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Chapter 19: Problem 42

Predict the sign of \(\Delta S_{s y s}\) for each of the following processes: (a) Gaseous \(\mathrm{H}_{2}\) reacts with liquid palmitoleic acid \(\left(\mathrm{C}_{16} \mathrm{H}_{30} \mathrm{O}_{2},\right.\) unsaturated fatty acid) to form liquid palmitic acid $\left(\mathrm{C}_{16} \mathrm{H}_{32} \mathrm{O}_{2}\right.$ saturated fatty acid). (b) Liquid palmitic acid solidifies at \(1^{\circ} \mathrm{C}\) to solid palmitic acid. (c) Silver chloride precipitates upon mixing \(\mathrm{AgNO}_{3}(a q)\) and \(\mathrm{NaCl}(a q) .\) (d) Gaseous \(\mathrm{H}_{2}\) dissociates in an electric arc to form gaseous H atoms (used in atomic hydrogen welding).

Short Answer

Expert verified
(a) \(\Delta S_{sys}<0\) (b) \(\Delta S_{sys}<0\) (c) \(\Delta S_{sys}<0\) (d) \(\Delta S_{sys}>0\)

Step by step solution

01

Identify the phases of the reactants and products

The reactants include gaseous \(\mathrm{H}_{2}\) and liquid palmitoleic acid, while the product is liquid palmitic acid.
02

Determine the change in disorder

In this reaction, a gaseous molecule reacts with liquid to form a liquid. The loss of a gaseous molecule means that the system becomes more ordered.
03

Predict the sign of \(\Delta S_{sys}\)

Since the system becomes more ordered, the entropy change will be negative: \(\Delta S_{sys}<0\). (b) Liquid palmitic acid solidifies at \(1^{\circ} \mathrm{C}\) to solid palmitic acid.
04

Identify the phase change

The process involves the transition from a liquid to a solid.
05

Determine the change in disorder

Going from a liquid to a solid means that the molecules become more ordered and less randomly distributed.
06

Predict the sign of \(\Delta S_{sys}\)

Since the system becomes more ordered, the entropy change will be negative: \(\Delta S_{sys}<0\). (c) Silver chloride precipitates upon mixing \(\mathrm{AgNO}_{3}(a q)\) and \(\mathrm{NaCl}(a q)\).
07

Identify the process

The process involves the formation of a solid precipitate (silver chloride) from two aqueous solutions.
08

Determine the change in disorder

The formation of a solid precipitate means that the system becomes more ordered.
09

Predict the sign of \(\Delta S_{sys}\)

Since the system becomes more ordered, the entropy change will be negative: \(\Delta S_{sys}<0\). (d) Gaseous \(\mathrm{H}_{2}\) dissociates in an electric arc to form gaseous H atoms (used in atomic hydrogen welding).
10

Identify the process

The process involves the dissociation of a gaseous molecule into single gaseous atoms.
11

Determine the change in disorder

During the dissociation, one gaseous molecule is converted into two individual gaseous atoms, leading to an increase in the number of particles and disorder.
12

Predict the sign of \(\Delta S_{sys}\)

Since the system becomes more disordered, the entropy change will be positive: \(\Delta S_{sys}>0\).

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Most popular questions from this chapter

Indicate whether each of the following statements is trueor false. If it is false, correct it. (a) The feasibility of manufacturing \(\mathrm{NH}_{3}\) from \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) depends entirely on the value of $\Delta H\( for the process \)\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) .$ (b) The reaction of \(\mathrm{Na}(s)\) with \(\mathrm{Cl}_{2}(g)\) to form \(\mathrm{NaCl}(s)\) is a spontaneous process. (c) A spontaneous process can in principle be conducted reversibly. (d) Spontaneous processes in general require that work be done to force them to proceed. (e) Spontaneous processes are those that are exothermic and that lead to a higher degree of order in the system.

Using data from Appendix \(\mathrm{C}\), calculate the change in Gibbs free energy for each of the following reactions. In each case, indicate whether the reaction is spontaneous at \(298 \mathrm{~K}\) under standard conditions. (a) \(2 \mathrm{Ag}(s)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{AgCl}(s)\) (b) $\mathrm{P}_{4} \mathrm{O}_{10}(s)+16 \mathrm{H}_{2}(g) \longrightarrow 4 \mathrm{PH}_{3}(g)+10 \mathrm{H}_{2} \mathrm{O}(g)$ (c) $\mathrm{CH}_{4}(g)+4 \mathrm{~F}_{2}(g) \longrightarrow \mathrm{CF}_{4}(g)+4 \mathrm{HF}(g)$ (d) $2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(I)+\mathrm{O}_{2}(g)$

When most elastomeric polymers (e.g., a rubber band) are stretched, the molecules become more ordered, as illustrated here: Suppose you stretch a rubber band. (a) Do you expect the entropy of the system to increase or decrease? (b) If the rubber band were stretched isothermally, would heat need to be absorbed or emitted to maintain constant temperature? (c) Try this experiment: Stretch a rubber band and wait a moment. Then place the stretched rubber band on your upper lip, and let it return suddenly to its unstretched state (remember to keep holding on!). What do you observe? Are your observations consistent with your answer to part (b)?

Using \(S^{\circ}\) values from Appendix \(\mathrm{C}\), calculate $\Delta S^{\circ}$ values for the following reactions. In each case, account for the sign of \(\Delta S\). (a) $\mathrm{NH}_{4} \mathrm{Cl}(s) \longrightarrow \mathrm{NH}_{4}^{+}(a q)+\mathrm{Cl}^{-}(a q)$ (b) $\mathrm{CH}_{3} \mathrm{OH}(g) \longrightarrow \mathrm{CO}(g)+2 \mathrm{H}_{2}(g)$ (c) $\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$ (d) $\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$

The oxidation of glucose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\( in body tissue produces \)\mathrm{CO}_{2}$ and \(\mathrm{H}_{2} \mathrm{O} .\) In contrast, anaerobic decomposition, which occurs during fermentation, produces ethanol $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\( and \)\mathrm{CO}_{2}$. (a) Using data given in Appendix \(\mathrm{C}\), compare the equilibrium constants for the following reactions: $$ \begin{array}{r} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \rightleftharpoons 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \\ \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s) \rightleftharpoons 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(I)+2 \mathrm{CO}_{2}(g) \end{array} $$ (b) Compare the maximum work that can be obtained from these processes under standard conditions.
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