where k is the proportionality constant, usually referred to as the rate constant. If k is large, the reaction is fast; if k is small, the reaction is slow. In this case, the reaction rate (-d[D]/dt) is said to be frrst-order in D and first-order in A.
If A is present in excess of D, that is, [A] >> [D], then even though some of A is consumed during the reaction, effectively only D is lost. Under these circumstances,
where kobs is said to be the observed rate constant, a pseudo-first-order constant. In most studies of the stability of pharmaceuticals, especially in aqueous solution, the kinetics can often be simplified to pseudo-fist-order conditions.
More generally, the degradation rate of a drug, D, depends on the drug concentration, [D], and the concentrations (more accurately, the activities) of chemical species participating in the reaction [A], [B], . . . . The rate at which [D] decreases, -d[D] /dt, is described by summing the terms for all the reactions that D might undergo:
where ko,AB... and ko,EF...etc., are rate constants of reactions in which species AB... and species EF..., respectively, react with D. The terms n, l, m, o, and p are reaction orders for each species, and the sum of these is considered to be the overall reaction order. For example, assuming that an ester is hydrolyzed by both hydronium ion catalysis and water attack, the rate can described by Eq. (2.5). If additional species participate in the hydrolysis, their terms would be added to this expression.
Assuming that degradation of drug D is a result of the direct reaction with a species A, the rate is proportional to the concentration of "activated complex," often referred to as the "transition state," Xt formed between D and A:
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