Macroscopic ionization constant

To accurately measure these n macroscopic values by standard methods, it is necessary to obtain information abont the ratio of eqnilibrinm concentrations of the n ionized and one neutral form of the acid by the most noninvasive method possible, while monitoring pH, temperature and ionic strength of the solntion. Ionization constants of bases and mixed systems are determined nsing the same principle. The problem of macroscopic determination thus becomes a problem of accurate measurement of relative concentrations in water solntion. Widely applied methods for this purpose are ... 

Microspeciation explained in the preceding chapter of this book has profound consequences for in silico prediction of ionization constants. Since macroscopic pK values are predicted from molecular stracture, having a uniquely defined structure with unambiguously positioned protons is a necessary condition of a successful prediction. Unfortunately, unique structures are characteristic of microstates, not macrostates. Consequently, macroconstants cannot be derived directly from the structure. On the other hand, experimental microconstants are available only for a handful of compounds, while the scientific literature is rich in macroconstants for tens of thousands of chemicals. 

For detailed understanding of many chemical reactions, more knowledge about ionization constants is needed than has been considered so far. The macroscopic constants K yKi,--. of polybasic acids can have several components arising from the detailed ionization processes. It has been shown that, if a dibasic add has two equivalent and independent ionization processes, the minimum value of KJK2 is 4. 

Table I. Macroscopic Ionization Constants for Anisindione, Phenindione, and Clorindione determined spectrophotometrically at 25 OT and p = 0.1 with sodium chloride.

The carboxyl ionization [pK]) is low and easily identified. However, the ammonium and thiol groups have similar pK values (compare methylamine with methyl mercaptan, Table 2.1) and so an uncertainty exists as to which group ionizes first. Ki, K2, and K3 represent macroscopic ionization constants determined experimentally from a titration curve. K2 and are the composite of four microscopic ionization constants. Once the proton is lost from the carboxyl group, one of two ionization pathways may be followed ... 

The first computations of ionization constants of residues in proteins for structures derived from molecular dynamics trajectories were described by Wendoloski and Matthew for tuna cytochrome c. In that study, conformers were generated using molecular dynamics simulations with a range of solvents, simulating macroscopic dielectric formalisms, and one solvent model that explicitly included solvent water molecules. The authors calculated individual pR values, overall titration curves, and electrostatic potential surfaces for average structures and structures along each simulation trajectory. However, the computational scheme for predicting electrostatic interactions in proteins used by Wendoloski and Matthew was not based on a FDPB model but on the modified Tanford-Kirkwood approach, which is not discussed in this chapter. 

The constants Kai and Ka2 are called macroscopic constants (see Chap. 4). The knowledge of their values and that of their analytical concentration is sufficient to calculate the solution s pH value. However, it is interesting to make a further study of the ionization constants of species A° and A + taken separately. By definition, we can write... 

Fig. 11.3 Macroscopic and microscopic ionization constants of malic acid...

Recall that the behavior of polyacids depends on macroscopic and microscopic ionization constants. The former can be determined experimentally. They globally quantify the more or less simultaneous ionization of several acid functions. Their value cannot be assigned in totality to only one acidity constant if the initial acid is dissymmetric. Let us consider malic acid (Fig. 11.1). It exhibits two different microscopic ionization methods (Fig. 11.3). 

The first ionization constant (pK = 3.40) corresponds to the formation of the two monoacid forms whose concentrations ratio is constant regardless of the pH value. Likewise, the two monoacid forms give the same dibase by ionization according to the second macroscopic constant (pK 2 = 5.82). 

Another kind of titration after transformation is provided by the formol titration of a-amino acids (Sprensen s method). We have already seen that it is impossible to titrate them in water with sodium hydroxide, because of their macroscopic ionization constant on the order of 10 -. The reaction with the hydroxide ion is not sufficiently quantitative to be used as a titration reaction ... 

Let s recall (see Chap. 5) that the macroscopic ionization constant Ka is defined by the following scheme ... 

We considered micro-pA), values in Section 3.6. A parallel concept applies to partition coefficients (of multiprotic molecules) namely, if an ionizable substance of a particular stoichiometric composition can exist in different structural forms, then it is possible for each form to have a different micro-log P [224,243,273,275], When logP is determined by the potentiometric method (below), the constant determined is the macro-log P. Other log/1 methods may also determine only the macroscopic constant. 

Though the original work is difficult to understand very good reviews about the van der Waals interaction between macroscopic bodies have appeared [114,120], In the macroscopic treatment the molecular polarizability and the ionization frequency are replaced by the static and frequency dependent dielectric permittivity. The Hamaker constant turns out to be the sum over many frequencies. The sum can be converted into an integral. For a material 1 interacting with material 2 across a medium 3, the non-retarded5 Hamaker constant is... 

We resume here the nature and number of macroscopic parameters used in this version of PCM the temperature T, the density ps of the solvent, its permittivity (here reduced to a constant T dependent s), and its refractive index ns. Among the constitutive parameters there is the hard sphere radius of the solvent molecule and its first ionization potential Is. 

The macroscopic dissociation constants are those determined directly from titration curves and can be used directly for calculation of the charge of the molecules at various pH values. They do not reveal which protons and acid groups are involved in the different ionization steps. For the simple monoamino monocarboxylic acids it is well known that the first pK value corresponds to that of the COOH group, the second to that of the NHJ group in agreement with the top part of the following scheme ... 

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