Reversible Reaction in an Adiabatic Plug Flow Reactor
 A reversible reaction, A ↔ B, takes place in an adiabatic plug-flow reactor (PFR). Select either an exothermic (ΔH < 0) or an endothermic (ΔH > 0) reaction. The black curve is the equilibrium conversion as a function of temperature from the van't Hoff equation.  The blue line is conversion as a function of temperature from the adiabatic energy balance.  The intersection of the curve and the line is the conversion at equilibrium (Xe)and the adiabatic temperature at equilibrium (Te). You can vary the feed temperature and the molar ratio of inert to reactant in the feed.

Download the CDF file to view the simulation using the free Wolfram CDF player.

Details
For the reversible reaction A ↔ B with both reactant A and inert component I in the adiabatic PFR feed, the equilibrium constant is:
where Km is the equilibrium constant at temperature Tm (K), ΔH is the heat of reaction (J/mol), R is the ideal gas constant (J/[mol K]), and T is the temperature of the reaction (K).

The equilibrium conversion is obtained from the equilibrium constant, assuming ideal gases:
where XE is the equilibrium conversion, XEB is the conversion calculated from the energy balance, α is the ratio in the feed of total mols/mols of reactant, cP is the heat capacity (J/[mol K]) of both the reactant and inert, and Tf is the feed temperature (K).

Reference
  1. H. S. Fogler, Essentials of Chemical Reaction Engineering, Upper Saddle River, NJ: Prentice Hall, 2011 pp. 503-505.