Chapter 18

Solid \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) is placed in a beaker containing water at \(25^{\circ} \mathrm{C}\). When the solid has completely dissolved, the temperature of the solution is \(23.5^{\circ} \mathrm{C}.\) (a) Was the process exothermic or endothermic? (b) Was the process spontaneous? (c) Did the entropy of the system increase? (d) Did the entropy of the universe increase?

Identify the following processes as either spontaneous or not spontaneous. (a) Ice melts when placed in a flask containing water at \(5^{\circ} \mathrm{C}.\) (b) Hydrogen iodide molecules decompose at \(400 \mathrm{K}\) to give a mixture of \(\mathrm{H}_{2}, \mathrm{I}_{2},\) and \(\mathrm{HI}\) (c) Ethanol and water are mixed to form a solution. (d) Slightly soluble \(\mathrm{PbCl}_{2}\left(K_{\mathrm{sp}}=1.7 \times 10^{-5}\right)\) dissolves in water to form a saturated solution.

Identify the following processes as either spontaneous or not spontaneous. (a) Liquid water turns to ice when placed in a freezer at \(-5^{\circ} \mathrm{C}\) (b) Nitrogen gas is compressed to one half its original volume. (c) Sodium reacts with water forming \(\mathrm{H}_{2}(\mathrm{g})\) and \(\mathrm{NaOH}(\mathrm{aq})\) (d) Slightly soluble \(\operatorname{CaSO}_{4}\left(K_{\mathrm{sp}}=4.5 \times 10^{-5}\right)\) dis- solves in water to form a saturated solution.

Predict whether each of the following processes results in an increase in entropy in the system. (Define reactants and products as the system.) (a) Water vapor condenses as dew (liquid water) at \(0^{\circ} \mathrm{C}\) and 1 atm pressure. (b) An exothermic reaction of \(\mathrm{Al}(\mathrm{s})\) and \(\mathrm{Br}_{2}(\ell)\) forms \(\mathrm{Al}_{2} \mathrm{Br}_{6}(\mathrm{s})\) (c) The endothermic decomposition of solid \(\mathrm{CaCO}_{3}\) at \(800^{\circ} \mathrm{C}\) to produce an equilibrium mixture containing solid \(\mathrm{CaCO}_{3},\) solid \(\mathrm{CaO}\) and gaseous \(\mathrm{CO}_{2}\) (d) One mol of AgCl(s) decomposes, forming 1.0 mole of \(\mathrm{Ag}(\mathrm{s})\) and \(0.5 \mathrm{mol} \mathrm{Cl}_{2}(\mathrm{g})\)

Predict whether each of the following processes results in an increase in entropy in the system. (Define reactants and products as the system.) (a) Water vapor condenses to liquid water at \(90^{\circ} \mathrm{C}\) and 1 atm pressure. (b) The exothermic reaction of \(\mathrm{Na}(\mathrm{s})\) and \(\mathrm{Cl}_{2}(\mathrm{g})\) forms \(\mathrm{NaCl}(\mathrm{s})\) (c) The endothermic reaction of \(\mathrm{H}_{2}\) and \(\mathrm{I}_{2}\) produces an equilibrium mixture of \(\mathrm{H}_{2}(\mathrm{g})\) \(\mathrm{I}_{2}(\mathrm{g}),\) and \(\mathrm{HI}(\mathrm{g})\) (d) Solid NaCl dissolves in water forming a saturated solution.

Indicate which of the following processes are reversible. (a) Nitrogen gas expands into a vacuum. (b) Dry ice, \(\mathrm{CO}_{2}(\mathrm{s}),\) sublimes at \(25^{\circ} \mathrm{C}\) and 1.0 atm. (c) Energy as heat is added to a mixture of ice and water at \(0^{\circ} \mathrm{C},\) causing some of the ice to melt. (d) Methanol and ethanol mix forming a homogeneous solution.

