An evacuated glass vessel weighs `50.0 g` when empty, `148.0 g` when filled with a liquid of density `0.98 g mL^(-1)`, and `50.5 g` when filled with an ideal gas at `760 mm Hg` at `300 K`. Determine the molar mass of the gas.

Explanation

Mas of water filled in the glass vessel,
`m_(1)=(148.0-50.0)g=98.0 g`
Volume of the glass vessel,
`V=(m_(1))/(rho)=(98.0)/(0.98 g mL^(-1))=100 mL=0.1dm^(3)`
Mass of gass filled in the vessel, `m=(50.5-50.0)g=0.5 g`
If `M` is the molar mass of the gas, we will have
`pV=nRT=(m)/(M)RT`
or `M=(mRT)/(pV)`
`=((0.5g)(8.314 JK^(-1)mol^(-1))(300 K))/((101.325 kPa)(0.1 dm^(3))`
`=123 g mol^(-1)`