The volume occupied by the molecules contained in $4.5 \, kg$ of water at $STP$,if the intermolecular forces vanish away,is ........ $m^{3}$.

In a process,the pressure of an ideal gas varies with volume as $P = \frac{a}{1 + (V/b)^2}$,where $a$ and $b$ are constants. What is the temperature of the gas when the volume of $1$ mole of the gas is $V = b$?

At a given temperature,the pressure of an ideal gas of density $\rho$ is proportional to

$28\, g$ of $N_2$ gas is contained in a flask at a pressure of $10\, atm$ and at a temperature of $57^\circ C$. It is found that due to leakage in the flask,the pressure is reduced to half and the temperature is reduced to $27^\circ C$. The quantity of $N_2$ gas that leaked out is

$A$ container holds $1$ mole of $O_2$ (molar mass $32$) at temperature $T$. The pressure is $P$. Another identical container holds $1$ mole of $He$ (molar mass $4$) at temperature $2T$. Find the pressure in the second container.

What is a mole? Write two equations for a mole.