Chapter 8, Problem 8.131QP

Interpretation Introduction

Interpretation: The energy difference between the incomplete and complete combustion of one mole of methane is to be calculated.

Concept introduction: The energy which is required in a molecule to break one mole of a covalent bond in its gaseous phase is known as bond energy of that bond. It is expressed in terms of enthalpy change denoted by $\left(\Delta H\right)$.

To determine: The energy difference between the incomplete and complete combustion of one mole of methane.

Answer to Problem 8.131QP

The energy difference between the incomplete and complete combustion of one mole of methane is $\underset{\_}{-278.5kJ/mol}$.

Explanation of Solution

Explanation

The reaction for incomplete combustion of methane is,

${\text{2CH}}_4\left(g\right)+3{\text{O}}_2\left(g\right)\stackrel{}{\to }\text{2CO}\left(g\right)+4{\text{H}}_{\text{2}}\text{O}\left(g\right)$

The change in enthalpy for the given reaction is calculated by using the formula,

$\Delta H_{\text{rxn}}={\displaystyle \sum \Delta H_{\text{bond}\text{breaking}}-{\displaystyle \sum \Delta H_{\text{bond}\text{forming}}}}$

Bond energy of a $\text{C}-\text{H}$ bond is $413\text{kJ/mol}$.

Bond energy of a $\text{O}=\text{O}$ bond is $495\text{kJ/mol}$.

Bond energy of a $\text{C}\equiv \text{O}$ bond is $1072\text{kJ/mol}$.

Bond energy of a $\text{O}-\text{H}$ bond is $463\text{kJ/mol}$.

Substitute the value of average bond energies of $\text{C}-\text{H}$, $\text{O}=\text{O}$, $\text{C}\equiv \text{O}$ and $\text{O}-\text{H}$ bond in the above formula to calculate the enthalpy change for the reaction.

$\begin{array}{c}\Delta H_{\text{rxn}}=\left(8\times \text{C}-\text{H}+3\times \text{O}=\text{O}\right)-\left(2\times \text{C}\equiv \text{O}+8\times \text{O}-\text{H}\right)\\ =\left(8\times 413\text{kJ/mol}+3\times 495\text{kJ/mol}\right)-\left(2\times 1072+8\times 463\text{kJ/mol}\right)\\ =\left(3304+1485\text{kJ/mol}\right)-\left(2144+3704\text{kJ/mol}\right)\\ =4789-5848\text{kJ/mol}\end{array}$

Simplify the above equation,

$\Delta H=-1059\text{kJ/mol}$

The change in enthalpy for two moles of methane is $-1059\text{kJ/mol}$. For one mole of methane the change in enthalpy is,

$\begin{array}{c}\Delta H=\frac{-1059\text{kJ/mol}}{2}\\ =-529.5\text{kJ/mol}\end{array}$

Hence, the enthalpy of incomplete combustion of methane is $-529.5\text{kJ/mol}$.

The equation for complete combustion of methane is,

${\text{CH}}_4\left(g\right)+2{\text{O}}_2\left(g\right)\stackrel{}{\to }{\text{CO}}_2\left(g\right)+2{\text{H}}_{\text{2}}\text{O}\left(g\right)$

The change in enthalpy for the given reaction is calculated by using the formula,

$\Delta H_{\text{rxn}}={\displaystyle \sum \Delta H_{\text{bond}\text{breaking}}-{\displaystyle \sum \Delta H_{\text{bond}\text{forming}}}}$

Bond energy of a $\text{C}-\text{H}$ bond is $413\text{kJ/mol}$.

Bond energy of a $\text{O}=\text{O}$ bond is $495\text{kJ/mol}$.

Bond energy of a $\text{C}=\text{O}$ bond is $799\text{kJ/mol}$.

Bond energy of a $\text{O}-\text{H}$ bond is $463\text{kJ/mol}$.

Substitute the value of average bond energies of $\text{C}-\text{H}$, $\text{O}=\text{O}$, $\text{C}=\text{O}$ and $\text{O}-\text{H}$ bond in the above formula to calculate the enthalpy change for the reaction.

$\begin{array}{c}\Delta H_{\text{rxn}}=\left(4\times \text{C}-\text{H}+2\times \text{O}=\text{O}\right)-\left(2\times \text{C}=\text{O}+4\times \text{O}-\text{H}\right)\\ =\left(4\times 413\text{kJ/mol}+2\times 495\text{kJ/mol}\right)-\left(2\times 799+4\times 463\text{kJ/mol}\right)\\ =\left(1652+990\text{kJ/mol}\right)-\left(1598+1852\text{kJ/mol}\right)\\ =2642-3450\text{kJ/mol}\end{array}$

Simplify the above equation,

$\Delta H=-808\text{kJ/mol}$

The change in enthalpy for one mole of methane is $-808\text{kJ/mol}$

Hence, the enthalpy of complete combustion of methane is. $-808\text{kJ/mol}$.

The difference between the enthalpy of complete combustion of methane and the incomplete combustion of methane is,

$\begin{array}{c}\text{Difference}\text{in}\text{enthalpy}=-808\text{kJ/mol}-\left(-5\text{29}\text{.5}\text{kJ/mol}\right)\\ =-808+529.5\text{kJ/mol}\\ =\underset{\_}{-278.5kJ/mol}\end{array}$

Hence, the incomplete combustion reaction releases $\underset{\_}{278.5kJ/mol}$ less heat than the complete combustion reaction.

Conclusion

The energy difference between the incomplete and complete combustion of one mole of methane is $\underset{\_}{-278.5kJ/mol}$.