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9.4 Problems for Chapter 9 257
contact. At the very least, mobility in one of the solids is required to bring the reactants
together. In the reduction of a metal oxide, MO, by carbon, carbon oxides are thought
to mediate this “solid-state” reaction through the two-step mechanism:
MO(s) + CO + M(s or 9 + CO, (1)
co, + C(s) + 2co (2)
This provides a means whereby the gas pressure can influence the kinetics, but these
reactions are sufficiently complex that rarely are mechanistic rate laws used in practice.
9.4 PROBLEMS FOR CHAPTER 9
9-1 For an isothermal spherical particle (at the surrounding bulk-gas temperature) of species B
reacting with gaseous species A as in Example 9-1, derive the time (t)-conversion (fa) relation
from the SCM for each of the following three cases individually, and show that additivity of
the three results for t agrees with the overall result reached in Example 9- 1:
(a) gas-film mass transfer is the rds;
(b) surface reaction (first-order) is the rds; (already done in Example 9-2)
(c) ash-layer diffusion of A is the rds.
(Any combination of two of the three may be similarly considered to obtain a corresponding
total time in each case.)
9-2 Repeat Example 9-1 and problem 9-1 for an isothermal particle of “flat-plate” geometry rep-
resented in Figure 8.10, assuming only one face permeable.
9-3 Repeat Example 9-1 and problem 9-1 for an isothermal cylindrical particle of radius R and
length L; assume that only the circumferential area is permeable (“ends sealed”).
9-4 In the use of the shrinking-core model for a gas-solid reaction, what information could be
obtained about the possible existence of a rate-controlling step (gas-film mass transfer or ash-
layer diffusion or surface reaction) from each of the following:
(a) t for given fn decreases considerably with increase in temperature (series of experiments);
(b) linear relationship between t and fs;
(c) change of relative fluid-particle velocity;
(d) effect on t of change of particle size (series of experiments).
9-5 For a certain fluid-particle reaction, represented by A(g) + bB(s) -+ products, it is proposed
to change some of the operating parameters as follows: the particle size RI is to be tripled to
Rz. and the temperature is to be increased from T1 = 800 K to T2 = 900 K. What would the
partial pressure (P,Q~) be, if the original partial pressure (P.Q~) was 2 bar, in order that the
fractional conversion (fa) be unchanged for a given reaction time? The particles are spher-
ical, and reaction rate is controlling for the shrinking-core model. For the reaction, EAIR =
12,000 K.
9-6 For a certain fluid-particle reaction, represented by A(g) + bB(s) -+ products, suppose the
time required for complete reaction of cylindrical particles of radius RI, at T1 = 800 K and
partial pressure p&l, is ti. If it is proposed to use particles of double the size at one-third
the partial pressure (R2, PA@), what should the temperature (T2) be to maintain the same
value of tl? Assume reaction control with the shrinking-core model, and for the reaction,
EAIR = 10,000 K.
9-7 An experimental reactor for a gas-solid reaction, A(g) + bB(s) + products, is used in which
solid particles are carried continuously at a steady flow-rate on a horizontal grate 5 m long and
moving at a constant speed. Pure gas reactant A is in continuous cross-flow upward through
the solid particles, which form a relatively thin layer on the moving grate.
(a) For a solid consisting of cylindrical particles 1 mm in radius, calculate the value of each
appropriate kinetics parameter tl (that is, for each appropriate term in the expression
given in Table 9.1), specifying the units, if, at a certain T and P, fB was 0.8 when the