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Problem 109

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?

Answer

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## Discussion

## Video Transcript

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## Recommended Questions

Predict which solid in each pair will have the higher melting point. Explain your answers.

a. NaCl or CsCl

b. Ag or Cu

c. $\mathrm{Na}_{2} \mathrm{O}$ or MgO

Which compound in each of the following pairs should have the higher melting point? Explain briefly.

(a) NaCl or RbCl

(b) BaO or $\mathrm{MgO}$

(c) NaCl or MgS

For each pair, choose the compound with the smaller lattice energy, and explain your choice: (a) CaS or BaS; (b) NaF or MgO.

In each of the following groups of substances, pick the one that has the given property. Justify each answer.

a. highest boiling point: $\mathrm{CCl}_{4}, \mathrm{CF}_{4}, \mathrm{CBr}_{4}$

b. lowest freezing point: LiF, $\mathrm{F}_{2}, \mathrm{HCl}$

c. smallest vapor pressure at $25^{\circ} \mathrm{C} : \mathrm{CH}_{3} \mathrm{OCH}_{3}, \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}$ , $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}$

d. greatest viscosity: $\mathrm{H}_{2} \mathrm{S}, \mathrm{HF}, \mathrm{H}_{2} \mathrm{O}_{2}$

e. greatest heat of vaporization: $\mathrm{H}_{2} \mathrm{CO}, \mathrm{CH}_{3} \mathrm{CH}_{3}, \mathrm{CH}_{4}$

f. smallest enthalpy of fusion: $\mathrm{I}_{2}, \mathrm{CsBr}, \mathrm{CaO}$

Locate the following metals in the periodic table, and predict whether they are likely to be found in nature as oxides, sulfides, or in uncombined form:

(a) Copper

(b) Zirconium

(c) Palladium

(d) Bismuth

In each of the following groups of substances, pick the one that has the given property. Justify each answer.

a. highest boiling point: $\mathrm{CCl}_{4}, \mathrm{CF}_{4}, \mathrm{CBr}_{4}$

b. lowest freezing point: $\mathrm{LiF}, \mathrm{F}_{2}, \mathrm{HCl}$

c. smallest vapor pressure at $25^{\circ} \mathrm{C}: \mathrm{CH}_{3} \mathrm{OCH}_{3}, \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}$ $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}$

d. greatest viscosity: $\mathrm{H}_{2} \mathrm{S}, \mathrm{HF}, \mathrm{H}_{2} \mathrm{O}_{2}$

e. greatest heat of vaporization: $\mathrm{H}_{2} \mathrm{CO}, \mathrm{CH}_{3} \mathrm{CH}_{3}, \mathrm{CH}_{4}$

f. smallest enthalpy of fusion: $\mathrm{I}_{2}, \mathrm{CsBr}, \mathrm{CaO}$

Write chemical formulas for the following minerals:

(a) calcite, (b) dolomite, (c) fluorite, (d) halite, (e) corundum, (f) magnetite, (g) beryl, (h) galena, (i) epsomite, (j) anhydrite.

Specify which compound in each of the following pairs of ionic compounds should have the higher lattice energy: (a) $\mathrm{AIN}$ or $\mathrm{CaO},(\mathrm{b}) \mathrm{NaF}$ or $\mathrm{CsF},(\mathrm{c}) \mathrm{MgCl}_{2}$ or $\mathrm{MgF}_{2} .$ Explain your choice.

Which substance has the higher entropy in each of the following pairs?

(a) dry ice (solid $\mathrm{CO}_{2}$ ) at $-78^{\circ} \mathrm{C}$ or $\mathrm{CO}_{2}(\mathrm{g})$ at $0^{\circ} \mathrm{C}$

(b) liquid water at $25^{\circ}$ C or liquid water at $50^{\circ} \mathrm{C}$

(c) pure alumina, $\mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s}),$ or ruby (Ruby is $\mathrm{Al}_{2} \mathrm{O}_{3}$ in which some of the Al $^{3+}$ ions in the crystalline lattice are replaced with $\mathrm{Cr}^{3+}$ ions.)

(d) one mole of $\mathrm{N}_{2}(\mathrm{g})$ at 1 bar pressure or one mole of $\left.\mathrm{N}_{2}(\mathrm{g}) \text { at } 10 \text { bar pressure (both at } 298 \mathrm{K}\right)$

Which of the substances in each of the following sets would be expected to have the lowest melting point? Explain why.

a. $\mathrm{H}_{2}, \mathrm{N}_{2}, \mathrm{O}_{2}$

b. $\mathrm{Xe}, \mathrm{NaCl}, \mathrm{C}$ (diamond)

c. $\mathrm{Cl}_{2}, \mathrm{Br}_{2}, \mathrm{I}_{2}$