The density of vapours of a particular volatile diatomic species $A_2$ was found to be $10 \ mg/mL$ at $1 \ atm$ and $273 \ K$. Its atomic weight is given by: [Assume ideal gas behaviour].

$A$ gas occupies $10 \ L$ at $STP$. Which of the following conditions will result in the same volume?

How many moles of $He$ gas occupy $22.4 \, L$ at $30^{\circ}C$ and $1 \, atm$ pressure?

For $0.09 \, \text{mol}$ of $CO_2$ at $300 \, K$,the volume is $112.0 \times 10^{-3} \, m^3$ at a pressure of $2.0 \times 10^4 \, Pa$. What will be the volume at a pressure of $4.0 \times 10^4 \, Pa$?

If $R = 0.082$,write it with its units and state the value with full precision.

Consider the figure provided. $1 \ mol$ of an ideal gas is kept in a cylinder,fitted with a piston,at the position $A$,at $18^{\circ} C$. If the piston is moved to position $B$,keeping the temperature unchanged,then '$x$' $L \ atm$ work is done in this reversible process. $x=$ . . . . . . $L \ atm$. (nearest integer) [Given : Absolute temperature $=^{\circ} C + 273.15$,$R=0.08206 \ L \ atm \ mol^{-1} \ K^{-1}$]