Chapter 15.3, Problem 25PP

Interpretation Introduction

Interpretation:

The mass of methane that must be burned to produce 12880kJ of heat is to be determined.

Concept introduction:

Enthalpy of combustion: It is the amount of heat produced when one mole of a substance burns completely in oxygen.

Answer to Problem 25PP

Heat released $\mathrm{Q}=-12880kJ$

Enthalpy of combustion ( $\Delta H_{comb}$ ) for methane $=-891\raisebox{1ex}{$kJ$}\!\left/ \!\raisebox{-1ex}{$mol$}\right.$

Molar mass of methane ${\mathrm{CH}}_4=12\times 1+1\times 4=16\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right.$

Number of moles in mass m of methane $\mathrm{N}=\frac{mass}{16\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right.}=\frac{m}{16\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right.}$

$\begin{array}{l}Q=N\times D{H}_{comb}\\ -12880kJ=\frac{m}{16\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right.}\times -891\raisebox{1ex}{$kJ$}\!\left/ \!\raisebox{-1ex}{$mol$}\right.\\ m=12880\times \frac{16}{891}g\\ m\approx 231.3g\end{array}$

Explanation of Solution

The following steps are needed to calculate the heat released:

• Calculate the molar mass of methane
• Write the expression for the number of moles contained in mass m of ammonia.
• Calculate the mass m of methane that wouldrelease the given amount of heat using the formula,
$Q=\mathrm{N}\times \Delta H_{comb}$

Conclusion

231.3 g of methane will burn in oxygen to produce -12880kJ of heat.