Chapter 17

Which of the following processes are spontaneous? (a) building a sand castle (b) outlining your chemistry notes (c) wind scattering leaves in a pile

Which of the following processes are spontaneous? (a) a snowman melting in the sun (b) building a house of cards (c) sorting clothes in a laundry basket

Which of the following processes are spontaneous? (a) a ball rolling down a hill (b) a drop of ink dispersing in water (c) melting wax at \(10^{\circ} \mathrm{C}\)

On the basis of your experience, predict which of the following reactions are spontaneous. (a) \(\mathrm{Zn}(s)+2 \mathrm{H}^{+}(a q) \longrightarrow \mathrm{Zn}^{2+}(a q)+\mathrm{H}_{2}(g)\) (b) \(\mathrm{CaCO}_{3}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(s)+\mathrm{H}_{2} \mathrm{CO}_{3}(a q)\) (c) \(\mathrm{CH}_{4}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\) (d) \(\mathrm{Ag}^{+}(a q)+\mathrm{Cl}^{-}(a q) \longrightarrow \mathrm{AgCl}(s)\)

On the basis of your experience, predict which of the following reactions are spontaneous. (a) \(\mathrm{CO}_{2}(s) \longrightarrow \mathrm{CO}_{2}(g)\) at \(25^{\circ} \mathrm{C}\) (b) \(\mathrm{NaCl}(s) \longrightarrow \mathrm{NaCl}(l)\) at \(25^{\circ} \mathrm{C}\) (c) \(2 \mathrm{NaCl}(s) \longrightarrow 2 \mathrm{Na}(s)+\mathrm{Cl}_{2}(g)\) (d) \(\mathrm{CO}_{2}(g) \longrightarrow \mathrm{C}(s)+\mathrm{O}_{2}(g)\)

In each of the following pairs, choose the substance with a lower entropy. (a) \(\mathrm{H}_{2} \mathrm{O}(l)\) at \(10^{\circ} \mathrm{C}, \mathrm{H}_{2} \mathrm{O}(l)\) at \(30^{\circ} \mathrm{C}\) (b) C (graphite), \(\mathrm{C}\) (diamond) (c) \(\mathrm{Cl}_{2}(l), \mathrm{Cl}_{2}(g)\), both at room temperature

In each of the following pairs, choose the substance with a lower entropy. (a) One mole of \(\mathrm{O}_{2}(g)\) with \(758 \mathrm{~mm} \mathrm{Hg}\) pressure, one mole of \(\mathrm{O}_{2}(\mathrm{~g})\) with \(493 \mathrm{~mm} \mathrm{Hg}\) pressure, both at room temperature (b) glucose \((s)\), glucose \((a q)\) (c) \(\mathrm{Hg}(l), \mathrm{Hg}(\mathrm{g})\), both at room temperature

Predict the sign of \(\Delta S\) for the following. (a) ice cream melting (b) boiling water (c) dissolving instant coffee in hot water (d) sugar, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\), decomposing to carbon and steam

Predict the sign of \(\Delta S\) for the following. (a) a lake freezing (b) precipitating lead chloride (c) a candle burning (d) weeding a garden

Predict the sign of \(\Delta S^{\circ}\) for each of the following reactions. (a) \(2 \mathrm{Na}(s)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NaCl}(s)\) (b) \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)\) (c) \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+3 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l)\) (d) \(\mathrm{NH}_{4} \mathrm{NO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{NH}_{3}(g)+\mathrm{O}_{2}(g)\)

Predict the sign of \(\Delta S^{\circ}\) for each of the following reactions. (a) \(\mathrm{CCl}_{4}(l)+5 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{~g})+4 \mathrm{ClO}_{2}(g)\) (b) \(8 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{S}_{8}(s) \longrightarrow 8 \mathrm{H}_{2} \mathrm{~S}(g)+4 \mathrm{O}_{2}(g)\) (c) \(\mathrm{Br}_{2}(l) \longrightarrow \mathrm{Br}_{2}(s)\) (d) \(2 \mathrm{NH}_{3}(\mathrm{~g}) \longrightarrow \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g)\)

Predict the sign of \(\Delta S^{\circ}\) for each of the following reactions. (a) \(\mathrm{O}_{3}(g) \longrightarrow \mathrm{O}_{2}(g)+\mathrm{O}(g)\) (b) \(\mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow \mathrm{PCl}_{5}(g)\) (c) \(\mathrm{CuSO}_{4}(s)+5 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}(s)\)

