An evacuated vessel weighs 50 g when empty, 144 g when filled with a liquid of density 0.47 g `mL^(-1)` and 50.5 g when filled with an ideal gas at 760 mm Hg at 300 K. The molar mass of the ideal gas is (Given R=0.082 L atm `K^(-1)mol^(-1)`)

Options

A. 61.575
B. 130.98
C. 87.943
D. 123.75

Answer

A

Explanation

Mass of liquid filling the vessel =144-50=94 g
Volume of liquid=Volume of vessel`=(94 g)/(0.47" g "mL^(-1))`
`:.` Volume of gas(V)=200mL=0.02L
Pressure (P)=760 mm=1 atm
Temperature (T)=300 K
Mass of the gas=50.5-50=0.5 g
PV=nRT`=(w)/(M)RT`
`:. M=(wRT)/(PV)=(0.5xx0.0821xx300)/(1xx0.2)=61.575`