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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The major industrial use of hydrogen is in the production of ammonia by the Haber process:

$$

3 \mathrm{H}_{2}(g)+\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)

$$

a. Using data from Appendix $4,$ calculate $\Delta H^{\circ}, \Delta S^{\circ},$ and $\Delta G^{\circ}$ for the Haber process reaction.

b. Is the reaction spontaneous at standard conditions?

c. At what temperatures is the reaction spontaneous at standard conditions? Assume $\Delta H^{\circ}$ and $\Delta S^{\circ}$ do not depend on temperature.