Page 72 - Introduction to chemical reaction engineering and kinetics

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

More generally, for an nth-order reaction, the half-life is given (from equation 3.4-9)
by

1

Both equations 3.4-14 and -15 lead to the same conclusion:

‘-l = a constant (all n) (3.4-16)
t1/‘2CAo
This may be used as a test to establish the value of n, by trial, from a series of experi-
ments carried out to measure t1,2 for different values of c&,. The value of kA can then
be calculated from the value of n obtained, from equation 3.4-14 or -15. Alternatively,
equation 3.4-15 can be used in linear form (ln t1,2 versus ln cAO) for testing similar to
that described in the previous section.

3.4.1.2 Use of a CSTR
Consider a constant-density reaction with one reactant, A + products, as illustrated
for a liquid-phase reaction in a CSTR in Figure 3.6. One experiment at steady-state
generates one point value of (-TA) for the conditions (CA, 4, T) chosen. This value is
given by the material balance obtained in Section 2.3.2:

(2.3-12)
(- rA) = tcAo - cA)dv
To determine the form of the rate law, values of (-IA) as a function of CA may be
obtained from a series of such experiments operated at various conditions. For a given
reactor (V) operated at a given K conditions are changed by varying either CA0 or 4.
For a rate law given by (-rA) = kAck, the parameter-estimation procedure is the same
as that in the differential method for a BR in the use of equation 3.4-2 (linearized form
of the rate law) to determine kA and IZ. The use of a CSTR generates point ( -rA) data
directly without the need to differentiate CA data (unlike the differential method with
a BR).
If there is more than one reactant, as in Examples 3-3 or 3-5, with a rate law given by
(-IA) = k&C; , the procedure to determine (-rA) is similar to that for one reactant,
and the kinetics parameters are obtained by use of equation 3.4-4, the linearized form
of the rate law.

How would the procedure described above have to be modified if density were not con-
stant?

Figure 3.6 Steady-state operation of a CSTR for measurement of ( -I-*);
constant density