Differntial-algebraic equation DAE - chemical reactor

Hi,

I have a question to solve a DAE-system of a chemical reactor. In the picture you can see a minimal example. Its a simple reaction A to B with a first order kinetic multiplicated with an arhenius equation and an empirical pressure factor. To solve the DGL system, I have to predict the pressure p, wich depends on the mol fractions and temperatur. So this is my algebraic equation. This equation is combined with a DGL of the energy balance and two mass balnce. How can I solve such a system? With the example of mathcad, i can't solve this. Is there a simple way or standard method? I want to solve the system with RADAU so i have to built the vector function D. How i have to implement the pressure equation?

Thanks for your help