If \(8.84 \mathrm{~kJ}\) heat is liberated for formation of \(3 \mathrm{~g}\) ethane, calculate its \(\Delta_{\mathrm{f}} \mathrm{H}^{\circ}\).

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 \(\mathrm{C}_2 \mathrm{H}_6=-88.4 \mathrm{~kJ}\)