Chapter 17

How is the entropy change that accompanies a reaction related to the entropy change that happens when the reaction runs in reverse?

Identify the following systems as isolated or not isolated, identify the processes as spontaneous or nonspontaneous, and explain your choice. a. A photovoltaic cell in a solar panel produces electricity. b. Helium gas escapes from a latex party balloon. c. A sample of pitchblende (uranium ore) emits alpha particles.

Ice cubes melt in a glass of lemonade, cooling the lemonade from \(10.0^{\circ} \mathrm{C}\) to \(0.0^{\circ} \mathrm{C} .\) If the ice cubes are the system, what are the signs of \(\Delta S_{\text {sys }}\) and \(\Delta S_{\text {surr }} ?\)

Adding sidewalk deicer (calcium chloride) to water causes the temperature of the water to increase. If solid \(\mathrm{CaCl}_{2}\) is the system, what are the signs of \(\Delta S_{\mathrm{sys}}\) and \(\Delta S_{\mathrm{surr}} ?\)

Which of the following combinations of entropy changes for a process are mathematically possible? a. \(\Delta S_{x y y}>0, \Delta S_{\text {surr }}>0, \Delta S_{\text {univ }}>0\) b. \(\Delta S_{\text {sy }}>0, \Delta S_{\text {surr }}<0, \Delta S_{\text {univ }}>0\) c. \(\Delta S_{\text {eys }}>0, \Delta S_{\text {surr }}>0, \Delta S_{\text {univ }}<0\)

Which of the following combinations of entropy changes for a process are mathematically possible? a. \(\Delta S_{\text {sys }}<0, \Delta S_{\text {surr }}>0, \Delta S_{\text {univ }}>0\) b. \(\Delta S_{\text {rys }}<0, \Delta S_{\text {surr }}<0, \Delta S_{\text {univ }}>0\) c. \(\Delta S_{\text {sys }}<0, \Delta S_{\text {surr }}>0, \Delta S_{\text {univ }}<0\)

What are the signs of \(\Delta S_{\mathrm{sy}}\), and \(\Delta S_{\text {univ }}\) for the photosynthesis of glucose from carbon dioxide and water?

What are the signs of \(\Delta S_{\text {sys }}, \Delta S_{\text {surr }},\) and \(\Delta S_{\text {univ }}\) for the complete combustion of propane in which the products include water vapor and carbon dioxide?

For the following reactions, indicate whether the entropy of the system increases, decreases, or remains nearly the same. a. \(\mathrm{Al}^{3+}(a q)+3 \mathrm{OH}^{-}(a q) \rightarrow \mathrm{Al}(\mathrm{OH})_{3}(s)\) b. \(\mathrm{CaCO}_{3}(s) \rightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)\) c. \(\mathrm{Mg}(s)+\mathrm{Cu}^{2+}(a q) \rightarrow \mathrm{Mg}^{2+}(a q)+\mathrm{Cu}(s)\)

Which of the following processes would not result in an entropy increase for the indicated system? a. Melting of an ice cube b. Evaporation of a sample of an alcohol c. Sublimation of a mothball d. Cooling of hot water to room temperature

Digestion During digestion, complex carbohydrates decompose into simple sugars. Do the carbohydrates experience an increase or decrease in entropy?

Diamond and the fullerenes are two allotropes of carbon. On the basis of their different structures and properties, predict which has the higher standard molar entropy.

Super fluids The 1996 Nobel Prize in Physics was awarded to Douglas Osheroff, Robert Richardson, and David Lee for discovering super-fluidity (apparently frictionless flow) in "He. When \(^{3} \mathrm{He}\) is cooled to \(2.7 \mathrm{mK}\), the liquid settles into an ordered super-fluid state. What is the predicted sign of the entropy change for the conversion of liquid ' He into its super-fluid state?

Rank the compounds in each of the following groups in order of increasing standard molar entropy \(\left(S^{\circ}\right):\) a. \(\mathrm{CH}_{4}(g), \mathrm{CF}_{4}(g),\) and \(\mathrm{CCl}_{4}(g)\) b. \(\mathrm{CH}_{2} \mathrm{O}(g), \mathrm{CH}_{3} \mathrm{CHO}(g),\) and \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CHO}(g)\) c. \(\mathrm{HF}(g), \mathrm{H}_{2} \mathrm{O}(g),\) and \(\mathrm{NH}_{3}(g)\)

Under standard conditions, the products of a reaction have, overall, greater entropy than the reactants. What is the sign of \(\Delta S_{\mathrm{rm}}^{\prime} ?\)

Do polymerization reactions tend to have \(\Delta S_{\mathrm{rxn}}^{*}\) values that are greater than zero or less than zero? Why?

Do precipitation reactions tend to have \(\Delta S_{r x n}\) values that are greater than zero or less than zero? Why?

