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

The van der Waals equation is given by:
(P + a(n/V)²)(V - nb) = nRT
where:
P = pressure
V = volume
T = temperature
n = number of moles
a and b are van der Waals constants

At low pressures, the term 'a(n/V)²' becomes negligible compared to P, and the term 'nb' becomes negligible compared to V. Therefore, the van der Waals equation simplifies to:
P(V - nb) ≈ nRT
P V ≈ nRT

The compressibility factor Z is defined as:
Z = PV/nRT

Substituting the simplified van der Waals equation, we get:
Z ≈ 1

However, a more accurate approximation at low pressures considers the correction for intermolecular forces (the 'a' term). Expanding the van der Waals equation and making the approximations mentioned above, we get:
PV = nRT + Pb - a(n/V)
Dividing by nRT gives:
PV/nRT = 1 + Pb/RT - a/(VRT)
At low pressures, the term a/(VRT) is much smaller than Pb/RT, so we can ignore it. This simplifies the expression to:
Z ≈ 1 + Pb/RT

Therefore, at low pressure, the van der Waals equation can be written as Z = 1 + Pb/RT