Kyanite, sillimanite, and andalusite all have the formula $\mathrm{Al}_{2} \mathrm{SiO}_{5}$. Each is stable under different conditions (see the graph at right). At the point where the three phases intersect:

(a) Which mineral, if any, has the lowest free energy?

(b) Which mineral, if any, has the lowest enthalpy?

(c) Which mineral, if any, has the highest entropy?

(d) Which mineral, if any, has the lowest density?

## Discussion

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## Recommended Questions

The oxidation of glucose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)$ in body tissue produces $\mathrm{CO}_{2}$ and $\mathrm{H}_{2} \mathrm{O}$ . In contrast, anaerobic decomposition, which occurs during fermentation, produces ethanol $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)$ and $\mathrm{CO}_{2} .$ (a) Using data given in Appendix $\mathrm{C},$ compare the equilibrium constants for the following reactions:

$$

\begin{array}{c}{\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \rightleftharpoons 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l)} \\ {\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s) \rightleftharpoons 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+2 \mathrm{CO}_{2}(g)}\end{array}

$$

(b) Compare the maximum work that can be obtained from

these processes under standard conditions.

Calculate $\Delta H_{\mathrm{rxn}}$ for the reaction:

$$

5 \mathrm{C}(s)+6 \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{5} \mathrm{H}_{12}(l)

$$

Use the following reactions and given $\Delta H^{\prime} \mathrm{s} :$

$$

\begin{aligned} \mathrm{C}_{5} \mathrm{H}_{12}(l)+8 \mathrm{O}_{2}(g) \longrightarrow 5 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) & \\ \Delta H &=-3244.8 \mathrm{kJ} \end{aligned}

$$

$$

\begin{array}{ll}{\mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)} & {\Delta H=-393.5 \mathrm{kJ}} \\ {2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)} & {\Delta H=-483.5 \mathrm{kJ}}\end{array}

$$