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Problem 98

Propylene (propene; $\mathrm{CH}_{3} \mathrm{CH}=\mathrm{CH}_{2} )$ is used to produce
polypropylene and many other chemicals. Although most is obtained from the cracking of petroleum, about 2$\%$ is produced by catalytic dehydrogenation of propane $\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}\right) :$
$$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3} \stackrel{\mathrm{P} / \mathrm{A}_{2} \mathrm{O}_{3}}{\longrightarrow} \mathrm{CH}_{3} \mathrm{CH}=\mathrm{CH}_{2}+\mathrm{H}_{2}$$
Because this reaction is endothermic, heaters are placed between the reactor vessels to maintain the required temperature.
(a) If the molar entropy, $S^{\circ},$ of propylene is 267.1 $\mathrm{J} / \mathrm{mol} \cdot \mathrm{K}$ , find its entropy of formation, $S_{\mathrm{f}}^{\circ}$
(b) Find $\Delta G_{\mathrm{f}}^{\circ}$ of propylene $\left(\Delta H_{\mathrm{f}}^{\circ} \text { for propylene }=20.4 \mathrm{kJ} / \mathrm{mol}\right)$
(c) Calculate $\Delta H_{\mathrm{rxn}}^{\circ}$ and $\Delta G_{\mathrm{ran}}^{\circ} \mathrm{for}$ the dehydrogenation.
(d) What is the theoretical yield of propylene at $580^{\circ} \mathrm{C}$ if the initial pressure of propane is 1.00 atm?
(e) Would the yield change if the reactor walls were permeable to H. $?$ Explain.
(f) At what temperature is the dehydrogenation spontaneous, with all substances in the standard state?

Answer
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Chapter 20
Thermodynamics: Entropy, Free Energy, and the Direction of Chemical Reactions
CHEMISTRY: The Molecular Nature of Matter and Change 2016

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