Chapter 17

Determine whether each of the following statements is true or false. If false, modify it to make it true. (a) An exothermic reaction is spontaneous. (b) When \(\Delta G^{\circ}\) is positive, the reaction cannot occur under any conditions. (c) \(\Delta S^{\circ}\) is positive for a reaction in which there is an increase in the number of moles. (d) If \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) are both negative, \(\Delta G^{\circ}\) will be negative.

Which of the following quantities can be taken to be independent of temperature? Independent of pressure? (a) \(\Delta H\) for a reaction (b) \(\Delta S\) for a reaction (c) \(\Delta G\) for a reaction (d) \(S\) for a substance

Fill in the blanks: (a) \(\Delta H^{\circ}\) and \(\Delta G^{\circ}\) become equal at _____ \(K\). (b) \(\Delta G^{\circ}\) and \(\Delta G\) are equal when \(Q=\) _____. (c) \(S^{\circ}\) for steam is _____ than \(S^{\circ}\) for water.

Fill in the blanks: (a) At equilibrium, \(\Delta G\) is _____. (b) For \(\mathrm{C}_{6} \mathrm{H}_{6}(l) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{6}(g), \Delta H^{\circ}\) is _____ \((+,-, 0)\) (c) When a pure solid melts, the temperature at which liquid and solid are in equilibrium and \(\Delta G^{\circ}=0\) is called ____.

In your own words, explain why (a) \(\Delta S^{\circ}\) is negative for a reaction in which the number of moles of gas decreases. (b) we take \(\Delta S^{\circ}\) to be independent of \(T\), even though entropy increases with \(T\). (c) a solid has lower entropy than its corresponding liquid.

Consider the following reaction with its thermodynamic data: \(2 \mathrm{~A}(\mathrm{~g})+\mathrm{B}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{AB}(\mathrm{g}) \quad \Delta H^{\circ}<0 ; \Delta S^{\circ}<0 ; \Delta G^{\circ}\) at \(60^{\circ} \mathrm{C}=+10 \mathrm{~kJ}\) Which statements about the reaction are true? (a) When \(\Delta G=1\), the reaction is at equilibrium. (b) When \(Q=1, \Delta G=\Delta G^{\circ}\). (c) At \(75^{\circ} \mathrm{C}\), the reaction is definitely nonspontaneous. (d) At \(100^{\circ} \mathrm{C}\), the reaction has a positive entropy change. (e) If \(\mathrm{A}\) and \(\mathrm{B}_{2}\) are elements in their stable states, \(S^{\circ}\) for \(\mathrm{A}\) and \(\mathrm{B}_{2}\) at \(25^{\circ} \mathrm{C}\) is \(0 .\) (f) \(K\) for the reaction at \(60^{\circ} \mathrm{C}\) is less than 1 .

The normal boiling point for ethyl alcohol is \(78.4^{\circ} \mathrm{C} .5^{\circ}\) for \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g)\) is \(282.7 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}\). At what temperature is the vapor pressure of ethyl alcohol \(357 \mathrm{~mm} \mathrm{Hg} ?\)

The overall reaction that occurs when sugar is metabolized is $$ \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s)+12 \mathrm{O}_{2}(g) \longrightarrow 12 \mathrm{CO}_{2}(g)+11 \mathrm{H}_{2} \mathrm{O}(l) $$ For this reaction, \(\Delta H^{\circ}\) is \(-5650 \mathrm{~kJ}\) and \(\Delta G^{\circ}\) is \(-5790 \mathrm{~kJ}\) at \(25^{\circ} \mathrm{C}\). (a) If \(25 \%\) of the free energy change is actually converted to useful work, how many kilojoules of work are obtained when one gram of sugar is metabolized at body temperature, \(37^{\circ} \mathrm{C}\) ? (b) How many grams of sugar would a 120 -lb woman have to eat to get the energy to climb the Jungfrau in the Alps, which is \(4158 \mathrm{~m}\) high? \(\left(w=9.79 \times 10^{-3} \mathrm{mh}\right.\), where \(w=\) work in kilojoules, \(m\) is body mass in kilograms, and \(h\) is height in meters.)

Hydrogen has been suggested as the fuel of the future. One way to store it is to convert it to a compound that can be heated to release the hydrogen. One such compound is calcium hydride, \(\mathrm{CaH}_{2}\). This compound has a heat of formation of \(-186.2 \mathrm{~kJ} / \mathrm{mol}\) and a standard entropy of \(42.0 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}\). What is the minimum temperature to which calcium hydride would have to be heated to produce hydrogen at one atmosphere pressure?

\(K_{a}\) for acetic acid \(\left(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\right)\) at \(25^{\circ} \mathrm{C}\) is \(1.754 \times 10^{-5} .\) At \(50^{\circ} \mathrm{C}, K_{\mathrm{a}}\) is \(1.633 \times 10^{-5}\). Assuming that \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) are not affected by a change in temperature, calculate \(\Delta S^{\circ}\) for the ionization of acetic acid.

Consider the reaction $$ 2 \mathrm{HI}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) $$ At \(500^{\circ} \mathrm{C}\), a flask initially has all three gases, each at a partial pressure of \(0.200\) atm. When equilibrium is established, the partial pressure of HI is determined to be \(0.48\) atm. What is \(\Delta G^{\circ}\) for the reaction at \(500^{\circ} \mathrm{C}\) ?