# The standard heat of formation

Question:

The standard heat of formation $\left(\Delta_{f} \mathrm{H}_{298}^{0}\right)$ of ethane (in $\mathrm{kJ} / \mathrm{mol}$ ), if the heat of combustion of ethane, hydrogen and graphite are $-1560,-393.5$ and $-286 \mathrm{~kJ} / \mathrm{mol}$, respectively is __________________ .

Solution:

$(-192.5)$

$\mathrm{C}+\mathrm{O}_{2} \rightarrow \mathrm{CO}_{2} ; \Delta_{\mathrm{C}} \mathrm{H}^{0}=-286.0 \mathrm{~kJ} / \mathrm{mol}$ ...(i)

$\mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2} \rightarrow \mathrm{H}_{2} \mathrm{O} ; \Delta_{\mathrm{C}} \mathrm{H}^{0}=-393.5 \mathrm{~kJ} / \mathrm{mol}$   ....(ii)

$\mathrm{C}_{2} \mathrm{H}_{6}+\frac{1}{2} \mathrm{O}_{2} \rightarrow 2 \mathrm{CO}_{2}+3 \mathrm{H}_{2} \mathrm{O} ; \Delta_{\mathrm{C}} \mathrm{H}^{0}=-1560 \mathrm{~kJ} / \mathrm{mol}$   ....(iii)

$\Delta_{f} \mathrm{H}^{0}$ of $\mathrm{C}_{2} \mathrm{H}_{6}(g)=$

$2 \times \Delta_{\mathrm{C}}^{0} \mathrm{H}\left[\mathrm{C}_{\text {graphite }}\right]+3 \times \Delta_{\mathrm{C}} \mathrm{H}^{0}\left[\mathrm{H}_{2}(g)\right]-\Delta_{\mathrm{C}} \mathrm{H}^{0}\left[\mathrm{C}_{2} \mathrm{H}_{6}(g)\right]$

$=2 \times(-286.0)+3(-393.5)-(-1560)$

$=-192.5 \mathrm{~kJ} / \mathrm{mol}$

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