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26    Modeling of Chemical Kinetics and Reactor Design

                               ACID-BASE CATALYSIS: HOMOGENEOUS LIQUID PHASE

                                A catalyst is defined as a substance that influences the rate or the
                              direction of a chemical reaction without being consumed. Homogeneous
                              catalytic processes are where the catalyst is dissolved in a liquid
                              reaction medium.  The varieties of chemical species that may act as
                              homogeneous catalysts include anions, cations, neutral species, enzymes,
                              and association complexes. In acid-base catalysis, one step in the
                              reaction mechanism consists of a proton transfer between the catalyst
                              and the substrate.  The protonated reactant species or intermediate
                              further reacts with either another species in the solution or by a
                              decomposition process. Table 1-1 shows typical reactions of an acid-
                              base catalysis.  An example of an acid-base catalysis in solution is
                              hydrolysis of esters by acids.

                                                 Acid
                                 R COOR +   H O [   R COOH +    R OH                    (1-113)
                                   1     2    2       1           2

                              Mechanism
                                                      1 (
                                                               +
                                               +
                                 R COOR +    H [    R COOR H )   *                      (1-114)
                                    1    2                   2
                                   1 (
                                              *
                                            +
                                 R COOR H ) +     H O [   R COOH +  R OH +  H +         (1-115)
                                          2        2       1          2
                                             AUTOCATALYTIC REACTIONS

                                There are many reactions in which the products formed often act
                              as catalysts for the reaction.  The reaction rate accelerates as the
                              reaction continues, and this process is referred to as autocatalysis. The
                              reaction rate is proportional to a product concentration raised to a
                              positive exponent for an autocatalytic reaction. Examples of this type
                              of reaction are the hydrolysis of several esters.  This is because the
                              acids formed by the reaction give rise to hydrogen ions that act as
                              catalysts for subsequent reactions.  The fermentation reaction that
                              involves the action of a micro-organism on an organic feedstock is a
                              significant autocatalytic reaction.
                                Normally, when a material reacts, its initial rate of disappearance
                              is high and the rate decreases continuously as the reactant is consumed.
                              However, in autocatalytic reaction, the initial rate is relatively slow
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