An evacuated vessel weighs 50.0g when empty, 148g when filled with a liquid (d=0.98`g*mL^(-1)`) & 50.5g when filled with an ideal gas at 760 mm Hg at 300K. Determine molar mass of the gas.

Explanation

Mass of the evacuated vesssel=50.0g
Mass of the vessel when filled with a liquid of density `0.98g*mL^(-1)=148g`
`therefore`Mass of the liquid=(148-50)g=98g
Volume of 98g of liquid`=(98)/(0.98)=100mL=0.1L`
Volume of the vessel=volume of the liquid=0.1L
Mass of the gas=mass of the vessel filled with the gas-mass of the vessel=(50.5-50.0)g=0.5g
Volume of the vessel=volume of the gas=0.1L
Let molar mass of the gas=`Mg*mol^(-1)`
Number of moles corresponding to 0.5g of the gas
`=(0.5)/(M)` mol
to calculate M, we use ideal gas equation, PV=nRT.
`therefore (760)/(760)xx0.1=(0.5)/(M)xx0.0821xx300` or, M=123.15
`therefore`Molar mass of the gas=`123.15g*mol^(-1)`