Chapter 16

Define the terms "product-favored system" and "reactant-favored system." Give one example of each.

What are the two ways that a final chemical state of a system can be more probable than its initial state?

Define the term "entropy," and give an example of a sample of matter that has zero entropy. What are the units of entropy? How do they differ from the units of enthalpy?

State five useful qualitative rules for predicting entropy changes when chemical or physical changes occur.

State the second law of thermodynamics.

In terms of values of \(\Delta_{r} H^{\circ}\) and \(\Delta_{r} S^{\circ},\) under what conditions can you be sure that a reaction is product-favored? When can you be sure that it is not product-favored?

Define the Gibbs free energy change of a chemical reaction in terms of its enthalpy and entropy changes. Why is the Gibbs free energy change especially useful in predicting whether a reaction is product-favored?

Why are materials whose reactions release large quantities of Gibbs free energy useful to society? Give two examples of such materials.

Define the terms "endergonic" and "exergonic."

Define these important biochemistry terms: metabolism, nutrients, ATP, ADP, coupled reactions, photosynthesis.

Describe two ways to cause reactant-favored reactions to form products.

Describe the process by which sunlight is employed to convert high-entropy, low-Gibbs-free-energy substances into low-entropy, high-Gibbs-free-energy substances.

For each process, write a chemical equation and classify the process as reactant-favored or product-favored. (a) Water decomposes to its elements, hydrogen and oxygen. (b) Gasoline spilled on the ground evaporates (use octane, \(\mathrm{C}_{8} \mathrm{H}_{18},\) to represent gasoline). (c) Sugar dissolves in water at room temperature.

For each process, write a chemical equation and classify the process as reactant-favored or product-favored. (a) Carbon dioxide gas decomposes to its elements, carbon and oxygen. (b) The steel (mostly iron) body of an automobile rusts. (c) Gasoline reacts with oxygen to form carbon dioxide and water (use octane, \(\mathrm{C}_{8} \mathrm{H}_{18},\) to represent gasoline).

Suppose you flip a coin. (a) What is the probability that the coin will come up heads? (b) What is the probability that it will come up tails? (c) If you flip the coin 100 times, what is the most likely number of heads and tails you will see?

Suppose you make a tetrahedron and put numbers \(1,2,3,\) and 4 on each of the four sides. You toss the tetrahedron in the air and observe it after it comes to rest. (a) What is the probability that the tetrahedron will come to rest with the numbers \(2,3,\) and 4 visible? (b) What is the probability that the tetrahedron will come to rest with the numbers \(1,2,\) and 3 visible? (c) If you toss the tetrahedron 100 times, what is the most likely number of times you will see a 1 after it comes to rest?

For each process, tell whether the entropy change of the system is positive or negative. (a) Water vapor (the system) deposits as ice crystals on a cold windowpane. (b) A can of carbonated beverage loses its fizz. (Consider the beverage but not the can as the system. What happens to the entropy of the dissolved gas?) (c) A glassblower heats glass (the system) to its softening temperature.

For each process, tell whether the entropy change of the system is positive or negative. (a) Water boils. (b) A teaspoon of sugar dissolves in a cup of coffee. (The system consists of both sugar and coffee.) (c) Calcium carbonate precipitates out of water in a cave to form stalactites and stalagmites. (Consider only the calcium carbonate to be the system.)

For each pair of items, predict which has the higher entropy, and explain why. (a) Item 1, a sample of solid \(\mathrm{CO}_{2}\) at \(-78^{\circ} \mathrm{C}\), or item \(2, \mathrm{CO}_{2}\) vapor at \(0{ }^{\circ} \mathrm{C}\) (b) Item 1, solid sugar, or item 2 , the same sugar dissolved in a cup of tea (c) Item 1, a 100-mL sample of pure water and a \(100-\mathrm{mL}\) sample of pure alcohol, or item 2 , the same samples of water and alcohol after they had been poured together and stirred

For each pair of items, predict which has the higher entropy, and explain why. (a) Item 1, a sample of pure silicon (to be used in a computer chip), or item 2 , a piece of silicon having the same mass but containing a trace of some other element, such as \(\mathrm{B}\) or \(\mathrm{P}\) (b) Item \(1,\) an ice cube at \(0^{\circ} \mathrm{C},\) or item \(2,\) the same mass of liquid water at \(0{ }^{\circ} \mathrm{C}\) (c) Item 1, a sample of pure \(\mathrm{I}_{2}\) solid at room temperature, or item \(2,\) the same mass of iodine vapor at room temperature

