KCET · Chemistry · Thermodynamics (C)
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
- A \( x+y \)
- B \( x-y \)
- C \( 2 x-y \)
- D \( 2 x+y \)
Answer & Solution
Correct Answer
(C) \( 2 x-y \)
Step-by-step Solution
Detailed explanation
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
\[
S(s)+O_{2}(g) \rightarrow S O_{2}(g) ; \Delta H_{3}=(2 x-y) k J
\]
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