Chapter 6, Problem 6.72P

Interpretation Introduction

Interpretation:Whetherbenzene or acetylene releases more energy per mole of CH needs to be determined.

Concept introduction: Balanced chemical equation for the combustion reaction of benzene is:

  ${\text{C}}_{\text{6}}{\text{H}}_{\text{6}}\text{(g)}\text{+}\raisebox{1ex}{$\text{15}$}\!\left/ \!\raisebox{-1ex}{$\text{2}$}\right.{\text{O}}_2\to {\text{6CO}}_{\text{2}}\text{(g)}\text{+}{\text{3H}}_2\text{O}\text{(g)}$

Balanced chemical equation for the combustion reaction of acetylene is as follows:

  ${\text{C}}_{\text{2}}{\text{H}}_{\text{2}}\text{(g)}\text{}\text{}\text{}\text{+}\raisebox{1ex}{$\text{5}$}\!\left/ \!\raisebox{-1ex}{$\text{2}$}\right.\text{}\text{}\text{}\text{}{\text{O}}_{\text{2}}\text{(g)}\to \text{2}{\text{CO}}_{\text{2}}\text{(g)}\text{+}{\text{H}}_{\text{2}}\text{O}\text{(g)}$

Answer to Problem 6.72P

Acetylene releases more energy per CH than benzene.

Explanation of Solution

Balanced chemical equation for the combustion reaction of benzene is:

  ${\text{C}}_{\text{6}}{\text{H}}_{\text{6}}\text{(g)}\text{+}\raisebox{1ex}{$\text{15}$}\!\left/ \!\raisebox{-1ex}{$\text{2}$}\right.{\text{O}}_2\to {\text{6CO}}_{\text{2}}\text{(g)}\text{+}{\text{3H}}_2\text{O}\text{(g)}$

Here,

  $\begin{array}{l}\text{(}{\text{ΔH}}^{\text{0}}{}_{\text{f}}{\text{CO}}_{\text{2}}\text{(g)}\text{)}\text{=(}-\text{393}\text{.5}\text{kJ/L}\text{),}\\ \text{(}{\text{ΔH}}^{\text{0}}{}_{\text{f}}{\text{H}}_{\text{2}}\text{O}\text{(g)}\text{)}\text{=(}-\text{241}\text{.86}\text{kJ/L}\text{),}\\ \text{(}{\text{ΔH}}^{\text{0}}{}_{\text{f}}{\text{C}}_{\text{6}}{\text{H}}_{\text{6}}\text{(g)}\text{)}\text{=}\text{(}\text{82}\text{.9}\text{kJ/L}\text{)}\\ \text{(}{\text{ΔH}}^{\text{0}}{}_{\text{f}}{\text{O}}_{\text{2}}\text{(g)}\text{)=(}\text{0}\text{.0}\text{kJ/L}\text{)}\end{array}$

Putting the values,

  $\begin{array}{c}{\text{ΔH}}^{\text{0}}{}_{\text{rxn}}\text{=}\left[\text{6}\text{mol}{\text{ΔH}}^{\text{0}}{}_{\text{rxn}}\text{(}{\text{ΔH}}^{\text{0}}{}_{\text{f}}{\text{CO}}_{\text{2}}\text{(g)}\text{)}\text{+}\text{3}\text{mol}\text{(}{\text{ΔH}}^{\text{0}}{}_{\text{f}}{\text{H}}_{\text{2}}\text{O}\text{(g)}\text{)}-\left[\begin{array}{l}\text{1}\text{mol}\text{(}{\text{ΔH}}^{\text{0}}{}_{\text{f}}{\text{C}}_{\text{6}}{\text{H}}_{\text{6}}\text{(g)}\text{)}\\ \text{+}\raisebox{1ex}{$\text{15}$}\!\left/ \!\raisebox{-1ex}{$\text{2}$}\right.\text{mol}\text{(}{\text{ΔH}}^{\text{0}}{}_{\text{f}}{\text{O}}_{\text{2}}\text{(g)}\text{)}\end{array}\right]\right]\\ {\text{ΔH}}^{\text{0}}{}_{\text{rxn}}\text{=}\left[\text{6}\text{mol}\text{(}-\text{393}\text{.5}\text{kJ/L}\text{)}\text{+}\text{3}\text{mol}\text{(}-\text{241}\text{.86}\text{kJ/L}\text{)}-\left[\begin{array}{l}\text{1}\text{mol}\text{(}\text{82}\text{.9}\text{kJ/L}\text{)}\\ \text{+}\raisebox{1ex}{$\text{15}$}\!\left/ \!\raisebox{-1ex}{$\text{2}$}\right.\text{mol}\text{(}\text{0}\text{.0}\text{kJ/L}\text{)}\end{array}\right]\right]\\ \text{=}-\text{2361}\text{kJ/L}-725.58\text{kJ/L}-\left[82.9\text{kJ/L}\right]\\ =-\text{3169}\text{.48}\text{kJ}\end{array}$

