$A$ $3.7 \ g$ mass of a gas occupies a certain volume at $25 \ ^\circ C$. The same volume is occupied by $0.184 \ g$ of $H_2$ gas at the same pressure and $17 \ ^\circ C$. Calculate the molar mass of the gas.

At $298 \, K$ temperature,$4 \, g$ of $H_2$ gas is filled in a $500 \, mL$ vessel. Due to a small hole in the vessel,after some time,the pressure in the vessel becomes $50 \, bar$. Find the number of $H_2$ molecules that have escaped from the vessel? $(R = 8.314 \times 10^{-2} \, L \, bar \, mol^{-1} \, K^{-1})$

Three bulbs are filled with $CH_4$,$CO_2$,and $Ne$ as shown in the picture. The bulbs are connected through pipes of zero volume. When the stopcocks are opened and the temperature is kept constant throughout,the pressure of the system is found to be $...... \ atm$. (Nearest integer)

At the same conditions of pressure,volume,and temperature,work done is maximum for which gas if all gases have equal masses?

An air tank has a volume of $10 \, L$ and is filled with air at a pressure of $200 \, atm$. If an adult human breathes in $0.50 \, L$ of air per breath at $1 \, atm$ pressure and $37 \, ^\circ C$,how many breaths can be taken from this tank? (Assume temperature remains constant)

Air entering the lungs ends up in tiny sacs called alveoli. It is from the alveoli that oxygen diffuses into the blood. The average radius of the alveoli is $0.0050 \ cm$ and the air inside contains $14$ per cent oxygen. Assuming that the pressure in the alveoli is $1.0 \ atm$ and the temperature is $37 \ ^oC$,calculate the number of oxygen molecules in one of the alveoli.