Chapter 17

For ammonia $\left({\mathrm{NH}}_3\right),$ the enthalpy of fusion is 5.65 $\mathrm{kJ}/\mathrm{mol}$ and the entropy of fusion is 28.9 $\mathrm{J}/\mathrm{K}\cdot$ mol. a. Will ${\mathrm{NH}}_3(s)$ spontaneously melt at $200.\mathrm{K}$ ? b. What is the approximate melting point of ammonia?

The enthalpy of vaporization of ethanol is 38.7 kJ/mol at its boiling point $\left({78}^{\circ }\mathrm{C}\right).$ Determine $\mathrm{\Delta }{S}_{\mathrm{sys}},\mathrm{\Delta }{S}_{\mathrm{surr}},$ and $\mathrm{\Delta }{S}_{\mathrm{univ}}$ when 1.00 mole of ethanol is vaporized at ${78}^{\circ }\mathrm{C}$ and 1.00 atm.

Predict the sign of $\mathrm{\Delta }{S}^{\circ }$ for each of the following changes. a. $\mathrm{K}(s)+\frac{1}{2}{\mathrm{Br}}_2(g)⟶\mathrm{KBr}(s)$ b. ${\mathrm{N}}_2(g)+3{\mathrm{H}}_2(g)⟶2{\mathrm{NH}}_3(g)$ c. $\mathrm{KBr}(s)⟶{\mathrm{K}}^{+}(aq)+{\mathrm{Br}}^{-}(aq)$ d. $\mathrm{KBr}(s)⟶\mathrm{KBr}(l)$

For each of the following pairs of substances, which substance has the greater value of $S^{\circ }?$ a. ${\mathrm{C}}_{\text{ graphite }}(s)$ or ${\mathrm{C}}_{\text{ diamond }}(s)$ b. ${\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH}(l)$ or ${\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH}(g)$ c. ${\mathrm{CO}}_2(s)$ or ${\mathrm{CO}}_2(g)$

For each of the following pairs, which substance has the greater value of S? a. ${\mathrm{N}}_2\mathrm{O}(\text{ at }0\mathrm{K})$ or He (at 10 $\mathrm{K})$ b. ${\mathrm{N}}_2\mathrm{O}(g)$ (at $1\mathrm{atm},{25}^{\circ }\mathrm{C})$ or He(g) (at 1 atm, ${25}^{\circ }\mathrm{C})$ c. ${\mathrm{NH}}_3(s)$ (at 196 $\mathrm{K})⟶{\mathrm{NH}}_3(l)(\text{ at }196\mathrm{K})$

Predict the sign of $\mathrm{\Delta }{S}^{\circ }$ and then calculate $\mathrm{\Delta }{S}^{\circ }$ for each of the following reactions. a. $2{\mathrm{H}}_2\mathrm{S}(g)+{\mathrm{SO}}_2(g)⟶3{\mathrm{S}}_{\text{ rhombic}}(s)+2{\mathrm{H}}_2\mathrm{O}(g)$ b. $2{\mathrm{SO}}_3(g)⟶2{\mathrm{SO}}_2(g)+{\mathrm{O}}_2(g)$ c. ${\mathrm{Fe}}_2{\mathrm{O}}_3(s)+3{\mathrm{H}}_2(g)⟶2\mathrm{Fe}(s)+3{\mathrm{H}}_2\mathrm{O}(g)$

Predict the sign of $\mathrm{\Delta }{S}^{\circ }$ and then calculate $\mathrm{\Delta }{S}^{\circ }$ for each of the following reactions. a. ${\mathrm{H}}_2(g)+\frac{1}{2}{\mathrm{O}}_2(g)⟶{\mathrm{H}}_2\mathrm{O}(l)$ b. $2{\mathrm{CH}}_3\mathrm{OH}(g)+3{\mathrm{O}}_2(g)⟶2{\mathrm{CO}}_2(g)+4{\mathrm{H}}_2\mathrm{O}(g)$ c. $\mathrm{HCl}(g)⟶{\mathrm{H}}^{+}(aq)+{\mathrm{Cl}}^{-}(aq)$

For the reaction $${\mathrm{CS}}_2(g)+3{\mathrm{O}}_2(g)⟶{\mathrm{CO}}_2(g)+2{\mathrm{SO}}_2(g)$$ $\mathrm{\Delta }{S}^{\circ }$ is equal to $-143\mathrm{JK}$ . Use this value and data from Appendix 4 to calculate the value of $S^{\circ }$ for ${\mathrm{CS}}_2(g).$

It is quite common for a solid to change from one structure to another at a temperature below its melting point. For example, sulfur undergoes a phase change from the rhombic crystal structure to the monoclinic crystal form at temperatures above ${95}^{\circ }\mathrm{C}$ a. Predict the signs of $\mathrm{\Delta }H$ and $\mathrm{\Delta }S$ for the process ${\mathrm{S}}_{\text{ rhombic}}(s)⟶{\mathrm{S}}_{\text{ monoclinic }}(s)$ b. Which form of sulfur has the more ordered crystalline structure (has the smaller positional probability)?

Two crystalline forms of white phosphorus are known. Both forms contain ${\mathrm{P}}_4$ molecules, but the molecules are packed together in different ways. The $\alpha$ form is always obtained when the liquid freezes. However, below $-{76.9}^{\circ }\mathrm{C},$ the $\alpha$ form spontaneously converts to the $\beta$ form: $${\mathrm{P}}_4(s,\alpha )⟶{\mathrm{P}}_4(s,\beta )$$ a. Predict the signs of $\mathrm{\Delta }H$ and $\mathrm{\Delta }S$ for this process. b. Predict which form of phosphorus has the more ordered crystalline structure (has the smaller positional probability).