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52    Modeling of Chemical Kinetics and Reactor Design
























                                     Figure 1-7. Lineweaver-Burk plot of (1/C urea ) versus (1/V ).
                                                                                      o





                                The overall reaction is:

                                 CH =   CH     +  H
                                  2  6    2  4    2
                                The reaction is first order in the temperature range of 550–640°C
                              and at pressure in excess of 50 mm Hg. The rate law is given by

                                              dC
                                                  2
                                 − ( r  ) =−    CH 6  = kC
                                   CH 6         dt         CH 6
                                                             2
                                    2
                                (1) Develop a mechanism to account for the first-order rate law for
                              the case where only methane is formed as a byproduct. Assume that
                              the chain length is large.

                              Mechanism

                              Initiation


                                1. C H →      CH +   CH * 3                           (1-222)
                                                   *
                                           k 1
                                                   3
                                     2
                                       6
                                                 
                                2. CH +  C H  →      CH +  C H * 5                     (1-223)
                                      *
                                                 k 2
                                                              2
                                                         4
                                             6
                                           2
                                      3
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