Several modifications of Peng-Robinson (and other equations of state) have been developed to enable prediction of VLE for mixtures including non-ideal (polar) components. For example PRSV (PR-Stryjek-Vera), PR-Twu. These EOS have added a term to improve the notoriously mediocre volume predictions. The typical approach for VLE is to enter binary interaction parameters for each component pair based on experimental data.

2 caveats come to mind - compounds such as acetic acid which associate in the vapour phase would need extra care. If all components in the mixture are highly non-ideal polar, then an activity coefficient method (such as UNIQUAC or NRTL) is preferred or a hybrid method using activity coefficients for liquid phase, but EOS for the vapour phase. For pure substances, specific EOS have been developed such as Span and Wagner for CO2.

Thanks for your answer, Dr Limb.

As we can use EOS with Van der Waals mixing rule for vapor phase for mixtures with all polar compounds, can we use EOS with Van der Waals mixing rule to calculate hydrocarbon dew point for mixtures with all polar compounds as hydrocarbon dew point is a vapor phase property?

Also, can we use EOS with Van der Waals mixing rule to find hydrocarbon dew point for mixtures containing both polar and nonpolar compounds?

Yes, may be you can do it. This can be considered based on the two points of view, including physical and mathematical. From mathematical point of view, you must work on the the correlation of alfa and b parameters of the PR EOS. May be you should consider volume correction parameter or a coefficient for b similar to Heyen EOS or even an alfa parameter like the one for Heyen. From physical point of view, these corrections are not logical. You must add polar term or consider dipole-dipole interactions for the EOS. Therefore, it depends on you what point of view you have. Mathematical or physical. May be you can combine useful aspects of both.

I am not sure if you are still interested in an answer, or if mine will help. Pure component behavior such as you have described can be captured because all intermolecular interactions are about the same in a pure species and the equation includes theoretically sound descriptions of intermolecular interactions and excluded volume. The success of the equations in these cases is based on the general success of their ability to match corresponding states behavior (similar behavior for all pure components with some consistent perturbations based on molecular structure/shape) and the ability of the equation to capture this behavior. Mixtures, however, are different. Here, the interaction parameters differ among pairs if there are polar molecules, or even if there is just one polar molecule, involved. This commonly leads to local concentration differences and other complex and quite fascinating behaviors that cannot exist in pure components. In general mixture behavior is not well described by the corresponding states curves for any simple mixture critical properties. These corresponding states curves are the basis of PR and all other cubic EOSs and are therefore too simple for polar molecules generally.