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.

Options

A. `120g//mol`
B. `123g//mol`
C. `246g//mol`
D. `61.5g//mol`

Answer

B

Explanation

Mass of liquid `= 148 - 50 = 98g`
Volume of liquid `= ("mass")/("density") = (98)/(0.98) = 100 mL`
Volume of vessel = Volume of liquid
Mass of gas `= 50.5 - 50 = 0.5 g`
On applying ideal gas equation, we have,
`PV = (w)/(m) RT`
`(760)/(760) xx (100)/(1000) = (0.5)/(m) xx 0.0821 xx 300`
`m = 123`