Chapter 16

Suppose that at a certain temperature \(T,\) a chemical reaction is found to have a standard equilibrium constant \(K^{\circ}\) of 1.0 . Indicate whether each statement is true or false and explain why. (a) The enthalpy change for the reaction, \(\Delta_{\mathrm{r}} H^{\circ},\) is zero. (b) The entropy change for the reaction, \(\Delta_{t} S^{\circ},\) is zero. (c) The Gibbs free energy change for the reaction, \(\Delta_{r} G^{\circ},\) is zero. (d) \(\Delta_{\mathrm{r}} H^{\circ}\) and \(\Delta_{\mathrm{r}} \mathrm{S}^{\circ}\) have the same sign. (e) \(\Delta_{\mathrm{r}} H^{\circ} / T=\Delta_{\mathrm{r}} S^{\circ}\) at the temperature \(T\).

When you eat a candy bar, how does your body store the Gibbs free energy that is released during oxidation of the sugars (glucose and other carbohydrates) in the candy bar? What was the original source of the Gibbs free energy needed to synthesize the sugars before they went into the candy bar?

Explain how biological systems make use of coupled reactions to maintain the high degree of order found in all living organisms.

How can kinetically stable substances exist at all if they are not thermodynamically stable?

Criticize this statement: Provided it occurs at an appreciable rate, any chemical reaction for which \(\Delta_{\mathrm{r}} G<0\) will proceed until all reactants have been converted to products.

Calculate the entropy change for formation of exactly \(1 \mathrm{~mol}\) of each of these gaseous hydrocarbons under standard conditions from carbon (graphite) and hydrogen. What trend do you see in these values? Does \(\Delta_{r} S^{\circ}\) increase or decrease on adding \(\mathrm{H}\) atoms? (a) acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{~g})\) (b) ethylene, \(\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})\) (c) ethane, \(\mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{~g})\)

Without consulting tables of \(\Delta_{\mathrm{f}} H^{\circ}, S^{\circ},\) or \(\Delta_{\mathrm{f}} G^{\circ}\) values, predict which of these reactions is (i) always product-favored. (ii) product-favored at low temperatures, but not productfavored at high temperatures. (iii) not product-favored at low temperatures, but productfavored at high temperatures. (iv) never product-favored. (a) \(2 \mathrm{NO}_{2}(\mathrm{~g}) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g})\) (b) \(\mathrm{C}_{5} \mathrm{H}_{12}(\mathrm{~g})+8 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 5 \mathrm{CO}_{2}(\mathrm{~g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (c) \(\mathrm{P}_{4}(\mathrm{~g})+10 \mathrm{~F}_{2}(\mathrm{~g}) \longrightarrow 4 \mathrm{PF}_{5}(\mathrm{~g})\)

Using the reactions $$ \begin{array}{l} 2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(\ell) \\ 2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \end{array} $$ as an example, explain why it may be incorrect to assun for reactions involving solids or liquids that \(\Delta_{\mathrm{r}} S^{\circ}\) and \(\Delta_{1} H^{\circ}\) do not change appreciably with increasing temperature.

For the reaction $$ \mathrm{CH}_{3} \mathrm{OH}(\ell)+\frac{3}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(\ell)+\mathrm{CO}_{2}(\mathrm{~g}) $$ the value of \(\Delta_{\mathrm{r}} G^{\circ}\) is \(-702.35 \mathrm{~kJ} / \mathrm{mol}\) at \(25^{\circ} \mathrm{C}\). Other data $$ \text { at } 25^{\circ} \mathrm{C} \text { are } $$ $$ \begin{array}{lcc} \hline & \Delta_{\mathrm{f}} H^{\circ}(\mathrm{k} \mathrm{J} / \mathrm{mol}) & \mathrm{S}^{\circ}\left(\mathrm{J} \mathrm{mol}^{-1} \mathrm{~K}^{-1}\right) \\\ \hline \mathrm{CH}_{3} \mathrm{OH}(\ell) & -238.66 & 126.8 \\ \mathrm{H}_{2} \mathrm{O}(\ell) & -285.83 & 69.91 \\ \mathrm{CO}_{2}(\mathrm{~g}) & -393.509 & 213.74 \\ \hline \end{array} $$ Calculate the standard molar entropy, \(S^{\circ},\) for \(\mathrm{O}_{2}(\mathrm{~g})\)

The standard equilibrium constant is \(2.1 \times 10^{9}\) for this reaction at \(25^{\circ} \mathrm{C}\) $$ \mathrm{Zn}^{2+}(\mathrm{aq})+4 \mathrm{NH}_{3}(\mathrm{aq}) \rightleftharpoons \mathrm{Zn}\left(\mathrm{NH}_{3}\right)_{4}^{2+}(\mathrm{aq}) $$ (a) Calculate \(\Delta_{r} G^{\circ}\) at this temperature. (b) If standard-state concentrations of the reactants and products are combined, in which direction will the reaction proceed? (c) Calculate \(\Delta_{\mathrm{r}} G\) when \(\left[\mathrm{Zn}\left(\mathrm{NH}_{3}\right)_{4}^{2+}\right]=0.010 \mathrm{M},\left[\mathrm{Zn}^{2+}\right]=\) $$ 0.0010 \mathrm{M}, \text { and }\left[\mathrm{NH}_{3}\right]=3.5 \times 10^{-4} \mathrm{M} $$