An evacuated glass vessel weighs 50g when empty, 148.0 g when filled with a liquid of density `0.98gml^(-1)` and 50.5g when filled with an ideal gas at 760mm Hg at 300K . The molar mass of the ideal gas is ( Given R = 0.0821 L atm `K^(-1) mol^(-1)` )

Options

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

Answer

A

Explanation

Mass of liquid `= 144 - 58 = 94g `
Density of liquid `= 0.47 g mL ^(-1)`
Volume of glass vessel `= ( " Mass")/( " Density")`
`= ( 94)/( 0.47) = 200mL`
Pressure of gas, p = 760 mm Hg = 1 atm
Temperature, T = 300K
Mass of gas in vessel = 50.5 - 50.0 = 0.5 g
pV = nRT
or pV = `( m )/( M ) RT `
or `M = ( m RT)/( pV) = ( 0.5 xx 0.082 xx 300)/( 1 xx 0.2)`
`= 61.575g mol^(-1)`