eq = (Z == Vm /R/T(R T/(Vm-b)-a/Vm^2))

eq /. Vm->Z R T / P /. a-> 27 R^2 Tcrit^2/64/Pcrit /. b-> R Tcrit/8 / Pcrit

seq =Simplify[%]

Solve[seq /. Tcrit->Tc /. Pcrit->Pc  /. T->300,Z][[2,1]]

Show[{ListPlot[ztable],Plot[Abs[Z] /. %,{P,1,400}]}]

Simplify[seq /. Z->1+x]

FullSimplify[%]

FullSimplify[Expand[% Pcrit T (1+x)]]

x[x_,p_] := (1/(8(1+x)-p/Pc Tc/300) - 27/64 Tc/300 /(1+x)) p/Pc Tc/300

x[1,1]

Show[{ListPlot[ztable],Plot[1+x[x[1,p],p],{p,1,300},PlotStyle->Yellow],Plot[RKZ[RKZ[RKZ[1,p],p],p],{p,1,400},PlotStyle->Red]}]

ztable={{1,0.9999},{5, 0.9987},{10, 0.9974},{20, 0.9950},{40, 0.9917},{60, 0.9901},{80, 0.9903},{100, 0.9930},{150, 1.0074},{200, 1.0326},{250, 1.0669},{300, 1.1089},{400 ,1.2073}}

ListPlot[ztable]

RKZ[Z_,p_] := 1/(1-0.08664 Tc/300 p/Pc 1/Z) - 0.42748 (Tc/300)^(3/2) / (300/Tc Pc/p Z + 0.08664)

Show[ListPlot[ztable],Plot[RKZ[RKZ[RKZ[1,p],p],p],{p,1,400}]]