The Bacillus cereus beta-lactamase I catalyzes the hydrolysis of a wide variety of penicillins and cephalosporins with values of k(cat)/K(m) varying over several orders of magnitude. The values of this parameter for the most reactive of these compounds, benzylpenicillin, I, and furylacryloyl-penicillin, II (k(cat)/K(m) = 2.43 x 10(7) M(-1) s(-1) and 2.35 x 10(7) M(-1) s(-1), respectively, at pH 7.0 in potassium phosphate buffer containing 0.17 M KCl, I(c) = 0.63, 25 degrees C) are decreased markedly by increasing viscosity in sucrose- or glycerol-containing buffers. The relative sensitivities to viscosity of k(cat)/K(m) values for I and for cephaloridine, III, were found to be virtually unchanged at pH 3.8 from those observed at pH 7.0. The differential effects of viscosity on the reactive vs. the sluggish [e.g., cephalothin (IV), k(cat)/K(m) = 1 x 10(4) M(-1) s(-1)] substrates support the contention that the rates of reaction of the former with the enzyme are in part diffusion controlled. Quantitative analysis gives values for the association rate constants, k(1), of 7.6 x 10(7) M(-1) s(-1), 4 x 10(7) M(-1) s(-1), and 1.1 x 10(7) M(-1) s(-1) for I, II, and III, respectively. As both reactive and sluggish substrates associate with the active site of the enzyme with relatively similar rate constants, the variation in k(cat)/K(m) values is primarily due to the variation in the partition ratios k(-1)/k(2), for the ES complex, which are 2.3, 0.77, and 30 for I, II, and III, respectively. The preceding analysis is based on direct application of the Stokes-Einstein diffusion law to enzyme kinetics. The range of applicability of this law to the diffusion of substrate size molecules and the mechanics of diffusion of ionic species through viscous solutions of sucrose vs. polymers are explored.