Equilibria constant, apparent

The equilibrium constant for the overall reaction is related to an apparent equilibrium constant Ki for carbonic acid ionization by the expression... 

The component reactions in eqn. (2) are very fast, and the system exists in equilibrium. Additional carbon dioxide entering the sea is thus quickly converted into anions, distributing carbon atoms between the dissolved gas phase, carbonate and bicarbonate ions. This storage capacity is clear when the apparent equilibrium constants for the two reactions in eqn. (2) are examined, namely... 

As the titration begins, mostly HAc is present, plus some H and Ac in amounts that can be calculated (see the Example on page 45). Addition of a solution of NaOH allows hydroxide ions to neutralize any H present. Note that reaction (2) as written is strongly favored its apparent equilibrium constant is greater than lO As H is neutralized, more HAc dissociates to H and Ac. As further NaOH is added, the pH gradually increases as Ac accumulates at the expense of diminishing HAc and the neutralization of H. At the point where half of the HAc has been neutralized, that is, where 0.5 equivalent of OH has been added, the concentrations of HAc and Ac are equal and pH = pV, for HAc. Thus, we have an experimental method for determining the pV, values of weak electrolytes. These p V, values lie at the midpoint of their respective titration curves. After all of the acid has been neutralized (that is, when one equivalent of base has been added), the pH rises exponentially. 

The role of biocatalysis in two-phase systems has many parallels with the subject we have covered under extractive reactions. It appears that a two-phase system was originally considered for transformations of water insoluble substances like steroids. Now, a series of treatises are available which teach us that the maximum value of the apparent equilibrium constant for a second-order reaction in a two-phase system can exceed the equilibrium... 

For a binding reaction we can pick whether we show the reaction as favorable or unfavorable by picking the substrate concentration we use. Association constants have concentration units (M-1)- The equilibrium position of the reaction (how much ES is present) depends on what concentration we pick for the substrate. At a concentration of the substrate that is much less than the dissociation constant for the interaction, most of the enzyme will not have substrate bound, the ratio[ES]/[E] will be small, and the apparent equilibrium constant will also be small. This all means that at a substrate concentration much less than the dissociation constant, the binding of substrate is unfavorable. At substrate concentrations higher than the dissociation constant, most of the enzyme will have substrate bound and the reaction will be shown as favorable (downhill). (See also the discussion of saturation behavior in Chap. 8.)... 

The second reaction studied using lipase as catalyst was the reversible re-gioselective esterification of propionic acid and 2-ethyl- 1,3-hexanediol [180]. While the previously described reaction was almost irreversible, this reaction is equilibrium limited with an apparent equilibrium constant of 0.6 0.1. In addition, the accumulated water inhibits the enzyme. Therefore, only the removal of the water from the reaction zone assures high enzymatic activity as well as drives the reaction beyond thermodynamic equilibrium. Experiments with two... 

With an aqueous fluid phase of high ionic strength, the problem of obtaining activity coefficients may be circumvented simply by using apparent equilibrium constants expressed in terms of concentrations. This procedure is recommended for hydro-metallurgical systems in which complexation reactions are important, e.g., in ammonia, chloride, or sulfate solutions. 

Whenever reporting equilibrium constants, detailed information concerning the reaction conditions should always be indicated. Alberty has also presented an important review of biochemical thermodynamics in which he discusses the apparent equilibrium constant for biochemical reactions (K ) in terms of sums of reactant species. 

The now classical example is lactate dehydrogenase. Sil-verstein and Boyer were the first to determine the rates of exchange between cognate pairs of reactants ie., lactate and pyruvate as well as NAD and NADH). Convenient [NADH]/[NAD ] and [pyruvate]/[lactate] ratios were chosen such that when combined they satisfied the apparent equilibrium constant for the LDH reaction. These investigators first established that each exchange rate was directly proportional to the duration of exchange and likewise directly proportional to enzyme concentration. As an additional control, they also demonstrated the equality of the pyruvate lactate exchange... 

STEREOCHEMICAL TERMINOLOGY, lUPAC RECOMMENDATIONS Apical and equatorial ligand interchange, PSEUDOROTATION APICOPHILIOITY APOACTIVATOR Apolar side-chain interactions, HYDROPHOBIC EFFECT Apparent equilibrium constant,... 

Magnitude of the flux vector Equilibrium constant partition coefficient Apparent equilibrium constant... 

Now, if some experimental method allows the determination of the ratio p of the gross concentration of neutral to protonated species (C + Cb)/Cc, the apparent equilibrium constant, K pp, is given by... 

Activity coefficients and concentration equilibrium constants. Strictly speaking, Eq. 6-31 applies only to thermodynamic equilibrium constants -that is, to constants that employ activities rather than concentrations. The experimental determination of such constants requires measurements of the apparent equilibrium constant or concentration equilibrium constant21 Kc at a series of different concentrations and extrapolation to infinite dilution (Eq. 6-32). 

It may seem surprising that a coenzyme is needed for these carboxylation reactions. However, unless the cleavage of ATP were coupled to the reactions, the equilibria would lie far in the direction of decarboxylation. For example, the measured apparent equilibrium constant K for conversion of propionyl-CoA to S methyl-malonyl-CoA at pH 8.1 and 28°C51 is given by Eq. 14-4. 

Apical position 260 Apoe nzyme 458 Apparent binding energies 428 relationship with incremental binding energies 435 Apparent equilibrium constants 109, 110... 

Suppose that an enzyme E has an alternative conformation E and that both take part in ionization equilibria. This happens with a-chymotrypsin on deprotonation of Ile-16, which is protonated in the active conformation. The equilibrium constants in scheme 3 are defined by K = [E ]/[E] K = [E H+]/[EH+] Ka = [H+][E]/[EH+] and K A = [H+][E ]/[E H+], The apparent equilibrium constant between E and E must consider all ionic forms and is defined by... 

Fig. 8. Apparent equilibrium constant, KA for the system living a-methylstyrene-living tetramer in THF at 0° C. (o) Experiment series 4 (o) experiment series 5 (A) experiment series 6. Reproduced, with permission, from Vrancken, Smid, and Szwaro Trans. Faraday Soc. 58, 2036 (1962).

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