Q50 / 150 · MHT CET 2023 (10 May Shift 2) · Chemistry

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

  • A
    $-8.00 \mathrm{~kJ}$
  • B
    $15.0 \mathrm{~kJ}$
  • C
    $30.0 \mathrm{~kJ}$
  • Correct answer
    D
    $-88.4 \mathrm{~kJ}$

Solution

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

Hence, the correct answer is option: 'D'.

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