The compression factor (compressibility factor) for `1 mol` of a van der Waals gas at `0^(@)C` and `100 atm` pressure is found to be `0.5`. Assuming that the volume of a gas molecule is neligible, calculate the van der Waals constant `a`.

Options

A. `0.253 L^(2) " mol"^(-2)` atm
B. `0.53 L^(2) " mol"^(-2) `atm
C. `1.83 L^(2) "mol"^(-2)`atm
D. `1.253 L^(2) "mol"^(-2)` atm

Answer

D

Explanation

We know that , `Z = (PV)/(RT) rArr 0.5 = (100 xx V)/(0.821 xx 273) rArr V = 0.112 ` litre
According to van der Waals equation
`(P+a/(V^(2)))(V-b) = RT`
`(100+a/((0.112)^(2)))(0.112-0)=0.0821 xx 273 `
`a = 1.253 L^(2) " mol"^(-2) " atm".`