If the density of dioxygen gas at $STP$ is $1.43 \, g \, L^{-1}$,calculate its density at $17 \, ^\circ C$ and $800 \, torr$ pressure.

$A$ $10 \, L$ cylinder contains $0.4 \, g$ of helium,$1.6 \, g$ of oxygen,and $1.4 \, g$ of nitrogen at $27 \, ^\circ C$. Calculate the total pressure of the mixture and the partial pressure of helium gas. Assume ideal gas behavior. $(R = 0.082 \, L \, atm \, K^{-1} \, mol^{-1})$

The ratio of densities of two gases is $1 : 2$. If the ratio of their temperatures is $2 : 1$,find the ratio of their corresponding pressures. (Assume the molar masses of the gases are equal.)

At $21\, ^oC$ temperature,the volume of $212\, g$ of $O_2$ gas is $34\, dm^3$. If the pressure of the gas becomes $1.24\, bar$,then how many grams of $O_2$ gas are left in the container? $(R = 0.083\, dm^3\, bar\, K^{-1}\, mol^{-1})$

At what temperature in $^\circ C$ will the volume of a gas become double its volume at $0\,^\circ C$?

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 $R = 0.083 \, bar \, dm^{3} \, K^{-1} \, mol^{-1}$).