Smog Use the standard molar entropies in Appendix 4 to calculate \(\Delta S^{\circ}\) values for each of the following atmospheric reactions that contribute to the formation of photochemical smog. a. \(\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}(g)\) b. \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)\) c. \(\mathrm{NO}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{NO}_{2}(g)\) d. \(2 \mathrm{NO}_{2}(g) \rightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g)\)

What is the entropy change to the surroundings when a small decorative ice sculpture at a temperature of \(0^{\circ} \mathrm{C}\) and weighing 456 g melts on a granite tabletop, if the temperature of the granite is \(12^{\circ} \mathrm{C}\) and the process occurs reversibly? Assume a final temperature for the water of \(0^{\circ} \mathrm{C}\). The heat of fusion of ice is \(6.01 \mathrm{kJ} / \mathrm{mol} .\)

Another decorative "ice" sculpture is carved from dry ice (solid \(\mathrm{CO}_{2}\) ) and held at its sublimation point of \(-78.5^{\circ} \mathrm{C} .\) What is the entropy change to the universe when the \(\mathrm{CO}_{2}\) sculpture, weighing \(389 \mathrm{g},\) sublimes on a granite tabletop if the temperature of the granite is \(12^{\circ} \mathrm{C}\) and the process occurs reversibly? Assume a final temperature for the \(\mathrm{CO}_{2}\) vapor of \(-78.5^{\circ} \mathrm{C} .\) The heat of sublimation of \(\mathrm{CO}_{2}\) is \(26.1 \mathrm{kJ} / \mathrm{mol}\).

What single criterion allows us to determine whether a process is spontaneous? a. The sign of the equilibrium constant, \(K\) b. The sign of the enthalpy change, \(\Delta H\) c. The sign of the free-energy change, \(\Delta G\) d. The sign of the entropy change, \(\Delta S\)

If \(\Delta G\) for a reaction is negative, then which of the following is true? a. The reaction is spontaneous in the forward direction as written. b. The reaction system is at equilibrium. c. The reverse of the given reaction is spontancous. d. No reaction would ever have a negative \(\Delta G\).

Many 19 th-century scientists believed that all exothermic reactions were spontaneous. Why did so many scientists share this belief?

In which direction does a reaction proceed when its \(\Delta G\) value is (a) less than zero; (b) equal to zero; (c) greater than zero?

What are the signs of \(\Delta S, \Delta H,\) and \(\Delta G\) for the sublimation of dry ice (solid \(\mathrm{CO}_{2}\) ) at \(25^{\circ} \mathrm{C} ?\)

What are the signs of \(\Delta S, \Delta H,\) and \(\Delta G\) for the formation of dew on a cool night?

Which of the following processes is/are spontaneous? a. A hurricane forms. b. A corpse decomposes. c. You get an \(A\) in this course. d. Ice cream melts on a hot summer day.

Which of the following processes is/are spontaneous? a. Wood burns in air. b. Water vapor condenses on the sides of a glass of iced tea. c. Salt dissolves in water. d. Photosynthesis.

The values of \(\Delta H_{\mathrm{rxn}}^{\circ}\) and \(\Delta S_{\mathrm{rxn}}^{\circ}\) for the reaction $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)$$are \(-12 \mathrm{kJ}\) and \(-146 \mathrm{J} / \mathrm{K},\) respectively. a. Use these values to calculate \(\Delta G_{\mathrm{rxn}}^{\circ}\) at \(298 \mathrm{K}\) b. Explain why the value of \(\Delta G_{\text {rxn }}^{\circ}\) is negative.

Using appropriate data from Appendix \(4,\) calculate \(\Delta G^{\circ}\) for the following reaction: $$\mathrm{N}_{2} \mathrm{O}_{3}(g) \rightarrow \mathrm{NO}(g)+\mathrm{NO}_{2}(g)$$

Acid Precipitation Aerosols (fine droplets) of sulfuric acid form in the atmosphere as a result of the reaction below. Use the appropriate \(\Delta G_{f}^{a}\) data from Appendix 4 to calculate \(\Delta G_{\text {ren }}^{\circ}\) for the combination reaction: $$\mathrm{SO}_{3}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(\ell)$$

Are exothermic reactions spontaneous only at low temperature? Explain your answer.

Are endothermic reactions never spontaneous at low temperature? Explain your answer.

Determine the normal melting point of carbon tetrachloride in degrees Celsius given the following data: \(\Delta H_{\text {fins }}^{\circ}=2.67 \mathrm{kJ} / \mathrm{mol} \quad \Delta S_{\text {fits }}^{\circ}=10.86 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K})\)

If the value of \(K\) for a reaction is less than \(1,\) what is the sign of \(\Delta G_{\mathrm{rxn}}^{\circ} ?\)

The equation \(\Delta G^{\circ}=-R T \ln K\) relates the value of \(K_{\mathrm{p}},\) not \(K_{c},\) to \(\Delta G^{*}\) for gas-phase reactions. Explain why.

If a reaction mixture contains only reactants and no products, will the reaction proceed in the forward direction even if \(\Delta G^{\circ}>0 ?\) Explain why or why not.