Comparing the formulas or states for each pair of substances, predict which has the higher entropy per mole at the same temperature, and explain why. (a) \(\mathrm{NaCl}(\mathrm{s})\) or \(\mathrm{CaO}(\mathrm{s})\) (b) \(\mathrm{Cl}_{2}(\mathrm{~g})\) or \(\mathrm{P}_{4}(\mathrm{~g})\) (c) \(\mathrm{NH}_{4} \mathrm{NO}_{3}(\mathrm{~s})\) or \(\mathrm{NH}_{4} \mathrm{NO}_{3}(\mathrm{aq})\)

From each pair of substances, select the one having the larger standard molar entropy at \(25^{\circ} \mathrm{C}\). Give reasons for your choice. (a) \(\mathrm{Ga}(\mathrm{s})\) or \(\mathrm{Ga}(\ell)\) (b) \(\mathrm{AsH}_{3}(\mathrm{~g})\) or \(\mathrm{Kr}(\mathrm{g})\) (c) \(\mathrm{NaF}(\mathrm{s})\) or \(\mathrm{MgO}(\mathrm{s})\)

Without doing a calculation, predict whether the entropy change is positive or negative when each reaction occurs in the direction it is written. (a) \(\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{~g})\) (b) \(\mathrm{CH}_{3} \mathrm{OH}(\ell)+\frac{3}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (c) \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{~g})\) (d) \(\mathrm{CaCO}_{3}(\mathrm{~s}) \longrightarrow \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g})\)

Without doing a calculation, predict whether the entropy change is positive or negative when each reaction occurs in the direction it is written. (a) \(\mathrm{CH}_{3} \mathrm{OH}(\ell) \longrightarrow \mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{~g})\) (b) \(\mathrm{Br}_{2}(\ell)+\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{HBr}(\mathrm{g})\) (c) \(\mathrm{C}_{3} \mathrm{H}_{8}(\mathrm{~g}) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})+\mathrm{CH}_{4}(\mathrm{~g})\) (d) \(\mathrm{Ag}^{+}(\mathrm{aq})+\mathrm{I}^{-}(\mathrm{aq}) \longrightarrow \mathrm{AgI}(\mathrm{s})\)

Without consulting a table of standard molar entropies, predict whether \(\Delta_{\mathrm{r}} S_{\text {system }}^{\circ}\) is positive or negative for each of these reactions. (a) \(2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})\) (b) \(2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(\ell)\) (c) \(2 \mathrm{O}_{3}(\mathrm{~g}) \longrightarrow 3 \mathrm{O}_{2}(\mathrm{~g})\)

Without consulting a table of standard molar entropies, predict whether \(\Delta_{1} S_{\text {system }}^{\circ}\) is positive or negative for each of these reactions. (a) \(2 \mathrm{NH}_{3}(\mathrm{~g}) \longrightarrow \mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g})\) (b) \(2 \mathrm{Na}(\mathrm{s})+\mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NaCl}(\mathrm{s})\) (c) \(\mathrm{H}_{2}(\mathrm{~g})+\mathrm{I}_{2}(\mathrm{~s}) \longrightarrow 2 \mathrm{HI}(\mathrm{g})\)

Calculate the entropy change, \(\Delta_{\mathrm{r}} S^{\circ},\) for the vaporization of ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH},\) at the boiling point of \(78.3{ }^{\circ} \mathrm{C}\). The heat of vaporization of the alcohol is \(39.3 \mathrm{~kJ} / \mathrm{mol}\). $$ \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{g}) \quad \Delta_{\mathrm{r}} S^{\circ}=? $$

Diethyl ether, \(\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{O},\) was once used as an anesthetic. Calculate the entropy change, \(\Delta_{\mathrm{r}} S^{\circ},\) for the vaporization of ether if its heat of vaporization is \(26.0 \mathrm{~kJ} / \mathrm{mol}\) at the boiling point of \(35.0^{\circ} \mathrm{C}\).

