Chapter U5.104, Problem 8E

Interpretation Introduction

Interpretation:

The net energy change for the given reaction is to be calculated.

Concept introduction:

The difference between bond broken energy and bond formed energy is termed as bond energy. The formula to calculate enthalpy change using bond energy is shown below:

$\Delta H_{\text{rxn}}^{\text{o}}=\Sigma H_{\text{bond}\text{broken}}-\Sigma H_{\text{bond}\text{formed}}$

Answer to Problem 8E

The net energy change for the given reaction is $124\text{kJ/mol}$.

Explanation of Solution

The given reaction is shown below.

${\text{C}}_{\text{2}}{\text{H}}_{\text{6}}\left(g\right)\to {\text{C}}_{\text{2}}{\text{H}}_{\text{4}}\left(g\right)+{\text{H}}_{\text{2}}\left(g\right)$

The ${\text{C}}_{\text{2}}{\text{H}}_{\text{6}}$ has six $\text{C-H}$ bonds and one $\text{C-C}$ bond. The ${\text{C}}_{\text{2}}{\text{H}}_{\text{4}}$ has four $\text{C-H}$ bonds and one $\text{C=C}$ bond.

The net energy change for the given reaction is calculated by the formula shown below:

$\begin{array}{c}\Delta H_{\text{rxn}}^{\text{o}}=\Sigma H_{\text{bond}\text{broken}}-\Sigma H_{\text{bond}\text{formed}}\end{array}$

   $\begin{array}{c}=\left[6\cdot H_{\text{C-H}}+1\cdot H_{\text{C-C}}\right]-\left[4\cdot H_{\text{C-H}}+1\cdot H_{\text{C=C}}+1\cdot H_{\text{H-H}}\right]\end{array}$ …(i)

Substitute the bond energies values in equation (i).

$\begin{array}{c}\Delta H_{\text{rxn}}^{\text{o}}=\left[6\cdot H_{\text{C-H}}+1\cdot H_{\text{C-C}}\right]-\left[4\cdot H_{\text{C-H}}+1\cdot H_{\text{C=C}}+1\cdot H_{\text{H-H}}\right]\end{array}$

   $\begin{array}{c}=\left[6\times 413\text{kJ/mol}+1\times 348\text{kJ/mol}\right]-\left[4\times 413\text{kJ/mol}+1\times 614\text{kJ/mol}+1\cdot 436\text{kJ/mol}\right]\end{array}$

   $\begin{array}{c}=2826\text{kJ/mol}-2702\text{kJ/mol}\end{array}$

   $\begin{array}{c}=\text{124}\text{kJ/mol}\end{array}$

Therefore, the energy change for the given reaction is $124\text{kJ/mol}$.

Conclusion

The energy change for the given reaction is $124\text{kJ/mol}$.