Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

356 TREATMENT OF EXPERIMENTAL DATAThe two constants of eqns. (24) and (25) differ by ~a+b)-l}log,,[A],. Eqns.(23), (24), or (25) show that, as a or [A] decreases throughout the particularexperiment, the time interval for a given fractional change increases if (u+b) > 1,remains constant if (u+b) = 1 and decreases if (u+b) < 1. The choice off isdetermined in part by the need to avoid large uncertainties in the interpolatedvalues of z,; iff is too close to unity, the points on the log,, z, log,, aj-, (orlog,, [A],-,) graph become widely scattered about the true straight line thusgiving rise to a large degree of uncertainty in the value of the total order. At thesame time, unlike the former fractional life treatment of several experiments, toolow a value off cannot be used; if a low value offis chosen, the reaction has to befollowed to very high degrees of conversion to obtain a reasonable number ofpoints to define the slope of the straight line of log,, zj against log,, a,- ,; evenwith a value f = 0.8, the reaction has to be followed to nearly 70 % conversionfor five points to be obtained on this graph. Clearly this method of treating thedata of a single experiment has few advantages over the superimposition method.(iii) Method of tangentsThe slope of the tangent to the a, t curve at any time is related to the value ofa at that time by eqn. (15)provided that the initial concentration ratio [B],/[A], has been chosen equal tothe stoichiometric ratio vs/vA. Consequently if a series of tangents are drawn to thea, t curve at a series of values of a and their slopes measured, the total order (u+b)can be obtained from a logarithmic plot of (- da/dt) against a sincelog,, (-da/dt) = constant+(u+b) log,, a (26)From a practical point of view, there is little virtue in converting all the experimentalvalues of [A] to a when utilizing this method. In terms of the directlymeasured quantities, eqn. (26) becomeslog,, (- d[A]/dt) = constant + (u + b) log,, [A] (27)The two constants of eqns. (26) and (27) differ byHa+b)-l) log,, [A10 .The construction of tangents to concentration-time curves is greatly facilitatedby the use of a front-surfaced plane mirror to find the normal. It is still, however,