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

$$\begin{aligned} & \mathrm{C}_2 \mathrm{H}_6(\mathrm{~g})+\frac{7}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{CO}_2(\mathrm{~g})+3 \mathrm{H}_2 \mathrm{O}(\mathrm{l}) \Delta \mathrm{H}_1^{\circ}=-1550 \\ & \mathrm{C}(\text { graphite })+\mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g}) \Delta \mathrm{H}_2^{\circ}=-393.5 \\ & \mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{l}) \Delta \mathrm{H}_3^{\circ}=-286 \end{aligned}$$

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

<p>$$ \begin{aligned} & \mathrm{C}_2 \mathrm{H}_6(\mathrm{~g})+\frac{7}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{CO}_2(\mathrm{~g})+3 \mathrm{H}_2 \mathrm{O}(\mathrm{I}) \Delta \mathrm{H}_1^{\circ} =-1550 \ldots \text { (i) } \\\\ & \mathrm{C} \text { (graphite) }+\mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g}) \Delta \mathrm{H}_2^{\circ}=-393.5 \ldots \text { (ii) } \\\\ & \mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{I}) \Delta \mathrm{H}_3^{\circ}=-286 .......(iii) \end{aligned} $$</p> $\begin{aligned} & \text { From } 2 \times \mathrm{eq}^{\mathrm{n}}(\mathrm{ii})+3 \times \mathrm{eq}^{\mathrm{n}}(\mathrm{iii})-\mathrm{eq}^{\mathrm{n}}(\mathrm{i}) \\\\ & 2 \mathrm{C}_{\text {(graphite) }}+3 \mathrm{H}_2(\mathrm{~g}) \rightarrow \mathrm{C}_2 \mathrm{H}_6(\mathrm{~g}): \Delta \mathrm{H}_{f \mathrm{C}_2 \mathrm{H}_6}^{\circ} \\\\ & \left(\Delta \mathrm{H}_f^{\circ}\right)_{\mathrm{C}_2 \mathrm{H}_6}=2 \times(-393.5)+3 \times(-286)-(-1550) \\\\ & =-95 \mathrm{~kJ} / \mathrm{mol}\end{aligned}$