Overall dissociation constants

3 Overall dissociation constants. Alternatively the reactions can be written as overall dissociation constants, in which case all the reactions are defined in terms of the dissociation of protons from H3L  

The stepwise and overall constants are related to each other as follows  

As can be seen above there are several ways in which an equilibrium constant can be expressed, e.g. see Table 5.2. From a modelling perspective the chemical reaction (stoichiometry) to which the constants relate should be known before embarking on any calculation. 

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The substrate concentration when the half maximal rate, (Vmax/2), is achieved is called the Km. For many simple reactions it can easily be shown that the Km is equal to the dissociation constant, Kd, of the ES complex. The Km, therefore, describes the affinity of the enzyme for the substrate. For more complex reactions, Km may be regarded as the overall dissociation constant of all enzyme-bound species. 

Ionization constant A , dissociation constant K, and overall dissociation constant A rx are defined ... 

The ionization eonstant should be a function of the intrinsic heterolytic ability (e.g., intrinsic acidity if the solute is an acid HX) and the ionizing power of the solvents, whereas the dissoeiation constant should be primarily determined by the dissociating power of the solvent. Therefore, Ad is expeeted to be under the eontrol of e, the dieleetrie eonstant. As a consequenee, ion pairs are not deteetable in high-e solvents like water, which is why the terms ionization constant and dissociation constant are often used interchangeably. In low-e solvents, however, dissociation constants are very small and ion pairs (and higher aggregates) become important species. For example, in ethylene chloride (e = 10.23), the dissociation constants of substituted phenyltrimethylammonium perchlorate salts are of the order 10 . Overall dissociation constants, expressed as pArx = — log Arx, for some substanees in aeetie acid (e = 6.19) are perchloric acid, 4.87 sulfuric acid, 7.24 sodium acetate, 6.68 sodium perchlorate, 5.48. Aeid-base equilibria in aeetie acid have been earefully studied beeause of the analytical importance of this solvent in titrimetry. 

The overall dissociation constant obtained comprises the intrinsic dissociation constants for the ligands and the equilibrium constant for the conformational transition [68],... 

The approximation of taking concentrations instead of activities was justified by the authors on the basis of the small degree of dissociation owing to the low e, and by the assumption that activity coefficients of neutral molecules and ion pairs are not significantly different from unity in the low range of concentrations studied. From eqns. 4.54 and 4.55 one obtains for the overall dissociation constant of HX... 

Usually there is a small amount of water in the solvent where it behaves as a base also, so that according to eqn. 4.61 we may write for its overall dissociation constant... 

Rule The KM is an apparent dissociation constant that may be treated as the overall dissociation constant of all enzyme-bound species. 

The apparent dissociation constant may be treated as an overall dissociation constant for much more complex situations involving several linked rate constants °. 

The formation of a tetrahedral hemiacetal adduct was analyzed for the interaction between the inhibitor aldehyde and the catalytic serine residue (18)35>. The overall dissociation constants for an enzyme and an interacting transition state analog may be given by ... 

Reversible Ligand Binding The protein calcineurin binds to the protein calmodulin with an association rate of 8.9 X 10s M-1s-1 and an overall dissociation constant, Kd, of 10 nM. Calculate the dissociation rate, kd, including appropriate units. 

Care must be taken when interpreting ionization measurements since the enolic form of the ketone may also be present in the reaction solution. In aqueous solutions of 2-acetylcyclohexanone, for example, the enol is present to the extent of 29.2 % [82]. This can be measured by titrating the enol (EH) with bromine under conditions where the interconversion of ketone (KH) and enol and the reaction of ketone with bromine are slow. The measured overall dissociation constant of the ketone (K0) can be corrected to give the true ionization constant (Kk ) as in (66)... 

In terms of ion pairs and free ions the usual overall dissociation constant Xha is... 

An acid may, rather arbitrarily, be called a strong acid in glacial acetic acid if HAjp - 1- Thus perchloric acid is a strong acid, and yet the pAT for the overall dissociation constant is only 4.87 because it exists largely as ion pairs. Hydrochloric acid has an overall pAT value of 8.55 ammonia, 6.40 pyridine, 6.10 sodium acetate, 6.68 potassium chloride, 6.88 and sodium perchlorate, 5.48. Perchloric acid is the strongest acid and the one used for titration of bases that may be too weak to be titrated in water as solvent. At first it appears that an attempt to titrate a base such as pyridine with perchloric acid would fail, since both have small overall dissociation constants. Critical to the success of such titrations is the small dissociation constant of the salt formed, which results in a large favorable equilibrium constant for the reaction. 

For the titration of an acid HA in en (pATsH = 15.3) with overall dissociation constant of 10 with sodium aminoethoxide, calculate the pH at the following percentages of the stoichiometric amount of reagent added 0, 50, 90, 100, 110. Take the initial concentration of acid to be 0.01 M, neglect dilution, and assume that the salt has an overall dissociation constant of 10 and that pATj for sodium aminoethoxide is 5.84. 

Calculate as in Problem 4-5, but with the salt having an overall dissociation constant of 10 instead of 10 . ... 

Kti ( denotes again the equilibrium constant of inter-conversion, while K is the dissociation constant of loose ion-pairs. Tire latter is related to the overall dissociation constant Kdiss by... 

Determine the propagation rate constants and k and the overall dissociation constant K for polystyryl sodium in THF at 25°C. (The dissociation constant of NaBPlH in THF at 25°C is 8.52x10" mol/L.)... 

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