Page 419 - Elements of Chemical Reaction Engineering Ebook

390 Nonelementary Reaction Kinetics Chap. 7

Because this reaction is liquid phase, the mole balance can be put in the fol-
lowing form:

(7-92)

The rate law for urea decomposition is

Rate law - (7-93)

Substituting Equation (7-93) into Equation (7-92) and then rearranging and
integrating, we get

Combine

(7-94)

We can write Equation (7-94) in terms of conversion as

Cum = CureaO(1 - X)
Time to achieve a
conversion X in a
batch enzymatic
reaction (7-95)

The parameters K, and Vm, can readily be determined from batch reactor data
by using the integral method of ,analysis. Dividing both sides of Equation
(7-95) by tK,l V,, and rearranging yields

(7-96)

We see that K, and Vma can be determined from the slope and intercept of a plot
of llt ln[l/(l - X)] versus Xlt. We could also express the Michaelis-Menten
equation in terms of the substrate concentration S:

(7-97)

where So is the initial concentration of substrate. In cases similar to Equation
(7-97) where there is no possibility of confusion, we shall not bother to
enclose the substrate or other species in parentheses to represent concentration
[i.e., Cs 5 (S) = SI. The corresponding plot in terms of substrate concentra-
tion is shown in Figure 7-12.