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Chapter 19: Problem 5

Indicate whether the entropy of the system would increase or decrease in each of the following reactions. If you cannot be certain simply by inspecting the equation, explain why. (a) \(\mathrm{CCl}_{4}(1) \longrightarrow \mathrm{CCl}_{4}(\mathrm{g})\) (b) \(\mathrm{CuSO}_{4} \cdot 3 \mathrm{H}_{2} \mathrm{O}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \longrightarrow\) \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}(\mathrm{s})\) (c) \(\mathrm{SO}_{3}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g}) \longrightarrow \mathrm{SO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (d) \(\mathrm{H}_{2} \mathrm{S}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{SO}_{2}(\mathrm{g})\) (not balanced)

Short Answer

Expert verified
a) Increases, b) Decreases, c) Uncertain from the equation alone, d) Uncertain due to unbalanced equation.

Step by step solution

01

Analyze Reaction (a)

In the reaction \(\mathrm{CCl}_{4}(1) \longrightarrow \(\mathrm{CCl}_{4}(\mathrm{g})\), the carbon tetrachloride transitions from liquid to gaseous state. For all spontaneous physical and chemical changes, the system always tends toward greater randomness. Since gases have higher entropy than liquids, the entropy increases in this reaction.
02

Analyze Reaction (b)

In the reaction \(\mathrm{CuSO}_{4} \cdot 3 \mathrm{H}_{2} \mathrm{O}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \longrightarrow \mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}(\mathrm{s})\), the number of gaseous molecules decreases (we go from 2 moles to 0 moles of gas). The reaction is forming an ordered solid, in which the molecules have less freedom to move around. This decrease in randomness translates to a decrease in entropy.
03

Analyze Reaction (c)

The reaction \(\mathrm{SO}_{3}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g}) \longrightarrow \mathrm{SO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) includes two moles of gas on the left of the equation and two moles of gas on the right of the equation. No change in the number of gas molecules or the phase, so we may not be able to determine this reaction's change in entropy just by looking at the reaction.
04

Analyze Reaction (d)

In this final unbalanced reaction, \(\mathrm{H}_{2} \mathrm{S}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{SO}_{2}(\mathrm{g})\), it's difficult to analyze the entropy change just through the equation due to imbalance. It's recommended to balance the equation first. However, an initial analysis suggests that both reactants and products are in gaseous state, thus it's uncertain whether entropy increases or decreases without further detailed balance and calculations.

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Most popular questions from this chapter

Comment on the difficulties of solving environmental pollution problems from the standpoint of entropy changes associated with the formation of pollutants and with their removal from the environment.

Two correct statements about the reversible reaction \(\mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})\) are \((\mathrm{a}) K=K_{\mathrm{p}}\) (b) the equilibrium amount of NO increases with an increased total gas pressure; (c) the equilibrium amount of NO increases if an equilibrium mixture is transferred from a \(10.0 \mathrm{L}\) container to a \(20.0 \mathrm{L}\) container; (d) \(K=K_{c} ;\) (e) the composition of an equilibrium mixture of the gases is independent of the temperature.

The following equilibrium constants have been determined for the reaction \(\mathrm{H}_{2}(\mathrm{g})+\mathrm{I}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{HI}(\mathrm{g})\) \(K_{\mathrm{p}}=50.0\) at \(448^{\circ} \mathrm{C}\) and 66.9 at \(350^{\circ} \mathrm{C} .\) Use these data to estimate \(\Delta H^{\circ}\) for the reaction.

Which of the following changes in a thermodynamic property would you expect to find for the reaction \(\mathrm{Br}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{Br}(\mathrm{g})\) at all temperatures: \((\mathrm{a}) \Delta H<0\) (b) \(\Delta S>0 ;\) (c) \(\Delta G<0 ;\) (d) \(\Delta S<0 ?\) Explain.

Use thermodynamic data from Appendix D to calculate values of \(K_{\mathrm{sp}}\) for the following sparingly soluble solutes: (a) \(\operatorname{AgBr} ;\) (b) \(\operatorname{CaSO}_{4} ;\) (c) \(\operatorname{Fe}(\text { OH })_{3}\). [Hint: Begin by writing solubility equilibrium expressions.
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