Chapter 18

Calculate $\mathrm{\Delta }{S}_{\text{sys }}$ for (a) the isothermal compression of 0.0050 mol of an ideal gas from $112\mathrm{mL}$ to $52.5\mathrm{mL}$ (b) the isothermal compression of $0.015\mathrm{mol}$ of an ideal gas from $225\mathrm{mL}$ to $22.5\mathrm{mL},$ and $(\mathrm{c})$ the isothermal expansion of $22.1\mathrm{mol}$ of an ideal gas from 122 L to $275\mathrm{L}$.

For each pair of substances listed here, choose the one having the larger standard entropy value at ${25}^{\circ }\mathrm{C}$. The same molar amount is used in the comparison. Explain the basis for your choice. (a) $\mathrm{Li}(s)$ or $\mathrm{Li}(l),(b)C_2{H}_{5}OH(l)$ or ${\mathrm{CH}}_3{\mathrm{OCH}}_3(l)$ (Hint: Which molecule can hydrogen- (d) $\mathrm{CO}(g)$ or ${\mathrm{CO}}_2(g),$ (e) ${\mathrm{O}}_2(g)$ bond?), (c) $\mathrm{Ar}(g)$ or $\mathrm{Xe}(g)$, or ${\mathrm{O}}_3(g),(\mathrm{f}){\mathrm{NO}}_2(g)$ or ${\mathrm{N}}_2{\mathrm{O}}_4(g).$

Arrange the following substances ( 1 mole each) in order of increasing entropy at ${25}^{\circ }\mathrm{C}:$ (a) $\mathrm{Ne}(g)$, (b) ${\mathrm{SO}}_2(g),$ (c) $\mathrm{Na}(s)$ (d) $\mathrm{NaCl}(s)$ (e) ${\mathrm{H}}_2(g)$. Give the reasons for your arrangement.

State the second law of thermodynamics in words, and express it mathematically.

State the third law of thermodynamics in words, and explain its usefulness in calculating entropy values.

Define free energy. What are its units?

Why is it more convenient to predict the direction of a reaction in terms of $\mathrm{\Delta }{G}_{\mathrm{sys}}$ instead of $\mathrm{\Delta }{S}_{\text{univ }}$ ? Under what conditions can $\mathrm{\Delta }{G}_{\mathrm{sys}}$ be used to predict the spontaneity of a reaction?

From the following combinations of $\mathrm{\Delta }H$ and $\mathrm{\Delta }$ 3, predict if a process will be spontaneous at a high or low temperature: (a) both $\mathrm{\Delta }H$ and $\mathrm{\Delta }S$ are negative, (b) $\mathrm{\Delta }H$ is negative and $\mathrm{\Delta }S$ is positive, $(\mathrm{c})$ both $\mathrm{\Delta }H$ and $\mathrm{\Delta }S$ are positive, (d) $\mathrm{\Delta }H$ is positive and $\mathrm{\Delta }S$ is negative.

From the values of $\mathrm{\Delta }H$ and $\mathrm{\Delta }S$, predict which of the following reactions would be spontaneous at ${25}^{\circ }\mathrm{C}:$ reaction A: $\mathrm{\Delta }H=10.5\mathrm{kJ}/\mathrm{mol},\mathrm{\Delta }S=30\mathrm{J}/\mathrm{K}\cdot \mathrm{mol};$ reaction B: $\mathrm{\Delta }H=1.8\mathrm{kJ}/\mathrm{mol},\mathrm{\Delta }S=-113\mathrm{J}/\mathrm{K}\cdot \mathrm{mol}$. If either of the reactions is nonspontaneous at ${25}^{\circ }\mathrm{C},$ at what temperature might it become spontaneous?

The molar heats of fusion and vaporization of ethanol are 7.61 and $26.0\mathrm{kJ}/\mathrm{mol}$, respectively. Calculate the molar entropy changes for the solid-liquid and liquidvapor transitions for ethanol. At 1 atm pressure, ethanol melts at $-{117.3}^{\circ }\mathrm{C}$ and boils at ${78.3}^{\circ }\mathrm{C}$.