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?

## Discussion

## Video Transcript

No transcript available

## Recommended Questions

Given the values of $\Delta H_{\mathrm{rxn}}, \Delta S_{\mathrm{rxn}}$ and $T,$ determine $\Delta S_{\text { univ }}$ and predict whether or not each reaction is spontaneous. (Assume that all reactants and products are in their standard states.)

\begin{equation}\begin{array}{l}{\text { a. } \Delta H_{\mathrm{rxn}}^{\circ}=-95 \mathrm{kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-157 \mathrm{J} / \mathrm{K} ; T=298 \mathrm{K}} \\ {\text { b. } \Delta H_{\mathrm{rxn}}^{\circ}=-95 \mathrm{kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-157 \mathrm{J} / \mathrm{K} ; T=855 \mathrm{K}} \\ {\text { c. } \Delta H_{\mathrm{rxn}}^{\circ}=+95 \mathrm{kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-157 \mathrm{J} / \mathrm{K} ; T=298 \mathrm{K}} \\ {\text { d. } \Delta H_{\mathrm{rxn}}^{\circ}=-95 \mathrm{kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=+157 \mathrm{J} / \mathrm{K} ; T=398 \mathrm{K}}\end{array}\end{equation}

A reaction has $\Delta H_{\mathrm{rxn}}^{\circ}=-112 \mathrm{kJ}$ and $\Delta S_{\mathrm{rxn}}^{\circ}=354 \mathrm{J} / \mathrm{K}$ . At what temperature is the change in entropy for the reaction equal to the change in entropy for the surroundings?

In photosynthesis, plants form glucose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)$ and oxygen from carbon dioxide and water. Write a balanced equation for photosynthesis and calculate $\Delta H_{\mathrm{rxn}}^{\circ}, \Delta S_{\mathrm{rxn}}^{\circ},$ and $\Delta G_{\mathrm{ren}}^{\circ}$ at $25^{\circ} \mathrm{C}$ . Is photosynthesis spontaneous?