Chapter 15, Problem 85A

Grilling What mass of propane $(C_3{H}_8)$ must be burnedin a barbecue grill to release 4560 kJ of heat? The $\Delta H_{comb}$ of propane is -2219 kJ/mol.

Interpretation Introduction

Interpretation:

Mass of propane ${\text{(C}}_{\text{6}}^{}{\text{H}}_{\text{8}}^{})$ burned during combustion is to be calculated.

Concept introduction:

Thermochemical equation: It is the balanced chemical equation that includes the physical states of all the reactants and products and their energy change. Thermochemical equation is usually expressed as change in enthalpy, $\text{ΔH}$.

Answer to Problem 85A

$\text{90}\text{.62g}$ of propane ${\text{(C}}_{\text{6}}^{}{\text{H}}_{\text{8}}^{})$ is burned in a barbecue grill to release $\text{4560}\text{kJ}$ of heat.

Explanation of Solution

The balanced thermochemical equation for the combustion of 1 mol of ${\text{C}}_{\text{6}}^{}{\text{H}}_{\text{8}}^{}$ is

${\text{C}}_{\text{6}}^{}{\text{H}}_{\text{8}}^{}{\text{(g)+5O}}_{\text{2}}^{}\text{(g)}\to {\text{3CO}}_{\text{2}}^{}{\text{(g)+4H}}_{\text{2}}^{}\text{O(l)}$

${\text{ΔH}}_{\text{comb}}^{}\text{=}\text{-2219kJ/mol}$

Molar mass of ${\text{C}}_{\text{6}}^{}{\text{H}}_{\text{8}}^{}$

Since, ${\text{C}}_{\text{6}}^{}{\text{H}}_{\text{8}}^{}$ contain 6 atoms of carbon and 8 atoms of hydrogen. The molar mass would be $\begin{array}{l}\text{C=3×12}\text{.0107g/mol}\\ \text{=36}\text{.0321g/mol}\end{array}$

$\begin{array}{l}\text{H=8×1}\text{.0079g/mol}\\ \text{=8}\text{.0632g/mol}\end{array}$

$\text{Molar}\text{mass=Sum}\text{of}\text{atomic}\text{weight}\text{of}\text{each}\text{element}\text{present}\text{the}\text{compound}$

$\begin{array}{l}\text{=36}\text{.0}\text{.321+8}\text{.0632g/mol}\\ \text{=44}\text{.0953g/mol}\end{array}$

Now, using the molar mass of ${\text{C}}_{\text{6}}^{}{\text{H}}_{\text{8}}^{}$ as conversion factor to convert moles of ${\text{C}}_{\text{6}}^{}{\text{H}}_{\text{8}}^{}$ to kJ.

$\text{1mol=44}\text{.0953g/mol}$

$\begin{array}{l}\text{=-4560}\frac{\text{1mole}\text{of}{\text{C}}_{\text{3}}^{}{\text{H}}_{\text{8}}^{}}{\text{-2219}}\text{.}\frac{\text{44}{\text{.0953gC}}_{\text{3}}^{}{\text{H}}_{\text{8}}^{}}{\text{1mole}\text{of}{\text{C}}_{\text{3}}^{}{\text{H}}_{\text{8}}^{}}\\ \text{=90}\text{.62g}{\text{C}}_{\text{3}}^{}{\text{H}}_{\text{8}}^{}\end{array}$

Conclusion

Mass can be calculated by heat released..