An Introduction to Environmental Chemistry

atmosphere at about 1.7 ppm (Box 3.1). Methane could be imagined to react with

O 2 in the following way:

eqn. 3.2

The reaction can be represented as an equilibrium situation (Box 3.2) and

described by the conventional equation:

eqn. 3.3

which can be written in terms of pressure (Box 3.1):

eqn. 3.4

The equilibrium constant (K) is about 10^140 (Box 3.2). This is an extremely large

number, which suggests that the equilibrium position of this reaction lies very

much to the right and that CH 4 should tend to be at low concentrations in the

atmosphere. How low? We can calculate this by rearranging the equation and

solving for CH 4. Oxygen, we can see from Table 3.1, has a concentration of about

21%, i.e. 0.21 atm, while CO 2 and H 2 O have values of 0.000 36 and about 0.01

atm respectively. Substituting these into equation 3.4 and solving the equation

gives an equilibrium concentration of 8¥ 10 -^147 atm. This is very different from

the value of 1.7¥ 10 -^6 atm actually found present in air.

What has gone wrong? This simple calculation tells us that gases in the atmos-

phere are not necessarily in equilibrium. This does not mean that atmospheric

composition is especially unstable, but just that it is not governed by chemical

equilibrium. Many trace gases in the atmosphere are in steady state. Steady state

describes the delicate balance between the input and output of the gas to the

atmosphere. The notion of a balance between the source of a gas to the atmos-

phere and sinks for that gas is an extremely important one. The situation is often

written in terms of the equation:

eqn. 3.5

where Finand Foutare the fluxes in and out of the atmosphere, Ais the total

amount of the gas in the atmosphere and tis the residence time of the gas.

To be in steady state the input term must equal the output term. Imagine the

atmosphere as a leaky bucket into which a tap is pouring water. The bucket

would fill for a while until the pressure rose and the leaks were rapid enough to

match the inflow rate. At that point we could say that the system was in steady

state.

Methane input into the atmosphere occurs at a rate of 500 Tg yr-^1 (i.e. 500¥

109 kg yr-^1 ). We have seen that the atmosphere has CH 4 at a concentration of

1.7 ppm. The total atmospheric mass is 5.2¥ 1018 kg. If we allow for the slight

differences between the molecular mass of CH 4 and that of the atmosphere as a

whole (i.e. 16/29), the total mass of CH 4 in the atmosphere can be estimated as

4.8¥ 1012 kg. Substituting these values in equation 3.5 gives a residence time of

FFin==out At

K

pp

pp

=

◊

◊

CO H O

CH O

22

2

422

K

cc

cc

=

◊

◊

CO H O

CH O

222

42

2

CH 42 ()gg+Æ + 22 O() CO2 2()gH O()g

36 Chapter Three