Problem: The standard enthalpies of formation of gaseous propyne (C3H4), propylene (C3H6), and propane (C3H8) are +185.4, +20.4, and -103.8 kJ/mol, respectively.Which is the most efficient fuel in terms of heat evolved per unit mass?

For propyne (C₃H₄)

C₃H₄ + 4 O₂ → 3 CO₂ + 2 H₂O

$\boxed{\mathbf{\Delta H}{\mathbf{°}}_{\mathbf{rxn}}\mathbf{=}\mathbf{H}{\mathbf{°}}_{\mathbf{f}\mathbf{,}\mathbf{ }\mathbf{prod}}\mathbf{-}\mathbf{H}{\mathbf{°}}_{\mathbf{f}\mathbf{,}\mathbf{ }\mathbf{react}}}$

$$\begin{gathered} \mathbf{\Delta H}{\mathbf{°}}_{\mathbf{rxn}}\mathbf{=}\left[\mathbf{(}\mathbf{3}\mathbf{ }\cancel{\mathbf{mol}\mathbf{ }{\mathbf{CO}}_{\mathbf{2}}}\mathbf{)}\left(\frac{\mathbf{-}\mathbf{393}\mathbf{.}\mathbf{5}\mathbf{ }\mathbf{kJ}}{\mathbf{1}\mathbf{ }\cancel{\mathbf{mol}\mathbf{ }{\mathbf{CO}}_{\mathbf{2}}}}\right)\mathbf{+}\mathbf{(}\mathbf{2}\mathbf{ }\cancel{\mathbf{mol}\mathbf{ }{\mathbf{H}}_{\mathbf{2}}\mathbf{O}}\mathbf{)}\mathbf{\left(}\frac{\mathbf{-}\mathbf{241}\mathbf{.}\mathbf{8}\mathbf{ }\mathbf{kJ}}{\mathbf{1}\mathbf{ }\cancel{\mathbf{mol}\mathbf{ }{\mathbf{H}}_{\mathbf{2}}\mathbf{O}}}\mathbf{\right)}\right] \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{-}\left[\mathbf{(}\mathbf{1}\mathbf{ }\cancel{\mathbf{mol}\mathbf{ }{\mathbf{C}}_{\mathbf{3}}{\mathbf{H}}_{\mathbf{4}}}\mathbf{)}\left(\frac{\mathbf{+}\mathbf{185}\mathbf{.}\mathbf{4}\mathbf{ }\mathbf{kJ}}{\mathbf{1}\mathbf{ }\cancel{\mathbf{mol}\mathbf{ }{\mathbf{C}}_{\mathbf{3}}{\mathbf{H}}_{\mathbf{4}}}}\right)\mathbf{+}\mathbf{0}\right] \end{gathered}$$

ΔH˚_rxn = –1849.5 kJ/mol

molar mass propyne = 40.062 g/mol

$\mathbf{∆}\mathbf{H}{\mathbf{°}}_{\mathbf{rxn}}\mathbf{=}\mathbf{-}\mathbf{1849}\mathbf{.}\mathbf{5}\frac{\mathbf{kJ}}{\cancel{\mathbf{mol}}}\mathbf{\times }\frac{\cancel{\mathbf{mol}}}{\mathbf{40}\mathbf{.}\mathbf{062}\mathbf{ }\mathbf{g}}$

ΔH˚_rxn = –46.16 kJ/g

For propylene (C₃H₆)

C₃H₆ + 9/2 O₂ → 3 CO₂ + 3 H₂O

$\boxed{\mathbf{\Delta H}{\mathbf{°}}_{\mathbf{rxn}}\mathbf{=}\mathbf{H}{\mathbf{°}}_{\mathbf{f}\mathbf{,}\mathbf{ }\mathbf{prod}}\mathbf{-}\mathbf{H}{\mathbf{°}}_{\mathbf{f}\mathbf{,}\mathbf{ }\mathbf{react}}}$

$$\begin{gathered} \mathbf{\Delta H}{\mathbf{°}}_{\mathbf{rxn}}\mathbf{=}\left[\mathbf{(}\mathbf{3}\mathbf{ }\cancel{\mathbf{mol}\mathbf{ }{\mathbf{CO}}_{\mathbf{2}}}\mathbf{)}\left(\frac{\mathbf{-}\mathbf{393}\mathbf{.}\mathbf{5}\mathbf{ }\mathbf{kJ}}{\mathbf{1}\mathbf{ }\cancel{\mathbf{mol}\mathbf{ }{\mathbf{CO}}_{\mathbf{2}}}}\right)\mathbf{+}\mathbf{(}\mathbf{3}\mathbf{ }\cancel{\mathbf{mol}\mathbf{ }{\mathbf{H}}_{\mathbf{2}}\mathbf{O}}\mathbf{)}\mathbf{\left(}\frac{\mathbf{-}\mathbf{241}\mathbf{.}\mathbf{8}\mathbf{ }\mathbf{kJ}}{\mathbf{1}\mathbf{ }\cancel{\mathbf{mol}\mathbf{ }{\mathbf{H}}_{\mathbf{2}}\mathbf{O}}}\mathbf{\right)}\right] \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{-}\left[\mathbf{(}\mathbf{1}\mathbf{ }\cancel{\mathbf{mol}\mathbf{ }{\mathbf{C}}_{\mathbf{3}}{\mathbf{H}}_{\mathbf{6}}}\mathbf{)}\left(\frac{\mathbf{+}\mathbf{20}\mathbf{.}\mathbf{4}\mathbf{ }\mathbf{kJ}}{\mathbf{1}\mathbf{ }\cancel{\mathbf{mol}\mathbf{ }{\mathbf{C}}_{\mathbf{3}}{\mathbf{H}}_{\mathbf{6}}}}\right)\mathbf{+}\mathbf{0}\right] \end{gathered}$$