Partitioning equilibrium constant definition

Although this equation reduces to an identity whenever solute-solvent interactions are embodied in the definition of the Henry s law standard state (cf section 10.2), it must be noted that K[ is the molar ratio of trace element i in the two phases and not the weight concentration ratio usually adopted in trace element geochemistry. As we will see later in this section, this double conversion (from activity ratio to molar ratio, and from molar ratio to weight concentration ratio) complicates the interpretation of natural evidence in some cases. To avoid ambiguity, we define here as conventional partition coefficients (with the same symbol K ) all mass concentration ratios, to distinguish them from molar ratios and equilibrium constants. 

We can now utilize some of the statistical mechanics relationships derived in Chapter 8 to find expressions for the free energy and the equilibrium constant in term of the molecular partition functions. From the definition of the free energy (Eq. 9.1) the expression for the enthalpy of an ideal gas (Eq. 8.121), and recalling that Ho = Eq (for an ideal gas), we obtain... 

This equilibrium or partitioning of a solute between micelles and the aqueous surroundings has not been uniformly described in the literature. We speak of distribution coefficient or constant, partition coefficient or constant, or equilibrium constant to describe equilibria that are the same qualitiatively speaking. However, the definition of the above-mentioned coefficients or constants varies. In this chapter we refer to the process as a partitioning of a molecule between micelles and the aqueous surroundings, and we term it the partition coefficient regardless of the concentration units used to define it. 

Combining Equations 18.1-18.4 and using the definitions of the partition coefficients, the apparent equilibrium constant biphasic fo " the biphasic system can be expressed as... 

This separation has the advantage that it allows arbitrary distortions of the molecule to be considered. The nuclear repulsion energy nn does not have to be kept constant. With this scheme of partitioning and the definition of a resonance coordinate which interpolates the situation between the equilibrium structure of benzene and the two Kekule structures, it can be shown that the energy curve for the a energy Ea has a positive curvature upon distortion from the... 

Because of their definition as equilibrium constants, partition coefficients do not refer to the total amount of chemicals in the system but rather indicate how large a fraction of the release tends to transfer into the different phases. Partition coefficients may be used as an extrathermodynamic reference scale for characterizing lipophilicity as one of the most important properties of small molecules acting on macromolecular systems in aqueous solutions for a comprehensive review of hydrophobicity see, for example, Taylor (1990). In QSAR analyses, the log P term is frequently used to account for two major processes related to partitioning ... 

The constant K issned from the partition function wonld be the constant of an equilibrium between the activated complex and reactants. Considering the definitions of equilibrium constants, the free energy related to the reaction can be introduced and the reaction rate coefficient becomes ... 

Distribution constant. KQ(K). The ratio of the concentration of a sample component in a single definite form in the stationary phase to its concentration in the mobile phase at equilibrium. Both concentrations should be calculated per unit volume of the phase. IUPAC recommends this term rather than partition coefficient. 

The dimensionless partition coefficient K = cp/cl = Sr, also known as a relative solubility coefficient, is defined as the ratio of the concentration of a substance in the polymer cP to that in the liquid (food) cLat equilibrium. While D is practically independent of the liquid phase in contact with the polymer in these measurements, the K values are determined by the nature of the polymer and liquid contact phases. From the definition Sr = K, a relative peremeability coefficient can be calculated, Pr = Sr D, with the dimension D. Here, accordingly to Eq. (9-2) and the solubility constant in the polymer and in the liquid phases expressed as SP = cP/p and Sl = C Jp, respectively, the following relationship results between the absolute and relative permeability coefficients ... 

In the past few years, development of new theories have led to completely new ways of determining free energy changes. Traditionally, the difference in the free energy of two equilibrium state is (AFi 2) and the free energy change of a process can be obtained directly from the statistical mechanical definition of the free energy, F, in terms of the partition function. For the canonical ensemble F = —k T In J = —ksTln Z, where ka is Boltzmann s constant, //(F) is the phase... 

The numerical values of chromatographic partition coefficient, regarded as a constant of physical equilibrium, depend on the standard states chosen for the solute in the two phases that participate in the distribution process. Consequently the standard thermodynamic properties take values which depend on this choice. A standard thermodynamic property should always be accompanied by an explicit definition of standard states. 

The partition function defines the thermodynamic potential. The partition function is a function of the thermodynamic state variables that are kept constant in the definition of the equilibrium ensemble. The expression of the thermodynamic potential in terms of these state variables constitutes a fundamental equation of thermodynamics. 

Given the definitions of solubility and vapor pressure presented in Section 1.7.1, consider the equilibrium between aqueous and gas phases that would occur if a pure chemical were in contact with and in equilibrium with both of those phases. The way in which a chemical partitions between aqueous and gas phases at equilibrium is based on the chemical s solubility and vapor pressure. The ratio of a chemical s partial pressure in air to its concentration in water at equilibrium is known as the Henry s law constant H or Kh). 

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