If in a given container there are $N$ number of molecules,then what will be the number of moles?

What is the number of molecules in $1 \, litre$ of an ideal gas at $S.T.P.$?

$A$ cylinder of volume $30 \, L$ contains oxygen at an initial gauge pressure of $15 \, atm$ and a temperature of $27^{\circ}C$. After some oxygen is withdrawn from the cylinder,the gauge pressure drops to $11 \, atm$ and its temperature drops to $17^{\circ}C$. The mass of oxygen taken out of the cylinder is approximately ........ $kg$. (Given: $R = 8.31 \, J \, mol^{-1} K^{-1}$,molar mass of $O_2 = 32 \, g/mol$ or $32 \times 10^{-3} \, kg/mol$)

$A$ tyre of a vehicle is filled with air having pressure $270 \text{ kPa}$ at $27^{\circ}C$. The air pressure in the tyre when the temperature increases to $37^{\circ}C$ is (in $\text{ kPa}$)

The pressure $P$,volume $V$,and temperature $T$ of a gas in jar $A$ are given. Another gas in jar $B$ has pressure $2P$,volume $V/4$,and temperature $2T$. The ratio of the number of molecules in jar $A$ to jar $B$ is:

Two spherical vessels of equal volume $V$ are connected by a narrow tube. The apparatus contains an ideal gas at $1 \text{ atm}$ and $300 \text{ K}$. Now,if one vessel is immersed in a bath of constant temperature $600 \text{ K}$ and the other in a bath of constant temperature $300 \text{ K}$,then the common pressure will be ...... $\text{atm}$.