PLEASE HELP ME ASAP IN THIS REACTION ENGINEERING PROBLEM. SOLVE ALL PARTS BY HAND, INCLUDING #3. Be as detailed as you can. do not copy other solutions please. don't copy AI solutions online pls. use your own knowledge.

A catalytic reaction A+BC+D takes place in an isothermal spherical catalyst pellet. Experimental studies have shown that the reaction follows Langmuir-Hinshelwood kinetics with a rate expression given by r(cA)=(1+KcA)2kvcA 1) Show how this rate expression can be obtained by considering the elementary steps of the reactions occurring on the catalyst surface. List all the assumptions that may lead to this rate expression. 2) Derive the steady state mass balance equation for the spherical pellet and render it dimensionless using the following definitions for the dimensionless variables, the Thiele modulus, and the dimensionless reaction rate: u=cAfcA,x=Rr,=RDe(1+Kcaf)2kv,r(u)=r(cAf)r(cA) where cAf is the bulk concentration of A,R is the radius of the pellet, and De is the effective diffusion coefficient of A in the pellet. State and dedimensionalize the boundary conditions assuming that external mass transfer is much faster than intraparticle diffusion (Bim). 3) Use the definition of effectiveness factor to derive a general formula that gives as a function of the dimensionless concentration profile u(x) and other parameters of the BVP