Verified Solution • 2025–26 Session moderate

QJEEM25Ch42c7: JEE Main 2025 Chemistry - Class 11 JEEM25Ch42c7 Solution: Consider the following cases of standard enthalpy of reaction…

Consider the following cases of standard enthalpy of reaction (ΔHr∘\left(\Delta \mathrm{H}_{\mathrm{r}}^{\circ}\right. in kJmol−1)\left.\mathrm{kJ} \mathrm{mol}^{-1}\right)

amp;C2H6( g)+72O2( g)→2CO2( g)+3H2O(l)ΔH1∘=−1550amp;C( graphite )+O2( g)→CO2( g)ΔH2∘=−393.5amp;H2( g)+12O2( g)→H2O(l)ΔH3∘=−286\begin{aligned}& \mathrm{C}_2 \mathrm{H}_6(\mathrm{~g})+\frac{7}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{CO}_2(\mathrm{~g})+3 \mathrm{H}_2 \mathrm{O}(\mathrm{l}) \Delta \mathrm{H}_1^{\circ}=-1550 \\& \mathrm{C}(\text { graphite })+\mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g}) \Delta \mathrm{H}_2^{\circ}=-393.5 \\& \mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{l}) \Delta \mathrm{H}_3^{\circ}=-286\end{aligned}

The magnitude of ΔHfC2H6( g)∘\Delta \mathrm{H}_{f \mathrm{C}_2 \mathrm{H}_6(\mathrm{~g})}^{\circ} is ____________ kJmol−1\mathrm{kJ} \mathrm{mol}^{-1} (Nearest integer).

Step-by-Step Verified Solution

amp;C2H6( g)+72O2( g)→2CO2( g)+3H2O(I)ΔH1∘=−1550… (i) amp;C (graphite) +O2( g)→CO2( g)ΔH2∘=−393.5… (ii) amp;H2( g)+12O2( g)→H2O(I)ΔH3∘=−286.......(iii)\begin{aligned} & \mathrm{C}_2 \mathrm{H}_6(\mathrm{~g})+\frac{7}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{CO}_2(\mathrm{~g})+3 \mathrm{H}_2 \mathrm{O}(\mathrm{I}) \Delta \mathrm{H}_1^{\circ} =-1550 \ldots \text { (i) } \\\\ & \mathrm{C} \text { (graphite) }+\mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g}) \Delta \mathrm{H}_2^{\circ}=-393.5 \ldots \text { (ii) } \\\\ & \mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{I}) \Delta \mathrm{H}_3^{\circ}=-286 .......(iii) \end{aligned}

amp; From 2×eqn(ii)+3×eqn(iii)−eqn(i)amp;2C(graphite) +3H2( g)→C2H6( g):ΔHfC2H6∘amp;(ΔHf∘)C2H6=2×(−393.5)+3×(−286)−(−1550)amp;=−95 kJ/mol\begin{aligned} & \text { From } 2 \times \mathrm{eq}^{\mathrm{n}}(\mathrm{ii})+3 \times \mathrm{eq}^{\mathrm{n}}(\mathrm{iii})-\mathrm{eq}^{\mathrm{n}}(\mathrm{i}) \\\\ & 2 \mathrm{C}_{\text {(graphite) }}+3 \mathrm{H}_2(\mathrm{~g}) \rightarrow \mathrm{C}_2 \mathrm{H}_6(\mathrm{~g}): \Delta \mathrm{H}_{f \mathrm{C}_2 \mathrm{H}_6}^{\circ} \\\\ & \left(\Delta \mathrm{H}_f^{\circ}\right)_{\mathrm{C}_2 \mathrm{H}_6}=2 \times(-393.5)+3 \times(-286)-(-1550) \\\\ & =-95 \mathrm{~kJ} / \mathrm{mol}\end{aligned}

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