Indicate which of the following processes are reversible. (a) Nitrogen and oxygen gases diffuse to give a homogeneous mixture. (b) Ice sublimes at \(-5^{\circ} \mathrm{C}\) and 1.0 atm. (c) Energy as heat is transferred to the surroundings from a mixture of ice and water at \(0^{\circ} \mathrm{C}\) causing more ice to form. (d) Bromine evaporates and the gaseous molecules diffuse into the atmosphere.

Calculate the entropy change that occurs when 0.50 mol of ice is converted to liquid water at \(0^{\circ} \mathrm{C}\) in a reversible process. \(\left(q_{\text {fus }}=333 \mathrm{J} / \mathrm{g}\right).\)

Calculate the entropy change that occurs when 1.00 mol of steam is converted to liquid water at \(100^{\circ} \mathrm{C}\) in a reversible process. \(\left(q_{\mathrm{vap}}=40.7 \mathrm{kJ} /\right.\)mol)

Calculate the change in entropy for a system in going from a condition of 5 accessible microstates to 30 accessible microstates.

Which substance has the higher entropy? (a) dry ice (solid \(\mathrm{CO}_{2}\) ) at \(-78^{\circ} \mathrm{C}\) or \(\mathrm{CO}_{2}(\mathrm{g})\) at \(0^{\circ} \mathrm{C}\) (b) liquid water at \(25^{\circ} \mathrm{C}\) or liquid water at \(50^{\circ} \mathrm{C}\) (c) pure alumina, \(\mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s}),\) or ruby (ruby is \(\mathrm{Al}_{2} \mathrm{O}_{3}\) in which some \(\mathrm{Al}^{3+}\) ions in the crystalline lattice are replaced with \(\mathrm{Cr}^{3+}\) ions) (d) one mole of \(\mathrm{N}_{2}(\mathrm{g})\) at 1 bar pressure or one mole of \(\mathrm{N}_{2}(\mathrm{g})\) at 10 bar pressure (both at \(298 \mathrm{K})\)

Which substance has the higher entropy? (a) a sample of pure silicon (to be used in a computer chip) or a piece of silicon containing a trace of another element such as boron or phosphorus (b) \(\mathrm{O}_{2}(\mathrm{g})\) at \(0^{\circ} \mathrm{C}\) or \(\mathrm{O}_{2}(\mathrm{g})\) at \(-50^{\circ} \mathrm{C}\) (c) \(\mathrm{I}_{2}(\mathrm{s})\) or \(\mathrm{I}_{2}(\mathrm{g}),\) both at room temperature (d) one mole of \(\mathrm{O}_{2}(\mathrm{g})\) at 1 bar pressure or one mole of \(\mathrm{O}_{2}(\mathrm{g})\) at 0.01 bar pressure (both at \(298 \mathrm{K})\)

Determine whether the reactions listed below are entropy-favored or disfavored under standard conditions. Predict how an increase in temperature will affect the value of \(\Delta_{\mathrm{r}} G^{\circ}.\) (a) \(\mathrm{I}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{I}(\mathrm{g})\) (b) \(2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{SO}_{3}(\mathrm{g})\) (c) \(\operatorname{sicl}_{4}(g)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \mathrm{SiO}_{2}(\mathrm{s})+4 \mathrm{HCl}(\mathrm{g})\) (d) \(\mathrm{P}_{4}(\mathrm{s}, \text { white })+6 \mathrm{H}_{2}(\mathrm{g}) \rightarrow 4 \mathrm{PH}_{3}(\mathrm{g})\)

The ionization constant, \(K_{\mathrm{a}},\) for acetic acid is \(1.8 \times\) \(10^{-5}\) at \(25^{\circ} \mathrm{C} .\) What is the value of \(\Delta_{\mathrm{r}} \mathrm{G}^{\circ}\) for this reaction? Is this reaction product- or reactantfavored at equilibrium?

The formation constant, \(K_{i}\) for the reaction $$\mathrm{Ag}^{+}(\mathrm{aq})+2 \mathrm{NH}_{3}(\mathrm{aq}) \rightleftharpoons\left[\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right]^{+}(\mathrm{aq})$$ is \(1.1 \times 10^{7} .\) What is the value of \(\Delta_{\mathrm{r}} \mathrm{G}^{\circ}\) for this reaction? Is the reaction product- or reactant- favored at equilibrium?

