Keeping temperature constant,the pressure of $11.2 \ dm^3$ of a gas was increased from $105 \ kPa$ to $420 \ kPa$. What is the new volume of the gas (in $dm^3$)?

At $740 \ torr$ pressure,the volume of $N_2$ gas is $800 \ mL$. If the volume becomes $540 \ mL$ at constant temperature,calculate the pressure of the gas. (in $torr$)

The volume occupied by $4.75 \, g$ of acetylene gas at $50^{\circ} C$ and $740 \, mm \, Hg$ pressure is ....... $L$.
(Rounded off to the nearest integer)
$[$ Given $R = 0.0826 \, L \, atm \, K^{-1} \, mol^{-1} ]$

The gram molecular volume of an ideal gas at $STP$ is $22400 \ cm^{3}$. However,for oxygen gas,the question asks for the volume. Given the options provided,the correct value for $1 \ \text{mole}$ of any ideal gas at $STP$ is $22400 \ cm^{3}$. Please note that the provided solution in the prompt was incorrect. (in $cm^{3}$)

Pay load is defined as the difference between the mass of displaced air and the mass of the balloon. Calculate the pay load when a balloon of radius $10 \, m$,mass $100 \, kg$ is filled with helium at $1.66 \, bar$ at $27^{\circ} C$. (Density of air $= 1.2 \, kg \, m^{-3}$ and $R = 0.083 \, bar \, dm^{3} \, K^{-1} \, mol^{-1}$).

When an ideal gas undergoes free expansion,then: