Page 417 - Elements of Chemical Reaction Engineering Ebook

388 Nonelementary Reaction Kinetics Chap. 7

then

-- - Vrnax(S1d (7-90)
Vmax
2 Km+(sl,,)
Solving Equation (7-90) for the Michaelis constant yields
Interpretation of
Michaelis constant Km = (S112) (7-91)
The Michaelis constant is equal to the substrate concentration at which the rate
of reaction is equal to one-half the maximum rate.
The parameters V,, and Km characterize the enzymatic reactions that are
described by Michaelis-Menten kinetics. V,,, is dependent on total enzyme
concentration, whereas K, is not.

Example 7-7 Evaluation of Michaelis-Menten Parameters V,, and K,,,

Determine the Michaelis-Menten parameters V,,, and K, for the reaction
’ k,
urea + urease (-> [ureasurease]* k3 > ~NH, + CO, + urease
-H,O
k2
The rate of reaction is given as a function of urea concentration in the following
table:

cure, (kmoi/m3) I 0.2 0.02 0.01 0.005 0.002
I
Ir,,, (kmol/m3.s) 1.08 0.55 0.38 0.2 0.09

Solution
Inverting Equation (7-89) gives us

(E7-7.1)

or

(E7-7.2)

A plot of the reciprocal reaction rate versus the reciprocal urea concentration should
be a straight line with an intercept llVma and slope Km/Vm,. This type of plot is
caIled a Lineweaver-Burk plot. The data in Table E7-7.1 are presented in Figure
E7-7.1 in the form of a Lineweaver-Burk plot. The intercept is 0.75, so
- 0.75 m3.s/kmo1
=
Vmax
Therefore, the maximum rate of reaction is
V,, = 1.33 kmol/m3-s = 1.33 mol/dm3-s