Page 63 - Introduction to chemical reaction engineering and kinetics

3.2 Experimental Measurements: General Considerations 45

value of the energy of activation, E,,,, if this rule is applied for an increase from (a) 300 to
310 K, and (b) 800 to 810 K.

SOLUTION

From equations 3. l-l and -2, we write

(-r*) = k*(T>rjJconc.>

and assume that k,(T) is given by equation 3.1-8, and that ra(conc.), although unknown,
is the same form at all values of T. If we let subscript 1 refer to the lower T and subscript
2 to the higher T(T, = T, + lo), then, since r, = 2rl,

A exp(-EdRT&(conc.) = A exp(-EAIRTI)2r~(conc.)
From this,

EA = RT, T2 In 2l(T, - T,)

(4 EA = 8314(300)310(1n2)/10 = 53,600 J mol-’
0.4 EA = 8.314(800)810(1n2)/10 = 373,400 J mol-’

These are very different values, which shows that the rule is valid for a given reaction
only over a limited temperature range.

3.2 EXPERIMENTAL MEASUREMENTS: GENERAL CONSIDERATIONS

Establishing the form of a rate law experimentally for a particular reaction involves
determining values of the reaction rate parameters, such as (Y, /I, and y in equation
3.1-2, and A and EA in equation 3.1-8. The general approach for a simple system would
normally require the following choices, not necessarily in the order listed:

(1) Choice of a species (reactant or product) to follow the extent of reaction (e.g., by
chemical analysis) and/or for specification of the rate; if the reaction stoichiom-
etry is not known, it may be necessary to establish this experimentally, and to
verify that the system is a simple one.
(2) Choice of type of reactor to be used and certain features relating to its mode of
operation (e.g., a BR operated at constant volume); these establish the numer-
ical interpretation of the rate from the appropriate material balance equation
(Chapter 2).
(3) Choice of method to follow the extent of reaction with respect to time or a time-
related quantity (e.g., by chemical analysis).
(4) Choice of experimental strategy to follow in light of points (1) to (3) (i.e., how to
perform the experiments and the number and type required).
(5) Choice of method to determine numerically the values of the parameters, and
hence to establish the actual form of the rate law.
We consider these points in more detail in the remaining sections of this chapter.
Points (1) and (3) are treated together in Section 3.3, and points (2) and (4) are treated
together in Section 3.4.1. Unless otherwise indicated, it is assumed that experiments are
carried out at fixed T. The effect of T is considered separately in Section 3.4.2. Some
comments on point (5) are given in Section 3.5.