Page 68 - Introduction to chemical reaction engineering and kinetics

50 Chapter 3: Experimental Methods in Kinetics: Measurement of Rate of Reaction

If there were two reactants A and B in reaction (A), Section 3.1.2, and the rate law were
of the form

(-rA) = k,c:c,p (3.4-3)

how would values of (Y, p, and kA be obtained using the differentiation procedure?

SOLUTION

The procedure is similar to that for one reactant, although there is an additional constant
to determine. From equation 3.4-3,

ln(-rA) = InkA + aIncA + plnc, (3.4-4)

Like equation 3.4-2, this is a linear relation, although in three-dimensional ln( - t-,&h CA-
In cn space. It is also linear with respect to the constants In kA, (Y, and p, and hence their
values can be obtained by linear regression from an experiment which measures CA as a
function of t. Values of (-rA) can be generated from these as a function of CA by differ-
entiation, as described above for the case of a single reactant. The concentrations CA and
cn are not independent but are linked by the reaction stoichiometry:

CA -cAo _ cB-cBo (3.4-5)
-
VA VB
0 where CA0 and cnO are the initial (known) concentrations. Values of cn can thus be cal-
can be obtained directly
and p
Alternatively, kA, Q,
culated from measured values of CA.
V
from equation 3.4-3 by nonlinear regression using E-Z Solve.
“O-v
method. This method is similar to the previous one, but only uses values of
Initial-rate
rates measured at t = 0, obtained by extrapolation from concentrations measured for
a relatively short period, as indicated schematically in Figure 3.3.

rAol = dope at CAol, t = 0
CA

o3 =slope atcAo3,t= 0

Figure 3.3 Initial-rate method