Page 67 - Basic physical chemistry for the atmospheric sciences

Chemical kinetics .'i i

bimolecular chemical reaction at I atm and 0°C, given that p = 3 x
10-10 m and c = 5 x 1 0 2 m s - 1 • How long would it take to consume the

reacting gases at this rate?
Solution. We must first determine the number of molecules per unit
volume (n0) of each gas at I atm and 0°C. This can be found using the
ideal gas equation in the form of Eq. ( l . 8g)
p = n0kT

where k is the Boltzmann constant. Substituting p I atm = 1 . 0 1 x 1 0 5
=
g
Pa, T= 273K and k = l . 3 x 8 1 0 - 23 J de - 1 molecule-' into this equa­
2
tion, we obtain n0 = 2.68 x 1 0 5 m - 3 • Hence, the total rate of collision
i
( i . e . , the maximum chemical reaction rate) s equal to
2
10 2
7Tp2cnAn8 = (3 . 1 4)(3 x 1 0 - ) (5 x 1 0 2)(2.68 x 1 0 25) molecules - 3 s - 1
m
= I x 1035 molecule s m - 3 s _ ,
2
Or, since there are Avogadro's number ( = 6.022 x 1 0 3) of molecules
3
in I mole, and I L = 10 - 3 m , the maximum chemical reaction rate is
3
1 0 5 x 1 0 - 3
I x 1
2
6_022 x 1 0 3 2 x 0 8 mol liter- 1 s - 1
The time required to consume one of the gases, cons1stmg of
2
3
2 . 6 8 x 1 0 5 molecules m- , at a rate of I x 1 0 35 molecules m - 3 s - 1
would be
2
2. 6 8 x 1 0 5
---=-=- = 3 x 1 0 - 10 s
I x 1 0 35
Although a few chemical reactions actually proceed at the enormous
rate calculated in Exercise . 5 , most reactions occur at a much slower
3
rate. Hence, factors other than the mere collisions of molecules must
be involved in chemical reactions. Since the rate of many chemical
reactions varies markedly with temperature, we must now consider
n
how temperature may affect a chemical reactio .
Shown in Figure . 1 i s the distribution of the kinetic energies of the
3
molecules in a gas for two temperatures. The number of molecules
with kinetic energy :=::: Ea is proportional to the shaded area in Figure
. It can be seen that if Ea is fairly large, the number of molecules
3 . 1
with energy :=::: Ea is very sensitive to temperature. Hence, if a certain
minimum value of Ea is required for two colliding molecules to react
y
chemicall , it is apparent why the chemical reaction rate should be
hoth smaller and more temperature sensitive than the collision rate.