Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

2 CONSISTENCY WITH EQNS. OF TYPE -d[A]/dt = k[A]"[B]* 387very close to zero. When c is zero, k and its standard error become indeterminateinthis situation, the special forms of the integrated expressions which are shown inTable 1 must be used. When c is small, it is advisable to transform the equationsunder discussion by suitable expansion in terms of c/a. A case in point is eqn. (50)In ("'"1a(l +c)= k~[A]~r(t-f~)(i-1) - c- [-- 1 -1) = k[Alor(t-t0)2 a2On expanding the logarithm as far as second order terms in c, we obtainEqn. (79) reduces to the special form (51) when c = 0. Thus, at sufficiently lowvalues of c so that terms in c3/a3 can be neglected, we write eqn. (50) in the form1 cf(a) = - --a 2a2Similar transformations can be made for the other equations mentioned.We should also note that the expressions for f(a) simplify considerably whenc is very large. In this case I>> r and so the concentration of B remains almostunchanged as A reacts; the integrated form of the rate expression, eqn. (32),reduces to$ = k[A]",-'[B]b,(t-to)(79)The integral on the left-hand side of the above equation is particularly simple.For example, eqn. (50), in which a = b = 1, reduces to1In - = k[B]o(tato)(d) Special proceduresThe major part of our previous discussion has been cast in terms of the variablea defined byIt happens in certain types of work that the absolute values of [A] and [Alecannot be determined with any accuracy; this occurs when the quantitative relation-References p. 407