Predict the sign of \(\Delta S^{\circ}\) for each of the following reactions. (a) \(\mathrm{H}_{2}(g)+\mathrm{Ni}^{2+}(a q) \longrightarrow 2 \mathrm{H}^{+}(a q)+\mathrm{Ni}(s)\) (b) \(\mathrm{Cu}(s)+2 \mathrm{H}^{+}(a q) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{Cu}^{2+}(a q)\) (c) \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)\)

Use Table \(17.1\) to calculate \(\Delta S^{\circ}\) for each of the following reactions. (a) \(\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(l)\) (b) \(\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}(g)\) (c) \(\mathrm{BaCO}_{3}(s) \longrightarrow \mathrm{BaO}(s)+\mathrm{CO}_{2}(g)\) (d) \(2 \mathrm{NaCl}(s)+\mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{NaF}(s)+\mathrm{Cl}_{2}(g)\)

Use Table \(17.1\) to calculate \(\Delta S^{\circ}\) for each of the following reactions. (a) \(2 \mathrm{Cl}^{-}(a q)+\mathrm{I}_{2}(s) \longrightarrow \mathrm{Cl}_{2}(g)+2 \mathrm{I}^{-}(a q)\) (b) \(\mathrm{SO}_{4}{\underline{\phantom{xx}}}^{2-}(a q)+4 \mathrm{H}^{+}(a q)+\mathrm{Cd}(s) \longrightarrow\) \(\mathrm{Cd}^{2+}(a q)+\mathrm{SO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)\) (c) \(2 \mathrm{Br}^{-}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Br}_{2}(l)+\mathrm{H}_{2}(g)+2 \mathrm{OH}^{-}(a q)\)

Calculate \(\Delta G^{\circ}\) at \(45^{\circ} \mathrm{C}\) for reactions for which (a) \(\Delta H^{\circ}=293 \mathrm{~kJ} ; \Delta S^{\circ}=-695 \mathrm{~J} / \mathrm{K}\) (b) \(\Delta H^{\circ}=-1137 \mathrm{~kJ} ; \Delta S^{\circ}=0.496 \mathrm{~kJ} / \mathrm{K}\) (c) \(\Delta H^{\circ}=-86.6 \mathrm{~kJ} ; \Delta S^{\circ}=-382 \mathrm{~J} / \mathrm{K}\)

Use standard entropies and heats of formation to calculate \(\Delta G_{i}^{\circ}\) at \(25^{\circ} \mathrm{C}\) for (a) cadmium(II) chloride (s). (b) methyl alcohol, \(\mathrm{CH}_{3} \mathrm{OH}(l)\). (c) copper(I) sulfide (s).

I Sodium carbonate, also called "washing soda," can be made by heating sodium hydrogen carbonate: $$ \begin{gathered} 2 \mathrm{NaHCO}_{3}(s) \longrightarrow \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \\ \Delta H^{\circ}=+135.6 \mathrm{~kJ} ; \Delta G^{\circ}=+34.6 \mathrm{~kJ} \text { at } 25^{\circ} \mathrm{C} \end{gathered} $$ (a) Calculate \(\Delta S^{\circ}\) for this reaction. Is the sign reasonable? (b) Calculate \(\Delta G^{\circ}\) at \(0 \mathrm{~K} ;\) at \(1000 \mathrm{~K}\).

Oxygen can be made in the laboratory by reacting sodium peroxide and water. $$ \begin{gathered} 2 \mathrm{Na}_{2} \mathrm{O}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 4 \mathrm{NaOH}(s)+\mathrm{O}_{2}(g) \\ \Delta H^{\circ}=-109.0 \mathrm{~kJ} ; \Delta G^{\circ}=-148.4 \mathrm{~kJ} \text { at } 25^{\circ} \mathrm{C} \end{gathered} $$ (a) Calculate \(\Delta S^{\circ}\). Is the sign reasonable? (b) Calculate \(S^{\circ}\) for \(\mathrm{Na}_{2} \mathrm{O}_{2}(s)\). (c) Calculate \(\Delta H_{f}^{\circ}\) for \(\mathrm{Na}_{2} \mathrm{O}_{2}(s)\).

