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. 123.75
D. 43.87

Answer

A

Explanation

`"Mass of glass vessel"=50g`
`"Mass of liquid "=144-50=94g`
`"Density of liquid "="0.47 g mL"^(-1)`
`"Density"=("Mass")/("Volume")`
`therefore" Volume of glass vessel, V"=("Mass")/("Density")`
`=(94g)/("0.47 g mL"^(-1))`
`="200 mL = 0.2 L"`
Pressure of gas, p = 760 mm Hg = 1 atm.
`"Temperature of gas, T = 300 K"`
`"Mass of gas in glass vessel "=(50.5-50)g=0.5g`
`pV=nRT or pV=(m)/(M)RT`
`"1 atm "xx0.2L=(0.5g)/(M)xx"0.0821 L atm K"^(-1)" mol"^(-1)xx300K`
`therefore" M"=(0.5gxx"0.0821 L atm K"^(-1)"mol"^(-1)xx300K)/("1 atm"xx0.2L)`
`="61.575 g mol"^(-1)`