Mixing ratio-concentration relationship

Fig. 2.95 Relationship between atmospheric CO2 mixing ratio and seawater pH assuming a pH of 8.25 at a CO2 mixing ratio of 280 ppm and constant seawater carbonate concentration.

Extreme values of concentrations occur for the fraction on the right-hand side being equal to 0 (pure contaminant melt) and 1 (no contamination). These relationships show a fairly simple behavior of the AFC model the isotopic ratio (Ci2/Cil)liq should be linearly correlated with the inverse of the element concentration Cm,11, a property which it shares with all bulk mixing models. Such a linear relationship, initially suggested by Briqueu and Lancelot (1979) from the evidence of a numerical solution, was demonstrated by Fleck and Criss (1985) and Taylor and Sheppard (1986). The present analytical solution will help the reader to work out tests on geological cases. 

In this section the distinction between dissolved and sorbed species is introduced into the box model concept in the simplest possible manner, that is, by assuming a reversible linear equilibrium relationship between the dissolved concentration, C (molm 3), and the species sorbed on solids, Cs(mol kg 1). (The units m3 and kgs refer to water volume and solid mass, respectively.) The sorption/ desorption process shall be fast compared to other processes which affect the chemical (e.g., mixing, chemical transformation). As discussed in Chapter 9 (Eq. 9-7), the (observed) solid-water distribution ratio Kd is defined by. 

The internal equilibrium constant can be measured after finding conditions under which all of the substrate and product will be bound to the enzyme. This is done by working at concentrations of enzyme in 5- or 10-fold excess of the dissociation constants for each substrate. Accordingly, the ratio of [P]/[S] measured will reflect the ratio of [E-P]/[E-S] = Kim- The time required for the reaction to come to equilibrium can be approximated from the relationship /tobs itcai + kai to provide a minimum estimate of the rate of reaction at the active site. Usually the time calculated will be in the millisecond domain, but incubation for S sec is more convenient for manual mixing and usually no side products are formed on this time scale. Although in some cases it may be difficult to obtain concentrations of enzyme in excess of the dissociation constants for the substrates and products, the quantitation of the product/substrate ratio can be done quite accurately thanks to the fundamental property of enzyme catalysis that leads to an internal equilibrium constant close to unity for most enzymes (78-20). 

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