Distribution constant at equilibrium

From Equations 12.2 through 12.4, the expression for the overall distribution constant at equilibrium for the extraction from the donor to the acceptor is obtained ... 

Organic chemicals are often much more soluble in organic solvents and fats than in water and are said to be lipophilic. The BCF and also to a great extent the binding to soil are dependent on the lipophilic nature of the compound. In principle, this is simple to measure experimentally by shaking a small amount of the substance in a separating funnel with n-octanol and water. The two solvents separate into two phases, and the substance distributes between them. The distribution constant at equilibrium (KOW) is defined as... 

If we have an isolated system which cannot exchange energy with its surroundings, we have seen that entropy will remain constant at equilibrium or will increase if an observable change occurs. Observable changes will continue to occur until the entropy attains a maximum value at which time the system will be in equilibrium. Thus the gas in our example expands until it is uniformly distributed and then no further changes occur. This can be expressed as follows in a system at constant energy and volume (and which can do no work) the entropy is a maximum at equilibrium (dS)u>K = 0 (see Section 3.3). 

Lipophilicity is a molecular property expressing the relative affinity of solutes for an aqueous phase and an organic, water-immiscible solvent. As such, lipophilicity encodes most of the intermolecular forces that can take place between a solute and a solvent, and represents the affinity of a molecule for a lipophilic environment. This parameter is commonly measured by its distribution behavior in a biphasic system, described by the partition coefficient of the species X, P. Thermodynamically, is defined as a constant relating the activity of a solute in two immiscible phases at equilibrium [111,112]. By convention, P is given with the organic phase as numerator, so that a positive value for log P reflects a preference for the lipid phase ... 

In its simplest form a partitioning model evaluates the distribution of a chemical between environmental compartments based on the thermodynamics of the system. The chemical will interact with its environment and tend to reach an equilibrium state among compartments. Hamaker(l) first used such an approach in attempting to calculate the percent of a chemical in the soil air in an air, water, solids soil system. The relationships between compartments were chemical equilibrium constants between the water and soil (soil partition coefficient) and between the water and air (Henry s Law constant). This model, as is true with all models of this type, assumes that all compartments are well mixed, at equilibrium, and are homogeneous. At this level the rates of movement between compartments and degradation rates within compartments are not considered. 

Soil Sorption Constant - Soil/Water (Knp.). The distribution of a chemical between soil and water can be described with an equilibrium expression that relates the amount of chemical sorbed to soil or sediment to the amount in the water at equilibrium. 

It is very important to realise that if many processes share a component in reaction pathways or controls then this is readily achieved if the binding of that component is at equilibrium with closely the same binding constant at sites within the different paths and controls. This is often true of components such as metal ions, coenzymes and energy-distributing molecules such as ATP. 

Thus, in according to the concept of equilibrium distribution, the relation of an organic pollutant concentration in the soil solid and liquid phase is constant at any moment (Vasilyeva and Shatalov, 2004). The example of such an approach application for assessing exposure pathways of POPs to living biota is shown in Box 1. 

Transition State Theory [1,4] is the most frequently used theory to calculate rate constants for reactions in the gas phase. The two most basic assumptions of this theory are the separation of the electronic and nuclear motions (stemming from the Bom-Oppenheimer approximation [5]), and that the reactant internal states are in thermal equilibrium with each other (that is, the reactant molecules are distributed among their states in accordance with the Maxwell-Boltzmann distribution). In addition, the fundamental hypothesis [6] of the Transition State Theory is that the net rate of forward reaction at equilibrium is given by the flux of trajectories across a suitable phase space surface (rather a hypersurface) in the product direction. This surface divides reactants from products and it is called the dividing surface. Wigner [6] showed long time ago that for reactants in thermal equilibrium, the Transition State expression gives the exact... 

Because the chemical potentials of water distributed in two phases (i.e., solution and vapor) must be equal, the water activity of a food can be measured by bringing the food into equilibrium with the air above it. At equilibrium, under conditions of constant temperature and pressure, the aw values of the aqueous phase of a food (aw l) and of the air (aw v) are equal and can be estimated from the ratio of the partial vapor pressure of water above the food (pv) to the vapor pressure of pure water (p") at the same temperature (Walstra, 2003) ... 

The rate constant is measured in units of moles dnr3 sec /(moles dnr3)", where n = a + b. Time may also be in minutes or hours. It should be noted that in case where the reaction is slow enough, the thermal equilibrium will be maintained due to constant collisions between the molecules and k remains constant at a given temperature. However, if the reaction is very fast the tail part of the Maxwell-Boltzmann distribution will be depleted so rapidly that thermal equilibrium will not be re-established. In such cases rate constant will not truly be constant and it should be called a rate coefficient. 

Thermodynamic calculations based on the compositional dependence of the equilibrium constant are applied to solubility data in the KCl-KBr-H20 system at 25°C. The experimental distribution coefficient and activity ratio of Br /Cl in solution is within a factor of two of the calculated equilibrium values for compositions containing 19 to 73 mole percent KBr, but based on an assessment of uncertainties in the data, the solid solution system is clearly not at equilibrium after 3-4 weeks of recrystallization. Solid solutions containing less than 19 and more than 73 mole percent KBr are significantly farther from equilibrium. As the highly soluble salts are expected to reach equilibrium most easily, considerable caution should be exercised before reaching the conclusion that equilibrium is established in other low-temperature solid solution-aqueous solution systems. 

The equilibrium condition for the distribution of one solute between two liquid phases is conveniently considered in terms of the distribution law. Thus, at equilibrium, the ratio of the concentrations of the solute in the two phases is given by CE/CR = K, where K1 is the distribution constant. This relation will apply accurately only if both solvents are immiscible, and if there is no association or dissociation of the solute. If the solute forms molecules of different molecular weights, then the distribution law holds for each molecular species. Where the concentrations are small, the distribution law usually holds provided no chemical reaction occurs. 

The distribution ratio of a solute between two liquid phases at equilibrium is a constant, provided that the solute forms a dilute ideal solution in each phase. 

The partition or distribution coefficient between a gas and a liquid is constant at a given temperature and pressure. The relative volatility is used in defining the equilibrium between a volatile liquid mixture and the atmosphere. The partition coefficient expresses the relative volatility of a species A distributed between a vapor phase (Al) and a liquid phase (A2). Henry s law applies to the distribution of dilute solutions of chemicals in a gas, liquid, or solid at a specific ambient condition. Equilibrium is defined by... 

The first term in parentheses on the right side of equation 5.213 is the distribution coefficient (K ), and the second groups activity coefficients related to the mixing behavior of components in the two phases. The equilibrium constant is thus related to the interaction parameters of the two phases at equilibrium. For example, the equilibrium between two regular mixtures is defined as... 

By comparing Eq. (2.176) to Eq. (2.78) for the desired diffusion equation, we may identify the reduced equilibrium distribution vl/ ( ) at each point on the constraint surface, to within a constant of proportionality, with the value of eq(6) on the constraint surface. In this model, the behavior of Peq(G) away from the constraint surface is dynamically irrelevant, since only the values of the derivatives of lnTeq(2) with respect to the soft coordinates, evaluated infinitesimally close to the constraint surface, enter diffusion Eq. (2.175). 

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