At 298 K , the enthalpy change ( in kJ ) for the reaction given below is

$$ \mathrm{CH}_4(g)+\mathrm{O}_2(g) \longrightarrow \mathrm{C}(s)+2 \mathrm{H}_2 \mathrm{O}(l) $$

$$ \begin{aligned} Given:\mathrm{H}_2(g)+\frac{1}{2} \mathrm{O}_2(g) & \longrightarrow \mathrm{H}_2 \mathrm{O}(l) ; \Delta H^{\ominus}=-286 \mathrm{~kJ} \\ \mathrm{C}(s)+\mathrm{O}_2(g) & \longrightarrow \mathrm{CO}_2(g) ; \Delta H^{\ominus}=-394 \mathrm{~kJ} \\ \mathrm{CH}_4(g)+2 \mathrm{O}_2(g) & \longrightarrow \mathrm{CO}_2(g)+2 \mathrm{H}_2 \mathrm{O}(l) \Delta H^{\ominus}=-890 \mathrm{~kJ}\end{aligned} $$

At $300 \mathrm{~K}, 3.0$ moles of an ideal gas at 3.0 atm pressure is compressed isothermally to one half of its volume by an external pressure of 6.0 atm . The work done (in kJ ) is (Given, $\left.R=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)(1 \mathrm{~L} \mathrm{~atm}=1013 \mathrm{~J})$

The $\Delta_{f} H^{\theta}$ of $\mathrm{AO}(s), \mathrm{BO}_{2}(g)$ and $A B \mathrm{O}_{3}(s)$ is $-635, x$ and $-1210 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively. $\left.\mathrm{ABO}_{3}(s) \rightarrow \mathrm{AO}(s)+\mathrm{BO}_{2}(g): \Delta_{r} H^{\Theta}=175 \mathrm{~kJ} \mathrm{~mol}^{-1}\right)$. What is the value of $x$ (in $\mathrm{kJ} \mathrm{mol}^{-1}$ )?

The standard enthalpy of combustion of C (graphite). $\mathrm{H}_2(g)$ and $\mathrm{CH}_3 \mathrm{OH}(l)$ respectively are $-393,-286$ and $-726 \mathrm{~kJ} \mathrm{~mol}^{-1}$. What is the standard enthalpy of formation of methanol?