Page 163 - Modelling in Transport Phenomena A Conceptual Approach
P. 163

5.3.  RATE OF GENERATION IN MASS TRANSPORT                          143

          where c,  is the initial total molar concentration.
             When more than one reaction takes place in a reactor,  Eq.  (5.3-10) takes the

                                                                           (5.3-19)
          where

                   nij  = number of moles of ith species in the jth reaction
                  nij, = initial number of  moles of ith species in the jth reaction
                   aij  = stoichiometric coefficient of  ith species in the jth reaction
                    ~j  = extent of the jth reaction

          Summation of  Eq.  (5.3-19) over all reactions taking place in a reactor gives






                                                                           (5.3-21)



          Example 5.4  The following  two reactions occur simultaneously  in a batch reac-
           tor:
                                     C2H6 = C2H4 + H2
                                     C2Hs + H2  = 2CH4
          A mixture of  85 mol % C2Hs and 15% anerts is fed into a reactor and the reactions
          proceed until 25% C2H4 and 5% CH4 are formed. Determine the percentage of  each
          species in a reacting mixture.

          Solution
          Basis: 1 mole of  a reacting mixture
          Let  ~1  and  ~2  be  the extents of  the first and second  reactions,  respectively.  Then,
          the number of  moles of  each species can be  expressed as
                                    nCzH6 = 0.85 -  -  €2
                                    nCzH4 = El
                                      nH2 = €1 - EP
                                     ncH, = 2E2
                                    ninert  = 0.15
           The total number of moles, nT, is

                                         nT=l+El
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