Page 240 - Introduction to chemical reaction engineering and kinetics

222 Chapter 8: Catalysis and Catalytic Reactions

(b) Solve the equation in (a) to give the nondimensional concentration profile +(A z), on the
assumption that $ > 0 for all values of z.
(c) Derive the result for the catalyst effectiveness factor 77 from (b).
(d) At what value of 4 does the concentration’of A drop to zero at the impermeable face?
(e) What does it mean for both $ and 17 if 4 is greater than the value, &d), obtained in part
(d)? To illustrate this, sketch (on the same plot for comparison) three concentration profiles
(JI versus z) for (i) 4 < +(d); (ii) 4 = $(d); and (iii) 4 > $(d). Completion of part (e)
leads to a value of 17 in terms of 4 for the case, (iii), of $ > 4(d). (The result from part
(c) applies for cases (i) and (ii).)
8-15 Consider agas-solid (catalyst) reaction, A(g) + products, in which the reaction is zero-order,
and the solid particles are spherical with radius R.
(a) Derive the diffusion equation for A, together with the expression for the Thiele modulus,
4.
(b) Solve the equation in (a) to give the nondimensional concentration profile $(4, I), on
the assumption that $ > 0 throughout the particle, where + = c~/ch. (Hint: Use the
substitution y = dcaldr.)
(c) Derive the result for the catalyst effectiveness factor 17 from (b).
(d) At what value of 4 does the concentration of A drop to zero at the center of the particle
(r = O)?
(e) In terms of 4, under what condition does + become zero at r*, where 0 < r* < R? Relate
(i) do and r*, and (ii) 7~ and r* for this situation.
8-16 (a) For a solid-catalyzed reaction (e.g., A + products), calculate the value of the catalyst
effectiveness factor (7) for the following case: EA = 83 kJ mol-‘; A is a gas at 500 K, 2.4
bar (partial pressure); the Thiele modulus (4) = 10; k, = 1.2 X 10m3 J s-l cm-’ K-l;
D, = 0.03 cm2 s-l; AH,, = +135 kJ mol-i. Use the Weisz-Hicks solution (Figure
8.12) for a first-order reaction with a spherical particle. Assume gas-film resistance is
negligible for both heat and mass transfer.
(b) Repeat (a), if AHRA = - 135 kJ mol-‘.
(c) Compare the results in (a) and (b) with the result for the case of an isothermal particle.
8-17 In the use of the observable modulus, a’, defined by equation 8.525, in the Weisz-Prater
criterion, cAs must be assessed. If cAs is replaced by cAg, the directly measurable gas-phase
concentration, what assumption is involved?
8-18 For a first-order, gas-solid (catalyst) reaction, A(g) -+ product(s), the (isothermal) overall
effectiveness factor (vO) is related to the catalyst effectiveness factor (17) by

(from 8.549)

where kA is the reaction rate constant, and kAg is the gas-film mass transfer coefficient. From
this and other considerations, complete the table below for the following cases, with a brief
justification for each entry, and a sketch of the concentration profile for each case:
(a) The surface reaction is rate controlling.
(b) Gas-film mass transfer is rate controlling.
(c) The combination of surface reaction and intraparticle diffusion is rate controlling.
(d) The combination of surface reaction and gas-film mass transfer is rate controlling.