Page 241 - Introduction to chemical reaction engineering and kinetics

v
7O-v
0 8-19 Experimental values for the rate constant k in the Eklund equation (1956) for the oxidation
8.7 Problems for Chapter 8 223

of SOz
described over VzOs catalyst are as follows for two different sizes/shapes of particle (A and B,
below):
t/T 416 420 429 437 455 458 474 488 504 525 544
106k* (for A+) - 6.7 - 17.7 47 - 99 - - - -
106k* (for B+) 1.43 - 2.23 5.34 - 11.1 - 17.7 28.0 38.6 37.7
*units of k: moles SO2 reacted (g cat)-’ s-l atm-’
+A particles are spherical with diameter of 0.67 mm
+B particles are cylindrical, 8 mm in diameter and 25 mm in length

(a) From these data, what activation energy is indicated for the surjiice reaction?
(b) Do the data for the cylindrical particles suggest significant pore-diffusion resistance? If
they do, what is the apparent activation energy for this range? See also Jensen-Holm and
Lyne (1994).
(c) One particular plant used cylindrical pellets 5 mm in diameter and 5 to 10 mm in length.
What value of the rate constant should be used for these pellets at (i) 525”C, and (ii)
429”C?
0 8-20 Suppose experiments were conducted to characterize the performance of a catalyst for a cer-
N.B. For a cylindrical pellet, L
in the Thiele modulus is R/2, where R is the radius.
(i.e., L,)
V
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tain reaction (A -+ products) that is first-order. The following data refer to experiments with
several sizes of spherical catalyst particles of diameter dp, with CA = 0.025 mol L-l:
d&m 0.1 0.5 1 5 10 20 25
lo4(-rA),&no1 L-’ s-l 5.8 5.9 5.3 2.4 1.3 0.74 0.59
Determine the following:
(a) the intrinsic reaction rate, (-T.&t, and kA;
(b) the effectiveness factor 71 for the 1,5,20, and 25-mm particles;
(c) the Thiele modulus (4’) for the 5,20, and 25-mm particles;
(d) the effective diffusivity D,.
State any other assumptions you make.
8-21 (a) For an n&order, solid-catalyzed, gas-phase reaction, A + products, obtain an expression
for the (catalyst) particle effectiveness factor (7) in terms of the overall effectiveness
factor (7,) and other relevant quantities.
(b) From the result in (a), obtain explicit expressions for q0 in terms of 17 and the other
quantities, for reaction orders n = 0, 1 (see equation 8.5-49), and 2.
products involving a catalyst with relatively porous
8-22 Consider the second-order reaction A +
v
particles (7 --z 1). If the ratio k&k,4 is 20 mol m- 3,
by what factor does the presence of
To\
= 0.2
external (film) mass-transfer resistance decrease the rate of reaction at 600 K and PA
0 8-23 Activated carbon has been studied as a means for removal of organic molecules from waste-
MPa?
water by adsorption. Using the following data for benzene (A) adsorption on activated carbon
(Leyva-Ramos and Geankopolis, 1994, as read from several points from a graph), determine
the adsorption coefficients mmax and b, assuming that the data follow a Langmuir isotherm
with the form mA* = m,,,bCA/(l + bCA). Comment on your results.
cc,%/mg cm-3 0.055 0.10 0.14 0.26 0.32 0.60
%gHga/mg (gc)-’ 12.2 13.4 14.4 15.4 16.9 17.7
where rnc6Qa is the amount of benzene adsorbed in mg g-l (carbon).