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Problem 110

Acetylene is produced commercially by the partial…

Problem 111

Synthesis gas, a mixture that includes the fuels CO and $\mathrm{H}_{2}$, is used to produce liquid hydrocarbons and methanol. It is made at pressures up to 100 atm by oxidation of methane followed by the steam reforming and water-gas shift reactions. Because the process is exothermic, temperatures reach $950-1100^{\circ} \mathrm{C}$, and the conditions are such that the amounts of $\mathrm{H}_{2}, \mathrm{CO}, \mathrm{CO}_{2}, \mathrm{CH}_{4}$, and $\mathrm{H}_{2} \mathrm{O}$ leaving the reactor are close to the equilibrium amounts for the steam re-forming and water-gas shift reactions:
$$\begin{aligned} \mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) & \rightleftharpoons \mathrm{CO}(g)+3 \mathrm{H}_{2}(g) \quad \text { (steam re-forming) } \\ \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) & \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) \quad \text { (water-gas shift) } \end{aligned}$$
(a) At $1000 .$ ', what are $\Delta G^{\circ}$ and $\Delta H^{\circ}$ for the steam re-forming
reaction and for the water-gas shift reaction?
(b) By doubling the steam re-forming step and adding it to the water-gas shift step, we obtain the following combined reaction:
$$2 \mathrm{CH}_{4}(g)+3 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{CO}(g)+7 \mathrm{H}_{2}(g)$$
Is this reaction spontaneous at $1000 .^{\circ} \mathrm{C}$ in the standard state?
(c) Is it spontaneous at 98 atm and $50 . \%$ conversion (when $50 . \%$ of the starting materials have reacted)?
(d) Is it spontaneous at 98 atm and $90 . \%$ conversion?

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?

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Video Transcript

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