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

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?

Summary Submit Skip Question

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:

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