You receive a Pt/Al2O3 catalyst of unknown surface area to be used for dehydrogenating cyclohexane to benzene. You think that the pores of the catalyst are narrow enough such that Knudsen diffusion can be assumed. You measure the rate at T = 705 K and find that it is 2.98 x 10-5 moles/sec-gcatalyst. Your colleague tells you that she has used the catalyst before, and that the effectiveness factor is around 0.42. Using the information below, find the specific surface area of the catalyst in m2/g. Check the validity of the assumption of Knudsen diffusion. (Hint: the mean free path equation is not useful, because d is NOT the pellet diameter in that equation.) VG = 0.48 cm³/gTortuosity - Τρ = 4.5Porosity = ɛ = 0.59 cm³ void/cm3 of catalystMolecular Weight of cyclohexane = 84 g/molDensity of particle = Pp = 1.332 g/cm3Particle diameter = dp = 0.32 cmAverage concentration of cyclohexane = 4.66 x 105 moles/cm3DK = Knudsen Diffusion coefficient in cm²/sec = (9.7 x 10°)(7)(T/M)/2where M = molecular weight in g/mol, T= temperature in K, and F = 2VG/SG, the equivalentpore radius in units of cm. Vg is the volume of pores and Sg is the specific surface area ofthe catalyst.Imeasured = nkı"SoCcyclohexane, where n is the effectiveness factor, k1" is the intrinsic rateconstant per unit surface area of catalyst, and Sg is the specific surface area of the catalyst.os = R(k:" pp SG/Deff.cyclohexane) 2 where os is the Thiele modulus for the spherical pellets, Ris the radius of the pellet, ki" is the intrinsic rate constant per unit surface area of catalyst,and SG is the specific surface area of the catalyst, Deff.cyclohexane is the effective diffusivityfor cyclohexane.n = (3/os)[1/tanhøs – 1/os]where n is the effectiveness factor and os is the Thiele modulus for the spherical pellets.

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Introduction to Chemical Engineering Thermodynamics

8th Edition

ISBN:9781259696527

Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Chapter1: Introduction

Section: Chapter Questions

Problem 1.1P

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You receive a Pt/Al2O3 catalyst of unknown surface area to be used for
dehydrogenating cyclohexane to benzene. You think that the pores of the catalyst are
narrow enough such that Knudsen diffusion can be assumed. You measure the rate at T
= 705 K and find that it is 2.98 x 10-5 moles/sec-gcatalyst. Your colleague tells you that she
has used the catalyst before, and that the effectiveness factor is around 0.42. Using the
information below, find the specific surface area of the catalyst in m2/g. Check the validity
of the assumption of Knudsen diffusion. (Hint: the mean free path equation is not
useful, because d is NOT the pellet diameter in that equation.)