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Heat of Formation

The heats of ...

Question

The heats of formation of $C O_{2} (g)$ and $H_{2} O (l)$ are $- 394$ kJ/mole and $- 285.8$ kJ/mole respectively. Using the data for the following combustion reaction, calculate the heat of formation of $C_{2} H_{2} (g)$ .
$2 C_{2} H_{2} (g) + 5 O_{2} (g) \to 4 C O_{2} (g) + 2 H_{2} O (l)$ , $Δ H^{o} = - 2601$ kJ.

A

- 238.6

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B

253.2

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C

238.7

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D

226.7

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Solution

The correct option is D $226.7$
Given, $C + O_{2} (g) ⟶ C O_{2} (g); Δ H_{1} = - 394 K J ⟶ (1)$
$H_{2} + \frac{1}{2} O_{2} (g) ⟶ H_{2} O (l); Δ H_{2} = - 285.8 K J ⟶ (2)$
$C_{2} H_{2} (g) + 5 O_{2} (g) ⟶ H C O_{2} (g) ⟶ H C O_{2} (g) + 2 H_{2} O (l); Δ H^{o} = - 2601 K J ⟶ (3)$
To find out, Heat of formation of $C_{2} H_{2} (g)$ i.e. $2 C + H_{2} ⟶ C_{2} H_{2} (g)$
Equation (1) $\times 2 +$ Equation (2) $\Rightarrow$
$2 C + 2 O_{2} (g) + H_{2} + \frac{1}{2} O_{2} (g) ⟶ 2 C O_{2} + H_{2} O$ $Δ H_{3} = - 1073.8 K J ⟶ (4)$
Reversing Equation (3)
$H C O_{2} (g) + 2 H_{2} O (l) ⟶ C_{2} H_{2} (g) + 5 O_{2} (g)$ $Δ H^{o} = 2601 K J ⟶ (5)$
Equation (4)+Equation (5/2)
$2 C (s) + H_{2} (g) ⟶ C_{2} H_{4} (g)$ $Δ H_{f}^{o} = 226.7 K J$

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