ou 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.)
ou 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.)
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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Question
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/g
Tortuosity - Τρ = 4.5
Porosity = ɛ = 0.59 cm³ void/cm3 of catalyst
Molecular Weight of cyclohexane = 84 g/mol
Density of particle = Pp = 1.332 g/cm3
Particle diameter = dp = 0.32 cm
Average concentration of cyclohexane = 4.66 x 105 moles/cm3
DK = Knudsen Diffusion coefficient in cm²/sec = (9.7 x 10°)(7)(T/M)/2
where M = molecular weight in g/mol, T= temperature in K, and F = 2VG/SG, the equivalent
pore radius in units of cm. Vg is the volume of pores and Sg is the specific surface area of
the catalyst.
Imeasured = nkı"SoCcyclohexane, where n is the effectiveness factor, k1" is the intrinsic rate
constant 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, R
is 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 diffusivity
for cyclohexane.
n = (3/os)[1/tanhøs – 1/os]
where n is the effectiveness factor and os is the Thiele modulus for the spherical pellets.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F68157290-0289-4316-a746-5bb4d295ffca%2F03fb1932-972f-4c74-820e-70132f543220%2Fvf1zzlv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:VG = 0.48 cm³/g
Tortuosity - Τρ = 4.5
Porosity = ɛ = 0.59 cm³ void/cm3 of catalyst
Molecular Weight of cyclohexane = 84 g/mol
Density of particle = Pp = 1.332 g/cm3
Particle diameter = dp = 0.32 cm
Average concentration of cyclohexane = 4.66 x 105 moles/cm3
DK = Knudsen Diffusion coefficient in cm²/sec = (9.7 x 10°)(7)(T/M)/2
where M = molecular weight in g/mol, T= temperature in K, and F = 2VG/SG, the equivalent
pore radius in units of cm. Vg is the volume of pores and Sg is the specific surface area of
the catalyst.
Imeasured = nkı"SoCcyclohexane, where n is the effectiveness factor, k1" is the intrinsic rate
constant 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, R
is 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 diffusivity
for 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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