Question

The third order rate coefficient for:

O + O₂ + M   -> O₃ + M

is given by the expression: k = 6.0x10^-34 *(T/300)^-2.4 cm⁶ molecule^-2 s^-1

This reaction is in the low pressure, i.e. termolecular, limit under all atmospheric conditions.

1) Find the effective bimolecular rate at 220K and a pressure of 50 mbar

2) An O₂ molecule undergoes photolysis giving O³P

Find the pseudo-first order rate of O₃ formation at 220K and a pressure of 50 mbar.

What is the lifetime of O³P at 220K and a pressure of 50 mbar.

Answer 1

1) A bimolecular reaction involves the collision of two reactants A and B to yield two products C and D. The collision produces an activated complex AB* which decomposes rapidly either to the original reactants A and B or to the products C and D. The reaction is written

A+B C+ D

and its rate is calculated as

- d[A] / dt = - d[B] / dt = d[C] / dt = d[D] / dt  = k [A] [B]

where k is the rate constant for the reaction. In this expression the concentrations are number densities so that the product [A] [B] is proportional to the frequency of collisions. The rate of the reaction depends on the frequency of collisions and on the rate of the activated complex. and k is given in units of cm³ molecule^-1 s-¹, in which case [A] and [B] must be in units of molecules cm^-3.

we can apply equestion for given example

- d[O] / dt = - d[O₂] / dt = d[O₃] / dt = k [O] [O₂]

we have k = 6.0 x 10-34 x (200/300) - 2.4 cm⁶ molecule^-2 s^-1

put values in equestion and solve.

2) Photolysis of O2 yields two O atoms

O₂ + hν O + O

where the O atoms are in the ground-level triplet state O(3 P) (section 9.4) and are highly reactive due to their two unpaired electrons. They combine rapidly with O2 to form ozone

O + O +2 M O₃ + M

where M is a third body

a mass balance equation for O_x as the sum of the mass balance equations for O3 and O:

d [Ox]/dt = d [O₃] + [O] /dt =  d [O₃]/dt +  d [O]/dt

The lifetime of Ox is given by

Ox= [Ox]/ 2k4 [O][O₃] = 1/ 2k4[O]

= 1/ 2 x 6.0 x 10^-34 x (200/300) - 2.4

= 1/12 x 10^-34 x 0.66 - 2.4

= 1/ 8 x 10^-34 - 2.4 = - 2.275 x 10^-34 cm⁶ molecule^-2 s^-1