Question

Compressibility factor `(Z = pV_(m)//RT)` of a real gas at low `T` and low `p` is usually less than one. It is due to the fact that in the van der Waals gas,
A. both the constants `a` and `b` are negligible
B. the constant `a` (i.e., molecular attraction) is not negligible whereas the constant `b`(i.e., molecular volume) is negligible
C. the constant `a` is negligible and the constant `b` is not negligible
D. both the constants `a` and `b` are not negligible

Answer 1

Correct Answer - B
For on emole of a gas, we can write the van der Waals equation as
`(p + (a)/(V_(m)^(2))) (V_(m) - b) = RT`
At low `p, V_(m)` is large. Thus, the constant `b` is negalected relative to `V_(m)` to give
`(p + (a)/(V_(m)^(2))) (V_(m)) = RT`
`pV_(m) + (a)/(V_(m)) = RT`
`pV_(m ) = RT - (a)/(V_(m))`
Dividing both the sides by `RT`, we get
`(pV_(m))/(RT) = (RT)/(RT) - (a)/(V_(m)RT)`
`Z = 1 - (a)/(V_(m)RT)`
i.e., `Z lt 1`