Page 165 - Modelling in Transport Phenomena A Conceptual Approach
P. 165

5.3.  RATE OF GENERATION IN MASS  TRANSPORT                         145

           then
                                                                            (5.3-26)
           Therefore, Xi is negative if  i appears as a reactant; Xi is positive if  i is a product.

           Example 5.5  For the reaction

                                         3A+B+C
            express the reaction rate in terms of  the time rate  of  change  of  species A, B, and
           C.
           Solution

           Application  of  Eq.  (5.3-24) gives the rate as




           If V is constant,  then Eq.  (1) reduces to




           Comment:  The rate of  reaction is equal to the time derivative of  a concentration
           only when the volume of the reacting mixture is constant.

                                        u                                   (5.3-27)
              In the case of  several reactions, Ri is defined by

                                        & =
                                                “ij rj

           where rj  is the rate of jth reaction.
              The reaction rate is a function of temperature and concentration and is assumed
           to be the product of  two functions, one is dependent only on the temperature and
           the other is dependent only on the concentration, i.e.,

                                      r(T Ci) = W)f (ci)                    (5.3-28)
           The function k(T) is called the rate constant and its dependence on the temperature
           is given by
                                      k(T) = ATrne-€lRT                     (5.3-29)
           where A is a constant, E  is the activation energy, R is the gas constant and T is
           the absolute temperature. The power of  temperature, m, is given by

                                 0     from the Arrhenius relation
                          m = { 1/2    from the kinetic theory of  gases    (5.3-30)
                                 1     from statistical mechanics
   160   161   162   163   164   165   166   167   168   169   170