The standard heat of formation, [tex]$\Delta H_{ f }^{\circ}$[/tex], is defined as the enthalpy change for the formation of one mole of substance from its constituent elements in their standard states. Thus, elements in their standard states have [tex]$\Delta H_{ f }^{\circ}=0$[/tex]. Heat of formation values can be used to calculate the enthalpy change of any reaction.

Consider, for example, the reaction

[tex]\[ 2 NO (g) + O_2(g) \rightleftharpoons 2 NO_2(g) \][/tex]

with heat of formation values given by the following table:

[tex]\[
\begin{tabular}{|c|c|}
\hline
Substance & \begin{tabular}{c}
$\Delta H_{ f }^{\circ}$ \\
$(kJ / mol)$
\end{tabular} \\
\hline
$NO (g)$ & 90.2 \\
\hline
$O_2(g)$ & 0 \\
\hline
$NO_2(g)$ & 33.2 \\
\hline
\end{tabular}
\][/tex]

Then the standard heat of reaction for the overall reaction is

[tex]\[
\begin{aligned}
\Delta H_{ \text{rxn} }^{\circ} &= \Delta H_{ f }^{\circ}(\text {products}) - \Delta H_{ f }^{\circ} (\text{reactants}) \\
&= [2 \times 33.2 - (2 \times 90.2 + 0)] \\
&= -114 \, \text{kJ}
\end{aligned}
\][/tex]

Part B

The combustion of propane, [tex]C_3 H_8[/tex], occurs via the reaction

[tex]\[ C_3 H_8(g) + 5 O_2(g) \rightarrow 3 CO_2(g) + 4 H_2O(g) \][/tex]

with heat of formation values given by the following table:

[tex]\[
\begin{tabular}{|c|c|}
\hline
Substance & \begin{tabular}{c}
$\Delta H_f$ \\
$(kJ / mol)$
\end{tabular} \\
\hline
$C_3 H_8(g)$ & -104.7 \\
\hline
$CO_2(g)$ & -393.5 \\
\hline
$H_2O(g)$ & -241.8 \\
\hline
\end{tabular}
\][/tex]

Calculate the enthalpy for the combustion of 1 mole of propane.
Express your answer to four significant figures and include the appropriate units.

[tex]\[ \Delta H_{\text{rxn}}^{\circ} = \, \square \, \text{Value} \, \text{Units} \][/tex]