Page 148 - [B._MURPHY,_C._MURPHY,_B._HATHAWAY]_A_working_meth

132 Chapter 9
R = Universal Gas Constant = 8.314 J K-' mol-'; T = absolute
temperature, measured in K; e = exponential = 2.71828 .......

Arrhenius Equation
The rate of a reaction therefore is dependent on three factors:

(a) Frequency of collision:
Rate = [Azl[B21
(b) Relative orientation of the molecules, i.e. the steric factor, p:
Rate ocp
(c) The Activation Energy of the Reaction

Rate oc e- EuJRT
Taking (a), (b) and (c) together,
Rate oc p[A2] [B2]e-EudRT
Rate = c p[A2] [B2]e-EsJRT
where c is a constant of proportionality.
But rate = k[A2][B2], from Chapter 8, where k = the specific rate
constant.
+ k[A2] [B2] = c p[A2] [B2]e-EsJRT
* k = Cpe-E-JRT
+ k = Ae-EUJRT

i.e. k is independent of the concentration terms. A is known as the
frequency factor, the Arrhenius parameter or the pre-exponential term.
A has the same units as k, ie. zero-order reaction, Ms-'; first-order
reaction, s-l, etc., where the order of a reaction is the sum of the
exponents of the concentration terms in the rate equation, as described
in Chapter 8.
If natural logs are now taken on both sides of this equation:
Ink = 1nAeAEsJRT
Ink = In e-E-JRT + In A (since log AB = log A + log B)
In k = (-Eact/RT) In e + In A (since log A" = x log A)
* Ink = (-Eact/RT) + 1nA (sincelne = 1)
This generates a much more useful expression for the Arrhenius
equation, as this represents the equation of a line, i.e. if a graph
(Figure 9.3) is plotted of In k versus l/T, the slope or gradient of the
graph, m = Ay/Ax, is given by -E,,/R, from which Eact, the
activation energy of the reaction, can be determined. The pre-