4)3PO4(aq)

When calcium nitrate and ammonium phosphate solutions are mixed, a precipitate of calcium phosphate forms. The process involves changing states from the more disordered aqueous ions to a more organized solid precipitate. Thus, the entropy change ΔS_sys for this process is negative as the system becomes more ordered.

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Most popular questions from this chapter

Propanol \(\left(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}\right)\) melts at \(-126.5^{\circ} \mathrm{C}\) and boils at \(97.4{ }^{\circ} \mathrm{C}\). Draw a qualitative sketch of how the entropy changes as propanol vapor at \(150^{\circ} \mathrm{C}\) and 1 atm is cooled to solid propanol at \(-150^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\).

The standard entropies at \(298 \mathrm{~K}\) for certain of the group \(4 \mathrm{~A}\) elements are as follows: \(\mathrm{C}(s,\) diamond \()=2.43 \mathrm{~J} / \mathrm{mol}-\mathrm{K},\) \(\mathrm{Si}(s)=18.81 \mathrm{~J} / \mathrm{mol}-\mathrm{K}, \mathrm{Ge}(s)=31.09 \mathrm{~J} / \mathrm{mol}-\mathrm{K},\) and \(\operatorname{Sn}(s)=\) \(51.818 \mathrm{~J} / \mathrm{mol}-\mathrm{K} .\) All but \(\mathrm{Sn}\) have the diamond structure. How do you account for the trend in the \(S^{\circ}\) values?

Suppose we vaporize a mole of liquid water at \(25^{\circ} \mathrm{C}\) and another mole of water at \(100{ }^{\circ} \mathrm{C}\). (a) Assuming that the enthalpy of vaporization of water does not change much between \(25^{\circ} \mathrm{C}\) and \(100^{\circ} \mathrm{C},\) which process involves the larger change in entropy? (b) Does the entropy change in either process depend on whether we carry out the process reversibly or not? Explain.

(a) What is special about a reversible process? (b) Suppose a reversible process is reversed, restoring the system to its original state. What can be said about the surroundings after the process is reversed? (c) Under what circumstances will the vaporization of water to steam be a reversible process? (d) Are any of the processes that occur in the world around us reversible in nature? Explain.

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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