Chapter 6, Problem 6.152QP

A sample of natural gas is 80.0% CH₄ and 20.0% C₂H₆ by mass. What is the heat from the combustion of 1.00 g of this mixture? Assume the products are CO₂(g) and H₂O(l).

Interpretation Introduction

Interpretation:

The amount of heat evolved from the combustion of $\text{1}\text{g}\text{of}$ the given mixture has to be calculated.

Answer to Problem 6.152QP

• The amount of heat evolved from the given combustion reaction is $\text{54}\text{.8}\text{kJ}\text{.}$

Explanation of Solution

Given information,

$\begin{array}{l}\text{Sample}\text{of}\text{natural}\text{gas}\text{is}\text{80}\text{\%}{\text{CH}}_{\text{4}}\text{and}\text{20\%}{\text{C}}_{\text{2}}{\text{H}}_{\text{6}}\text{by}\text{mass}\text{.}\\ \text{products}\text{are}{\text{CO}}_{\text{2}}{}_{\left(\text{g}\right)}\text{and}{\text{H}}_{\text{2}}{\text{O}}_{\left(\text{l}\right)}\text{.}\end{array}$

Write the balanced equation

$\begin{array}{l}{\text{CH}}_{\text{4}}{}_{\left(\text{g}\right)}\text{+}{\text{2O}}_{\text{2}}{}_{\left(\text{g}\right)}\stackrel{}{\to }{\text{CO}}_{\text{2}}{}_{\left(\text{g}\right)}\text{+}{\text{2H}}_{\text{2}}{\text{O}}_{\left(\text{l}\right)}\\ {\text{C}}_{\text{2}}{\text{H}}_{\text{6}}{}_{\left(\text{g}\right)}\text{+}\text{3}\text{.5}{\text{O}}_{\text{2}}{}_{\left(\text{g}\right)}\stackrel{}{\to }{\text{2CO}}_{\text{2}}{}_{\left(\text{g}\right)}\text{+}{\text{3H}}_{\text{2}}{\text{O}}_{\left(\text{l}\right)}\end{array}$

Calculate the moles of ${\text{CH}}_{\text{4}}\text{and}{\text{C}}_{\text{2}}{\text{H}}_{\text{6}}\left(\text{let}\text{80\%}\text{=}\text{0}\text{.800}\text{g}\text{and}\text{20\%}\text{=}\text{0}\text{.200}\text{g}\right)$

$\begin{array}{l}\text{Mol}{\text{CH}}_{\text{4}}\text{=}\text{0}\text{.800}\text{g}{\text{CH}}_{\text{4}}\text{×}\frac{\text{1}\text{mol}{\text{CH}}_{\text{4}}}{\text{16}\text{.04}\text{g}{\text{CH}}_{\text{4}}}\text{=}\text{0}\text{.04987}\text{mol}{\text{CH}}_{\text{4}}\\ \text{Mol}{\text{C}}_{\text{2}}{\text{H}}_{\text{6}}\text{=}\text{0}\text{.200}\text{g}{\text{C}}_{\text{2}}{\text{H}}_{\text{6}}\text{×}\frac{\text{1}\text{mol}{\text{C}}_{\text{2}}{\text{H}}_{\text{6}}}{\text{30}\text{.07}\text{g}{\text{C}}_{\text{2}}{\text{H}}_{\text{6}}}\text{=}\text{0}\text{.006651}\text{mol}{\text{C}}_{\text{2}}{\text{H}}_{\text{6}}\end{array}$

Calculate the heat of combustion by using enthalpies of formation

$\begin{array}{l}{\text{CH}}_{\text{4}}{}_{\left(\text{g}\right)}\text{+}{\text{2O}}_{\text{2}}{}_{\left(\text{g}\right)}\stackrel{}{\to }{\text{CO}}_{\text{2}}{}_{\left(\text{g}\right)}\text{+}{\text{2H}}_{\text{2}}{\text{O}}_{\left(\text{l}\right)}\\ \text{0}\text{.04987}\text{excess}\text{0}\text{.04987}\text{2}\text{×}\text{0}\text{.04987}\text{mol}\\ \text{-}\text{74}\text{.87}\text{0}\text{-}\text{393}\text{.5}\text{-}\text{285}\text{.8}\text{kJ/mol}\\ \text{-}\text{3}\text{.734}\text{0}\text{-}\text{19}\text{.62}\text{-}\text{28}\text{.51}\text{kJ/eqn}\\ \\ {\text{C}}_{\text{2}}{\text{H}}_{\text{6}}{}_{\left(\text{g}\right)}\text{+}\text{3}\text{.5}{\text{O}}_{\text{2}}{}_{\left(\text{g}\right)}\stackrel{}{\to }{\text{2CO}}_{\text{2}}{}_{\left(\text{g}\right)}\text{+}{\text{3H}}_{\text{2}}{\text{O}}_{\left(\text{l}\right)}\\ \text{0}\text{.006651}\text{excess}\text{0}\text{.04693}\text{3}\text{×}\text{0}\text{.006651}\text{mol}\\ \text{-84}\text{.68}\text{0}\text{-393}\text{.5}\text{-285}\text{.8}\text{kJ/mol}\\ \text{-0}\text{.5632}\text{0}\text{-}\text{5}\text{.234}\text{-5}\text{.703}\text{kJ/eqn}\end{array}$

Calculate the enthalpy change for the combustion of ${\text{CH}}_{\text{4}}$

$\begin{array}{l}\text{ΔH}\text{=}\left[\left(\text{-28}\text{.51}\right)\text{+}\left(\text{-19}\text{.62}\right)\right]\text{-}\left[\left(\text{-3}\text{.734}\right)\text{+}\text{0}\right]\\ \text{=}\text{-}\text{44}\text{.395}\text{kJ}\text{.}\end{array}$

Calculate the enthalpy change for the combustion of ${\text{C}}_{\text{2}}{\text{H}}_{\text{6}}$

$\begin{array}{l}\text{ΔH}\text{=}\left[\left(\text{-5}\text{.234}\right)\text{+}\left(\text{-5}\text{.703}\right)\right]\text{-}\left[\left(\text{-0}\text{.5632}\right)\text{+}\text{0}\right]\\ \text{=}\text{-}\text{10}\text{.373}\text{kJ}\text{.}\end{array}$

For the combustion of the total $\left(\text{1}\text{.00}\text{g}\right)\text{of}{\text{CH}}_{\text{4}}\text{and}{\text{C}}_{\text{2}}{\text{H}}_{\text{6}}\text{:}$

$\begin{array}{l}\text{ΔH}\text{=}\text{-44}\text{.395}\text{+}\left(\text{-}\text{10}\text{.373}\right)\\ \text{=}\text{-54}\text{.768}\text{=}\text{-54}\text{.8}\text{kJ}\text{.}\end{array}$

The amount of heat evolved from the given combustion reaction is $\text{54}\text{.8}\text{kJ}\text{.}$

Conclusion

The amount of heat evolved from the given reaction was calculated by using mole and enthalpy change calculations.