Page 74 - Introduction to chemical reaction engineering and kinetics

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

Depending on the method of analysis for species A, fA may be calculated from cA,
together with the flow rates, q and FA, by equations 2.3-5 and -7. By varying cAO at the
inlet, and/or by varying flow rate, in a series of experiments, each at steady-state at the
same ?; one can measure (-T*) as a function of cA at the given T to obtain values of
kA and n in the rate law, in the same manner as described for a BR.
If there were more than one reactant, the procedure would be similar, in conjunction
with the use of equations such as 3.4-4 and -5.

3.4.1.3.2 PFR us integral reactor. In Figure 3.8, the entire vessel indicated from sam-
pling points S, t0 Sout, over which a considerable change in fA or CA would normally
occur, could be called an integral PFR. It is possible to obtain values of kinetics pa-
rameters by means of such a reactor from the material balance equation 2.4-4 rear-
ranged as

(2.4-413)

If the rate law (for (-TA)) is such that the integral can be evaluated analytically,
then it iS Only necessary t0 make IIIeaSUreInentS (Of CA or fA) at the inlet and OUtlet,
Sin and Sout, respectively, of the reactor. Thus, if the rate law is given by equation 3.4-
1, integration of the right side of equation 2.4-4b results in an expression of the form
dfA)lkA,wheredfA) is in terms of the order II, values of which can be assumed by
trial, and kA is unknown. The left side of equation 2.4-4b for a given reactor (V) can
be varied by changing FAo, and g(fA) is a linear function of V/F,, with slope kA, if the
correct value of II is used.
If the rate law is such that the integral in equation 2.4-4b cannot be evaluated analyt-
ically, it is necessary to make measurements from samples at several points along the
length of the reactor, and use these in a numerical or graphical procedure with equation
2.4-4b.

If the gas-phase reaction A + B + C is first-order with respect to A, show how the value
Of the rate Constant kA can be obtained from IneaSUrementS Of cA (Or fA) at the inlet and
outlet of a PFR operated isothermally at T, and at (essentially) constant P.

SOLUTION

The rate law is

(-rA) = kACA

and CA and fA are related by, from equations 2.3-5 and -7,

CA = F,,(l - fA)b(fA)

where it is emphasized by q(fA) that the volumetric flow rate q depends on fA. If we
assume ideal-gas behavior, and that only A is present in the feed, the dependence is given
in this particular case by (with the aid of a stoichiometric table):

4 = qo(l + fA)