Page 101 - Elements of Chemical Reaction Engineering 3rd Edition

Sec. 3 1 Basic Definitions 73

Other exlpressions similar to the Arrheniu!; equation exist. One such
expression is the temperature dependence derived from transition-state theory,
which takes a form similar to Equation (3-2):

in which OSn5 1.
If Equations (3-2) and (3-4) are used to describe the te-mperature depen-
dence: for the same reaction data, it will be found that the activation energies E
and E' will differ slightly.

3.1.2 The Reaction Order and Rate Law

The dependence of the reaction rate -rA on the concentrations {of the
species present, fn( C, ), is almost without exception determined by experimen-
tal observation. Although the functional dependence may be postulated from
theory, experirnents are necessary to confirm the proposed form. One of the
most common general forms of this dependence is the product of concentra-
tions of the individual reacting species, each of which is raised to a power, for
example,

The exponents of the concentrations in Equation (3-5) lead to the concept
of reaction order. The order of a reaction refers to the powers to which the
concentrations are raised in the kinetic rate 1aw.t In Equation (3-5), the reac-
tion 11s a order with respect to reactant A, and p order with respect to reactant
B. The overall order of the reaction, n, is
Overall reaction
order n=a+p
For example, in the gas-phase reaction

2NO+0, --+ 2N40,

Strictly Speaking Strictly speakling, the reaction rates should be written in terms of the activities, a,
(a, = yzC,, where y, is the activity coefficient):

However, for many reacting systems, the activity coefficients, y,, do not change
appreciably during the course of the reaction and they are adsorbed in the specific
reaction rate: