Page 70 - Basic physical chemistry for the atmospheric sciences

56 Basic physical chemistry

3.5 The effect of temperature on reaction rates:
the Arrhenius' relation
The general tendency for chemical reactions to proceed faster at
higher temperatures can be understood qualitatively in terms of the
concepts presented in Section 3 . 4 . The higher the temperature, the
greater will be the probability that the relative kinetic energy associ­
ated with the collision between two molecules will exceed the required
activation energy, and therefore the more likely it will be for the
reaction to occur.
Arrhenius found that the rate coefficient k for a chemical reaction
generally varies with temperature according to the relation
( - Ea)
k = A exp (3 . 9 )
R * T
*
)
where Ea is the activation energy (units J mol - 1 , R the universal gas
constant, T the temperature, and A a constant (which has the same
units as A) called the f r equency f a ctor (which is related to the fre­
quency of molecular collisions and the probability that the collisions
are favorably oriented for a chemical reaction).
From Eq. (3 .9)

or,

( - Ea ) I
log k = + log A
2 . 303 R* T
I
Hence, a plot of log k versus should be a straight line of slope
T
I
- E a
--- and the intercept at - = 0 is log k = l og A . This provides a
2 . 303 R T
A
means for determining E a and .
Exercise 3 . 6 . The reaction
2N0 2 (g)� 2NO(g) + 0 2 (g)
1
has a rate coefficient of 1 . 0 x 1 0 - 0 s-1 at 300 K and an activation
K
• What is the rate coefficient at 273 ?
energy of 1 1 1 kJ mol - 1
(R = * 8 . 3 1 4 x 1 0 - 3 kJ mo1 - 1 K - 1 . )