Q51 / 180 · KCET 2015 · Chemistry
In the reaction
\( \mathrm{S}+\frac{3}{2} \mathrm{O}_{2} \rightarrow \mathrm{SO}_{3}+2 \times \mathrm{kJ} \) and \( \mathrm{SO}_{2}+\frac{1}{2} \mathrm{O}_{2} \rightarrow \mathrm{SO}_{3}+y \mathrm{~kJ} \)
heat of formation of \( \mathrm{SO}_{2} \) is
\( \mathrm{S}+\frac{3}{2} \mathrm{O}_{2} \rightarrow \mathrm{SO}_{3}+2 \times \mathrm{kJ} \) and \( \mathrm{SO}_{2}+\frac{1}{2} \mathrm{O}_{2} \rightarrow \mathrm{SO}_{3}+y \mathrm{~kJ} \)
heat of formation of \( \mathrm{SO}_{2} \) is
- A\( x+y \)
- B\( x-y \)
- Correct answerC\( 2 x-y \)
- D\( 2 x+y \)
Solution
Given
\[ \begin{array}{l} S(s)+\frac{3}{2} O_{2}(g) \rightarrow S O_{3}(g) ; \Delta H_{1}=2 x k J \rightarrow(1) \\ S O_{2}(g)+\frac{1}{2} O_{2}(g) \rightarrow S O_{3}(g) ; \Delta H_{2}=y k J \rightarrow(2) \end{array} \]
For reaction
\[ S(s)+O_{2}(g) \rightarrow S O_{2}(g) ; \Delta H_{3}=? k J \]
Inverting Eq. (2), we get
\[ \mathrm{SO}_{3}(g) \rightarrow \mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) ; \Delta \mathrm{H}_{4}=-y k J \rightarrow(3) \]
Adding Eq. (1) and (3), we get
\[ S(s)+O_{2}(g) \rightarrow S O_{2}(g) ; \Delta H_{3}=(2 x-y) k J \]
\[ \begin{array}{l} S(s)+\frac{3}{2} O_{2}(g) \rightarrow S O_{3}(g) ; \Delta H_{1}=2 x k J \rightarrow(1) \\ S O_{2}(g)+\frac{1}{2} O_{2}(g) \rightarrow S O_{3}(g) ; \Delta H_{2}=y k J \rightarrow(2) \end{array} \]
For reaction
\[ S(s)+O_{2}(g) \rightarrow S O_{2}(g) ; \Delta H_{3}=? k J \]
Inverting Eq. (2), we get
\[ \mathrm{SO}_{3}(g) \rightarrow \mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) ; \Delta \mathrm{H}_{4}=-y k J \rightarrow(3) \]
Adding Eq. (1) and (3), we get
\[ S(s)+O_{2}(g) \rightarrow S O_{2}(g) ; \Delta H_{3}=(2 x-y) k J \]
Hence, the correct answer is option: 'C'.