1.  The irreversible gas-phase isomerization reaction A+B→C+D is carried out in a packed bed of reactor. The reaction is given by 

The feed consists of 6% (mole) A, 6% (mole) B and 88% inerts.  The inlet temperature is 300 K. The entering volumetric flow rate is 100 L/s. The reactor operates at a flowrate in which the reaction rate is not external mass transfer limited so that you can assume that the bulk gas concentration is equal to the surface concentration.  Your task is to first determine the catalyst effectiveness factor (internal) and then assume this factor is constant with the packed bed reactor and determine the conversion of A in the reactor.

a) Derive an unsteady-state mole balance on A within a single spherical catalyst particle with a radius of 0.5 cm, effective Diffusivity of 0.5×10-8 m2/s, and catalyst density of 1515 kgcat/mcat

b) Assume steady-state and transform your mole balances and constitutive equations for the diffusive flux into 2 ODE’s that can be solved using POLYMATH or python.

c) Assuming steady-state give the Boundary conditions at r=0 and r=