Page 286 - Introduction to chemical reaction engineering and kinetics

10.3 Estimation of K, and V,,, 267

to the exact result.) Using the SSH, we set dc,,ldt = 0, and then, from equation 10.2-14,

klCEoCS (10.2-16)
cEs = k-, + k, + klcS
Substituting for cEs in the rate of reaction from the rate-determining step, 10.2-4, we
again obtain

(10.24)
rP = krcES = Km + cs

where

K,,, = (k-, + k,.)lk, (10.2-17)

This is a more general definition of the Michaelis constant than that given in Section
10.2.1. If k-, >> k,, it simplifies to the form developed in 10.2.1.
Again, V,,,,, may be substituted for krcEo, producing the Michaelis-Menten form of
the rate law, that is,

VitlLlXCS (10.2-9)
rp = Km + cs

10.3 ESTIMATION OF K,,, AND V,,,,,

The nonlinear form of the Michaelis-Menten equation, 10.2-9, does not permit simple
estimation of the kinetic parameters (Km and V,,,). Three approaches may be adopted:

(1) use of initial-rate data with a linearized form of the rate law;
(2) use of concentration-time data with a linearized form of the integrated rate law;
and
(3) use of concentration-time data with the integrated rate law in nonlinear form.
These approaches are described in the next three sections.

10.3.1 Linearized Form of the Michaelis-Menten Equation

The Michaelis-Menten equation, 10.2-9, in initial-rate form, is
Vmax%o
rP0 = (10.3-1)
Km + cso
Inverting equation 10.3-1, we obtain

1
1
-
-=- + Km 1 - (10.3-2)
rp, V,,, Vmax cso
This is a linear expression for l/r,, as a function of l/csO, and was first proposed by
Lineweaver and Burk (1934). A plot of l/r,, against l/csO, known as a Lineweaver-Burk
plot, produces a straight line with intercept l/V,,, and slope Km/V,,,.