@wikipedia

One of the cubic equations of real gas state defining the Compressibility factor as a function of fluid pressure and fluid temperature :

Z^3 - (1-B) \, Z^2 +(A-2B-3B^2) \, Z -(AB-B^2-B^3) = 0

A= 0.45724 \cdot \alpha \cdot \frac{p_r}{T_r^2}

B=0.07780 \cdot \frac{p_r}{T_r}

\alpha = \left( 1 + \kappa \, (1-T_r^{0.5}) \right)^2

\kappa = 0.37464 + 1.54226 \, \omega -0.26992 \, \omega^2

where

	Compressibility factor		Critical pressure
	Fluid pressure		Сritical temperature
	Fluid temperature		Reduced pressure
	Gas constant		Reduced Temperature
	Acentric factor

Once compressibility Z-factor is known the fluid density can be calculated as:

\rho(p, T) = \frac{1}{Z(p,T)} \cdot \frac{M}{R} \cdot \frac{p}{T}

where

fluid molar mass

Reference

Ding-Yu Peng and Donald B. Robinson, A New Two-Constant Equation of State, Industrial & Engineering Chemistry Fundamentals , 1976, 15 (1), 59-64, doi.org/10.1021/i160057a011