Chapter 19

What values of $\mathrm{\Delta }H,\mathrm{\Delta }S,$ and $\mathrm{\Delta }G$ would you expect for the formation of an ideal solution of liquid components? (Is each value positive, negative, or zero?)

Explain why (a) some exothermic reactions do not occur spontaneously, and (b) some reactions in which the entropy of the system increases do not occur spontaneously.

Explain why you would expect a reaction of the type $\mathrm{AB}(\mathrm{g})⟶\mathrm{A}(\mathrm{g})+\mathrm{B}(\mathrm{g})$ always to be spontaneous at high rather than at low temperatures.

From the data given in the following table, determine $\mathrm{\Delta }{S}^{\circ }$ for the reaction ${\mathrm{NH}}_3(\mathrm{g})+\mathrm{HCl}(\mathrm{g})⟶$ ${\mathrm{NH}}_4\mathrm{Cl}(\mathrm{s}).$ All data are at $298\mathrm{K}$ $$\overline{)\begin{array}{lcc}& \mathrm{\Delta }{H}_f^{\circ },\mathrm{kJ}{\mathrm{mol}}^{-1}& \mathrm{\Delta }{G}_{f,}^{\circ }\mathrm{kJ}{\mathrm{mol}}^{-1}\\ {\mathrm{NH}}_3(\mathrm{g})& -46.11& -16.48\\ \mathrm{HCl}(\mathrm{g})& -92.31& -95.30\\ {\mathrm{NH}}_4\mathrm{Cl}(\mathrm{s})& -314.4& -202.9\end{array}}$$

Use data from Appendix D to determine values of $\mathrm{\Delta }{G}^{\circ }$ for the following reactions at ${25}^{\circ }\mathrm{C}$ (a) ${\mathrm{C}}_2{\mathrm{H}}_2(\mathrm{g})+2{\mathrm{H}}_2(\mathrm{g})⟶{\mathrm{C}}_2{\mathrm{H}}_6(\mathrm{g})$ (b) $2{\mathrm{SO}}_3(\mathrm{g})⟶2{\mathrm{SO}}_2(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})$ (c) ${\mathrm{Fe}}_3{\mathrm{O}}_4(\mathrm{s})+4{\mathrm{H}}_2(\mathrm{g})⟶3\mathrm{Fe}(\mathrm{s})+4{\mathrm{H}}_2\mathrm{O}(\mathrm{g})$ (d) $2\mathrm{Al}(\mathrm{s})+6{\mathrm{H}}^{+}(\mathrm{aq})⟶2{\mathrm{Al}}^{3+}(\mathrm{aq})+3{\mathrm{H}}_2(\mathrm{g})$

At $298\mathrm{K},$ for the reaction $2{\mathrm{PCl}}_3(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})\stackrel{\text{ Lest }}{⟶}$ $2{\mathrm{POCl}}_3(1),\mathrm{\Delta }{H}^{\circ }=-620.2\mathrm{kJ}$ and the standard molar entropies are ${\mathrm{PCl}}_3(\mathrm{g}),311.8{\mathrm{JK}}^{-1};{\mathrm{O}}_2(\mathrm{g}),205.1{\mathrm{JK}}^{-1}$ and ${\mathrm{POCl}}_3(1),222.4{\mathrm{JK}}^{-1}.$ Determine (a) $\mathrm{\Delta }{G}^{\circ }$ at $298\mathrm{K}$ and (b) whether the reaction proceeds spontaneously in the forward or the reverse direction when reactants and products are in their standard states.

At $298\mathrm{K},$ for the reaction $2{\mathrm{H}}^{+}(\mathrm{aq})+2{\mathrm{Br}}^{-}(\mathrm{aq})+$ $2{\mathrm{NO}}_2(\mathrm{g})⟶{\mathrm{Br}}_2(1)+2{\mathrm{HNO}}_2(\mathrm{aq}),\mathrm{\Delta }{H}^{\circ }=-61.6\mathrm{kJ}$ and the standard molar entropies are ${\mathrm{H}}^{+}(\mathrm{aq}),0{\mathrm{JK}}^{-1}$ ${\mathrm{Br}}^{-}(\mathrm{aq}),82.4{\mathrm{JK}}^{-1};{\mathrm{NO}}_2(\mathrm{g}),240.1{\mathrm{JK}}^{-1};{\mathrm{Br}}_2(1),152.2$ $\mathrm{J}{\mathrm{K}}^{-1};{\mathrm{HNO}}_2(\mathrm{aq}),135.6{\mathrm{JK}}^{-1}.$ Determine (a) $\mathrm{\Delta }{G}^{\circ }$ at 298 K and (b) whether the reaction proceeds spontaneously in the forward or the reverse direction when reactants and products are in their standard states.

