Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

392 TREATMENT OF EXPERIMENTAL DATAtion times intermediate between the initial and final values. The basic reason forthis is that the integrated expressions for reactions other than the simple firstorder case discussed above require the values of the initial concentrations. Thus,if these data are not available, absolute values of the rate coefficients cannot becalculated.However, if we consider reactions in which the order with respect to the secondreactant B is zero or in which the concentration of the second reactant is in suchlarge excess that its time dependence can be neglected, it is possible to manipulatethe integrated rate equations so as to give a numerical value of the rate coefficientinvolving the dimensions of A [see eqn. (80)] and/or [B],. Two simple exampleswill suffice to make this clearer. Firstly, suppose we have a reaction which is firstorder with respect to A and first order with respect to B and suppose we can arrangeour conditions so that B is in considerable excess of A even though we may notactually know the value of [B],. Then we may apply either the Guggenheim orMangelsdorf methods to obtain the product of the second order rate coefficientand [B], . For the second example, consider a reaction which is second order withrespect to A and zero order with respect to B. The integrated form of the rateexpression for this case is eqn. (38), namely1- -1 = k[A]o(t-to)awhich in terms of the physical property 4 becomesk= - (t-to)4t-4m 40-4m A---1 1We may regard this equation as containing three unknowns: (4,-~$~), andk/A. Therefore, by taking any three pairs of (t, c$t) values, we can eliminate twoof these unknowns to find the third. Thus if we eliminate rPm and (40-4m), weobtain k/A (but not k). The computations are simpler if we take three observationsof 4 separated by equal time intervals, thus: $t, $,+,, 4t+Zz. The value of k/A isgiven 3* byClearly from a succession of triads, we can calculate a series of values of k/A if wewish. We shall not pursue this method any further except to point out that thereare problems to be solved concerning the optimum value oft and the methodof averaging the set of k/A values. Obvbusly there is no real need to use observationsat equally spaced time intervals to eliminate two of our three unknowns andso obtain a value of k/A; this problem has been examined by Sturtevant'.