[Cat.0 [Cat.0.S]

Under steady-state conditions YCat. °2. 8 = 0 and, assuming that decomposition of the intermediate complex (10.12) is rate determining and that (10.10) and (10.13) are very rapid, it follows from Eqs. (10.16) and (10.14) that

(10.18)

Substituting (10.18) into (10.17) we finally obtain the rate of formation of the product:

~2 [Cat] 0[8 ] KM + [8]

(10.19)

where fuw = (~-1 + ~2)/~1 is the Michaelis constant, and Eq. (10.19), which expresses the rate of reaction, is called the Michaelis-Menten equation and is used to describe the rate of enzymatic and homogeneous catalytic reactions. It was demonstrated by Schwab [15] that this equation is equivalent to the Hinshelwood-Langmuir equation used in heterogeneous catalysis.