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Enthalpy of Combustion

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Question

From the following data, calculate the enthalpy change for the combustion of cyclopropane at 298 K. The enthalpy of formation of $C O_{2} (g), H_{2} O (l)$ and propane (g) are -393.5, -285.8 & 20.42 kJ/mol respectively. The enthalpy of isomerisation of cyclopropane to propene is -33.0 kJ/mol.

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Solution

We are give:
(i) $C (s) + O_{2} (g) \to C O_{2} (g) Δ H = - 393.5 k J m o l^{- 1}$
(ii) $H_{2} (g) + \frac{1}{2} O_{2} (g) \to H_{2} O (l) Δ H = - 285.8 k J m o l^{- 1}$
(iii) $3 C (s) + 3 H_{2} (g) \to C_{3} H_{6} (g) Δ H = + 20.42 k J m o l^{- 1}$
Operating (iv)-(iii) $+ 3 \times (i) + 3 \times (i i)$ , we get the required equation and
$Δ H = - 33 - 20.42 + 3 (- 393.5) + 3 (- 285.8)$
$= - 2091.32 k J m o l^{- 1}$

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