Answer all question labeled and answer circled 1. Oxygen flux into a catalyst pa

Question

Answer all question labeled and answer circled 1. Oxygen flux into a catalyst particle (30 points) oxygen is consumed inside a spherical catalyst particle at a rate which is nearly independent of the O2 concentration. As a model of the particle, consider steady-state O2 diffusion inside a symmetrical sphere o radius R, with zeroth-order consumption of O2, where the reaction rate -Ko, a constant. Assume that the O2 concentration at the outer surface (r R is maintained constant at CR. The diffusion coefficient of O2 in the catalyst particle is DM. a) points) You are given the O2 concentration profile, Cun, where Ko (R -r 6D Determine NA,, the flux of O2 at the outer surface (r R). 0 points) Divide the flux Nur from part DA C a typical value of the flux into a (a by ere. Then, express the ratio in terms of a familiar dimensionless parameter. c) (10 points) If D s cm /s, R 1 mm, CR 10 and 106 mol/ocm3 s), the mol/cms, Ko is system in the slow reaction limit or fast reaction limit? Briefly your answer. explain

Explanation / Answer

given Cr=CR- Kg*(R2-r2)/6DA

dCr/dr = +Kg* 2r/6DA, NA = -DA* dCA/dr =-DA* Ko*2r/3DA

at r=R, NAr = -DA*K0*2R/D= -2Ko*R/3

NA/(-DACR/R)= (2K0*R/3)/DCR/R = 2Ko*R2/3DACR= Convective mass transfer/ Diffusive mass transfer =f( shrewood numner)= 2*10-6 mol/cm3.s*(10-1)2 cm2/ (3* 10-5* cm2/s. 10-7 mol/cm3= 6666

This is diffusionn controlled as indicated by the value of the given number. Hence it is fast reaction .

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