Distribution laws solutions

The theory of the process can best be illustrated by considering the operation, frequently carried out in the laboratory, of extracting an orgaiuc compound from its aqueous solution with an immiscible solvent. We are concerned here with the distribution law or partition law which, states that if to a system of two liquid layers, made up of two immiscible or slightly miscible components, is added a quantity of a third substance soluble in both layers, then the substance distributes itself between the two layers so that the ratio of the concentration in one solvent to the concentration in the second solvent remains constant at constant temperature. It is assumed that the molecular state of the substance is the same in both solvents. If and Cg are the concentrations in the layers A and B, then, at constant temperature ... 

The solute concentrations very close to the interface, and are assumed to be in equiUbrium, in the absence of any slow interfacial reaction. According to the linear distribution law, Cg. = thus from equation 14 the mass-transfer flux can be expressed in terms of an overall... 

The different location of polar and amphiphilic molecules within water-containing reversed micelles is depicted in Figure 6. Polar solutes, by increasing the micellar core matter of spherical micelles, induce an increase in the micellar radius, while amphiphilic molecules, being preferentially solubihzed in the water/surfactant interface and consequently increasing the interfacial surface, lead to a decrease in the miceUar radius [49,136,137], These effects can easily be embodied in Eqs. (3) and (4), aUowing a quantitative evaluation of the mean micellar radius and number density of reversed miceUes in the presence of polar and amphiphilic solubilizates. Moreover it must be pointed out that, as a function of the specific distribution law of the solubihzate molecules and on a time scale shorter than that of the material exchange process, the system appears polydisperse and composed of empty and differently occupied reversed miceUes [136],... 

Solvent extraction, sometimes called liquid-liquid extraction, involves the selective transfer of a substance from one liquid phase to another. Usually, an aqueous solution of the sample is extracted with an immiscible organic solvent. For example, if an aqueous solution of iodine and sodium chloride is shaken with carbon tetrachloride, and the liquids allowed to separate, most of the iodine will be transferred to the carbon tetrachloride layer, whilst the sodium chloride will remain in the aqueous layer. The extraction of a solute in this manner is governed by the Nernstpartition or distribution law which states that at equilibrium, a given solute will always be distributed between two essentially immiscible liquids in the same proportions. Thus, for solute A distributing between an aqueous and an organic solvent,... 

Distribution Laws For Simple Ideal solid solutions. If a solid solution of Formula (2) is in eguilibrium with an agueous phase (ag), the distribution of A and B ions between the agueous phase and the solid phase (s) can be represented by ... 

Distribution Laws for Complex Ideal Solid Solutions. Let AnX and BnX be two ionic compounds which form a series of solid solutions of the Formula ... 

Distribution Laws And Regular Solid Solutions. For so-called regular solid solutions (15), Equation (9) still holds but by definition the expression for their enthalpy of mixing is ... 

The behavioural pattern of two immiscible solvents, say a and ib is essentially nonideal with respect to one another. Now, if a third substance is made to dissolve in a two-phase mixture of the solvents (i.e., a and 3 ), it may behave ideally in either phases provided its concentration in each individual phase is approximately small. Therefore, under these prevailing experimental parameters the ratio of the mole fractions of the solute in the two respective immiscible phases ( a and A) is found to be a constant which is absolutely independent of the quantity of solute present. It is termed as the Nernst Distribution Law or the Partition Law and may be expressed as follows ... 

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. 

If the distribution law is followed, then the equilibrium curve becomes a straight line given by Y = mX. The material balance on the solute may then be rewritten as ... 

The distribution law, derived in 1898 by W. Nemst, relates to the distribution of a solute in the organic and in the aqueous phases. For the equilibrium reaction... 

Nemst distribution law for regular mixtures and solvents ) it The non-electrolyte solute A in water A... 

If the solute A does not undergo any reaction in the two solvents, except for the solubility caused by the solvation due to the nonspecific cohesive forces in the liquids, the distribution of the solute follows the Nernst distribution law, and the equilibrium reaction can be described either by a distribution constant or an (equilibrium) extraction constant... 

Difficult separations can often be effected by liquid-liquid solvent extraction, which depends on differences in the distribution of solute species between two immiscible or partially immiscible phases.4,9 For a solute species A, this distribution is governed by the Nemst partition law... 

Energy states in solution, 1462 1463 Boltzmann distribution law, 1466 distribution, 1462 1464 ground state, 1464, 1468 number of, 1462 Enthalpy... 

Electrons in metals obey a different distribution law (the law that indicates how the number of electrons varies with the energy state they are in) from the corresponding quantity for, say, molecules in gases. Because the electrons in solution are in equilibrium with the electrons in the Fermi level of the metal, electrochemists have referred... 

Before leaving this subject, it is a good idea to remark that the term Fermi energy of electrons in solution is not the most helpful one and has led to a degree of misunderstanding. Thus, as mentioned, the Fermi level in a metal deals with electrons that obey a certain distribution law. This law arises from Pauli s principle Only two... 

The electrons in the Fermi level in a metal—those that undergo the Fermi distribution law—are mobile and that is where the difference comes from electrons in solution which are, in fact, in the bound levels of ions. Such electrons are not mobile and the statement that they have a Fermi energy may therefore be misleading, for they do not obey the same distribution law as the electrons with which they are in equilibrium.4... 

Of course, this energy of electrons in solution is numerically equal to the Fermi energy of electrons in the metaL However, in respect to the applicable distribution law, that which applies to the electrons in solution is not that which applies to electrons in the metaL... 

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