If a gas-phase reaction mixture contains 1 mole of each reactant and product and has a 1: 1 stoichiometry, is the \(\Delta G_{\text {ran }}^{\circ}\) of the reaction mixture the same as \(\Delta H_{\mathrm{rm}}^{\circ}\) ? Explain why or why not.

Which of the following reactions has the largest \(K_{\mathrm{p}}\) value at \(25^{\circ} \mathrm{C} ?\) a. \(\mathrm{Cl}_{2}(g)+\mathrm{F}_{2}(g) \rightleftharpoons 2 \mathrm{ClF}(g) \quad \Delta G_{\text {rxn }}^{\circ}=115.4 \mathrm{kJ}\) b. \(\mathrm{Cl}_{2}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{ClBr}(g) \quad \Delta G_{\mathrm{mo}}^{*}=-2.0 \mathrm{kJ}\) c. \(\mathrm{Cl}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{ICl}(g) \quad \Delta G_{\mathrm{rm}}^{\circ}=-27.9 \mathrm{kJ}\)

Use the appropriate equilibrium constant from Appendix5 to calculate the value of \(\Delta G_{\max }^{\circ}\) for the reaction$$\mathrm{HClO}(a q)+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{ClO}^{-}(a q)+\mathrm{H}_{3} \mathrm{O}^{+}(a q)$$

The value of the equilibrium constant of a reaction decreases with increasing temperature. Is the reaction endothermic or exothermic?

The value of \(K_{\mathrm{p}}\) for the water-gas shift reaction $$\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g)$$ increases as the temperature decreases. Is the reaction exothermic or endothermic?

Air Pollution Automobiles and trucks pollute the air with NO. At \(2000^{\circ} \mathrm{C},\) the value of \(K_{c}\) for the reaction $$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)$$ is \(4.10 \times 10^{-4},\) and \(\Delta H^{\circ}=180.6 \mathrm{kJ} .\) What is the value of \(K_{c}\) at \(25^{\circ} \mathrm{C} ?\)

At \(400 \mathrm{K}\) the value of \(K_{\mathrm{p}}\) for the reaction $$\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)$$ is \(41,\) and \(\Delta H=-92.2 \mathrm{kJ} .\) What is the value of \(K_{\mathrm{p}}\) at \(700 \mathrm{K} ?\)

The equilibrium constant for the reaction $$\mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)$$ decreases from \(1.5 \times 10^{5}\) at \(430^{\circ} \mathrm{C}\) to 23 at \(1000^{\circ} \mathrm{C} .\) From these data, calculate the value of \(\Delta H^{\circ}\) for the reaction.

Describe the ways in which two chemical reactions must complement each other so that the decrease in free energy of the spontaneous reaction can drive the non-spontaneous reaction.

Why is it important that at least some of the spontaneous steps in glycolysis convert ADP to ATP?

Uses of Methane The methane in natural gas is an important starting material, or feedstock, for producing industrial chemicals, including \(\mathrm{H}_{2}\) gas. a. Use the appropriate \(\Delta G_{f}^{\circ}\) value(s) from Appendix 4 to calculate \(\Delta G_{\text {mn }}^{*}\) for the reaction known as steam-metbane reforming: $$\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{CO}(g)+3 \mathrm{H}_{2}(g)$$ b. To drive this nonspontancous reaction, the CO that is produced can be oxidized to \(\mathrm{CO}_{2}\) by using more steam: $$\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)$$ Use the appropriate \(\Delta G_{f}^{*}\) value(s) from Appendix 4 to calculate \(\Delta G_{\text {rxn }}^{*}\) for this reaction, which is known as the water- gas shift reaction. c. Combine these two reactions and write the chemical equation of the overall reaction in which methane and steam combine to produce hydrogen gas and carbon dioxide. d. Calculate the \(\Delta G_{\text {ren }}^{\circ}\) value of the overall reaction. Is it spontaneous under standard conditions?

Which of the following steps in glycolysis has the largest equilibrium constant? a. Fructose 1,6 -diphosphate \(\rightleftharpoons\) 2 glyceraldehyde-3-phosphate \(\quad \Delta G_{\text {ran }}^{*}=24 \mathrm{kJ}\) b. 3 -Phosphoglycerate \(\rightleftharpoons 2\) -phosphoglycerate \(\Delta G_{\mathrm{rxn}}^{\circ}=4.4 \mathrm{kJ}\) c. 2-Phosphoglycerate \(\rightleftarrows\) phosphocnolpyruvate \(\Delta G_{\mathrm{rxn}}^{\circ}=1.8 \mathrm{kJ}\)

In glycolysis, the hydrolysis of ATP to ADP drives the phosphorylation of glucose: $$\begin{array}{l}\text { Glucose }+\mathrm{ATP} \rightleftharpoons \mathrm{ADP}+\text { glucose } 6 \text { -phosphate } \\\\\qquad \Delta G_{\mathrm{rm}}^{\circ}=-17.7 \mathrm{kJ}\end{array}$$ What is the value of \(K_{c}\) for this reaction at \(298 \mathrm{K} ?\)