Phosgene, \(\mathrm{COCl}_{2}\), can be formed by the reaction of chloroform, \(\mathrm{CHCl}_{3}(l)\), with oxygen: $$ \begin{gathered} 2 \mathrm{CHCl}_{3}(l)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{COCl}_{2}(g)+2 \mathrm{HCl}(g) \\ \Delta H^{\circ}=-353,2 \mathrm{~kJ} ; \Delta G^{\circ}=-452.4 \mathrm{~kJ} \text { at } 25^{\circ} \mathrm{C} \end{gathered} $$ (a) Calculate \(\Delta S^{\circ}\) for the reaction. Is the sign reasonable? (b) Calculate \(S^{\circ}\) for phosgene. (c) Calculate \(\Delta H_{f}^{\circ}\) for phosgene.

Discuss the effect of temperature change on the spontaneity of the following reactions at 1 atm. $$ \text { (a) } \begin{aligned} 2 \mathrm{PbO}(s)+2 \mathrm{SO}_{2}(g) \longrightarrow 2 \mathrm{PbS}(s)+3 \mathrm{O}_{2}(g) \\ \Delta H^{\circ}=+830.8 \mathrm{~kJ} ; \Delta S^{\circ}=+168 \mathrm{~J} / \mathrm{K} \end{aligned} $$ (b) \(2 \mathrm{As}(s)+3 \mathrm{~F}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{AsF}_{3}(l)\) \(\Delta H^{\circ}=-1643 \mathrm{~kJ} ; \Delta S^{\circ}=-0.316 \mathrm{~kJ} / \mathrm{K}\) (c) \(\mathrm{CO}(\mathrm{g}) \longrightarrow \mathrm{C}(s)+\frac{1}{2} \mathrm{O}_{2}(g)\) \(\Delta H^{\circ}=110.5 \mathrm{~kJ} ; \Delta S^{\circ}=-89.4 \mathrm{~J} / \mathrm{K}\)

Discuss the effect of temperature change on the spontaneity of the following reactions at 1 atm. (a) \(\mathrm{Al}_{2} \mathrm{O}_{3}(s)+2 \mathrm{Fe}(s) \longrightarrow 2 \mathrm{Al}(s)+\mathrm{Fe}_{2} \mathrm{O}_{3}(s)\) $$ \Delta H^{\circ}=+851.5 \mathrm{~kJ} ; \Delta S^{\circ}=+38.5 \mathrm{~J} / \mathrm{K} $$ (b) \(\mathrm{N}_{2} \mathrm{H}_{4}(l) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2}(g)\) $$ \Delta H^{\circ}=-50.6 \mathrm{~kJ} ; \Delta S^{\circ}=0.3315 \mathrm{~kJ} / \mathrm{K} $$ (c) \(\mathrm{SO}_{3}(g) \longrightarrow \mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g)\) $$ \Delta H^{\circ}=98.9 \mathrm{~kJ} ; \Delta S^{\circ}=+0.0939 \mathrm{~kJ} / \mathrm{K} $$

For the reaction $$ 2 \mathrm{Cl}^{-}(a q)+\mathrm{Br}_{2}(l) \longrightarrow \mathrm{Cl}_{2}(g)+2 \mathrm{Br}^{-}(a q) $$ calculate the temperature at which \(\Delta G^{\circ}=0 .\)

Earlier civilizations smelted iron from ore by heating it with charcoal from a wood fire: $$ 2 \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{C}(s) \longrightarrow 4 \mathrm{Fe}(s)+3 \mathrm{CO}_{2}(g) $$ (a) Obtain an expression for \(\Delta G^{\circ}\) as a function of temperature. Prepare a table of \(\Delta G^{\circ}\) values at \(100-\mathrm{K}\) intervals between \(100 \mathrm{~K}\) and \(500 \mathrm{~K}\) (b) Calculate the lowest temperature at which the smelting could be carried out.

Two possible ways of producing iron from iron ore are (a) \(\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\frac{3}{2} \mathrm{C}(s) \longrightarrow 2 \mathrm{Fe}(s)+\frac{3}{2} \mathrm{CO}_{2}(g)\) (b) \(\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{Fe}(s)+3 \mathrm{H}_{2} \mathrm{O}(g)\) Which of these reactions proceeds spontaneously at the lower temperature?

