Chapter 19

Which substance has the higher entropy in each of the following pairs? (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 \(25^{\circ}\) 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 of the 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 \(\left.\mathrm{N}_{2}(\mathrm{g}) \text { at } 10 \text { bar pressure (both at } 298 \mathrm{K}\right)\)

Which substance has the higher entropy in each of the following pairs? (a) a sample of pure silicon (to be used in a computer chip) or a piece of silicon containing a trace of some other elements 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 \(\left.\mathrm{O}_{2}(\mathrm{g}) \text { at } 0.01 \text { bar pressure (both at } 298 \mathrm{K}\right)\)

By comparing the formulas for each pair of compounds, decide which is expected to have the higher entropy. Assume both are at the same temperature. Check your answers using data in Appendix L. (a) \(\mathrm{O}_{2}(\mathrm{g})\) or \(\mathrm{CH}_{3} \mathrm{OH}(\mathrm{g})\) (two substances with the same molar mass) (b) \(\mathrm{HF}(\mathrm{g}), \mathrm{HCl}(\mathrm{g}),\) or \(\mathrm{HBr}(\mathrm{g})\) (c) \(\mathrm{NH}_{4} \mathrm{Cl}(\mathrm{s})\) or \(\mathrm{NH}_{4} \mathrm{Cl}(\mathrm{aq})\) (d) HNOs \((\mathrm{g}), \mathrm{HNO}_{3}(\ell),\) or \(\mathrm{HNO}_{3}(\mathrm{aq})\)

Is the reaction $$ \mathrm{Si}(\mathrm{s})+2 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow \mathrm{SiH}_{4}(\mathrm{g}) $$ spontaneous? Answer this question by calculating \(\Delta S_{\mathrm{sw}}^{0}\) \(\Delta S_{\text {surr }}^{o},\) and \(\Delta S_{\text {unin. }}^{\circ}\) (The reactants and products are defined as the system and \(\mathrm{T}=298 \mathrm{K}\).)

Using values of \(\Delta H_{j}\) and \(S^{\circ},\) calculate the standard molar free energy of formation, \(\Delta G_{j}^{\circ},\) for each of the following: (a) \(\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{s})\) (b) \(\mathrm{Cl}(\mathrm{g})\) (c) \(\mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{s})\) Compare your calculated values of \(\Delta G_{1}^{\circ}\) with those listed in Appendix L. Which compounds are predicted to be formed spontancously?

Using values of \(\Delta G_{f}^{\circ},\) calculate \(\Delta G_{\text {rem }}^{\circ}\) for each of the following reactions. Which are product-favored? (a) \(\mathrm{HgS}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{Hg}(\ell)+\mathrm{SO}_{2}(\mathrm{g})\) (b) \(2 \mathrm{H}_{2} \mathrm{S}(\mathrm{g})+3 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+2 \mathrm{SO}_{2}(\mathrm{g})\) (c) \(\operatorname{sic} \mathrm{l}_{4}(\mathrm{g})+2 \mathrm{Mg}(\mathrm{s}) \longrightarrow 2 \mathrm{MgCl}_{2}(\mathrm{s})+\mathrm{Si}(\mathrm{s})\)

Determine whether each of the reactions listed below is entropy-favored or -disfavored under standard conditions. Predict how an increase in temperature will affect the value of \(\Delta G_{\text {ren }}^{\circ}\) (a) \(\mathrm{I}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{I}(\mathrm{g})\) (b) \(2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{SO}_{3}(\mathrm{g})\) (c) \(\operatorname{sicl}_{1}(g)+2 H_{2} O(\ell) \longrightarrow S i O_{2}(s)+4 H C l(g)\) (d) \(\mathrm{P}_{4}(\mathrm{s}, \text { white })+6 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow 4 \mathrm{PH}_{3}(\mathrm{g})\)

The formation of \(\mathrm{NO}(\mathrm{g})\) from its elements $$ \frac{1}{2} \mathrm{N}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{NO}(\mathrm{g}) $$ has a standard free energy change, \(\Delta G^{\circ},\) of \(+86.58 \mathrm{kJ} / \mathrm{mol}\) at \(25^{\circ} \mathrm{C}\). Calculate \(K_{\mathrm{p}}\) at this temperature. Comment on the connection between the sign of \(\Delta G^{\circ}\) and the magnitude of \(\bar{K}_{\mathrm{p}^{*}}\)

The formation of \(\mathbf{O}_{3}(\mathrm{g})\) from \(\mathbf{O}_{2}(\mathrm{g})\) has a standard free energy change, \(\Delta G^{\circ},\) of \(+163.2 \mathrm{kJ} / \mathrm{mol}\) at \(25^{\circ} \mathrm{C} .\) Calculate \(K_{\mathrm{p}}\) at this temperature. Comment on the connection between the sign of \(\Delta G^{\circ}\) and the magnitude of \(K_{\mathrm{p}}\)

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) a liquid to vapor usansformation and (b) a vapor to liquid transformation at \(35.0^{\circ} \mathrm{C}\)

When calcium carbonate is heated strongly, \(\mathrm{CO}_{2}\) gas is evolved. The equilibrium pressure of the gas is 1.00 bar at \(897^{\circ} \mathrm{C},\) and \(\Delta H_{\mathrm{rxn}}^{\mathrm{e}}\) at \(298 \mathrm{K}=179.0 \mathrm{kJ}\) $$ \mathrm{CaCO}_{3}(\mathrm{s}) \longrightarrow \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g}) $$ Estimate the value of \(\Delta S^{\circ}\) at \(897^{\circ} \mathrm{C}\) for the reaction.

