## Example

Calculation of the threshold concentration as a function of temperature

Consider the anaerobic catabolic system 4H2 + HCO— + H + » CH4 + 3H2O. One can calculate that DG£At = - 135.57 kJ, and dHCAT = -241 kJ. Using the Van't Hoff relation (DG = DH — TDS) one calculates DS£at = -0.354 kJ/molK.

Assuming PCH4 = 1 bar, HCO3 = 0.01 M, H+ = 10—8 M, T = 303 K, and DGCAT equals the threshold minimum of —20 kJ, one can calculate at threshold conditions:

From this follows that the threshold hydrogen pressure is PH = 7 x 10 — 5 bar at a temperature of 30 °C (303 K).

For a temperature of 75 °C ( = 348 K), one finds that (Ph2 )threshoid = 120 x 10 —5 bar. Such an increase of hydrogen threshold partial pressure with increasing temperature has indeed been observed (36). The calculated threshold H2 pressures are also in the correct range.

From the previous findings it is clear that, especially for systems with a low DGCAT (e.g., anaerobic, inorganic electron donors), threshold values can be found. For aerobic growth, DGCAT is so large that a measurable threshold value is not expected because the thermodynamically calculated Cs thresh would be extremely low.

The existence of threshold concentrations makes it desirable to change the kinetics of substrate uptake (qs, equation 14a) from the irreversible to reversible form qs =

In conclusion it appears that threshold concentrations of electron donor (or substrate) do exist and their value can be estimated from the catabolic reaction using the value of (D Gcat)thresh in equation 18. In addition a more proper kinetic expression for qs is then given by equation 19.

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