# If Z is a compressibility factor, van der Waals equation at low pressure can be written as

A. Z = 1 − (Pb/RT)

B. Z = 1 + (Pb/RT)

C. Z = 1 + (RT/Pb)

D. Z = 1 − (a/VRT)

[IIT-JEE(Main)-2014]
Van der Waals equation for 1 mole of real gas is-

(P + a/V^{2}) (V − b) = RT

At low pressure, volume is very large and hence correction term 'b' can be neglected in comparison to very large volume of V.

i.e. (V − b) ≈ V

Hence, the above equation becomes-

(P + a/V^{2}) V = RT

PV + a/V = RT

PV = RT − a/V

Dividing both sides by RT, we get-

PV/RT = 1 − (a/VRT)

So, the correct option is D.