"Are there any equations I can use to estimated the average property of this mixture." Yes there are. An excellent reference is The Properties of Gases and Liquids. The most recent edition, the 5th Edition, is by Robert C. Reid, John M. Prausnitz, and Bruce E. Poling.
You will have to estimate each property for each phase separately and then use an appropriate mixture formula to average the two. For example, for density a volume average would make sense. Ditto for Cp using a weight (or mole) average.
Good luck,
Latexman