Chapter 18

Large quantities of hydrogen are needed for the synthesis of ammonia. One preparation of hydrogen involves the reaction between carbon monoxide and steam at \(300^{\circ} \mathrm{C}\) in the presence of a copper-zinc catalyst: $$ \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) $$.

Consider two carboxylic acids (acids that contain the \(-\mathrm{COOH}\) group \(): \mathrm{CH}_{3} \mathrm{COOH}\) (acetic acid, \(K_{\mathrm{a}}=1.8 \times 10^{-5}\) ) and \(\mathrm{CH}_{2} \mathrm{ClCOOH}\) (chloroacetic acid, \(K_{\mathrm{a}}=1.4 \times 10^{-3}\) ). (a) Calculate \(\Delta G^{\circ}\) for the ionization of these acids at \(25^{\circ} \mathrm{C}\) (b) From the equation \(\Delta G^{\circ}=\Delta H^{\circ}-T \Delta S^{\circ},\) we see that the contributions to the \(\Delta G^{\circ}\) term are an enthalpy term \(\left(\Delta H^{\circ}\right)\) and a temperature times entropy term \(\left(T \Delta S^{\circ}\right)\). These contributions are listed below for the two acids: Which is the dominant term in determining the value of \(\Delta G^{\circ}\) (and hence \(K_{\mathrm{a}}\) of the acid)? (c) What processes contribute to \(\Delta H^{\circ} ?\) (Consider the ionization of the acids as a Bronsted acid-base reaction.) (d) Explain why the \(T \Delta S^{\circ}\) term is more negative for \(\mathrm{CH}_{3} \mathrm{COOH}\).

Derive the following equation $$ \Delta G=R T \ln (Q / K) $$ where \(Q\) is the reaction quotient and describe how you would use it to predict the spontaneity of a reaction.

Entropy has sometimes been described as "time's arrow" because it is the property that determines the forward direction of time. Explain.

A student looked up the \(\Delta G_{\mathrm{f}}^{\circ}, \Delta H_{\mathrm{f}}^{\circ}\), and \(S^{\circ}\) values for \(\mathrm{CO}_{2}\) in Appendix 2. Plugging these values into Equation \((18.10),\) he found that \(\Delta G_{\mathrm{f}}^{\circ} \neq \Delta H_{\mathrm{f}}^{\circ}-T S^{\circ}\) at \(298 \mathrm{~K}\). What is wrong with his approach?

As an approximation, we can assume that proteins exist either in the native (or physiologically functioning) state and the denatured state $$\text { native } \rightleftharpoons \text { denatured }$$ The standard molar enthalpy and entropy of the denaturation of a certain protein are \(512 \mathrm{~kJ} / \mathrm{mol}\) and \(1.60 \mathrm{~kJ} / \mathrm{K} \cdot \mathrm{mol}\), respectively. Comment on the signs and magnitudes of these quantities, and calculate the temperature at which the process favors the denatured state.

Which of the following are not state functions: \(S, H\) \(q, w, T ?\)

Which of the following is not accompanied by an increase in the entropy of the system? (a) mixing of two gases at the same temperature and pressure, (b) mixing of ethanol and water, (c) discharging a battery, (d) expansion of a gas followed by compression to its original temperature, pressure, and volume.

Hydrogenation reactions (for example, the process of converting \(\mathrm{C}=\mathrm{C}\) bonds to \(\mathrm{C}-\mathrm{C}\) bonds in food industry) are facilitated by the use of a transition metal catalyst, such as Ni or \(\mathrm{Pt}\). The initial step is the adsorption, or binding, of hydrogen gas onto the metal surface. Predict the signs of \(\Delta H, \Delta S,\) and \(\Delta G\) when hydrogen gas is adsorbed onto the surface of Ni metal.

Comment on the correctness of the analogy sometimes used to relate a student's dormitory room becoming untidy to an increase in entropy.