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`.

Explanation

For 1 mole of the gas,
`Z= ( pV)/( R T ) rArr 0.5 = ( 100 xx V)/( 0.0821 xx 273'), V=0.112 L`
Neglecting b, van der Waals equation reduces to
`( P + (a)/( V^(2)))V = RT`
or `pV + ( v)/( V) = RT `
or ` 100 xx 0.112 + ( a)/( 0.112 ) = 0.0821 xx 273 `
`a =1.25 L^(2) atm mol^(-2)`