Calculate \(\Delta_{\mathrm{r}} S^{\circ}\) for each substance when the quantity of thermal energy indicated is transferred reversibly to the system at the temperature specified. Assume that you have enough of each substance so that its temperature remains constant as the thermal energy is transferred. (a) \(\mathrm{H}_{2}(\mathrm{~g}), 0.775 \mathrm{~kJ} / \mathrm{mol}, 295 \mathrm{~K}\) (b) \(\mathrm{KCl}(\mathrm{s}), 500 . \mathrm{kJ} / \mathrm{mol}, 500 . \mathrm{K}\) (c) \(\mathrm{N}_{2}(\mathrm{~g}), 2.45 \mathrm{~kJ} / \mathrm{mol}, 1000 . \mathrm{K}\)

Calculate \(\Delta_{\mathrm{r}} S^{\circ}\) for each of these substances when the quantity of thermal energy indicated is transferred reversibly to the system at the temperature specified. Assume that you have enough of each substance so that its temperature remains constant as the thermal energy is transferred. (a) \(\mathrm{NaCl}(\mathrm{s}), 5.00 \mathrm{~kJ} / \mathrm{mol}, 500 . \mathrm{K}\) (b) \(\mathrm{N}_{2} \mathrm{O}(\mathrm{g}), 0.30 \mathrm{~kJ} / \mathrm{mol}, 300 . \mathrm{K}\)

Is this reaction predicted to favor the products at low temperatures, at high temperatures, or both? Explain your answer briefly. \(\mathrm{Mg}(\mathrm{s})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{MgO}(\mathrm{s}) \quad \Delta_{\mathrm{r}} H^{\circ}=-601.70 \mathrm{~kJ} / \mathrm{mol}\)

Is this reaction predicted to favor the products at low temperatures, at high temperatures, or both? Explain your answer briefly. \(\mathrm{MgCO}_{3}(\mathrm{~s}) \longrightarrow \mathrm{MgO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g}) \quad \Delta_{\mathrm{r}} H^{\circ}=100.59 \mathrm{~kJ} / \mathrm{mol}\)

Explain briefly why the exothermic combustion of propane is product-favored. $$ \mathrm{C}_{3} \mathrm{H}_{8}(\mathrm{~g})+5 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 3 \mathrm{CO}_{2}(\mathrm{~g})+4 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) $$

Explain briefly why the exothermic reaction of a metal carbonate with an acid is product-favored. \(\mathrm{CuCO}_{3}(\mathrm{~s})+\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}) \longrightarrow\) \(\mathrm{CuSO}_{4}(\mathrm{aq})+\mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\ell)\)

Hydrogen burns in air with considerable heat transfer to the surroundings. Consider the decomposition of water to gaseous hydrogen and oxygen. Without doing any calculations, and basing your prediction on the enthalpy change and the entropy change, is this reaction product-favored at \(25^{\circ} \mathrm{C} ?\) Explain your answer briefly.

Hydrogen gas combines with chlorine gas in an exothermic reaction to form \(\mathrm{HCl}(\mathrm{g})\). Consider the decomposition of gaseous hydrogen chloride to hydrogen and chlorine. Without doing any calculations, and basing your prediction on the enthalpy change and the entropy change, is this reaction product-favored at \(25^{\circ} \mathrm{C}\) ? Explain your answer briefly.

Use a mathematical equation to show how the statement leads to the conclusion cited: If a reaction is exothermic (negative \(\Delta_{1} H\) ) and if the entropy of the system increases (positive \(\Delta_{\\{} S\) ), then \(\Delta_{r} G\) must be negative, and the reaction is product-favored.

Use a mathematical equation to show how the statement leads to the conclusion cited: If \(\Delta_{\mathrm{r}} H\) and \(\Delta_{\mathrm{r}} S\) have the same sign, then the magnitude of \(T\) determines whether \(\Delta_{\mathrm{r}} G\) is negative and whether the reaction is product-favored.

Predict whether the reaction given is product-favored or reactant-favored by calculating \(\Delta_{\mathrm{r}} G^{\circ}\) from the entropy and enthalpy changes for the reaction at \(25^{\circ} \mathrm{C}\). \(\mathrm{H}_{2}(\mathrm{~g})+\mathrm{CO}_{2}(\mathrm{~g}) \longrightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{CO}(\mathrm{g})\) $$ \Delta_{r} H^{\circ}=41.17 \mathrm{~kJ} / \mathrm{mol} \quad \Delta_{r} S^{\circ}=42.08 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1} $$

Predict whether this reaction is product-favored at \(25^{\circ} \mathrm{C}\) by calculating the change in standard Gibbs free energy from the entropy and enthalpy changes. $$ \begin{aligned} \mathrm{H}_{2}(\mathrm{~g})+\mathrm{I}_{2}(\mathrm{~g}) & \rightleftharpoons 2 \mathrm{HI}(\mathrm{g}) \\ \Delta_{\mathrm{r}} H^{\circ} &=52.96 \mathrm{~kJ} / \mathrm{mol} \quad \Delta_{\mathrm{r}} S^{\circ}=21.81 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1} \end{aligned} $$