  $\left(\frac{\text{-393}\text{.5}\text{kJ/L}}{\text{1}\text{mol}{\text{C}}_{\text{6}}{\text{H}}_{\text{6}}}\right)\left(\frac{\text{1}\text{mol}{\text{C}}_{\text{6}}{\text{H}}_{\text{6}}}{\text{6}\text{mol}\text{CH}}\right)\text{=}\text{-528}\text{.2297}\text{=}\text{-528}\text{.2}\text{kJ/mol}\text{CH}$

Balanced chemical equation for the combustion reaction of acetylene is:

  ${\text{C}}_{\text{2}}{\text{H}}_{\text{2}}\text{(g)}\text{}\text{}\text{}\text{+}\raisebox{1ex}{$\text{5}$}\!\left/ \!\raisebox{-1ex}{$\text{2}$}\right.\text{}\text{}\text{}\text{}{\text{O}}_{\text{2}}\text{(g)}\to \text{2}{\text{CO}}_{\text{2}}\text{(g)}\text{+}{\text{H}}_{\text{2}}\text{O}\text{(g)}$

  $\begin{array}{c}\\ {\text{ΔH}}^{\text{0}}{}_{\text{rxn}}\text{=}\left[\text{2}\text{mol}{\text{ΔH}}^{\text{0}}{}_{\text{rxn}}\text{(}{\text{ΔH}}^{\text{0}}{}_{\text{f}}{\text{CO}}_{\text{2}}\text{(g)}\text{)}\text{+}\text{1}\text{mol}\text{(}{\text{ΔH}}^{\text{0}}{}_{\text{f}}{\text{H}}_{\text{2}}\text{O}\text{(g)}\text{)}\text{-}\left[\begin{array}{l}\text{1}\text{mol}\text{(}{\text{ΔH}}^{\text{0}}{}_{\text{f}}{\text{C}}_{\text{2}}{\text{H}}_{\text{2}}\text{(g)}\text{)}\\ \text{+}\raisebox{1ex}{$\text{5}$}\!\left/ \!\raisebox{-1ex}{$\text{2}$}\right.\text{mol}\text{(}{\text{ΔH}}^{\text{0}}{}_{\text{f}}{\text{O}}_{\text{2}}\text{(g)}\text{)}\end{array}\right]\right]\\ {\text{ΔH}}^{\text{0}}{}_{\text{rxn}}\text{=}\left[\text{2}\text{mol}\text{(}-\text{393}\text{.5}\text{kJ/L}\text{)}\text{+}\text{1}\text{mol}\text{(}-\text{241}\text{.86}\text{kJ/L}\text{)}-\left[\text{1}\text{mol}\text{(}\text{227}\text{kJ/L}\text{)}\text{+}\raisebox{1ex}{$\text{5}$}\!\left/ \!\raisebox{-1ex}{$\text{2}$}\right.\text{mol}\text{(}\text{0}\text{.0}\text{kJ/L}\text{)}\right]\right]\\ \text{=}-787\text{kJ}-\text{241}\text{.86}\text{kJ}-\text{227}\text{kJ}\\ \text{=}-\text{1255}\text{.826}\text{kJ}\end{array}$

Conclusion

Thus, acetylene releases more energy per CH than benzene.