CHAP. 9: CHEMICAL KINETICS [CONTENTS] 317
Solution
Substituting into relation (9.159) yieldsk= 1, 5 · 1015 e−^286600 /(8.^314 ·850)= 3. 657 · 10 −^3 s−^1.9.6.3 Collision theory
The collision theory was suggested for the calculation of the rate of reactions in the gas phase.
In this theory the reacting molecules are modelled using hard spheres. It is assumed that the
rate of reaction equals the number of collisions between molecules per unit time multiplied by
the probability that the collision will result in a reaction. It may be deduced that the number of
collisions is proportional to the concentrations of the reactants and to the root of temperature.
The probability that the reaction will take place is approximated by the term exp[−E∗/(RT)],
whereE∗is the lowest value of energy sufficient for the reaction to take place.
For the temperature dependence of the rate constant it follows from the collision theory
that
k=A
√
Te−B/T, (9.162)whereAandBare constants.
9.6.4 Theory of absolute reaction rates
The theory of absolute reaction rates (also called the “activated-complex theory” or the “transition-
state theory”) is an attempt at theoretical modelling of an elementary reaction. It assumes that
the molecules of reactants approach each other and form an unstable formation called theac-
tivated complex. This complex can either decompose back to the reactants, or it can change
into the reaction products. In the model it is assumed that the activated complex is in the
state of pre-equilibrium with the reactants [see section9.5.7]. The model may be symbolically
described using the sequence of “reactions”
reactants ⇀↽ activated complex → products, (9.163)