The standard free energy change, \(\Delta_{\mathrm{r}} G^{\circ},\) for the formation of \(\mathrm{NO}(\mathrm{g})\) from its elements is \(+86.58 \mathrm{kJ} / \mathrm{mol}-\mathrm{rxn}\) at \(25^{\circ} \mathrm{C} .\) Calculate \(K_{\mathrm{p}}\) at this temperature for the equilibrium $$1 / 2 \mathrm{N}_{2}(\mathrm{g})+1 / 2 \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{NO}(\mathrm{g})$$ Comment on the sign of \(\Delta_{\mathrm{r}} G^{\circ}\) and the magnitude of \(K_{\mathrm{p}}.\)

The standard free energy change, \(\Delta_{\mathrm{r}} G^{\circ},\) for the formation of \(\mathrm{O}_{3}(\mathrm{g})\) from \(\mathrm{O}_{2}(\mathrm{g})\) is \(+163.2 \mathrm{kJ} / \mathrm{mol}\) -ren at \(25^{\circ} \mathrm{C} .\) Calculate \(K_{\mathrm{p}}\) at this temperature for the equilibrium $$3 \mathrm{O}_{2}(\mathrm{g}) \rightleftarrows 2 \mathrm{O}_{3}(\mathrm{g})$$ Comment on the sign of \(\Delta_{r} G^{\circ}\) and the magnitude of \(K_{\mathrm{p}}.\)

About 5 billion kilograms of benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}\), are made each year. Benzene is used as a starting material for many other compounds and as a solvent (although it is also a carcinogen, and its use is restricted). One compound that can be made from benzene is cyclohexane, \(\mathrm{C}_{6} \mathrm{H}_{12}\) $$\begin{array}{c} \mathrm{C}_{6} \mathrm{H}_{6}(\ell)+3 \mathrm{H}_{2}(\mathrm{g}) \rightarrow \mathrm{C}_{6} \mathrm{H}_{12}(\ell) \\ \Delta_{\tau} H^{\circ}=-206.7 \mathrm{kJ} / \mathrm{mol}-\mathrm{rxn} ; \\\ \Delta_{\tau} \mathrm{S}^{\circ}=-361.5 \mathrm{J} / \mathrm{K} \cdot \mathrm{mol}-\mathrm{rxn} \end{array}$$ Is this reaction predicted to be product-favored at equilibrium at \(25^{\circ} \mathrm{C} ?\) Is the reaction enthalpy-or entropy-driven?

The enthalpy of vaporization of liquid diethyl ether, \(\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{O},\) is \(26.0 \mathrm{kJ} / \mathrm{mol}\) at the boiling point of \(35.0^{\circ} \mathrm{C} .\) Calculate \(\Delta S^{\circ}\) for a vapor-to-liquid transformation at \(35.0^{\circ} \mathrm{C}.\)

Calculate the entropy change, \(\Delta_{r} S^{\circ},\) for the vaporization of ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH},\) at its normal boiling point, \(78.0^{\circ} \mathrm{C} .\) The enthalpy of vaporization of ethanol is \(39.3 \mathrm{kJ} / \mathrm{mol}\).

Sodium reacts violently with water according to the equation $$\mathrm{Na}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \mathrm{NaOH}(\mathrm{aq})+1 / 2 \mathrm{H}_{2}(\mathrm{g})$$Without doing calculations, predict the signs of \(\Delta_{\mathrm{r}} H^{\circ}\) and \(\Delta_{\mathrm{r}} S^{\circ}\) for the reaction. Verify your prediction with a calculation.

