The solvent kinetic isotope effects (SKIE's) on k(cat) (D(V)) and on k(cat/Km[D(V/K)] were determined for the Bacillus cereus beta-lactamase I catalyzed hydrolysis of five substrates that have values of k(cat)/K(m) varying over the range (0.014-46.3) X 10(6)M(-1) s(-1) and of k(cat) between 0.5 and 2019 s(-1). The variation of D(V/K) was only from 1.06 to 1.25 among these compounds and that in D(V) was from 1.50 to 2.16. These results require that Dk(1), the SKIE on the enzyme-substrate association rate constant, and D(k-1/k2), that on the partition ratio of the ES complex, both be near 1. The larger SKIE observed on D(V) requires that an exchangeable proton be in flight for either or both the acylation and the deacylation reaction. The pH dependence of the values k(cat)/K(m) for three substrates shows identical pK(a)s of 5.5. and 8.4. This identity combined with the fact that only one of these three substrates is kinetically "sticky" proves that the substrates can combine productively with only one protonic form of the enzyme. There is considerable substrate variation in the pK(a) values of k(cat) observed vs. pH profiles; the inflection points for all substrates studied are at pH values more extreme than are observed in the pH profiles for k(cat)/K(m).