PV = nRT is the ideal gas law.
it assumes.
1) there are no intermolecular interactions
2) the volume of each individual gas molecule = 0
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the Van Der Waals equation corrects for those two assumptions.
(P - an² / V²) x (V - nb) = nRT.. is the Van Der Waals equation
the "a" term corrects for the intermolecular interactions
the "b" term corrects for the volume of the individual molecules.
see the source for other "equations of state" (equations relating P,V,n,&T for gases)
and details on the Van Der Waals equation.