Page 253 - Elements of Chemical Reaction Engineering 3rd Edition
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Sec. 5.1   Batch Reactor Data                                  225

                                                         -
                                                           "
                                                   k,=  - (dm3/mol)a+P-1/s
                                                              =
                                                        c:c;
                                 Both a and p can be determined by using the method of  excess, coupled with
                                 a differential analysis of  data for batch systems.
                                      To  outline the procedure  used in the differential method  of  analysis, we
                                 consider a reaction carried out isothermally in a constant-volume batch reactor
                                 and the concentration recorded  as a function of  time. By  combining  the  mole
                                 balance with  the rate law given by  Equation (5-l), we obtain

                   Constant-volume
                      batch reactor                                                            (5-6)

                                 After taking the natural logarithm of  both sides of.Equation (5-61,





                                                     I                          I
                                 observe that the slope of  a plot of  In( -dC,ldt)  as a function of (InC,)  is the
                                 reaction order (Figure 5-1).


                                      In                               In
                                               /


                            Plot



                      versus In CA              e.  e.   =  a
                                                     Slope
                          to find
                        (Y  and  k,






                                              Figure 5-1  Differential method to determine reaction order.

                                  Figure  S-l(a) shows  a plot  of  - (dC,/dt)  versus  CA on  log-log paper  where
                                  the slope is equal to the reaction order a. The specific reaction rate,  k,,  can be
                                  found by  first choosing  a concentration  in the plot,  say  C,,,  and then finding
                                  the corresponding  value of  - (dCA/dt) as shown in Figure  5-l(b). After rais-
                                  ing CAI, to the a power, we divide it into - (dC,/dt),  to determine k,:

                                                                - (dC,/dt),
                                                           k,  =
                                                                   ( CAp)a
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