Page 179 - Instant notes
P. 179

Rate law determination     165


        The determination of a rate law using the method of initial rates has a number of
        disadvantages:
        (i) determining tangents to a concentration versus time plot is generally subject to
           considerable uncertainty.
        (ii) the rate constant is obtained by extrapolation to an intercept which increases the error
           in k.
        (iii) observing only initial rates may be misleading if the rate of reaction is also affected
           by the formation of products. The rate constant and order may be correct at times close
           to t=0 but may not be valid over the whole course of the reaction. An example is the
           reaction between hydrogen and bromine to form HBr which has the rate law (see
           Topic F6) of:





        Initially, when [HBr] is small,              but as the reaction progresses the
        significance of the k′[HBr] term increases and the order with respect to Br 2 becomes
        undefined.


                                    Integrated rate laws

        Reaction rates are rarely measured directly because of the  difficulty  in  determining
        accurate values for slopes of graphs. Instead an integrated rate law may be used which
        expresses kinetic behavior directly in terms of the measurable  observables  of
        concentration and time. Analytical expressions for integrated rate laws of simple types of
        reaction are presented in Table 1 but even the most complex rate laws can usually be
        integrated numerically by computers. Table 1 contains expressions of integrated rate laws
        in terms of concentration of reactant A at time t but similar analytical expressions are
        readily derived for concentration of product P at time t. The advantage of these simple
        integrated rate laws is that the order of reaction with respect to a species is readily tested
        by means of a suitable plot of species concentration and time (Fig. 2).
                        Table 1. Integrated rate laws for reactions of
                        simple order

        Order   Rea   Differential    Integ      Straight       Half-life  Dime
            Ction   rate law      rated          line plot                nsions
             type                 rate law                                 of k
             0   A→P              kt=[A] 0 −[A]  [A]vs.t                  conc.
                                                                             −1
                                                                          time

                                                                             −1
             1   A→P              [A]=[A] 0 e −kt  ln[A]vs.t              time
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