I will use polymath so I would appreciate it if you answer it with appropriate equations.

In an isothermal packed bed reactor, the reaction given below is a simplified of a multiple reaction system and can be considered as an overall reaction for that real process. CO2+3H2CH3OH+H2O (A) (B) (C) (D) The rate of reaction and the rate constant of the above reaction are given below; r=k1KA(PAPB3/2K1PB3/2PCPD)kgcat.skmol where, PA,PB,PC, and PD are the partial pressures in bar, Reaction rate constant, k1=10.9exp[RT87500(J/mol)] in kmol/(s.bar1.5.kgcat) Adsorption equilibrium constant, KA=7.05107exp[RT61700(J/mol] in bar1, All temperature is in K. The feed having the mole ratio of H2 to CO2:1 enters the reactor at 220C and 50 bars. Inlet molar flow rate of CO2 is 0.01kmol/s. Determine the catalyst weight necessary for 81% of equilibrium conversion by neglecting the pressure drop. Use Polymath software with the design equations written by your hand, and show the results in table and graphical format. NOTE: Equilibrium conversion at the studied operating condition is about 37.1%