The following standard Gibbs energy changes are given for ${25}^{\circ }\mathrm{C}$ (1) ${\mathrm{N}}_2(\mathrm{g})+3{\mathrm{H}}_2(\mathrm{g})⟶2{\mathrm{NH}}_3(\mathrm{g})$ $\mathrm{\Delta }{G}^{\circ }=-33.0\mathrm{kJ}$ (2) $4{\mathrm{NH}}_3(\mathrm{g})+5{\mathrm{O}}_2(\mathrm{g})⟶4\mathrm{NO}(\mathrm{g})+6{\mathrm{H}}_2\mathrm{O}(1)$ $\mathrm{\Delta }{G}^{\circ }=-1010.5\mathrm{kJ}$ (3) ${\mathrm{N}}_2(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})⟶2\mathrm{NO}(\mathrm{g})$ $\mathrm{\Delta }{G}^{\circ }=+173.1\mathrm{kJ}$ (4) ${\mathrm{N}}_2(\mathrm{g})+2{\mathrm{O}}_2(\mathrm{g})⟶2{\mathrm{NO}}_2(\mathrm{g})$ $\mathrm{\Delta }{G}^{\circ }=+102.6\mathrm{kJ}$ (5) $2{\mathrm{N}}_2(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})⟶2{\mathrm{N}}_2\mathrm{O}(\mathrm{g})$ $\mathrm{\Delta }{G}^{\circ }=+208.4\mathrm{kJ}$ Combine the preceding equations, as necessary, to obtain $\mathrm{\Delta }{G}^{\circ }$ values for each of the following reactions. (a) ${\mathrm{N}}_2\mathrm{O}(\mathrm{g})+\frac{3}{2}{\mathrm{O}}_2(\mathrm{g})⟶2{\mathrm{NO}}_2(\mathrm{g})\mathrm{\Delta }{G}^{\circ }=?$ (b) $2{\mathrm{H}}_2(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})⟶2{\mathrm{H}}_2\mathrm{O}(1)\mathrm{\Delta }{G}^{\circ }=?$ (c) $2{\mathrm{NH}}_3(\mathrm{g})+2{\mathrm{O}}_2(\mathrm{g})⟶{\mathrm{N}}_2\mathrm{O}(\mathrm{g})+3{\mathrm{H}}_2\mathrm{O}(1)$ $\mathrm{\Delta }{G}^{\circ }=?$ Of reactions (a), (b), and (c), which would tend to go to completion at ${25}^{\circ }\mathrm{C}$, and which would reach an equilibrium condition with significant amounts of all reactants and products present?

The following standard Gibbs energy changes are given for ${25}^{\circ }\mathrm{C}$ (1) ${\mathrm{SO}}_2(\mathrm{g})+3\mathrm{CO}(\mathrm{g})⟶\mathrm{COS}(\mathrm{g})+2{\mathrm{CO}}_2(\mathrm{g})$ $\mathrm{\Delta }{G}^{\circ }=-246.4\mathrm{kJ}$ (2) ${\mathrm{CS}}_2(\mathrm{g})+{\mathrm{H}}_2\mathrm{O}(\mathrm{g})⟶\mathrm{COS}(\mathrm{g})+{\mathrm{H}}_2\mathrm{S}(\mathrm{g})$ $\mathrm{\Delta }{G}^{\circ }=-41.5\mathrm{kJ}$ (3) $\mathrm{CO}(\mathrm{g})+{\mathrm{H}}_2\mathrm{S}(\mathrm{g})⟶\mathrm{COS}(\mathrm{g})+{\mathrm{H}}_2(\mathrm{g})$ $\mathrm{\Delta }{G}^{\circ }=+1.4\mathrm{kJ}$ (4) $\mathrm{CO}(\mathrm{g})+{\mathrm{H}}_2\mathrm{O}(\mathrm{g})⟶{\mathrm{CO}}_2(\mathrm{g})+{\mathrm{H}}_2(\mathrm{g})$ $\mathrm{\Delta }{G}^{\circ }=-28.6\mathrm{kJ}$ Combine the preceding equations, as necessary, to obtain $\mathrm{\Delta }{G}^{\circ }$ values for the following reactions. (a) $\mathrm{COS}(\mathrm{g})+2{\mathrm{H}}_2\mathrm{O}(\mathrm{g})⟶$ $\begin{array}{rl}{\mathrm{SO}}_2(\mathrm{g})+\mathrm{CO}(\mathrm{g})+2{\mathrm{H}}_2(\mathrm{g})& \mathrm{\Delta }{G}^{\circ }=?\end{array}$ (b) $\cos (g)+3{\mathrm{H}}_2\mathrm{O}(\mathrm{g})⟶$ ${\mathrm{SO}}_2(\mathrm{g})+{\mathrm{CO}}_2(\mathrm{g})+3{\mathrm{H}}_2(\mathrm{g})\mathrm{\Delta }{G}^{\circ }=?$ $+{\mathrm{H}}_{\mathrm{O}}\mathrm{C}(\mathrm{d})={\mathrm{CO}}_{-}^{\circ }\mathrm{G})+{\mathrm{H}}_{-}^{-}\mathrm{S}(\mathrm{q})$ (c) $\cos (\mathrm{g})+{\mathrm{H}}_2\mathrm{O}(\mathrm{g})⟶{\mathrm{CO}}_2(\mathrm{g})+{\mathrm{H}}_2\mathrm{S}(\mathrm{g})$ $\mathrm{\Delta }{G}^{\circ }=?$ Of reactions (a), (b), and (c), which is spontaneous in the forward direction when reactants and products are present in their standard states?

For one of the following reactions, $K_c{K}_p=K.$ Identify that reaction. For the other two reactions, what is the relationship between $K_c,{\overline{K}}_{\mathrm{p}},$ and $K?$ Explain. (a) $2{\mathrm{SO}}_2(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})\rightleftharpoons 2{\mathrm{SO}}_3(\mathrm{g})$ (b) $\mathrm{HI}(\mathrm{g})\rightleftharpoons \frac{1}{2}{\mathrm{H}}_2(\mathrm{g})+\frac{1}{2}{\mathrm{I}}_2(\mathrm{g})$ (c) ${\mathrm{NH}}_4{\mathrm{HCO}}_3(\mathrm{s})\rightleftharpoons {\mathrm{NH}}_3(\mathrm{g})+{\mathrm{CO}}_2(\mathrm{g})+{\mathrm{H}}_2\mathrm{O}(1)$