Chapter 16

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. $\mathrm{HCl}(g)⟶{\mathrm{H}}^{+}(aq)+{\mathrm{Cl}}^{-}(aq)$

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 $S_{\text{rhombic }}(s)⟶S_{\text{monoclinic }}(s).$ b. Which form of sulfur has the more ordered crystalline structure (has the smaller positional probability)?

Consider the reaction $$2\mathrm{O}(g)⟶{\mathrm{O}}_2(g)$$ a. Predict the signs of $\mathrm{\Delta }H$ and $\mathrm{\Delta }S.$ b. Would the reaction be more spontaneous at high or low temperatures?

From data in Appendix $4,$ calculate $\mathrm{\Delta }{H}^{\circ },\mathrm{\Delta }{S}^{\circ },$ and $\mathrm{\Delta }{G}^{\circ }$ for each of the following reactions at ${25}^{\circ }\mathrm{C}.$ a. ${\mathrm{CH}}_4(g)+2{\mathrm{O}}_2(g)⟶{\mathrm{CO}}_2(g)+2{\mathrm{H}}_2\mathrm{O}(g)$ b. $6{\mathrm{CO}}_2(g)+6{\mathrm{H}}_2\mathrm{O}(l)⟶{\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_6(s)+6{\mathrm{O}}_2(g)$ c. ${\mathrm{P}}_4{\mathrm{O}}_{10}(s)+6{\mathrm{H}}_2\mathrm{O}(l)⟶4{\mathrm{H}}_3{\mathrm{PO}}_4(s)$ d. $\mathrm{HCl}(g)+{\mathrm{NH}}_3(g)⟶{\mathrm{NH}}_4\mathrm{Cl}(s)$

For the reaction at $298\mathrm{K}$, $$2{\mathrm{NO}}_2(g)\rightleftharpoons {\mathrm{N}}_2{\mathrm{O}}_4(g)$$ the values of $\mathrm{\Delta }{H}^{\circ }$ and $\mathrm{\Delta }{S}^{\circ }$ are $-58.03\mathrm{kJ}$ and $-176.6\mathrm{J}/\mathrm{K},$ respectively. What is the value of $\mathrm{\Delta }{G}^{\circ }$ at 298 K? Assuming that $\mathrm{\Delta }{H}^{\circ }$ and $\mathrm{\Delta }{S}^{\circ }$ do not depend on temperature, at what temperature is $\mathrm{\Delta }{G}^{\circ }=0?$ Is $\mathrm{\Delta }{G}^{\circ }$ negative above or below this temperature?

At $100{.}^{\circ }\mathrm{C}$ and $1.00\mathrm{atm},\mathrm{\Delta }{H}^{\circ }=40.6\mathrm{kJ}/\mathrm{mol}$ for the vaporiza- tion of water. Estimate $\mathrm{\Delta }{G}^{\circ }$ for the vaporization of water at $90{.}^{\circ }\mathrm{C}$ and $110{.}^{\circ }\mathrm{C}.$ Assume $\mathrm{\Delta }{H}^{\circ }$ and $\mathrm{\Delta }{S}^{\circ }$ at $100{.}^{\circ }\mathrm{C}$ and 1.00 atm do not depend on temperature.

Given the following data: $$2{\mathrm{H}}_2(g)+\mathrm{C}(s)⟶{\mathrm{CH}}_4(g)\mathrm{\Delta }{G}^{\circ }=-51\mathrm{kJ}$$ $$2{\mathrm{H}}_2(g)+{\mathrm{O}}_2(g)⟶2{\mathrm{H}}_2\mathrm{O}(l)\mathrm{\Delta }{G}^{\circ }=-474\mathrm{kJ}$$ $$\mathrm{C}(s)+{\mathrm{O}}_2(g)⟶{\mathrm{CO}}_2(g)\mathrm{\Delta }{G}^{\circ }=-394\mathrm{kJ}$$ Calculate $\mathrm{\Delta }{G}^{\circ }$ for ${\mathrm{CH}}_4(g)+2{\mathrm{O}}_2(g)\to {\mathrm{CO}}_2(g)+2{\mathrm{H}}_2\mathrm{O}(l)$

Given the following data: $$2{\mathrm{C}}_6{\mathrm{H}}_6(l)+15{\mathrm{O}}_2(g)⟶12{\mathrm{CO}}_2(g)+6{\mathrm{H}}_2\mathrm{O}(l)$$ $$\mathrm{\Delta }{G}^{\circ }=-6399\mathrm{kJ}$$ $$\mathrm{C}(s)+{\mathrm{O}}_2(g)⟶{\mathrm{CO}}_2(g)\mathrm{\Delta }{G}^{\circ }=-394\mathrm{kJ}$$ $${\mathrm{H}}_2(g)+\frac{1}{2}{\mathrm{O}}_2(g)⟶{\mathrm{H}}_2\mathrm{O}(l)\mathrm{\Delta }{G}^{\circ }=-237\mathrm{kJ}$$ calculate $\mathrm{\Delta }{G}^{\circ }$ for the reaction $$6\mathrm{C}(s)+3{\mathrm{H}}_2(g)⟶{\mathrm{C}}_6{\mathrm{H}}_6(l)$$

The value of $\mathrm{\Delta }{G}^{\circ }$ for the reaction $$2{\mathrm{C}}_4{\mathrm{H}}_{10}(g)+13{\mathrm{O}}_2(g)⟶8{\mathrm{CO}}_2(g)+10{\mathrm{H}}_2\mathrm{O}(l)$$ is $-5490.$ kJ. Use this value and data from Appendix 4 to calculate the standard free energy of formation for ${\mathrm{C}}_4{\mathrm{H}}_{10}(g).$

Consider the reaction $${\mathrm{Fe}}_2{\mathrm{O}}_3(s)+3{\mathrm{H}}_2(g)⟶2\mathrm{Fe}(s)+3{\mathrm{H}}_2\mathrm{O}(g)$$ a. Use $\mathrm{\Delta }{G}_{\mathrm{f}}^{\circ }$ values in Appendix 4 to calculate $\mathrm{\Delta }{G}^{\circ }$ for this reaction. b. Is this reaction spontaneous under standard conditions at $298\mathrm{K}?$ c. The value of $\mathrm{\Delta }{H}^{\circ }$ for this reaction is $100.$ kJ. At what temperatures is this reaction spontaneous at standard conditions? Assume that $\mathrm{\Delta }{H}^{\circ }$ and $\mathrm{\Delta }{S}^{\circ }$ do not depend on temperature.