$A$ glass vessel weighs $50.0 \, g$ when empty. When filled with a liquid of density $0.98 \, g \cdot mL^{-1}$,it weighs $148.0 \, g$. When filled with an ideal gas at $760 \, mm$ of $Hg$ pressure and $300 \, K$ temperature,it weighs $50.5 \, g$. Calculate the molar mass of the gas in $u$.

The density of $CO_2$ at $100\,^oC$ temperature and $400\,mm\,Hg$ pressure is .......... $g/L$.

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

If the pressure and absolute temperature of $2 \ L$ of $CO_2$ are doubled,the volume of $CO_2$ would become ............... $L$.

What is the density of $CO_2$ at $100\,^oC$ and $800\,mm\,Hg$ pressure in $g/L$?

If the pressure and temperature of $4 \, dm^3$ of carbon dioxide are doubled,what will be the volume of the carbon dioxide gas in $dm^3$?