It is desired to produce tin from its ore, cassiterite, \(\mathrm{SnO}_{2}\), at as low a temperature as possible. The ore could be (a) decomposed by heating, producing tin and oxygen. (b) heated with hydrogen gas, producing tin and water vapor. (c) heated with carbon, producing tin and carbon dioxide. Solely on the basis of thermodynamic principles, which method would you recommend? Show calculations.

Red phosphorus is formed by heating white phosphorus. Calculate the temperature at which the two forms are at equilibrium, given $$ \text { white } \text { P: } \Delta H_{\mathrm{f}}^{\circ}=0.00 \mathrm{~kJ} / \mathrm{mol} ; S^{\circ}=41.09 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} $$ red \(\mathrm{P}: \Delta H_{\mathrm{f}}^{\circ}=-17.6 \mathrm{~kJ} / \mathrm{mol} ; \mathrm{S}^{\circ}=22.80 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}\).

Sulfur has about 20 different allotropes. The most common are rhombic sulfur (the stable form at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) ) and monoclinic sulfur. They differ in their crystal structures. Given $$ \mathrm{S}(s, \text { monoclinic }): \Delta H_{\mathrm{f}}^{\circ}=0.30 \mathrm{~kJ} / \mathrm{mol}, S^{\circ}=0.0326 \mathrm{~kJ} / \mathrm{mol} \cdot \mathrm{K} $$ at what temperature are the two forms in equilibrium?

Pencil "lead" is almost pure graphite. Graphite is the stable elemental form of carbon at \(25^{\circ} \mathrm{C}\) and 1 atm. Diamond is an allotrope of graphite. Given $$ \text { diamond: } \Delta H_{\mathrm{f}}^{\circ}=1.9 \mathrm{~kJ} / \mathrm{mol} ; S^{\circ}=2.4 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} $$ at what temperature are the two forms in equilibrium at 1 atm? \(\mathrm{C}\) (graphite) \(\rightleftharpoons \mathrm{C}\) (diamond)

Given the following data for sodium $$ \begin{aligned} &\mathrm{Na}(s): S^{\circ}=51.2 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} \\\ &\mathrm{Na}(g): S^{\circ}=153.6 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} \quad \Delta H_{\mathrm{f}}^{\circ}=108.7 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$ estimate the temperature at which sodium sublimes at 1 atm. $$ \mathrm{Na}(s) \rightleftharpoons \mathrm{Na}(g) $$

Given the following data for bromine, $$ \begin{aligned} &\mathrm{Br}_{2}(l): S^{\circ}=152.2 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} \\ &\mathrm{Br}_{2}(g): S^{\circ}=245.4 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} \quad \Delta H_{\mathrm{f}}^{\circ}=30.91 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$ estimate the normal boiling point of bromine. $$ \mathrm{Br}_{2}(l) \rightleftharpoons \mathrm{Br}_{2}(g) $$

Mow by calculation, using Appendix 1, whether dissolving lead(II) chloride $$ \mathrm{PbCl}_{2}(s) \rightleftharpoons \mathrm{Pb}^{2+}(a q)+2 \mathrm{Cl}^{-}(a q) $$ is spontaneous at \(25^{\circ} \mathrm{C}\) (a) when \(\left[\mathrm{Pb}^{2+}\right]=1.0 \mathrm{M} ;\left[\mathrm{Cl}^{-}\right]=2.0 \mathrm{M}\). (b) when \(\left[\mathrm{Pb}^{2+}\right]=1.0 \times 10^{-5} ;\left[\mathrm{Cl}^{-}\right]=2.0 \times 10^{-5} \mathrm{M}\).

Show by calculation whether the reaction $$ \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-}(a q) \quad \Delta G^{\circ}=+27.2 \mathrm{~kJ} $$ is spontaneous at \(25^{\circ} \mathrm{C}\) (a) when \(\left[\mathrm{H}^{+}\right]=\left[\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-}\right]=0.85 M_{;}\left[\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\right]=0.15 \mathrm{M}\). (b) when \(\left[\mathrm{H}^{+}\right]=\left[\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-}\right]=2.0 \times 10^{-3} \mathrm{M} ;\left[\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\right]=1.0 \mathrm{M}\).

