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Fig. 5-4 The rate of bacterial sulfate reduction as a function of sulfate concentration. (Adapted from Berner (1984) with the permission of Pergamon Press.)

Fig. 5-4 The rate of bacterial sulfate reduction as a function of sulfate concentration. (Adapted from Berner (1984) with the permission of Pergamon Press.)

much less than 5 mM and the sulfate reduction rate does depend on the sulfate concentration (and may be independent of the concentration of organic carbon).

5.4.5 Kinetic Isotope Effects

Molecules containing different isotopic species of an element often react at different rates. The effect is noticeable if the rate-limiting step in a reaction is one in which a bond to the element in question is formed or broken. The primary kinetic isotope effect results from the lower vibrational frequencies of heavier isotopic species. The quantum mechanical zero point vibrational energies are also lower for heavier isotopes and thus slightly more energy is required to break a bond to 13C, for instance, than to 12C. Isotope ratios may be measured with high accuracy on small amounts of geo-chemical samples and thus one may infer something about the processes that form a compound from the observed isotope distribution.

For a kinetic isotope effect to exist, the reverse reaction must not occur to a significant extent (in which case we would have a thermodynamic isotope effect) and the molecules undergoing reaction must be drawn from a larger pool of molecules that do not react. If all the molecules are going to undergo reaction there will be no discrimination between isotopes and no kinetic isotopic effect. For these reasons, the kinetic isotope effect for 13C in living matter occurs in the early stages of the photosynthetic process when a small fraction of the C02 (or HC03 ) available is added to organic substrates to form carboxylic acids.

Photosynthesis begins with the transfer of C02 into the cell from the atmosphere or water. Photosynthetic enzymes then transfer the inorganic carbon to a five-carbon organic compound to form two three-carbon carboxylic acid molecules. (This is the case for the C3 photosynthetic mechanism.) In these steps, reaction of 12C02 occurs slightly faster than reaction of 13C02 and the organism has a more negative ¿13C than the atmosphere or ocean from which it grows. Thus, while marine inorganic carbon has <513C of about 0%o compared to the reference and atmospheric carbon has ¿13C of about -7%>, the <S13C values for plants range from —10 to — 30%o (Schid-lowski, 1988). The isotope distribution depends somewhat on the species of plant and it is a strong function of whether the plant fixes carbon by the C3 mechanism (most plants) or the C4 mechanism (a smaller group including corn, sugar cane, and some tropical plants).

Isotope effects also play an important role in the distribution of sulfur isotopes. The common state of sulfur in the oceans is sulfate and the most prevalent sulfur isotopes are 32S (95.0%) and S (4.2%). Sulfur is involved in a wide range of biologically driven and abiotic processes that include at least three oxidation states, S(VI), S(0), and S(-II). Although sulfur isotope distributions are complex, it is possible to learn something of the processes that form sulfur compounds and the environment in which the compounds are formed by examining the isotopic ratios in sulfur compounds.

5.5 Non-Equilibrium Natural Systems

Thus far we have studied thermodynamics and kinetics under the assumption that the systems of interest are in equilibrium. However, some natural systems have reaction rates so slow that they exist for long periods under non-equilibrium conditions. The formation of nitric oxide serves as an interesting example.

The net reaction for NO formation is N2 + 02 —> 2NO, although the actual mechanism by which NO forms does not include the direct reaction of N2 and 02 to any significant extent. This direct reaction would involve the breaking of two strong bonds and the formation of two new bonds, an unlikely event. Rather, the oxidation of nitrogen begins with a simple reaction:

This reaction occurs to only a small extent, but the oxygen atoms thus formed may form NO through the following catalytic cycle.

The reverse reactions of 1, 2, and 3 are also important in establishing the equilibrium between N2, 02, and N02.

At low temperatures the rates of these reactions are very slow either because the rate constants are very small or because the concentrations of O and N are very small. For these reasons, equilibrium is not maintained at the low temperatures typical of the atmosphere. However, as the temperature rises, the rate constants for the critical steps increase rapidly because they each have large activation energies - Ea = 494 kj/mol for reaction 1 and 316 kj/mol for reaction 2. The larger rate constants contribute to a faster rate of NO production, and equilibrium is maintained at higher temperatures. The time scale for equilibrium for the overall reaction N2 + 02 —► 2NO is less than a second for T > 2000 K.

It may seem unrealistic to consider such high temperatures, but in fact, many processes raise air to very high temperatures. Hydrocarbon or biomass combustion can produce temperatures of 1500-3000 K and lightning discharges can produce temperatures of the order of 30 000 K (Yung and McElroy, 1979). Other processes capable of producing high temperatures include shock waves from comet or meteorite impacts (Prinn and Fegley, 1987) and nuclear bomb explosions (Goldsmith et al, 1973).

As the temperature of an N2/02 mixture is increased above 2000 K the observed concentration of NO (as well as those for N02, N, O, and other species) will approach the equilibrium values appropriate for that temperature. As the temperature of the mixture of these gases decreases, the concentrations will follow the equilibrium values. Equilibrium will be maintained as long as the time scale for the chemical reaction is shorter than the time scale for the temperature change (that is, the chemical reaction is more rapid than the temperature change). The time scale for »• the chemical reaction increases rapidly as tjhe temperature decreases because of the large activation energies. The concentrations of NO at ambient conditions reflect the lowest temperature at which the system was in equilibrium as it cooled.

The example described above for nitric oxide illustrates the interplay between thermody namics and kinetics. At high temperatures, where the reaction rates are relatively high, the N2 -t- 02 —► NO system is in equilibrium. At lower temperatures, however, the rate constants are so low that the system cannot achieve equilibrium and many of the thermodynamic principles described in this chapter would not apply.

The presence of a high concentration of oxygen in the contemporary atmosphere and the prevalence of substances that can react with oxygen in the atmosphere and on the surface of the Earth is another example of a non-equilibrium system.

Photosynthesis produces oxygen by the following redox reaction:

but most of the oxygen thus produced is removed by respiration and decomposition,

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