Chapter 14

Predict the sign of the change in entropy in the system for the following processes (Section \(14.1)\) (a) Steam condensing on a cold window (b) A cloud forming in the atmosphere (c) Inflating a bicycle tyre with air (d) Dissolving sugar in hot coffee (e) \(P C l_{3}(g)+C l_{2}(g) \rightarrow P C l_{5}(g)\) (f) \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{CaSO}_{4}(\mathrm{s}) \rightarrow \mathrm{CaSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}(\mathrm{s})\) (g) \(\mathrm{SO}_{3}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}() \rightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq})\) (h) \(2 \mathrm{KCl}(\mathrm{s})+\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{I}) \rightarrow \mathrm{K}_{2} \mathrm{SO}_{4}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{g})\) \((i) \quad \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}()\)

An apparatus consists of two bulbs of the same volume connected by a tap. Initially, the tap is closed with one bulb containing nitrogen gas and the other oxygen gas. Both bulbs are at the same temperature and pressure. (Section 14.2 ) (a) What happens when the tap is opened? What will be the equilibrium state of the system? (b) What are the signs of \(\Delta H, \Delta S,\) and \(\Delta G\) for the process in (a)? (c) Is this consistent with the Second Law of thermodynamics?

Estimate the change in entropy when 1.00 mol of argon is heated from \(300 \mathrm{K}\) to \(1200 \mathrm{K}\). What assumptions have you made and how could you make your estimate more accurate? (Section 14.2 ) (The heat capacity, \(C_{p^{\prime}}\), of argon gas is \(20.8 \mathrm{JK}^{-1}\) mol \(^{-1}\).)

For each of the following reactions, suggest whether the entropy change in the system would be: (1) near zero; (il) positive; or (ii) negative. Explain your answers. (Section \(14.4)\) (a) \(\mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{NH}_{3}(\mathrm{g})\) (b) \(Z n(s)+C u^{2+}(a q) \rightarrow Z n^{2+}(a q)+C u(s)\) (c) \(3 \mathrm{Mg}(\mathrm{s})+2 \mathrm{Fe}^{3+}(\mathrm{aq}) \rightarrow 3 \mathrm{Mg}^{2+}(\mathrm{aq})+2 \mathrm{Fe}(\mathrm{s})\) (d) \(\mathrm{CH}_{4}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (e) C(diamond) \(\rightarrow\) C(graphite)

Dissolving solid potassium iodide in water results in a lowering of the temperature. Explain why this endothermic process can be spontaneous. (Section 14.2 )

\(100.0 \mathrm{g}\) of water at \(30^{\circ} \mathrm{C}\) were placed in a refrigerator at \(4^{\circ} \mathrm{C}\) When the water cools down, what is the entropy change of (a) the water and (b) the refrigerator? What is the overall entropy change? Comment on the results.

An ice cube of mass \(18 \mathrm{g}\) is added to a large glass of water just above \(0^{\circ} \mathrm{C}\). Calculate the change of entropy for the ice and for the water (without the ice). (Section 14.4 ) (The enthalpy change of fusion for water is \(+6.01 \mathrm{kJ} \mathrm{mol}^{-1}\).)

Calculate the change in entropy when \(100 \mathrm{g}\) of water at \(90^{\circ} \mathrm{C}\) are added to an insulated flask containing \(100 \mathrm{g}\) of water at \(\left.10^{\circ} \mathrm{C} . \text { (Section } 14.2\right)\)

Calculate the entropy changes for the system and surroundings when \(1.00 \mathrm{mol}\) of \(\mathrm{NaCl}\) melts at \(1100 \mathrm{K}\). Calculate \(\Delta_{\mathrm{us}} \mathrm{G}\) and estimate the melting point of NaCl. (Section 14.5 ) (For the melting of sodium chloride (NaCl), \(\Delta_{\text {ivs }} H=+30.2 \mathrm{kJmol}^{-1}\) and \(\Delta_{\text {fus }} S=+28.1 \mathrm{JK}^{-1} \mathrm{mol}^{-1}\).)

Calcium carbonate \(\left(\mathrm{CaCO}_{3}\right)\) decomposes to form \(\mathrm{CaO}\) and \(\mathrm{CO}_{2}\) with \(\Delta_{\mathrm{r}} \mathrm{H}_{29 \mathrm{g}}=+178 \mathrm{kJ} \mathrm{mol}^{-1}\) and \(\Delta_{r} \mathrm{S}_{2 \mathrm{SQ}}=+161 \mathrm{JK}^{-1} \mathrm{mol}^{-1}\) Estimate the temperature at which the decomposition becomes spontaneous. (Section \(14.6)\)

You expend about \(100 \mathrm{kJ}\) a day keeping your heart beating. What is the minimum mass of glucose you must oxidize per day in order to produce this much energy? (Section 14.5 ) $$\begin{array}{r}\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{s})+6 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 6 \mathrm{CO}_{2}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O} / \\\\\Delta G^{0}=-2872 \mathrm{kJ} \mathrm{mol}^{-1}\end{array}$$

Calculate the normal boling point of ethanol given that \(\Delta_{\text {vap }} H=+42.6 \mathrm{kJ} \mathrm{mol}^{-1}\) and \(\Delta_{\text {vap }} \mathrm{S}=+122.0 \mathrm{JK}^{-1} \mathrm{mol}^{-1}\) (Section \(14.5)\)

Impure nickel metal is purified using the Mond process where it is first reacted at \(80^{\circ} \mathrm{C}\) with carbon monoxide to form \(\mathrm{Ni}(\mathrm{CO})_{4}(\mathrm{g})\) $$\mathrm{Ni}(\mathrm{s})+4 \mathrm{CO}(\mathrm{g}) \rightarrow \mathrm{Ni}(\mathrm{CO})_{4}(\mathrm{g})$$ followed by heating to \(200^{\circ} \mathrm{C}\) when the reverse reaction occurs. Use the following thermodynamic data to show that this approach is thermodynamically feasible. $$\begin{array}{llll} & \mathrm{Ni}(\mathrm{s}) & \mathrm{Ni}(\mathrm{CO})_{4}(\mathrm{g}) & \mathrm{CO}(\mathrm{g}) \\\\\Delta_{1} \mathrm{G}_{289}^{\circ} / \mathrm{kJmol}^{-1}: & 0 & -601.6 & -110.5 \\\\\mathrm{S}_{298}^{\circ} / \mathrm{JK}^{-1} \mathrm{mol}^{-1}: & 29.9 & 415.5 & 197.6\end{array}$$