For the reaction at $$298 \mathrm{~K}, 2 \mathrm{~A}+\mathrm{B} \rightarrow \mathrm{C}, \Delta \mathrm{H}=400 \mathrm{~kJ} \mathrm{~mol}^{-1}$$ and $$\Delta S=0.2 \mathrm{~kJ} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$$. The reaction will become spontaneous above __________ $$\mathrm{K}$$.

An ideal gas, $$\overline{\mathrm{C}}_{\mathrm{v}}=\frac{5}{2} \mathrm{R}$$, is expanded adiabatically against a constant pressure of 1 atm untill it doubles in volume. If the initial temperature and pressure is $$298 \mathrm{~K}$$ and $$5 \mathrm{~atm}$$, respectively then the final temperature is _________ $$\mathrm{K}$$ (nearest integer).

[$$\overline{\mathrm{c}}_{\mathrm{v}}$$ is the molar heat capacity at constant volume]

Combustion of 1 mole of benzene is expressed at

$$\mathrm{C}_6 \mathrm{H}_6(\mathrm{l})+\frac{15}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow 6 \mathrm{CO}_2(\mathrm{~g})+3 \mathrm{H}_2 \mathrm{O}(\mathrm{l}) \text {. }$$

The standard enthalpy of combustion of $$2 \mathrm{~mol}$$ of benzene is $$-^{\prime} x^{\prime} \mathrm{kJ}$$. $$x=$$ __________.

Given :

1. standard Enthalpy of formation of $$1 \mathrm{~mol}$$ of $$\mathrm{C}_6 \mathrm{H}_6(\mathrm{l})$$, for the reaction $$6 \mathrm{C}$$ (graphite) $$+3 \mathrm{H}_2(\mathrm{g}) \rightarrow \mathrm{C}_6 \mathrm{H}_6(\mathrm{l})$$ is $$48.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$$.

2. Standard Enthalpy of formation of $$1 \mathrm{~mol}$$ of $$\mathrm{CO}_2(\mathrm{g})$$, for the reaction $$\mathrm{C}$$ (graphite) $$+\mathrm{O}_2(\mathrm{g}) \rightarrow \mathrm{CO}_2(\mathrm{g})$$ is $$-393.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$$.

3. Standard and Enthalpy of formation of $$1 \mathrm{~mol}$$ of $$\mathrm{H}_2 \mathrm{O}(\mathrm{l})$$, for the reaction $$\mathrm{H}_2(\mathrm{g})+\frac{1}{2} \mathrm{O}_2(\mathrm{g}) \rightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{l})$$ is $$-286 \mathrm{~kJ} \mathrm{~mol}^{-1}$$.

The heat of combustion of solid benzoic acid at constant volume is $$-321.30 \mathrm{~kJ}$$ at $$27^{\circ} \mathrm{C}$$. The heat of combustion at constant pressure is $$(-321.30-x \mathrm{R}) \mathrm{~kJ}$$, the value of $$x$$ is __________.