MHT CET · Chemistry · Thermodynamics (C)
Heat of combustion of \(\mathrm{C}_{(\mathrm{s})}, \mathrm{H}_{2(\mathrm{~g})}\) and \(\mathrm{C}_{2} \mathrm{H}_{6(\mathrm{~g})}\) are \(-x_{1},-x_{2}\) and \(-x_{3}\) respectively. Hence heat of formation of \(\mathrm{C}_{2} \mathrm{H}_{6(\mathrm{~g})}\) is
- A \(-x_{1}-x_{2}+x_{3}\)
- B \(-2 x_{1}-3 x_{2}+x_{3}\)
- C \(x_{1}+x_{2}-x_{3}\)
- D \(-x_{3}+2 x_{1}+3 x_{2}\)
Answer & Solution
Correct Answer
(B) \(-2 x_{1}-3 x_{2}+x_{3}\)
Step-by-step Solution
Detailed explanation
i. \(\mathrm{C}+\mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2} \quad \Delta \mathrm{H}_{1}=-\mathrm{x}_{1}\)
ii. \(\mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2} \longrightarrow \mathrm{H}_{2} \mathrm{O} \quad \Delta \mathrm{H}_{2}=-\mathrm{x}_{2}\)
iii. \(\mathrm{C}_{2} \mathrm{H}_{6}+\frac{7}{2} \mathrm{O}_{2} \rightarrow 2 \mathrm{CO}_{2}+3 \mathrm{H}_{2} \mathrm{O} \quad \Delta \mathrm{H}_{3}=-\mathrm{x}_{3}\)
Multiply equation (i) by \(2+\) multiply equation (ii) by 3 - equation (iii)
\(
\begin{array}{l}
\therefore 2 \mathrm{C}+3 \mathrm{H}_{2} \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6} \\
\therefore \Delta \mathrm{H}=2 \Delta \mathrm{H}_{1}+3 \Delta \mathrm{H}_{2}-\Delta \mathrm{H}_{3} \\
\therefore \Delta \mathrm{H}=-2 \mathrm{x}_{1}-3 \mathrm{x}_{2}+\mathrm{x}_{3}
\end{array}
\)
ii. \(\mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2} \longrightarrow \mathrm{H}_{2} \mathrm{O} \quad \Delta \mathrm{H}_{2}=-\mathrm{x}_{2}\)
iii. \(\mathrm{C}_{2} \mathrm{H}_{6}+\frac{7}{2} \mathrm{O}_{2} \rightarrow 2 \mathrm{CO}_{2}+3 \mathrm{H}_{2} \mathrm{O} \quad \Delta \mathrm{H}_{3}=-\mathrm{x}_{3}\)
Multiply equation (i) by \(2+\) multiply equation (ii) by 3 - equation (iii)
\(
\begin{array}{l}
\therefore 2 \mathrm{C}+3 \mathrm{H}_{2} \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6} \\
\therefore \Delta \mathrm{H}=2 \Delta \mathrm{H}_{1}+3 \Delta \mathrm{H}_{2}-\Delta \mathrm{H}_{3} \\
\therefore \Delta \mathrm{H}=-2 \mathrm{x}_{1}-3 \mathrm{x}_{2}+\mathrm{x}_{3}
\end{array}
\)
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