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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One of the important reactions in the biochemical pathway glycolysis is the reaction of glucose-6-phosphate $(\mathrm{G} 6 \mathrm{P})$ to fructose-6-phosphate (F6P):

$\mathrm{G} 6 \mathrm{P} \rightleftharpoons \mathrm{F} 6 \mathrm{P} \quad \Delta G_{298}^{\circ}=1.7 \mathrm{kJ}$

(a) Is the reaction spontaneous or nonspontaneous under standard thermodynamic conditions?

(b) Standard thermodynamic conditions imply the concentrations of G6P and $\mathrm{F} 6 \mathrm{P}$ to be $1 \mathrm{M},$ however, in a typical cell, they are not even close to these values. Calculate $\Delta G$ when the concentrations of $\mathrm{G} 6 \mathrm{P}$ and $\mathrm{F} 6 \mathrm{P}$ are 120$\mu M$ and 28 $\mu M$ respectively, and discuss the spontaneity of the forward reaction under these conditions. Assume the temperature is $37^{\circ} \mathrm{C} .$

The metabolic oxidation of glucose, $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},$ in our bodies produces $\mathrm{CO}_{2},$ which is expelled from our lungs as a gas:

$$\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q)+6 \mathrm{O}_{2}(g) \longrightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l)$$

(a) Calculate the volume of dry $\mathrm{CO}_{2}$ produced at body temperature $\left(37^{\circ} \mathrm{C}\right)$ and 0.970 atm when 24.5 $\mathrm{g}$ of glucose is consumed in this reaction. (b) Calculate the volume of oxygen you would need, at 1.00 $\mathrm{atm}$ and $298 \mathrm{K},$ to completely oxidize 50.0 $\mathrm{g}$ of glucose.