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If $8.84 \mathrm{~kJ}$ heat is liberated for formation of $3 \mathrm{~g}$ ethane, calculate its $\Delta_{\mathrm{f}} \mathrm{H}^{\circ}$.
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The correct answer is:
$-88.4 \mathrm{~kJ}$
Formation of ethane:
$2 \mathrm{C}_{(\mathrm{s})}+3 \mathrm{H}_{2(\mathrm{~g})} \longrightarrow \mathrm{C}_2 \mathrm{H}_{6(\mathrm{~g})} ; \Delta_{\mathrm{f}} \mathrm{H}^{\circ}=\text { ? }$
Molar mass of $\mathrm{C}_2 \mathrm{H}_6=30 \mathrm{~g} \mathrm{~mol}^{-1}$
$\therefore \quad 3 \mathrm{~g} \mathrm{C}_2 \mathrm{H}_6=\frac{3}{30}=\frac{1}{10} \cdot \mathrm{mol}$
$\therefore \quad$ For formation of $\frac{1}{10} \mathrm{~mol} \mathrm{C}_2 \mathrm{H}_6, 8.84 \mathrm{~kJ}$ heat is liberated.
$\therefore \quad$ Formation of $1 \mathrm{~mol} \mathrm{C}_2 \mathrm{H}_6$ will liberate $88.4 \mathrm{~kJ}$ of heat.
$\therefore \quad \Delta_{\mathrm{f}} \mathrm{H}^{\circ}$ of $\mathrm{C}_2 \mathrm{H}_6=-88.4 \mathrm{~kJ}$
$2 \mathrm{C}_{(\mathrm{s})}+3 \mathrm{H}_{2(\mathrm{~g})} \longrightarrow \mathrm{C}_2 \mathrm{H}_{6(\mathrm{~g})} ; \Delta_{\mathrm{f}} \mathrm{H}^{\circ}=\text { ? }$
Molar mass of $\mathrm{C}_2 \mathrm{H}_6=30 \mathrm{~g} \mathrm{~mol}^{-1}$
$\therefore \quad 3 \mathrm{~g} \mathrm{C}_2 \mathrm{H}_6=\frac{3}{30}=\frac{1}{10} \cdot \mathrm{mol}$
$\therefore \quad$ For formation of $\frac{1}{10} \mathrm{~mol} \mathrm{C}_2 \mathrm{H}_6, 8.84 \mathrm{~kJ}$ heat is liberated.
$\therefore \quad$ Formation of $1 \mathrm{~mol} \mathrm{C}_2 \mathrm{H}_6$ will liberate $88.4 \mathrm{~kJ}$ of heat.
$\therefore \quad \Delta_{\mathrm{f}} \mathrm{H}^{\circ}$ of $\mathrm{C}_2 \mathrm{H}_6=-88.4 \mathrm{~kJ}$
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