For each reaction, an equilibrium constant at \(298 \mathrm{~K}\) is given. Calculate \(\Delta_{\mathrm{r}} G^{\circ}\) for each reaction. $$ \begin{array}{lr} \text { (a) } \mathrm{Br}_{2}(\ell)+\mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{HBr}(\mathrm{g}) & K_{\mathrm{P}}=4.4 \times 10^{18} \\ \text { (b) } \mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) & K_{\mathrm{P}}=3.17 \times 10^{-2} \\ \text {(c) } \mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g}) & K_{\mathrm{c}}=3.5 \times 10^{8} \end{array} $$

The molecular structure shown is of one form of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) Glucose can be oxidized to carbon dioxide and water according to the equation $$ \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{~s})+6 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 6 \mathrm{CO}_{2}(\mathrm{~g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) $$

Another step in the metabolism of glucose, which occurs after the formation of glucose 6 -phosphate, is the conversion of fructose 6 -phosphate to fructose 1,6 -bisphosphate ("bis" means two): $$ \begin{aligned} \text { Fructose } 6 \text { -phosphate }(\mathrm{aq})+\mathrm{H}_{2} \mathrm{PO}_{4}^{-}(\mathrm{aq}) & \longrightarrow \\ & \text { fructose } 1,6 \text { -bisphosphate(aq) }+\mathrm{H}_{2} \mathrm{O}(\ell)+\mathrm{H}^{+}(\text {aq }) \end{aligned} $$ (a) This reaction has a Gibbs free energy change of \(+16.7 \mathrm{~kJ} / \mathrm{mol}\) of fructose 6 -phosphate. Is it endergonic or exergonic? (b) Write the equation for the formation of \(1 \mathrm{~mol}\) ADP from ATP, for which \(\Delta_{\mathrm{r}} G^{\circ}=-30.5 \mathrm{~kJ} / \mathrm{mol}\) (c) Couple these two reactions to get an exergonic process; write its overall chemical equation, and calculate the Gibbs free energy change.

In muscle cells under the condition of vigorous exercise, glucose is converted to lactic acid ("lactate"), \(\mathrm{CH}_{3} \mathrm{CHOHCOOH},\) by the chemical reaction \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \longrightarrow 2 \mathrm{CH}_{3} \mathrm{CHOHCOOH} \quad \Delta_{\mathrm{r}} G^{\circ \prime}=-197 \mathrm{~kJ} / \mathrm{mol}\) (a) If all of the Gibbs free energy from this reaction were used to convert ADP to ATP, calculate how many moles of ATP could be produced per mole of glucose. (b) The actual reaction involves the production of \(3 \mathrm{~mol}\) ATP per mole of glucose. Calculate the \(\Delta_{\mathrm{r}} G^{\circ}\) for this overall reaction. (c) Is the overall reaction in part (b) reactant-favored or product-favored?

What are the resources human society uses to supply Gibbs free energy?

A friend says that the boiling point of water is twice that of cyclopentane, which boils at \(50{ }^{\circ} \mathrm{C}\). Write a brief statement about the validity of this observation.

Using the second law of thermodynamics, explain why it is very difficult to unscramble an egg. Who was HumptyDumpty? Why did his moment of glory illustrate the second law of thermodynamics?

Appendix J lists standard molar entropies \(S^{\circ},\) not standard entropies of formation \(\Delta_{\mathrm{f}} S^{\circ} .\) Why is this possible for entropy but not for internal energy, enthalpy, or Gibbs free energy?

When calculating \(\Delta_{\mathrm{r}} S^{\circ}\) from \(S^{\circ}\) values, it is necessary to look up all substances, including elements in their standard state, such as \(\mathrm{O}_{2}(\mathrm{~g}), \mathrm{H}_{2}(\mathrm{~g}),\) and \(\mathrm{N}_{2}(\mathrm{~g}) .\) When calcu- lating \(\Delta_{\mathrm{r}} H^{\circ}\) from \(\Delta_{\mathrm{f}} H^{\circ}\) values, however, elements in their standard state can be ignored. Why is the situation different for \(S^{\circ}\) values?

Explain how the entropy of the universe increases when an aluminum metal can is made from aluminum ore. The first step is to extract the ore, which is primarily a form of \(\mathrm{Al}_{2} \mathrm{O}_{3},\) from the ground. After it is purified by freeing it from oxides of silicon and iron, aluminum oxide is changed to the metal by an input of electrical energy. $$ 2 \mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{~s}) \stackrel{\text { electrical energy }}{\longrightarrow} 4 \mathrm{Al}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{~g}) $$