Chapter 9, Problem 48PP

Interpretation Introduction

Interpretation:

Temperature condition is needed to be explained in the given dehydrogenation reaction.

Concept introduction:

Dehydrogenation: dehydrogenation is a process of elimination of hydrogen molecule from the substrate at high temperature condition.

Free energy: reaction is feasible when free energy is negative.

$\begin{array}{l}\text{ΔG}\text{=}\text{ΔH-TΔS}\\ \text{ΔG}\text{=}\text{free}\text{energy}\\ \text{ΔH}\text{=}\text{change}\text{in}\text{enthalpy}\\ \text{ΔS}\text{=}\text{change}\text{in}\text{entropy}\end{array}$

Answer to Problem 48PP

Reaction is feasible at higher temperature conditions only since $\text{ΔG}$ is negative at higher temperatures. Therefore, higher temperatures are needed for dehydrogenation process.

Explanation of Solution

To explain: the conditions for the given reaction.

Given reaction is shown below.

Clear from the reaction that the ethane molecule converted ethylene molecule at high temperature condition by releasing hydrogen gas.

Given reaction refers the dehydrogenation process at high temperatures. Given substrate is ethane and this ethane molecule heated at high temperature (750⁰ C) to produce ethylene and hydrogen gas.

To give: the reason for high temperatures needed for the dehydrogenation process.

Given reaction is favorable when $\text{ΔG}$ is negative and change in enthalpy is positive for this reaction because two sigma bonds are braking to form one pi-bond. In addition, change in entropy is positive because one molecule is converting into two molecules. So depending on these conditions, reaction temperature should be high then only $\text{ΔG}$ will be negative to feasible this reaction.

$\begin{array}{l}\text{ΔG}\text{=}\text{ΔH-TΔS}\\ \text{ΔH}\text{= -ve }\\ \text{ΔS}\text{=}\text{+ve}\end{array}$

At higher temperature condition, the given reaction is feasible since $\text{ΔG}$ is negative.

Conclusion

Conclusion

At higher temperature conditions, value of free energy will be negative so the dehydrogenation reaction is feasible at higher temperature conditions.