Page 278 - Introduction to chemical reaction engineering and kinetics

9.4 Problems for Chapter 9 259

9-14 For a gas-liquid reaction A(g) + bB(9 * products (B nonvolatile), sketch concentration pro-
files for A and B, according to the two-film model as in Figures 9.5 to 9.7, for each of the
following cases:
(a) instantaneous reaction for (i) gas-film control and (ii) liquid-film control;
(b) “slow” reaction for (i) gas-film + reaction control; (ii) liquid-film + reaction control; (iii)
reaction control; can there be gas-film and/or liquid-film control in this case?
(c) “fast” reaction in liquid film only.
9-15 For the (irreversible) gas-liquid reaction A(g) + bB(9 --f products, based on the information
below,
(a) sketch the concentration profiles for both A and B according to the two-film model, and
(b) derive the form of the rate law.
The reaction is zero-order with respect to A, and second-order with respect to B, which is
nonvolatile [(- Y*)int = kc;]. Assume reaction takes place only in the liquid film, that gas-
film mass-transfer resistance for A is negligible, and that es is uniform throughout the liquid
phase.
(c) Obtain an expression for the enhancement factor, E, for this case.
(d) Obtain an expression for the Hatta number, Ha, and relate E and Ha for this case.
9-16 Compare the (steady-state) removal of species A from a gas stream by the absorption of A in
a liquid (i) containing nonvolative species B such that the reaction A(g) + bB(9 + products
takes place, and (ii) containing no species with which it (A) can chemically react, in the
following ways:
(a) Assuming the reaction in case (i) is instantaneous, sketch (separately) concentration pro-
files for (i) and (ii) in accordance with the two-film model.
(b) Write the rate law for case (i) in terms of the enhancement factor (I?), and the correspond-
ing form for case (ii).
(c) Explain briefly, in words, in terms of the film theory, why the addition of B to the liquid
increases the rate of absorption of A in case (i) relative to that in case (ii).
(d) What is the limit of the behavior underlying the explanation in (c), how may it be
achieved, and what is the rate law in this situation?
9-17 An approximate implicit solution (van Krevelen and Hoftijzer, 1948) for the enhancement
factor (I?) for a second-order, “fast” gas-liquid reaction, A(g) + bB(9 + products (B non-
volatile), occurring in the liquid film, according to the two-film theory, is given by equations
9.2-51 and -52.
(a) Show that, under a certain condition, this solution may be put in a form explicit in E (in
terms of Ha and Ei); that is, E = E(Ha, Ei). State what the condition is, and derive the
explicit form from equations 9.2-51 and -52.
(b) Confirm the result obtained in (a) for Ha = 100 and Ei = 100.
(c) Show whether (i) equation 9.2-49 and (ii) equation 9.2-53 can each be obtained as a
limiting case from the result derived in (a) for “fast” pseudo-first-order and instantaneous
reaction, respectively. (cf. de Santiago and Farena, 1970).
9-18 Boron, because of its high hardness and low density, is important in providing protective
coatings for cutting tools and fibers for use in composite materials. The kinetics of deposition
of boron by CVD from Hz and BBr3 was studied by Haupfear and Schmidt (1994). The overall
reaction is 2BBr3 + 3H2 + 2B(s) + 6HBr.
(a) Assuming that the reaction occurs on open deposition sites on the growing boron film,
write as many mechanistic steps as possible for this reaction.
(b) Write the LH rate law that results from a mechanism in which the rds is the reaction of
adsorbed H atoms and adsorbed BBrs. Assume that the coverages of these species are
given by Langmuir competitive isotherms.
(c) For the proposed rate law in (b), obtain values of the adsorption constants and the surface
rate constant from the following data obtained with a deposition temperature of 1100 K
(regression or graphical techniques may be used). r, is the rate of growth of the thickness