Chapter 19

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 Al \(^{3+}\) ions in the crystalline lattice are replaced with \(\left.\mathrm{Cr}^{3+} \text { ions }\right)\) (d) one mole of \(\mathrm{N}_{2}(\mathrm{g})\) at 1 bar pressure or one mole of \(\left.\mathrm{N}_{2}(\mathrm{g}) \text { at } 10 \text { bar pressure (both at } 298 \mathrm{K}\right)\)

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 \(\left.\mathrm{O}_{2}(\mathrm{g}) \text { at } 0.01 \text { bar pressure (both at } 298 \mathrm{K}\right)\)

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) \(\mathrm{N}_{2}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{NO}_{2}(\mathrm{g})\) (b) \(2 \mathrm{C}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{CO}(\mathrm{g})\) (c) \(\mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g}) \rightarrow \mathrm{CaCO}_{3}(\mathrm{s})\) (d) \(2 \mathrm{NaCl}(\mathrm{s}) \rightarrow 2 \mathrm{Na}(\mathrm{s})+\mathrm{Cl}_{2}(\mathrm{g})\)

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 standard free energy change, \(\Delta_{\mathrm{r}} G^{\circ}\), for the formation of \(\mathrm{NO}(\mathrm{g})\) from its elements is \(+86.58 \mathrm{kJ} / \mathrm{mol}\) at \(25^{\circ} \mathrm{C} .\) Calculate \(K_{\mathrm{p}}\) at this temperature for the equilibrium $$1 / 2 \mathrm{N}_{2}(\mathrm{g})+1 / 2 \mathrm{O}_{2}(\mathrm{g}) \rightleftarrows \mathrm{NO}(\mathrm{g})$$ Comment on the sign of \(\Delta G^{\circ}\) 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 \(+163.2 \mathrm{kJ} / \mathrm{mol}\) 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 \(\Delta G^{\circ}\) and the magnitude of \(K_{\mathrm{p}}.\)

About 5 billion kilograms of benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}\), is 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, \(\mathrm{C}_{6} \mathrm{H}_{12}.\) $$\begin{aligned} \mathrm{C}_{6} \mathrm{H}_{6}(\ell)+3 \mathrm{H}_{2}(\mathrm{g}) \rightarrow & \mathrm{C}_{6} \mathrm{H}_{12}(\ell) \\ \Delta_{\mathrm{r}} H^{\circ}=-206.7 \mathrm{kJ} ; \Delta_{\mathrm{r}} S^{\circ} &=-361.5 \mathrm{J} / \mathrm{K} \end{aligned}$$ Is this reaction predicted to be product-favored at equilibrium at \(25^{\circ} \mathrm{C} ?\) Is the reaction enthalpy- or entropy-driven?

Hydrogenation, the addition of hydrogen to an organic compound, is an industrially important reaction. Calculate \(\Delta_{\mathrm{r}} H^{\circ}, \Delta_{\mathrm{r}} S^{\circ},\) and \(\Delta_{\mathrm{r}} G^{\circ}\) for the hydrogenation of octene, \(\mathrm{C}_{8} \mathrm{H}_{16},\) to give octane, \(\mathrm{C}_{8} \mathrm{H}_{18},\) at \(25^{\circ} \mathrm{C} .\) Is the reaction product- or reactant-favored at equilibrium? $$\mathrm{C}_{8} \mathrm{H}_{16}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g}) \rightarrow \mathrm{C}_{8} \mathrm{H}_{18}(\mathrm{g})$$ Along with data in Appendix \(L\), the following information is needed for this calculation. $$\begin{array}{lll} \text { Compound } & \Delta_{f} H^{\circ}(\mathrm{k} \mathrm{J} / \mathrm{mol}) & S^{\circ}(\mathrm{J} / \mathrm{K} \cdot \mathrm{mol}) \\ \hline \text { Octene } & -82.93 & 462.8 \\ \text { Octane } & -208.45 & 463.639 \\ \hline \end{array}$$

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, \(\Delta S^{\circ}\), 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 \(39.3 \mathrm{kJ} / \mathrm{mol}\).

The following reaction is reactant-favored at equilibrium at room temperature. $$\operatorname{COCl}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})$$ Will raising or lowering the temperature make it product-favored?

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 \(\Delta_{r} H^{\circ}\) and \(\Delta_{\mathrm{r}} S^{\circ}\) for the reaction. Verify your prediction with a calculation.

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

The equilibrium constant for the butane \(\rightleftarrows\) isobutane equilibrium at \(25^{\circ} \mathrm{C}\) is \(2.50 .\) Calculate \(\Delta_{\mathrm{r}} G^{\circ}\) at this temperature in units of \(\mathrm{kJ} / \mathrm{mol}\).

Sulfur undergoes a phase transition between 80 and \(100^{\circ} \mathrm{C}.\) $$\begin{array}{c} \mathrm{S}_{8}(\text { rhombic }) \rightarrow \mathrm{S}_{8}(\text { monoclinic }) \\ \Delta_{\mathrm{r}} H^{\circ}=3.213 \mathrm{kJ} / \text { mol-rxn } \Delta_{\mathrm{r}} S^{\circ}=8.7 \mathrm{J} / \mathrm{K} \cdot \text { mol- rxn } \end{array}$$ (a) Estimate \(\Delta_{\mathrm{r}} G^{\circ}\) 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 \(\Delta_{r} G^{\circ}=0 .\) What is the significance of this temperature?

Titanium(IV) oxide is converted to titanium carbide with carbon at a high temperature. $$\mathrm{TiO}_{2}(\mathrm{s})+3 \mathrm{C}(\mathrm{s}) \rightarrow 2 \mathrm{CO}(\mathrm{g})+\mathrm{TiC}(\mathrm{s})$$ $$\begin{array}{lc} & \text { Free Energies of Formation } \\ \text { Compound } & \text { at } 727^{\circ} \mathrm{C}, \mathrm{kJ} / \mathrm{mol} \\ \hline \mathrm{TiO}_{2}(\mathrm{s}) & -757.8 \\ \mathrm{TiC}(\mathrm{s}) & -162.6 \\ \mathrm{CO}(\mathrm{g}) & -200.2 \\ \hline \end{array}$$ (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 be spontaneous at \(727^{\circ} \mathrm{C} ?\)

Cisplatin [ cis-diamminedichloroplatinum(II)] is a potent treatment for certain types of cancers, but the trans isomer is not effective. What is the equilibrium constant at 298 K for the transformation of the cis to the trans isomer? Which is the favored isomer at \(298 \mathrm{K},\) the cis or the trans isomer? $$\begin{array}{lll} \text { Compound } & \left.\Delta_{f} H^{\circ}(\mathrm{k}] / \mathrm{mol}, 298 \mathrm{K}\right) & \Delta_{f} G^{\circ}(\mathrm{k} \mathrm{J} / \mathrm{mol}, 298 \mathrm{K}) \\ \hline \left. \text { Cis-Pt(NH }_{3}\right)_{2} \mathrm{Cl}_{2} & -467.4 & -228.7 \\\ \text { Trans-Pt(NH_) }_{2} \mathrm{Cl}_{2} & -480.3 & -222.8 \\ \hline\end{array}$$

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: $$\begin{array}{lccc} & \Delta_{f} H^{\circ}(\mathrm{k} \mathrm{J} / \mathrm{mol}) & S^{\circ}(\mathrm{J} / \mathrm{K} \cdot \mathrm{mol}) & \left.\Delta_{f} G^{\circ}(\mathrm{k}) / \mathrm{mol}\right) \\ \hline \mathrm{Hg}(\ell) & 0 & 76.02 & 0 \\ \mathrm{Hg}(\mathrm{g}) & 61.38 & 174.97 & 31.88 \\ \hline \end{array}$$ 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 whch 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 on page 570.)

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 \(\Delta_{\mathrm{r}} H^{\circ}\) and a positive \(\Delta_{\mathrm{r}} S^{\circ}\) can never be product-favored. (d) If \(\Delta_{\mathrm{r}} G^{\circ}\) for a reaction is negative, the reaction will have an equilibrium constant greater than 1.

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) \(\Delta H^{\circ}\) (b) \(\Delta S^{\circ}\) (c) \(\Delta G^{\circ}\) at \(5.5^{\circ} \mathrm{C}\) (d) \(\Delta G^{\circ}\) at \(0.0^{\circ} \mathrm{C}\) (e) \(\Delta G^{\circ}\) at \(25.0^{\circ} \mathrm{C}\)

For each of the following processes, predict the algebraic sign of \(\Delta_{\mathrm{r}} H^{\circ}, \Delta_{\mathrm{r}} S^{\circ},\) and \(\Delta_{\mathrm{r}} G^{\circ} .\) 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 explosive 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. $$2 \mathrm{C}_{8} \mathrm{H}_{18}(\mathrm{g})+25 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 16 \mathrm{CO}_{2}(\mathrm{g})+18 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$$

Oxygen dissolved in water can cause corrosion in hot-water heating systems. To remove oxygen, hydrazine \(\left(\mathrm{N}_{2} \mathrm{H}_{4}\right)\) is often added. Hydrazine reacts with dissolved \(\mathrm{O}_{2}\) to form water and \(\mathrm{N}_{2}.\) (a) Write a balanced chemical equation for the reaction of hydrazine and oxygen. Identify the oxidizing and reducing agents in this redox reaction. (b) Calculate \(\Delta_{\mathrm{r}} H^{\circ}, \Delta_{\mathrm{r}} S^{\circ},\) and \(\Delta_{\mathrm{r}} G^{\circ}\) for this reaction involving \(1 \mathrm{mol}\) of \(\mathrm{N}_{2} \mathrm{H}_{4}\) at \(25^{\circ} \mathrm{C}.\) (c) Because this is an exothermic reaction, energy is evolved as heat. What temperature change is expected in a heating system containing \(5.5 \times 10^{4} \mathrm{L}\) of water? (Assume no energy is lost to the surroundings.) (d) The mass of a hot-water heating system is \(5.5 \times 10^{4}\) kg. What amount of \(\mathrm{O}_{2}\) (in moles) would be present in this system if it is filled with water saturated with O \(_{2} ?\) (The solubility of \(\mathrm{O}_{2}\) in water at \(25^{\circ} \mathrm{C}\) is 0.000434 g per \(100 \mathrm{g}\) of water. (e) Assume hydrazine is available as a \(5.0 \%\) solution in water. What mass of this solution should be added to totally consume the dissolved \(\mathrm{O}_{2}[\text { described in part }(\mathrm{d})] ?\) (f) Assuming the \(\mathrm{N}_{2}\) escapes as a gas, calculate the volume of \(\mathrm{N}_{2}(\mathrm{g})\) (measured at \(273 \mathrm{K}\) and \(1.00 \mathrm{atm}\) ) that will be produced.

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.