Page 235 - Modeling of Chemical Kinetics and Reactor Design
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Reaction Rate Expression  205

                              on A and integrate it to derive the expression C  = C AO  exp(–kt), where
                                                                         A
                              C AO  is the concentration of A in the reactor at t = 0.
                                (2)  The gas-phase decomposition of sulfuryl chloride, SO Cl   →
                                                                                           2
                                                                                        2
                              SO  + Cl , is thought to follow a first order rate law. The reaction is
                                 2
                                      2
                              performed in a constant volume, isothermal batch reactor, and the
                              concentration of SO Cl  is measured at several reaction times, with
                                                 2
                                                    2
                              the following results.
                              t(min)           4.0     20.2    40.0     60.0     120.0    180.0
                              C (mol/l)      0.0158   0.0152  0.0144   0.0136   0.0116   0.0099
                               A

                                Use these results to verify the proposed law and determine the rate
                              constant k. Give both the value and units of k.

                              Solution

                                (1) Assuming that the reaction is first order in an isothermal batch
                              reactor of constant volume, then the rate equation for the reaction
                                  
                                   k 1
                              A → Products is

                                 − ( r A ) =−  1  dn A  = kC A                          (3-309)
                                                     1
                                           V dt
                              where the number of moles n  is
                                                          A
                                n  = C V                                                (3-310)
                                 A
                                       A
                              where C  = concentration of species A
                                      A
                                     V = volume of the batch reactor
                                Substituting Equation 3-310 into Equation 3-309 yields


                                 − ( r A ) =−  1  ( dVC A  ) = k C A
                                                       1
                                          V
                                      =−  dC A  = kC A                                  (3-311)
                                                  1
                                           dt

                              since V is constant.
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