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( 3 0 pts ) A spherical catalyst particle with a diameter R is suspended in a fluidized bed. C 2 H 6 diffuses, through

(30 pts) A spherical catalyst particle with a diameter R is suspended in a fluidized bed.
C2H6 diffuses, through a stationary gas layer, to the catalyst surfac
which the following reaction occurs:
C2H6C2H4+H2
(i) Express the ethane flux (NA) in terms of diffusion coefficient
total gas concentration C, and mole fraction of C2H6(xA) along
radial (r) direction in its most simplified form. State your
assumptions;
(ii) Write down the governing equation with respect to xA?Ny
performing shell mass balance (do NOT solve the equation);
(iii) If the rate constant on the catalyst surface is very large relative to the diffusion coefficient, i.e.k?
D, and boundary layer thickness is very small relative to the catalyst radius R, i.e.R0,
express NA in C,CAO,D, and . Assume first order reaction rate equation with A
being ethane), and bulk phase ethane concentration being CA0. Hint: Simplify the problem by
considering the effect of very large kD ratio on ethane concentration at the catalyst surface and small
R on surface curvature.
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