Steady state or equilibrium

Let us look at an individual trace gas in the atmosphere. We will take methane (CH4), not an especially reactive gas, as an illustration. It is present in the atmosphere at about 1.7 ppm (Box 3.1). Methane could be imagined to react with O2 in the following way:

The reaction can be represented as an equilibrium situation (Box 3.2) and described by the conventional equation:

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

The equilibrium constant (K) is about 10140 (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 CH4 should tend to be at low concentrations in the atmosphere. How low? We can calculate this by rearranging the equation and solving for CH4. Oxygen, we can see from Table 3.1, has a concentration of about 21%, i.e. 0.21 atm, while CO2 and H2O have values of 0.00036 and about 0.01 atm respectively. Substituting these into equation 3.4 and solving the equation gives an equilibrium concentration of 8 X 10-147atm. This is very different from the value of 1.7 X 10-6atm actually found present in air.

What has gone wrong? This simple calculation tells us that gases in the atmosphere 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 atmosphere and sinks for that gas is an extremely important one. The situation is often written in terms of the equation:

where Fn and Fout are the fluxes in and out of the atmosphere, A is the total amount of the gas in the atmosphere and t is 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 500Tgyr-1 (i.e. 500 X 109kgyr-1). We have seen that the atmosphere has CH4 at a concentration of

1.7 ppm. The total atmospheric mass is 5.2 X 1018kg. If we allow for the slight differences between the molecular mass of CH4 and that of the atmosphere as a whole (i.e. 16/29), the total mass of CH4 in the atmosphere can be estimated as

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

Box 3.2 Chemical equilibrium

Many chemical reactions occur in both directions such that the products are able to re-form the reactants. For instance, in rainfall chemistry, we account for the hydrolysis (i.e. reaction with water) of aqueous formaldehyde (HCHO) to methylene glycol (H2C(OH)2) according to the equation:

but the reverse reaction also occurs:

such that the system is maintained in dynamic equilibrium, symbolized by:

The relationship between the species at equilibrium is described in terms of the equation:

where a denotes the activities of the entities involved in the reaction. Remember from Section 2.6 that activities are the formal thermodynamic representations of concentration. However, in dilute solutions activity and concentration are almost identical. Dilute solutions, such as rainwater, are almost pure water. The activity of pure substances is defined as unity, so in the case of rainwater the equation can be simplified:

aH2C(OH)2 aHCHO

K is known as the equilibrium constant and in this case it has the value 2000. An equilibrium constant greater than unity suggests that equilibrium lies to the right-hand side and the forward reaction is favoured. Equilibrium constants vary with temperature, but not with concentration if the concentrations have been correctly expressed in terms of activities.

The equilibrium relationship is often called the law of mass action and may be remembered by the fact that an equilibrium constant is the numerical product of the activity of the products of a reaction divided by the numerical product of the reactants, such that in general terms:

eqn.7

It may be easier to grasp the notion of shifts in equilibrium in a qualitative way using the Le Chatelier Principle. This states that, if a system at equilibrium is perturbed, the system will react in such a way as to minimize this imposed change. Thus, looking at the formaldehyde equilibrium (eqn. 3), any increase in HCHO in solution would be lessened by the tendency of the reaction to shift to the right, producing more methylene glycol.

9.75 years. This represents the average lifetime of a CH4 molecule in the atmosphere (at least, it would if the atmosphere was very well mixed).

Residence time is the fundamental quantity that describes systems in steady state. It is a very powerful concept that plays a central role in much of environmental chemistry. Compounds with long residence times can accumulate to relatively high concentrations compared with those with shorter ones. However, even though gases with short residence times are removed quickly, their high reactivity can yield reaction products that cause problems.

The famous atmospheric chemist C.E. Junge made an important observation about residence times and the variability of gases in the atmosphere. If a gas has

Residence time (days)

Residence time (days)

"V

_ /

- CS2

SO2

/ A

/CH4

/ OCS

H2

CO2 n2o

1 1 1 1

100

101 102 103 104 Residence time (years)

Fig. 3.3 Variability of trace and other components in the atmosphere as a function of residence time. Large coefficients of variation indicate higher variability. From Brimblecombe (1986). With kind permission of Cambridge University Press.

a long residence time, then it will have ample time to become well mixed in the atmosphere and thus would be expected to show great constancy in concentration all around the globe. This is the case and the results of measurements are illustrated in Fig. 3.3.

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