Estimate the boiling point of water in Denver, Colorado (where the altitude is \(1.60 \mathrm{km}\) and the atmospheric pressure is \(630 \mathrm{mm} \mathrm{Hg} \text { or } 0.840 \mathrm{bar}).\)

Sulfur undergoes a phase transition between 80 and \(100^{\circ} \mathrm{C}$$$\mathrm{S}_{8}(\text { rhombic }) \rightarrow \mathrm{S}_{8}(\text { monoclinic })$$ $$\Delta_{\mathrm{r}} H^{\circ}=3.213 \mathrm{kJ} / \mathrm{mol}-\mathrm{rxn} \quad \Delta_{\mathrm{r}} S^{\circ}=8.7 \mathrm{J} / \mathrm{K} \cdot \mathrm{mol}-\mathrm{rxn}$$ (a) Estimate \)\Delta_{r} G^{\circ}\( for the transition at \)80.0^{\circ} \mathrm{C}\( and \)110.0^{\circ} \mathrm{C} .\( What do these results tell you about the stability of the two forms of sulfur at each of these temperatures? (b) Calculate the temperature at which \)\Delta_{\mathrm{r}} G^{\circ}=0$ What is the significance of this temperature?

Calculate \(\Delta_{f} G^{\circ}\) for \(\mathrm{HI}(\mathrm{g})\) at \(350^{\circ} \mathrm{C},\) given the following equilibrium partial pressures: \(P\left(\mathrm{H}_{2}\right)=\) 0.132 bar, \(P\left(\mathrm{I}_{2}\right)=0.295\) bar, and \(P(\mathrm{HI})=1.61\) bar. At \(350^{\circ} \mathrm{C}\) and \(1 \mathrm{bar}, \mathrm{I}_{2}\) is a gas. $$1 / 2 \mathrm{H}_{2}(\mathrm{g})+1 / 2 \mathrm{I}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{HI}(\mathrm{g})$$

Titanium(IV) oxide is converted to titanium carbide with carbon at a high temperature. $$\mathrm{TiO}_{2}(\mathrm{s})+3 \mathrm{C}(\mathrm{s}) \rightarrow 2 \mathrm{CO}(\mathrm{g})+\mathrm{TiC}(\mathrm{s})$$ $$\begin{array}{lc} & \text { Free Energies of Formation at } \\ \text { Compound } & 727^{\circ} \mathrm{C}, \mathrm{kJ} / \mathrm{mol} \\ \hline \mathrm{TiO}_{2}(\mathrm{s}) & -757.8 \\ \mathrm{TiC}(\mathrm{s}) & -162.6 \\\ \mathrm{CO}(\mathrm{g}) & -200.2 \end{array}$$ (a) Calculate \(\Delta_{\mathrm{r}} G^{\circ}\) and \(K\) at \(727^{\circ} \mathrm{C}.\) (b) Is the reaction product-favored at equilibrium at this temperature? (c) How can the reactant or product concentrations be adjusted for the reaction to proceed at \(727^{\circ} \mathrm{C} ?\)

Mercury vapor is dangerous because breathing it brings this toxic element into the lungs. We wish to estimate the vapor pressure of mercury at two different temperatures from the following data: (TABLE CAN'T COPY) Estimate the temperature at which \(K_{\mathrm{p}}\) for the process \(\mathrm{Hg}(\ell) \rightleftarrows \mathrm{Hg}(\mathrm{g})\) is equal to 1.00 (and the vapor pressure of Hg is 1.00 bar). Next, estimate the temperature at which the vapor pressure is \((1 / 760)\) bar. (Experimental vapor pressures are \(1.00 \mathrm{mm} \mathrm{Hg}\) at \(126.2^{\circ} \mathrm{C}\) and 1.00 bar at \(356.6^{\circ} \mathrm{C} .\) ) (Note: The temperature at which \(P=1.00\) bar can be calculated from thermodynamic data. To find the other temperature, you will need to use the temperature for \(P=1.00\) bar and the Clausius-Clapeyron equation in Section 11.6.)

Explain why each of the following statements is incorrect. (a) Entropy increases in all spontaneous reactions. (b) Reactions with a negative free energy change \(\left(\Delta_{\mathrm{r}} G^{\circ}<0\right)\) are product-favored and occur with rapid transformation of reactants to products. (c) All spontaneous processes are exothermic. (d) Endothermic processes are never spontaneous.

