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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
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