Consider the reaction $$ \mathrm{NH}_{4}{\underline{\phantom{xx}}}^{+}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{NH}_{3}(a q) $$ Use \(\Delta G_{i}^{\circ}\) for \(\mathrm{NH}_{3}(a q)\) at \(25^{\circ} \mathrm{C}=-26.7 \mathrm{~kJ} / \mathrm{mol}\) and the appropriate tables to calculate (a) \(\Delta G^{\circ}\) at \(25^{\circ} \mathrm{C}\) (b) \(K_{\mathrm{a}}\) at \(25^{\circ} \mathrm{C}\)

Consider the following reaction at \(25^{\circ} \mathrm{C}\) : $$ \mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{Cl}(g) \quad K=1.0 \times 10^{-37} $$ (a) Calculate \(\Delta G^{\circ}\) for the reaction at \(25^{\circ} \mathrm{C}\). (b) Calculate \(\Delta G_{\mathrm{f}}^{\circ}\) for \(\mathrm{Cl}(\mathrm{g})\) at \(25^{\circ} \mathrm{C}\).

Consider the reaction $$ \mathrm{N}_{2} \mathrm{O}(g)+\mathrm{NO}_{2}(g) \longrightarrow 3 \mathrm{NO}(g) \quad K=4.4 \times 10^{-19} $$ (a) Calculate \(\Delta G^{\circ}\) for the reaction at \(25^{\circ} \mathrm{C}\). (b) Calculate \(\Delta G_{i}^{\circ}\) for \(\mathrm{N}_{2} \mathrm{O}\) at \(25^{\circ} \mathrm{C}\).

For the reaction $$ \mathrm{CO}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) $$ \(K=2.2 \times 10^{11}\) at \(473 \mathrm{~K}\) and \(4.6 \times 10^{8}\) at \(533 \mathrm{~K}\), Calculate \(\Delta G^{\circ}\) at both temperatures.

For the reaction $$ \mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g) $$ \(K=50.0\) at \(721 \mathrm{~K}\) (a) What is \(\Delta G^{\circ}\) at \(721 \mathrm{~K} ?\) (b) What is \(K\) at \(25^{\circ} \mathrm{C}\) ? \(\left(\Delta G_{f}^{\circ} \mathrm{I}_{2}(g)=+19.4 \mathrm{~kJ} / \mathrm{mol}\right.\) )

Use the values for \(\Delta G_{i}^{o}\) in Appendix 1 to calculate \(K_{\text {ip }}\) for barium sulfate at \(25^{\circ} \mathrm{C}\). Compare with the value given in Chapter 16 .

Given that \(\Delta H_{\mathrm{f}}^{\circ}\) for \(\mathrm{HF}(a q)\) is \(-320.1 \mathrm{~kJ} / \mathrm{mol}\) and \(S^{\circ}\) for \(\mathrm{HF}(a q)\) is \(88.7 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}\), find \(K_{\mathrm{a}}\) for \(\mathrm{HF}\) at \(25^{\circ} \mathrm{C}\).

A \(0.143 M\) solution of the weak base \(\mathrm{RNH}_{2}\) has \(\mathrm{pH} 9.11\) at \(25^{\circ} \mathrm{C}\). What is \(\Delta G^{\circ}\) for the dissociation of the weak base in water? $$ \mathrm{RNH}_{2}(a q)+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{RNH}_{3}{\underline{\phantom{xx}}}^{+}(a q)+\mathrm{OH}^{-}(a q) $$

Given the following standard free energies at \(25^{\circ} \mathrm{C}\), $$ \begin{array}{ll} \mathrm{SO}_{2}(g)+3 \mathrm{CO}(g) \longrightarrow \operatorname{COS}(g)+2 \mathrm{CO}_{2}(g) & \Delta G^{\circ}=-246.5 \mathrm{~kJ} \\ \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) & \Delta G^{\circ}=-28.5 \mathrm{~kJ} \end{array} $$ find \(\Delta G^{\circ}\) at \(25^{\circ} \mathrm{C}\) for the following reaction. $$ \mathrm{SO}_{2}(g)+\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{COS}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) $$

Given the following standard free energies at \(25^{\circ} \mathrm{C}\), $$ \begin{array}{ll} \mathrm{N}_{2} \mathrm{O}_{5}(g) \longrightarrow 2 \mathrm{NO}(g)+\frac{3}{2} \mathrm{O}_{2}(g) & \Delta G^{\circ}=-59.2 \mathrm{~kJ} \\ \mathrm{NO}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{NO}_{2}(g) & \Delta G^{\circ}=-35.6 \mathrm{~kJ} \end{array} $$ calculate \(\Delta G^{\circ}\) at \(25^{\circ} \mathrm{C}\) for the reaction $$ 2 \mathrm{NO}_{2}(g)+{ }_{2}^{1} \mathrm{O}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{5}(g) $$

