Given below are two statement : one is labelled as Assertion $\mathrm{A}$ and the other is labelled as Reason $\mathrm{R}$.
Assertion $\mathrm{A}:{\mathrm{SO}}_2( \mathrm{g})$ is adsorbed to a large extent than ${\mathrm{H}}_2( \mathrm{g})$ on activated charcoal.

Reason $\mathrm{R}$ : ${\mathrm{SO}}_2( \mathrm{g})$ has a higher critical temperature than ${\mathrm{H}}_2( \mathrm{g})$

In the light of the above statements, choose the most appropriate answer from the options given below.

$2{\mathrm{SO}}_2( \mathrm{g})+{\mathrm{O}}_2( \mathrm{g})\to 2{\mathrm{SO}}_3( \mathrm{g})$ 

The above reaction is carried out in a vessel starting with partial pressure ${\mathrm{P}}_{{\mathrm{SO}}_2}=250 \mathrm{m} \mathrm{bar}$, ${\mathrm{P}}_{{\mathrm{O}}_2}=750 \mathrm{m} \mathrm{bar}$ and ${\mathrm{P}}_{{\mathrm{SO}}_3}=0 \mathrm{bar}$. When the reaction is complete, the total pressure in the reaction vessel is _____ $\mathrm{m} \mathrm{bar}$. 

(Round off of the nearest integer).

Two flasks I and II shown below are connected by a valve of negligible volume.

When the valve is opened, the final pressure of the system in bar is $\mathrm{x}\times {10}^{-2}$. The value of $\mathrm{x}$ is (Integer answer)
[Assume : Ideal gas; $1$ bar $={10}^5 \mathrm{Pa}$ : Molar mass of $\left.{\mathrm{N}}_2=28.0{ \mathrm{mol}}^{-1};\mathrm{R}=8.31 \mathrm{J}{ \mathrm{mol}}^{-1}{ \mathrm{K}}^{-1}\right]$

The unit of the van der Waals gas equation parameter $\text{'}\mathrm{a}\text{'}$ in $\left(\mathrm{P}+\frac{{\mathrm{an}}^2}{{\mathrm{V}}^2}\right)(\mathrm{V}-\mathrm{nb})=\mathrm{nRT}$ is:

A home owner uses $4.00\times {10}^3{ \mathrm{m}}^3$ of methane $\left({\mathrm{CH}}_4\right)$ gas, (assume ${\mathrm{CH}}_4$ is an ideal gas) in a year to heat his home. Under the pressure of $1.0$ atm and $300 \mathrm{K}$, mass of gas used is $\mathrm{x}\times {10}^5 \mathrm{g}$. The value of $\mathrm{x}$ is ______. (Nearest integer)

(Given $\mathrm{R}=0.083 \mathrm{L} \mathrm{atm} {\mathrm{K}}^{-1}{ \mathrm{mol}}^{-1}$)