Pr0 c0Xc072

Since the inorganic component, c0, is very dominant at thermodynamic equilibrium, then c0 >> Xn=1 c0, and expression (7.2) can be approximated as

As a result of the combination of Eqs. (7.1) and (7.3), we get

The equilibrium constant for the process describing the aerobic (presence of oxygen) decomposition of detritus at 300 K can be found based upon the above-mentioned values. We could presume that the detritus molecular weight is about 100,000 (more accurately 104,400; Morowitz, 1968) and its typical composition is 3500 carbon, 6000 hydrogen, 3000 oxygen and 600 nitrogen:

C3500H6000O3000N600 + 435002 —y 3500C02 + 2700H20 + 600N03 + 600H+. (7.5) Then the equilibrium constant

[C3500H6000 03000N600 ][O2]4350

since water is omitted from the expression of K. Then we have AG0 = — RTlnK(T), so that — AG0 = 18.7 kJ/g X 104,400 g/mol = 1952 MJ/mol = 8.2 J/mol X 300 ln K, which implies that ln K = 793,496 or K is about 10,344,998.

In other words, the equilibrium constant is enormous. The spontaneous formation of detritus in the form of a compound with the molecular weight of about 100,000 has therefore a very small probability. Even if we consider detritus with a low molecular weight corresponding to detritus partially decomposed, the K value is still very high. If we presume a 100 times smaller molecular weight, the exponent is 100 times smaller or is about 3500—still a very high K value. It is therefore understandable that detritus is decomposed spontaneously and thereby yields energy to the heterotrophic organisms. The opposite process corresponds to what may be the result of the photosynthesis, the conversion of solar radiation (energy) into chemical energy.

Fig. 2.4 shows the resulting biochemical reactions of an ecosystem, i.e. how the ecosystem works as a biochemical reactor. The biologically important elements are cycling

Ecosystem Lake
Fig. 2.4. An ecosystem is a biochemical reactor. The input of energy comes from the solar radiation. The biologically important elements cycle and carry the energy which is utilised by heterotrophic organisms to support the life processes.

and used again and again to build up biochemically important compounds, as for instance proteins, lipids and carbohydrates. These compounds are carrying the energy of the solar radiation and thereby supporting the maintenance of life and the cycling processes. The cycle may be compared with a Carnot cycle (given in detail in Chapter 5). The hot reservoir (the Sun) delivers the energy, which is utilised to do work. The heat energy is delivered to the cold reservoir at the ambient temperature (the temperature of the Earth). The work, after it

Fig. 2.5. The biochemical cycling of matter in ecosystems (from J0rgensen, 2000b).

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