Page 333 - Advanced thermodynamics for engineers
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322    CHAPTER 14 CHEMICAL KINETICS




             P14.3 The rate of formation of nitric oxide (NO) is controlled by the three reversible chemical
                    reactions

                                                     k þ 1
                                              O þ N 2 5 NO þ N
                                                     k   1
                                                     k þ 2
                                              N þ O 2 5 NO þ O
                                                     k   2
                                                     k þ 3
                                             N þ OH 5 NO þ H:
                                                     k   3
                       Use the steady state approximation for the nitrogen atom concentration and the assumption
                    of partial equilibrium for the reactions governing the concentrations of O, O 2 ,HandOH
                    show that
                                                     dR þ a
                                                 b ¼
                                                     aR þ 1
                    where b ¼ [N]/[N] e , d ¼ [N 2 ]/[N 2 ] e , a ¼ [NO]/[NO] e , R ¼ R 1 /(R 2 þR 3 ), and R j is the
                    equilibrium reaction rate of reaction j, and [ ] denotes the molar concentration, and [ ] e is the
                    equilibrium molar concentration. Derive an expression for d[NO]/dt in terms of R 1 , b, a and d.
                       At a particular stage in the formation of nitric oxide the values of R and a are 0.26 and 0.1 re
                    spectively. Why is d ¼ 1 likely to be a good approximation in this case? What is the error if the
                    rate of formation of NO is evaluated from the larger approximation d½NOŠ=dt ¼ 2R 1 ,rather than
                    the equation derived in this question?
                    [3.64%]
             P14.4 The rate of change of mole concentration of constituent A in a chemical reaction is
                    expressed as


                                                d½AŠ       n
                                                    ¼ k½AŠ :
                                                 dt
                       While mole concentration is the dominant property in the reaction it is much more usual for
                    engineers to deal in mole fractions of the constituents. Show that the rate of change of mole
                    fraction of constituent A is given by
                                               dx A     n n 1
                                                  f   kx r   :
                                                        A
                                               dt
                    where r ¼ density. Also show how the rate of change of mole fraction is affected by pressure.
                    ½dx A =dtfp n 1 Š
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