van der Waals gas is not real gas?

From van der Waals , (P+a/v^2)(v-b)=RT,
At critical temperature, I get (∂P/∂V)at constant temperature =0
and (∂^2P/∂V^2) at constant temperature ,T=0.
then critical pressure,P = a/(27b^2)--------1
critical volume,v=3b-----------2
critical temperature=8a/(27Rb)----------3
then simultaneous equation 1 and 3,
I get b=(RT/8P), b=(v/3) ------------------4
But from the experiment, we get T,P,v and then substitute into the two equation from 4,both b have different values. Why?

Thank you