What is the compressibility factor (Z) for 0.02 mole of a van der Waals's gas at pressure of 0.1 atm. Assume the size of gas molecules is negligible.
Given : RT=20 L atm `mol^(-1)` and a=1000 atm `L^(2) mol^(-2)`

Options

A. `2`
B. `1`
C. `0.02`
D. `0.01`

Answer

D

Explanation

`(0.1 +(1000xx(0.02)^(2))/(V^(2))) V = 20 xx 0.02 = 0.1 V^(2) - 0.4 V + 0.4 = 0`
`V^(2) - 4V +4 = 0`
`rArr V = 2L`
`Z = (PV)/(RT) = (0.1 xx 2)/(20) = 0.01`