Equilibrium distribution ratio

Study the effect of the extraction stage on reactor performance by varying the magnitudes of the the mass transfer coefficient Ka, the equilibrium distribution ratio m, the recycle ratio R, the relative reactor and extraction volumes and solvent flowrate. 

Note that is not necessarily constant with varying p,. In fact, evaluation of the air-water equilibrium distribution ratio as a function ofp, is one of the methods that can be used to assess the concentration dependence of y-w of an organic compound, regardless whether the compound is a gas, liquid, or solid at the temperature considered (see below). 

A variation of this equation is to re-arrange the equation to obtain the equilibrium distribution ratio, yjx as shown in Equation (1.50). This distribution ratio is also known as the K-value for component i. Numerous correlations for K-values exist for a variety of pure components and pseudocomponents. The Braun-KlO (BK-10) correlation is a popular correlation of this type [6]. 

This distinction between Kd and D is important. The partition coefficient is an equilibrium constant and has a fixed value for the solute s partitioning between the two phases. The value of the distribution ratio, however, changes with solution conditions if the relative amounts of forms A and B change. If we know the equilibrium reactions taking place within each phase and between the phases, we can derive an algebraic relationship between Kd and D. 

Since the position of an acid-base equilibrium depends on the pH, the distribution ratio must also be pH-dependent. To derive an equation for D showing this dependency, we begin with the acid dissociation constant for HA. 

A recent paper by Singh et al. summarized the mechanism of the pyrazole formation via the Knorr reaction between diketones and monosubstituted hydrazines. The diketone is in equilibrium with its enolate forms 28a and 28b and NMR studies have shown the carbonyl group to react faster than its enolate forms.Computational studies were done to show that the product distribution ratio depended on the rates of dehydration of the 3,5-dihydroxy pyrazolidine intermediates of the two isomeric pathways for an unsymmetrical diketone 28. The affect of the hydrazine substituent R on the dehydration of the dihydroxy intermediates 19 and 22 was studied using semi-empirical calculations. ... 

Of course, even in the case of acyclic alkenes reaction enthalpy is not exactly zero, and therefore the product distribution is never completely statistically determined. Table V gives equilibrium data for the metathesis of some lower alkenes, where deviations of the reaction enthalpy from zero are relatively large. In this table the ratio of the contributions of the reaction enthalpy and the reaction entropy to the free enthalpy of the reaction, expressed as AHr/TASr, is given together with the equilibrium distribution. It can be seen that for the metathesis of the lower linear alkenes the equilibrium distribution is determined predominantly by the reaction entropy, whereas in the case of the lower branched alkenes the reaction enthalpy dominates. If the reaction enthalpy deviates substantially from zero, the influence of the temperature on the equilibrium distribution will be considerable, since the high temperature limit will always be a 2 1 1 distribution. Typical examples of the influence of the temperature are given in Tables VI and VII. 

Using the formalism of statistical mechanics, Giddings et al. [135] investigated the effects of molecular shape and pore shape on the equilibrium distribution of solutes in pores. The equilibrium partition coefficient is defined as the ratio of the partition function in the pore... 

Cfs-butene should lead initially to the anti form trrms-butene should lead initially to the syn form and 1-butene should give rise initially to both. The equilibrium distribution of syn and anti forms usually differs greatly from the equilibrium distribution of cis- and frans-butene for cobalt complexes 59, 60) the syn form, precursor of irans-butene, is by far the most stable. By way of contrast for the corresponding carbanion, the cis anion seems by far the more stable. This preference for the cis carbanion is presumed to be the source of the high initial cis-to-trans ratio in the initial products of base catalyzed isomerization. In the base catalyzed isomerization of more complex cf-s-olefins (cfs-S-methyl-stilbene), the ions corresponding to syn and anti are not interconvertible and cis-trans isomeriza-... 

Assuming a homogeneous distribution of crosslinks, the equality, given by Eq. (4), becomes independent of conversion. Thus on complete conversion (x = 1), Qx(x)reduces to Q°° (initial degree of dilution of the monomers) and Qv(x) can be replaced by the experimentally determined equilibrium swelling ratio Qv. Accordingly, the condition of phase separation becomes... 

In many practical situations solute A may dissociate, polymerize or form complexes with some other component of the sample or interact with one of the solvents. In these circumstances the value of KD does not reflect the overall distribution of the solute between the two phases as it refers only to the distributing species. Analytically, the total amount of solute present in each phase at equilibrium is of prime importance, and the extraction process is therefore better discussed in terms of the distribution ratio D where... 

Batch extraction is the simplest and most useful method, the two phases being shaken together in a separatory funnel until equilibrium is reached and then allowed to separate into two layers. If the distribution ratio is large, a solute may be transferred essentially quantitatively in one extraction, otherwise several may be necessary. The optimum conditions for quantitative extraction have been discussed on p. 57. If several extractions are required, it is advantageous to use a solvent more dense than water, e.g. carbon tetrachloride or chloroform, so that the aqueous phase can be left in the separatory funnel until the procedure is complete. 

An aqueous dispersion of a disperse dye contains an equilibrium distribution of solid dye particles of various sizes. Dyeing takes place from a saturated solution, which is maintained in this state by the presence of undissolved particles of dye. As dyeing proceeds, the smallest insoluble particles dissolve at a rate appropriate to maintain this saturated solution. Only the smallest moieties present, single molecules and dimers, are capable of becoming absorbed by cellulose acetate or polyester fibres. A recent study of three representative Cl Disperse dyes, namely the nitrodiphenylamine Yellow 42 (3.49), the monoazo Red 118 (3.50) and the anthraquinone Violet 26 (3.51), demonstrated that aggregation of dye molecules dissolved in aqueous surfactant solutions does not proceed beyond dimerisation. The proportion present as dimers reached a maximum at a surfactant dye molar ratio of 2 5 for all three dyes, implying the formation of mixed dye-surfactant micelles [52]. 

More complicated chemical systems may require a more universally applicable quantity called the distribution ratio to describe the system. These involve situations in which the analyte species may be found in different chemical states and different equilibrium species, some of which may be extracted while others are not. An example is an equilibrium system involving a weak acid. In such a system, there may be one (or several) protonated species and one unprotonated species. The distribution ratio, D, then takes into account all analyte species present ... 

Usually, however, the distribution coefficients determined experimentally are not equal to the ratios of the solubility product because the ratio of the activity coefficients of the constituents in the solid phase cannot be assumed to be equal to 1. Actually observed D values show that activity coefficients in the solid phase may differ markedly from 1. Let us consider, for example, the coprecipitation of MnC03 in calcite. Assuming that the ratio of the activity coefficients in the aqueous solution is close to unity, the equilibrium distribution may be formulated as (cf. Eq. A.6.11)... 

Table VI summarizes values of the activity coefficient ratio Ygr-/YC].- in the saturated solution for each average solid composition (as calculated from the model of Table II), the calculated provisional equilibrium distribution coefficient (Equation 12) and the provisional equilibrium aqueous solution activity ratio of Br to Cl- (Equation 13) based on the data of Table V.

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. 

It assumes that there are no significant solute-solute interactions and no strong solute-solvent interactions which would influence the distribution process. Concentrations are expressed as mass/unit volume, and usually C1 refers to an aqueous phase and C2 to a non-aqueous phase. The equilibrium constant (P or K) defining this system is referred to as the partition coefficient or distribution ratio. The thermodynamic partition coefficient (P ) is given by the ratio of the respective mole fractions as follows ... 

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