Consider the following chemical system:
Compounds A and B react reversibly, and B reacts irreversibly to C. Assume that the reversible reaction is rapid, compared with the timescale of conversion of B to C. Physically, this means that once a molecule of A reacts to form B, B is much more likely to react back to A than to go on to C; every once in a while, B does react to form C. In this case, A and B achieve an equilibrium on a short timescale, and this equilibrium slowly adjusts as some of the B reacts to form C. We recognize that the A-B equilibrium is just a pseudo-steady state.
Since A and B rapidly interchange, it is useful to view these two species as a chemical family. The overall process can then be depicted as shown below, where we enclose the family of A and B within the dashed box and denote the family as A v, where Ar = A + B,
Thus, the Ax family has a sink that occurs at a rate [B].
It turns out that the concept of chemical families is enormously useful in atmospheric chemistry. We will now analyze the properties of the general A,B,C system above; in subsequent chapters we will see how that analysis applies directly to several key atmospheric components.
Invoking the idea of a pseudo-steady state between A and B, because the rate of the reaction that returns B to A, kj [B], far exceeds that converting B to C, ¿3 [B], at any instant the concentrations of A and B are related by
Slow changes in the sink B —► C only serve to alter this instantaneous steady state between A and B.
What is often of interest with respect to a chemical family is the lifetime of the family. Let's write the full rate equations:
If ta, is the lifetime of Ax = A + B, and tb is the lifetime of B, then, by definition
or or where the [A]/[B] ratio is determined from (3.26) as [A]/[B] = k2/kl. Thus where the [A]/[B] ratio is determined from (3.26) as [A]/[B] = k2/kl. Thus
Because of the pseudo-steady state that exists between A and B, the lifetime of the chemical family A* = A + B is actually longer than that of B alone, by the factor (1 +k2/h).
In an atmospheric mechanism there is a source of A or B or both that sustains the cycle. Let us call these SA and SB. In this case, the family can be depicted as follows:
The existence of sources of A and/or B does not alter the instantaneous equilibrium between A and B or the lifetime of A*, given above. The overall steady state balance on the Ax family is then
As an example of a chemical family, consider photodissociation of ozone to produce 02 and ground-state atomic oxygen:
The oxygen atoms just combine with 02, most of the time, to reform ozone:
In most regions of the atmosphere, the interconversion between O and O3 is so rapid that the two species are often considered together as the chemical family, Ox = O + 03, which is denoted "odd oxygen."
In summary, a "chemical family" refers to two compounds that interchange with each other sufficiently rapidly such that they tend to behave chemically as a group. As noted, we will encounter a number of such systems in the chapters to come.
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