Volume of a balloon at $25^{\circ} C$ and $1 \ bar$ pressure is $2.27 \ L$. If the pressure of the gas in the balloon is reduced to $0.227 \ bar$,what is the rise in volume of the gas (in $L$)?

Two containers $A$ and $B$ contain $CO_2$ gas. Pressure, volume, and absolute temperature of the gas in $A$ are $4$ times more compared to that in $B$. If the mass of the gas in $B$ is $x \ g$, then the mass of the gas in $A$ will be:

Derive the relation between density $(d)$ and molar mass $(M)$ for an ideal gas.

The universal gas constant $R$ is defined as:

The value of the universal gas constant $R$ is the same for all gases. What is its physical significance?

At what new pressure will $100 \ mL$ of a gas at a pressure of $720 \ mm$ occupy a volume of $84 \ mL$,keeping the temperature constant (in $mm$)?