$S (s) + O_{2} (g) \to {S O}_{2} (g) Δ H^{\circ} = - 297 k J$
$2 {S O}_{2} (g) + O_{2} (g) \to 2 {S O}_{3} (g) Δ H^{\circ} = - 198 k J$
Given the above thermochemical reactions, what is the heat of reaction for the formation of ${S O}_{3} (g)$ provided below?
$S (s) + {3 / 2 O}_{2} (g) \to {S O}_{3} (g)$

-495 kJ

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-396 kJ

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-198 kJ

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+198 kJ

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Solution

The correct option is B -396 kJ
$S$ $+$ $O_{2}$ $=$ $S O_{2}$ , $Δ H^{o}$ $=$ $- 297 k J$ ..... $(1)$
$2 S O_{2}$ $+$ $O_{2}$ $=$ $2 S O_{3}$ , $Δ H^{o}$ $=$ $- 198 k J$ .... $(2)$
Dividing equation (2) by $2$ , we get-
$S O_{2}$ $+$ $\frac{1}{2} O_{2}$ $=$ $S O_{3}$ , $Δ H^{o}$ $=$ $- 99 k J$ .... $(3)$
Now, adding equation (1) and (3), we get-
$S$ $+$ $\frac{3}{2} O_{2}$ $+$ $S O_{2}$ $=$ $S O_{2}$ $+$ $S O_{3}$ ...... $(4)$ .
Cancelling $S O_{2}$ from both the sides of the equation, we get the equation $S$ $+$ $\frac{3}{2} O_{2}$ $=$ $S O_{3}$ .
Thus the value of $Δ H^{o}$ will also be added. Since we are adding the equations (1) and (3), which comes out to be equal to $[- 297 + (- 99)] k J$ , that is $- 396 k J$ .
Thus option $B$ is the correct answer.

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