Decide whether each of the following statements is true or false. If false, rewrite it to make it true. (a) The entropy of a substance increases on going from the liquid to the vapor state at any temperature. (b) An exothermic reaction will always be spontaneous. (c) Reactions with a positive \(\Delta_{r} H^{\circ}\) and a positive \(\Delta_{\mathrm{r}} S^{\circ}\) can never be product-favored. (d) If \(\Delta_{r} G^{\circ}\) for a reaction is negative, the reaction will have an equilibrium constant greater than 1.

Under what conditions is the entropy of a pure substance \(0 \mathrm{J} / \mathrm{K} \cdot \mathrm{mol} ?\) Could a substance at standard conditions at \(25^{\circ}\) C have a value of \(0 \mathrm{J} / \mathrm{K} \cdot\) mol? A negative entropy value? Are there any conditions under which a substance will have negative entropy? Explain your answer.

Write a chemical equation for the oxidation of \(\mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{g}) \mathrm{by} \mathrm{O}_{2}(\mathrm{g})\) to form \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) Defining this as the system: (a) Predict whether the signs of \(\Delta S^{\circ}\) (system), \(\Delta S^{\circ}\) (surroundings), and \(\Delta S^{\circ}\) (universe) will be greater than zero, equal to zero, or less than zero. Explain your prediction. (b) Predict the signs of \(\Delta_{\mathrm{r}} H^{\circ}\) and \(\Delta_{\mathrm{r}} G^{\circ} .\) Explain how you made this prediction. (c) Will the value of \(K_{\mathrm{p}}\) be very large, very small, or near \(1 ?\) Will the equilibrium constant, \(K_{\mathrm{p}}\), for this system be larger or smaller at temperatures greater than 298 K? Explain how you made this prediction.

The normal melting point of benzene, \(\mathrm{C}_{6} \mathrm{H}_{6},\) is \(5.5^{\circ} \mathrm{C} .\) For the process of melting, what is the sign of each of the following? (a) \(\Delta_{\mathrm{r}} H^{\circ}\) (b) \(\Delta_{\mathrm{r}} S^{\circ}\) (c) \(\Delta_{r} G^{\circ}\) at \(5.5^{\circ} \mathrm{C}\) (d) \(\Delta_{\mathrm{r}} G^{\circ}\) at \(0.0^{\circ} \mathrm{C}\) (e) \(\Delta_{r} G^{\circ}\) at \(25.0^{\circ} \mathrm{C}\)

For each of the following processes, predict the algebraic sign of \(\Delta_{r} H^{\circ}, \Delta_{r} S^{\circ},\) and \(\Delta_{r} G^{\circ} .\) No calculations are necessary; use your common sense. (a) The decomposition of liquid water to give gaseous oxygen and hydrogen, a process that requires a considerable amount of energy. (b) Dynamite is a mixture of nitroglycerin, \(\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{N}_{3} \mathrm{O}_{9},\) and diatomaceous earth. The explo- sive decomposition of nitroglycerin gives gaseous products such as water, \(\mathrm{CO}_{2}\), and others; much heat is evolved. (c) The combustion of gasoline in the engine of your car, as exemplified by the combustion of octane. $$2 \mathrm{C}_{8} \mathrm{H}_{18}(\mathrm{g})+25 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 16 \mathrm{CO}_{2}(\mathrm{g})+18 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$$

Iodine, I \(_{2}\), dissolves readily in carbon tetrachloride. For this process, \(\Delta H^{\circ}=0 \mathrm{kJ} / \mathrm{mol}\). $$\mathrm{I}_{2}(\mathrm{s}) \rightarrow \mathrm{I}_{2}\left(\text { in } \mathrm{CCl}_{4} \text { solution }\right)$$ What is the sign of \(\Delta_{r} G^{\circ} ?\) Is the dissolving process entropy-driven or enthalpy-driven? Explain briefly.

Determine if each of the following statements is true or false (a) For a reaction that can yield more than one product, the most stable product is always formed in the greatest amount. (b) For a reaction that can yield more than one product, the pathway that has the lowest activation energy always occurs more quickly. (c) Reactions that are thermodynamically favored are always fast. (d) Diamond is always more stable than graphite.