$$\begin{array}{c c} \\ \text{Substance} & \text{Standard Heat of Formation}, \\ & \Delta H_{\text{f}}^\degree \text{ in } \pu{kJ }\pu{ mol^{-1}} \\ \hline \ce{C(s)} & 0.00 \\ \ce{CO2(g)} & -393.5\\ \ce{H2(g)} & 0.00 \\ \ce{H2O(l)} & -285.85 \\ \ce{O2(g)} & 0.00 \\ \ce{C3H7COOH(l)} & ? \\ \end{array}$$

The enthalpy change for the combustion of butyric acid at $\pu{25\degree C}$, $\Delta H_{\text{comb}}$, is $-2{,}183.5$ kilojoules per mole. The combustion reaction is

$$\ce{C3H7COOH(l) + 5O2(g)-> 4CO2(g) + 4H2O(l)}$$

Which of the following is closest to the standard heat of formation, $\Delta H_{\text{f}}^\circ$, in $\pu{kJ mol^{-1}}$, for butyric acid?

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We are given $\Delta H_{\text{reaction}}^\circ$ which can be used to find $\Delta H_{\text{f}}^\circ$ for butyric acid.

$$\Delta H_{\text{reaction}}^\circ = \sum n_{\text{p}}\Delta H_{\text{f}}^\circ \text{(products)} - \sum n_{\text{r}}\Delta H_{\text{f}}^\circ \text{(reactants)}$$ $$\Delta H_{\text{reaction}}^\circ = 4\cdot \Delta H_{\text{f}}^\circ \text{ for }\ce{CO2(g)} + 4\cdot \Delta H_{\text{f}}^\circ \text{ for }\ce{H2O(l)}$$ $$- \Delta H_{\text{f}}^\circ \text{ for }\ce{C3H7COOH(l)} + 5\cdot \Delta H_{\text{f}}^\circ \text{ for }\ce{O2(g)}$$

Substituting known values from the table and equation:

$$-2{,}183.5 = 4(-393.5)+4(-285.85) - \Delta H_{\text{f}}^\circ \text{ for }\ce{C3H7COOH(l)}+5(0)$$ $$-2{,}183.5 = -1{,}574 - 1{,}143.4 - \Delta H_{\text{f}}^\circ \text{ for }\ce{C3H7COOH(l)}$$ $$\Delta H_{\text{f}}^\circ \text{ for }\ce{C3H7COOH(l)} = \boxed{\pu{-533.9 kJ mol^{-1}}}$$