The compressibility factor for definite amount of vander walls gas at `0^(@)C and 100` atm is found to be `0.5`. Assuming the volume of gas molecules negligible the vander Waal's constant 'a' for gas in `"litre"^(2)" mol"^(-2)` atm is :

Options

A. 1.256
B. 0.256
C. 2.256
D. 10.0256

Explanation

`Z=(PV)/(nRT) =0.5`
`(P+(n^(2)a)/(V^(2))(V-nb)=nRT)`
`rArr (P+(n^(2)a)/(V^(2))(V) =nRT` (b is negligible)
`therefore PV^(2) -nRTV +n^(2)a=0`
`V =(nRT pm sqrt(n^(2)R^(2)T^(2)-4n^(2)aP))/(2P)`
Since, V is constant at given P and T thus discriminant is zero
`therefore n^(2)R^(2)T^(2)=4n^(2) aP`
`therefore