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.

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For the reversible reaction A ↔ B with both reactant A and inert component I in the adiabatic PFR feed, the equilibrium constant is:
where K_m is the equilibrium constant at temperature T_m (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 X_E is the equilibrium conversion, X_EB is the conversion calculated from the energy balance, α is the ratio in the feed of total mols/mols of reactant, c_P is the heat capacity (J/[mol K]) of both the reactant and inert, and T_f is the feed temperature (K).