Overall equilibrium constant

The equilibrium constants for addition of alcohols to carbonyl compounds to give hemiacetals or hemiketals show the same response to structural features as the hydration reaction. Equilibrium constants for addition of metiianoHb acetaldehyde in both water and chloroform solution are near 0.8 A/ . The comparable value for addition of water is about 0.02 The overall equilibrium constant for formation of the dimethyl acetal of... 

Therefore, the overall equilibrium constant for the ionization of H2CO3 in equilibrium with C02(d) is given by... 

We derived the relation between the equilibrium constant and the rate constant for a single-step reaction. However, suppose that a reaction has a complex mechanism in which the elementary reactions have rate constants ku k2, and the reverse elementary reactions have rate constants kf, k2, . .Then, by an argument similar to that for the single-step reaction, the overall equilibrium constant is related to the rate constants as follows ... 

The symbol (a) denotes an adsorbed species. If all steps are at equilibrium and if the second step is believed to be rate controlling, what relation must exist between the overall equilibrium constant and the observed rate constants The rate of the forward reaction is to be taken as k2CH2 where k2 is the rate constant observed for the forward reaction. Start by determining the appropriate form of the rate constant observed for the reverse reaction in terms of the kt values used above. 

Figure 12 [115] shows a series of complex formation titration curves, each of which represents a metal ion-ligand reaction that has an overall equilibrium constant of 1020. Curve A is associated with a reaction in which Mz+ with a coordination number of 4 reacts with a tetradentate ligand to form an ML type complex. Curve B relates to a reaction in which Mz+ reacts with bidentate ligands in two steps, first to give ML complexes, and finally close to 100% ML2 complexes in the final stages of the titration. The formation constant for the first step is 1012, and for the second 108. Curve C refers to a unidentate ligand that forms a series of complexes, ML, ML2. .. as the titration proceeds, until ultimately virtually 100% of Mz+ is in the ML4 complex form. The successive formation constants are 108 for ML, 106 for ML2, 104 for ML3, and 102 for ML4 complexes. 

The overall equilibrium constant for binding y ligands to an empty molecule is defined for the reaction... 

Pertechnetate in neutral and alkaline media can be extracted into solutions of tetra-alkylammonium iodides in benzene or chloroform. With tetra-n-heptylammo-nium iodide (7.5 x 10 M) in benzene distribution coefficients up to 18 can be obtained . A solution of fV-benzoyl-iV-phenylhydroxylamine (10 M) in chloroform can be used to extract pertechnetate from perchloric acid solution with a distribution coefficient of more than 200, if the concentration of HCIO is higher than 6 M The distribution of TcO between solutions of trilauryl-ammonium nitrate in o-xylene and aqueous solutions of nitrate has been measured. In 1 M (H, Li) NOj and 0.015 M trilaurylammonium nitrate the overall equilibrium constant has been found to be log K = 2.20 at 25 °C. The experiments support an ion exchange reaction . Pertechnetate can also be extracted with rhodamine-B hydrochloride into organic solvents. The extraction coefficient of Tc (VII) between nitrobenzene containing 0.005 %of rhodamine-B hydrochloride and aqueous alcoholic " Tc solution containing 0.0025 % of the hydrochloride, amounts to more than 5x10 at pH 4.7 . 

A substance that accelerates a chemical reaction but does not become consumed, generated, or permanently changed by such reaction. Thus, a catalyst does not alter the overall stoichiometric expression for the reaction or the overall equilibrium constant. The enhanced reactivity produced by a catalyst is referred to as catalysis. 

The energetics of enzymatic and their corresponding uncatalyzed reference reactions can be understood by the cyclic path that allows for substrate conversion to product by the uncatalyzed and enzymatic routes (Fig. 2). Note that the uncatalyzed reaction is characterized by a transition state that is far less stable than its enzymatic counterpart. Note also that the initial and final conditions are the same for either route, an absolute requirement for any catalyzed process i.e., no effect on the overall equilibrium constant). 

Cyanide and Thiocyanate Complexes Among other unidentate anionic ligands commonly encountered, cyanide forms stable complexes with both Cu(II) and Cu(I) however, the CuCN salt is so insoluble (p gp = 19.5)[169] that only the reduced complex has been characterized, that is, the addition of cyanide to an aqueous solution initially containing Cu(II) results in autoreduction to Cu(I). The overall equilibrium constant ( 34) for the reaction of Cu(I) with four cyanide ions was determined as early as 1904 by Kunschert [170] and subsequent measurements have yielded virtually identical values ... 

If n reactions are added, the overall equilibrium constant is the product of n individual equilibrium constants. 

Now consider Eq. 17-42, step a, the ADP- and P -requiring oxidation of glyceraldehyde 3-phosphate (Fig. 15-6). Experimental measurements indicated that this reaction is also at equilibrium in the cytoplasm. In one series of experiments the measured phosphorylation state ratio [ATP]/[ADP] [PJ was 709, while the ratio [3-phosphoglycerate]/[glyceraldehyde 3-phosphate] was 55.5. The overall equilibrium constant for Eq. 17-42a is given by Eq. 17-44. That calculated from known equilibrium constants is 60. 

The above procedure is simple, but it can be time-consuming for more complex examples. One can write down the correct relationships between the equilibrium constants or the free energies by inspection as follows. The overall equilibrium constant between, say, A and C must be the same for any route. Therefore, the products of the equilibrium constant for one route from A to C must be the same as for another route. And so, KBIA - KcfB = KD/A Kan (i.e., equation 3.71). The difference in free energy between A and, say, D is similarly independent of route. Thus, AGc-a = AGb a + AGC B = AGd a + AGC D (i.e., equation 3.72). 

Thus, a plot of the pH vs. Dt will give at high Dt a slope (n) equal to the negative coordination number and an intercept (pKn) equal to minus the log of the overall equilibrium constant. 

Assess the likelihood of the occurrence of this reaction at a reasonable rate and the favorableness of its overall equilibrium constant. 

It should be kept in mind that although an enzyme can increase the rate at which a reaction occurs, it (or any other catalyst) cannot alter the overall equilibrium constant. Since A gq is equal to the ratio of the rate constants for the forward and reverse processes, the catalyst increases both of these rate constants without changing their ratio. 

Schematic illustration of the organization of metabolic sequences into oppositely directed pairs. The two sequences result in opposite conversions. The values for the overall equilibrium constant are a function of the conversion and the number of ATP-to-ADP conversions to which each sequence is coupled. Note the similarity to figure 11.6.

The stoichiometry of coupling to ATP-to-ADP conversions contributes to the overall equilibrium constant of a sequence and therefore can determine the direction of conversion that is thermodynamically favorable. Any conversion can be made favorable by coupling to an appropriate number of ATP-to-ADP conversions. 

Transalkylation is also catalyzed by acids, but requires more severe conditions than isomerization. As shown below, the methyl migration is intermolecular and ultimately produces a mixture of aromatic compounds ranging from benzene to hexamethylbenzene. The overall equilibrium constants for all possible methylbenzenes have been determined experimentally and calculated theoretically (Fig. 2 and Table 3). 

Only the unprotonated amine with the free electron pair on nitrogen participated in the reaction (6). The dependence of the height of the more positive wave on the logarithm of the amine concentration is shown in Fig. lb the slope corresponds to a reaction of one carbonyl molecule with one amine. From the ratio of the wave-heights of the first and second waves, it is possible to calculate values of the overall equilibrium constant Ks = K 2K3HOH-], provided that the effect of protonation of the amine and of the Schiff base expressed by equations (4 a) and (4 b) is taken into account. 

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