Page 239 - Introduction to chemical reaction engineering and kinetics

8.7 Problems for Chapter 8 221

8-10 (a) For the decomposition of NHs (A) on Pt (as catalyst), what is the form of the rate law,
according to the Langmuir-Hinshelwood model, if NHs (reactant) is weakly adsorbed and
Hz (product) strongly adsorbed on Pt? Explain briefly. Assume Nz does not affect the rate.
(b) Do the following experimental results, obtained by Hinshelwood and Burk (1925) in a
constant-volume batch reactor at 1411 K, support the form used in (a)?

tls 0 10 60 120 240 360 720
P/kPa 26.7 30.4 34.1 36.3 38.5 40.0 42.7

P is total pressure, and only NHs is present initially. Justify your answer quantitatively,
for example, by using the experimental data in conjunction with the form given in (a).
Use partial pressure as a measure of concentration.
8-11 (a) For a zero-order catalytic reaction, if the catalyst particle effectiveness factor is g, what
is the overall effectiveness factor, 7, (in terms of q)? Justify your answer.
(b) For a solid-catalyst, gas-phase reaction A(g) -+ product(s), if the gas phase is pure A
and the (normalized) Thiele modulus is 10, what is the value of the overall effectiveness
factor? Explain briefly.
8-12 Swabb and Gates (1972) have studied pore-diffusion/reaction phenomena in crystallites of
H(hydrogen)-mordenite catalyst. The crystallites were approximate parallelepipeds, the long
dimension of which was assumed to be the pore length. Their analysis was based on straight,
parallel pores in an isothermal crystallite (2 faces permeable). They measured (initial) rates of
dehydration of methanol (A) to dimethyl ether in a differential reactor at 101 kPa using catalyst
fractions of different sizes. Results (for two sizes) are given in the table below, together with
quantities to be calculated, indicated by (?).

Catalyst/reaction in general: Value
II, order of reaction (assumed) 1
T/“C 205
c,4slmol cm-3 2.55 x 1O-5
pP, catalyst (particle) density/g cme3 1.7
E,,, catalyst (particle) void fraction 0.28
kA, intrinsic rate constant/s-’
D,, effective diffusivity of A/cm2 s-l

Catalyst fraction:

8-13 Derive an expression for the catalyst effectiveness factor (7) for a spherical catalyst particle of
radius R. The effective diffusivity is D, and is constant; the reaction (A + product(s)) is first-
order [(-rA) = k*cA] and irreversible. Assume constant density, steady-state and equimolar
counterdiffusion. Clearly state the boundary conditions and the form of the Thiele modulus
(4). If the diffusion or continuity equation is solved in terms of r (variable radius from center)
and CA, the substitution y = rcA is helpful.
8-14 Consider a gas-solid (catalyst) reaction, A(g) + products, in which the reaction is zero-order,
and the solid particles have “slab” or “flat-plate” geometry with one face permeable to A.
(a) Derive the continuity or diffusion (differential) equation in nondimensional form for A,
together with the expression for the Thiele modulus, 4.