Theoretically, one can obtain zinc from an ore containing zinc sulfide, \(\mathrm{ZnS}\), by the reaction $$ \mathrm{ZnS}(s) \longrightarrow \mathrm{Zn}(s)+\mathrm{S}(s) $$ (a) Show by calculation that this reaction is not feasible at \(25^{\circ} \mathrm{C}\). (b) Show that by coupling the above reaction with the reaction $$ \mathrm{S}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g) $$ the overall reaction, in which \(\mathrm{Zn}\) is obtained by roasting in oxygen, is feasible at \(25^{\circ} \mathrm{C}\).

How many moles of ATP must be converted to ADP by the reaction \(\mathrm{ATP}(a q)+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{ADP}(a q)+\mathrm{HPO}_{4}^{2-}(a q)+2 \mathrm{H}^{+}(a q)\) $$ \Delta G^{\circ}=-31 \mathrm{~kJ} $$ to bring about a nonspontaneous biochemical reaction in which \(\Delta G^{\circ}=+372 \mathrm{~kJ}\) ?

Consider the following reactions at \(25^{\circ} \mathrm{C}\) : $$ \begin{aligned} &\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q)+6 \mathrm{O}_{2}(g) \longrightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O} \quad \Delta G^{\circ}=-2870 \mathrm{~kJ} \\ &\mathrm{ADP}(a q)+\mathrm{HPO}_{4}{\underline{\phantom{xx}}}^{2-}(a q)+2 \mathrm{H}^{+}(a q) \longrightarrow \mathrm{ATP}(a q)+\mathrm{H}_{2} \mathrm{O} \\ &\Delta G^{\circ}=31 \mathrm{~kJ} \end{aligned} $$ Write an equation for a coupled reaction between glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), and ADP in which \(\Delta G^{\circ}=-390 \mathrm{~kJ}\).

At \(1200 \mathrm{~K}\), an equilibrium mixture of \(\mathrm{CO}\) and \(\mathrm{CO}_{2}\) gases contains 98.31 mol percent CO and some solid carbon. The total pressure of the mixture is \(1.00 \mathrm{~atm}\). For the system $$ \mathrm{CO}_{2}(g)+\mathrm{C}(s) \rightleftharpoons 2 \mathrm{CO}(g) $$ calculate (a) \(P_{\mathrm{Co}}\) and \(P_{\mathrm{CO}_{2}}\) (b) \(K\) (c) \(\Delta G^{\circ}\) at \(1200 \mathrm{~K}\)

At \(25^{\circ} \mathrm{C}\), a \(0.13 \mathrm{M}\) solution of a weak acid, \(\mathrm{HB}\), has a \(\mathrm{pH}\) of \(3.71\). What is \(\Delta G^{\circ}\) for $$ \mathrm{H}^{+}(a q)+\mathrm{B}^{-}(a q) \rightleftharpoons \mathrm{HB}(a q) $$

A student is asked to prepare a \(0.030 \mathrm{M}\) aqueous solution of \(\mathrm{PbCl}_{2}\) (a) Is this possible at \(25^{\circ} \mathrm{C} ?\) (Hint: Is dissolving \(0.030 \mathrm{~mol}\) of \(\mathrm{PbCl}_{2}\) at \(25^{\circ} \mathrm{C}\) possible? \()\) (b) If the student used water at \(100^{\circ} \mathrm{C}\), would this be possible?

Some bacteria use light energy to convert carbon dioxide and water to glucose and oxygen: \(6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q)+6 \mathrm{O}_{2}(g) \quad \Delta G^{\circ}=2870 \mathrm{~kJ}\) at \(25^{\circ} \mathrm{C}\) Other bacteria, those that do not have light available to them, couple the reaction $$ \mathrm{H}_{2} \mathrm{~S}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{S}(s) $$ to the glucose synthesis above. Coupling the two reactions, the overall reaction is \(24 \mathrm{H}_{2} \mathrm{~S}(g)+6 \mathrm{CO}_{2}(g)+6 \mathrm{O}_{2}(g) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q)+18 \mathrm{H}_{2} \mathrm{O}(l)+24 \mathrm{~S}(s)\) Show that the reaction is spontaneous at \(25^{\circ} \mathrm{C}\).