How to use a modified Peng-Robinson equation to calculate a density?
According to this source:


  The popular EoSs such as Soave-Redlich-Kwong (SRK) [1] and Peng-Robinson (PR) [2] predict liquid density with an average absolute error of about 8%, much higher than several good density correlations. This large magnitude of error is not acceptable by industry; therefore, they are not used for this purpose. 


Which is what I first thought when I thought of your question. Liquid density is a hard issue, specially in compounds with hydrogen bonding like ethanol. I wouldn't predict a gas-oriented (as in its primary use) EoS to perform just as well for liquids.

The article further suggests


  In order to overcome this deficiency, volume translated methods have been developed.


So that's what I'd recommend you to look into.