Page 42 - Modeling of Chemical Kinetics and Reactor Design

12 Modeling of Chemical Kinetics and Reactor Design

TRANSITION STATE INTERMEDIATES

Each elementary step proceeds from reactants to products through
the formation of an intermediate called the transition state. Such
intermediates cannot be isolated, as they are species in transit. The
act of reaction will involve the breaking or making of a chemical bond,
whereby transition state intermediates are formed (see also “Transition
State Theory”).

THE ARRHENIUS EQUATION AND
THE COLLISION THEORY

THE ARRHENIUS EQUATION

Generally, the rate of reaction depends on three principal functions:
temperature, pressure, and composition. However, as a result of phase
rule and thermodynamics, there is a relationship between temperature,
pressure, and composition. This relationship can be expressed as:
r = ( (1-52)
f temperature, composition)
i
Consider the reaction:

A + B → C + D (1-53)

Here, a molecule of C is formed only when a collision between
molecules of A and B occurs. The rate of reaction r (that is, rate of
C
appearance of species C) depends on this collision frequency. Using
the kinetic theory of gases, the reaction rate is proportional to the
product of the concentration of the reactants and to the square root
of the absolute temperature:

r ∝ C C T 05 (1-54)
.
B
A
C
The number of molecules reacting per unit time is smaller than the
number of binary collisions between A and B. Also, temperature is
known to have a much greater effect on the reaction rate than one
0.5
would expect from T . For binary collisions between A and B to
result in a reaction, the collision must involve energies of translation
and vibration that are in excess of energy E, known as the activation