Most metal oxides can be reduced with hydrogen to the pure metal. (Although such reactions work well, this expensive method is not used often for large- scale preparations.) The equilibrium constant for the reduction of iron(II) oxide is 0.422 at \(700^{\circ} \mathrm{C}\). Fstimate \(\Delta G_{\text {ren }}^{\circ}\) $$ \mathrm{FeO}(\mathrm{s})+\mathrm{H}_{2}(\mathrm{g}) \longrightarrow \mathrm{Fe}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) $$

Almost 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 benzenc is cyclohexanc, \(\mathbf{C}_{6} \mathbf{H}_{12}\) $$ \begin{aligned} \mathrm{C}_{6} \mathrm{H}_{6}(\ell)+3 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow & \mathrm{C}_{6} \mathrm{H}_{12}(\ell) \\ \Delta H_{\mathrm{ran}}^{\circ}=-206.7 \mathrm{k} \mathrm{J} ; \quad \Delta S_{\mathrm{ran}}^{\circ} &=-361.5 \mathrm{J} / \mathrm{K} \end{aligned} $$ Is this reaction predicted to be spontancous under standard conditions at \(25^{\circ} \mathrm{C} ?\) Is the reaction enthalpy-or entropy-driven?

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

Based on your experience and common sense, which of the following processes would you describe as productfavored and which as reactant-favored under standard conditions? (a) \(\mathrm{Hg}(\ell) \longrightarrow \mathrm{Hg}(\mathrm{s})\) (b) \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \longrightarrow \mathrm{H}_{2} \mathrm{O}(\ell)\) (c) \(2 \mathrm{HgO}(\mathrm{s}) \longrightarrow \mathrm{Hg}(\ell)+\mathrm{O}_{2}(\mathrm{g})\) (d) \(\mathrm{C}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{g})\) (e) \(\mathrm{NaCl}(\mathrm{s}) \longrightarrow \mathrm{NaCl}(\mathrm{aq})\) (f) \(\operatorname{CaCO}_{3}(\mathrm{s}) \longrightarrow \mathrm{Ca}^{2+}(\mathrm{aq})+\mathrm{CO}_{3}^{2-}(\mathrm{aq})\)

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

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 \(\Delta H_{\mathrm{rxn}}^{\circ}\) and a positive \(\Delta S_{\mathrm{rxm}}^{\circ}\) can never be product-favored. (d) If \(\Delta G_{\text {ran }}^{\circ}\) 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 \(0 \mathrm{J} / \mathrm{K} \cdot\) mol? Could a substance at standard conditions 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.

In Chapter 14 you learned that entropy, as well as enthalpy, plays a role in the solution process. If \(\Delta H^{\circ}\) for the solution process is zero, explain how the process can be driven by entropy.

Write a chemical equation for the oxidation of \(\mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{g})\) 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 \(\Delta S_{\mathrm{m}}^{\circ}, \Delta S_{\text {surr }}^{\mathrm{o}},\) and \(\Delta S_{\text {univ }}^{\mathrm{e}}\) will be greater than zero, equal to zero, or less than zero. Explain your prediction. (b) Predict the signs of \(\Delta H^{\circ}\) and \(\Delta G^{\circ} .\) 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, \(K_{p},\) for this system be larger or smaller at temperatures greater than \(298 \mathrm{K} ?\) 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) \(\Delta H^{\circ}\) (c) \(\Delta G^{\circ}\) at \(5.5^{\circ} \mathrm{C}\) (c) \(\Delta G^{\circ}\) at \(25.0^{\circ} \mathrm{C}\) (b) \(\Delta S^{\circ}\) (d) \(\Delta G^{\circ}\) at \(0.0^{\circ} \mathrm{C}\)

Explain why the entropy of the system increases on dissolving solid NaCl in water \(| S^{\circ}[\mathrm{NaCl}(\mathrm{s})]=72.1 \mathrm{J} / \mathrm{K} \cdot\) mol and \(\left.S^{0}[\mathrm{NaCl}(\mathrm{aq})]=115.5 \mathrm{J} / \mathrm{K} \cdot \mathrm{mol}\right]\)

For each of the following processes, give the algebraic sign of \(\Delta H^{\circ}, \Delta S^{\circ},\) and \(\Delta G^{\circ} .\) 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, \(C_{3} H_{5} N_{3} O_{9},\) and diatomaceous earth. The explosive decomposition of nitroglycerin gives gaseous products such as water, CO \(_{2}\), and others; much heat is cvolved. (c) The combustion of gasoline in the engine of your car, as exemplified by the combustion of octane. \(2 \mathrm{C}_{8} \mathrm{H}_{1 \mathrm{s}}(\mathrm{g})+25 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 16 \mathrm{CO}_{2}(\mathrm{g})+18 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\)

If gaseous \(\mathrm{H}_{2}\) and \(\mathrm{O}_{2}\) are carefully mixed and left alone, they can remain intact for millions of years. Is this "stability" a function of thermodynamics or of kinetics? (You may wish to revicw the General ChemistryNow CD-ROM or website Screen \(6.3 .)\)