Equilibria partition ratios

Gmehhng and Onken (Vapor-Liquid Equilibrium Data Collection, DECHEMA, Frankfurt, Germany, 1979) have reported a large collection of vapor-liqnid equilibrium data along with correlations of the resulting activity coefficients. This can be used to predict liqnid-hqnid equilibrium partition ratios as shown in Example 1. 

In Fig. 9.26, the thermodynamic equilibrium, solid-liquid phase diagram of a binary (species A and B) system is shown for a nonideal solid solution (i.e., miscible liquid but immiscible solid phase). The melting temperatures of pure substances are shown with Tm A and Tm B. At the eutectic-point mole fraction, designated by the subscript e, both solid and liquid can coexist at equilibrium. In this diagram the liquidus and solidus lines are approximated as straight lines. A dendritic temperature T and the dendritic mass fractions of species (p)7(p)s and (p)equilibrium partition ratio kp is used to relate the solid- and liquid-phase mass fractions of species (p)7(p)J and (p)f/(p)f on the liquidus and solidus lines at a given temperature and pressure, that is,... 

Assuming an equilibrium phase diagram, such as that shown in Fig. 9.28b, the definition of the equilibrium partition ratio kp was given by Eq. 9.148 and is repeated here. 

Only about half of the annual C02 emissions remain in the atmosphere the remainder partition primarily into the near-surface ocean layer. The equilibrium ratio is about 0.7 1.0 for C02 partitioning between the atmosphere and the near-surface ocean water. At present, the total amount of C02 in the atmosphere is about 750 Pg C, with approximately 900 Pg C in the near-surface ocean layer. If humans add 700 Pg C by the year 2050, this C02 will partition by equilibration (with the roughly 35-year relaxation time) between the atmosphere and the surface ocean layer. Neglecting any significant uptake by biomass, the total C in the atmosphere/surface ocean will be 750 + 900 + 700 = 2350 Pg C. At an equilibrium partitioning ratio of 0.7 1.0, this will lead to 950 Pg C in the atmosphere and 1400 Pg C in the near-surface ocean. The atmospheric C02 mixing ratio will be 475 ppm. 

Finally we reach the discussion of the most easily adjusted variable controlling GC peak elution. Recall from Chapter 11 that for a given stationary phase the temperature of the column is the primary determinant of the equilibrium partition ratio between the stationary and mobile phases. The larger the percentage of time the analyte spends in the gas flow of the mobile phase the more quickly it elutes from the column. A modern GC instrument is designed to very precisely and reproducibly control the temperature of the oven compartment in which the coiled-up column resides. This will promote reproducible retention times to enable peak identification. 

Finally, we reach the discussion of the most easily adjusted variable controlling GC peak elution. Recall from Chapter 11 that for a given stationary phase, the temperature of the column is the primary determinant of the equilibrium partition ratio between the stationary and mobile phases. 

The separation of components by liquid-liquid extraction depends primarily on the thermodynamic equilibrium partition of those components between the two liquid phases. Knowledge of these partition relationships is essential for selecting the ratio or extraction solvent to feed that enters an extraction process and for evaluating the mass-transfer rates or theoretical stage efficiencies achieved in process equipment. Since two liquid phases that are immiscible are used, the thermodynamic equilibrium involves considerable evaluation of nonideal solutions. In the simplest case a feed solvent F contains a solute that is to be transferred into an extraction solvent S. 

The weight fraction of solute in the extract phase y divided by the weight fraction of solute in the raffinate phase x at equilibrium is called the partition ratio, K [Eq. (15-1)]. 

Gmehhng and Onken (op. cit.) give the activity coefficient of acetone in water at infinite dilution as 6.74 at 25 C, depending on which set of vapor-liquid equilibrium data is correlated. From Eqs. (15-1) and (15-7) the partition ratio at infinite dilution of solute can he calculated as follows ... 

Sorenson and Arlt Liquid-Liquid Equilihiium Data Collection, DECHEMA, Frankfurt, Germany, 1979) report several sets of liquid-liquid equilibrium data for the system acetone-water-chloroform, but the lowest solute concentrations reported at 25 C were. 3 weight percent acetone in the water layer in equilibrium with 9 weight percent acetone in the chloroform layer. This gives a partition ratio K of, 3.0. 

The working capacity of a sorbent depends on fluid concentrations and temperatures. Graphical depiction of soration equilibrium for single component adsorption or binary ion exchange (monovariance) is usually in the form of isotherms [n = /i,(cd or at constant T] or isosteres = pi(T) at constant /ij. Representative forms are shown in Fig. I6-I. An important dimensionless group dependent on adsorption equihbrium is the partition ratio (see Eq. 16-125), which is a measure of the relative affinities of the sorbea and fluid phases for solute. 

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... 

Solute Flux Solute partitioning between the upstream polarization layer and the solvent-filled membrane pores can be modeled by considering a spherical solute and a cylindrical pore. The equilibrium partition coefficient 0 (pore/bulk concentration ratio) for steric exclusion (no long-range ionic or other interactions) can be written as... 

Two general cases are considered (1) adsorption under conditions of constant or nearly constant external solution concentration (equivalent to infinite fluid volume) and (2) adsorption in a batch with finite volume. In the latter case, the fluid concentration varies from c°t to c7 when equilibrium is eventually attained. A = (c° - c /c = Ms(h7 — h0i)/(Vfc0i) is a partition ratio that represents the fraction of adsorbate that is ultimately adsorbed. It determines which general case should be considered in the analysis of experimental systems. Generally, when A90 > 0.1, solutions for the second case are required. 

We see here that one calculates an isotope effect on an equilibrium constant as a ratio of isotopic partition ratios. Moreover, we also see that the subtraction of... 

Distribution ratio is the total analytical concentration of a substance in the organic phase to its total analytical concentration in the aqueous phase, usually measured at equilibrium. Symbol D. D shall be defined and, preferably, specified by an index if the distribution of mercury is measured, the distribution ratio is written D(Hg) or The term partition ratio is not used for the distribution ratio. 

Now, because the water-borne radioactive element is predominantly associated with the colloids, we no longer have a need for the distribution coefficient. There will still be a partitioning because the major portion of the radioactive elements will still be adsorbed to the sediment. This is a separate equilibrium partitioning coefficient, requiring a new experiment on the clay sediments and the colloids present. The partitioning colloid-clay ratio would most likely be dependent on the surface areas of each present in the sediments. A separate size distribution analysis has resulted in a sediment-colloid surface area ratio of 99 1 for the sediment. This results in a colloid retardation coefficient oiRc = 100 rather than Ri = 4.2 x 10 or i 2 = 6 x 10. ... 

In the adsorption in batch (second case), the concentration of the fluid varies from its initial to the equilibrium concentration. The partition ratio is used to discriminate between these two cases, which for the case of the solid phase initially free from the solute, is defined as (Perry and Green, 1999 Ruthven, 1984)... 

Partition Coefficient A constant ratio that occurs when a heterogeneous system of two phases is in equilibrium the ratio of concentrations (or strictly activities) of the same molecular species in the two phases is constant at constant temperature. 

Where I is the initial amount (g) of excipient in the solution, Wc is the weight of the container (g), Fs is the solution volume (L), and E, is the equilibrium partitioning constant, the ratio of the concentration of solute in the film to that in water, at equilibrium (66). This can be calculated from the more familiar, and referenced, solvent solvent partition coefficients. Plastics and rubber stoppers can also leach stabilizers and plasticizers into the contained injection volume. The extent of this can be calculated by considering the same factors described above. 

Equilibrium Partition Constants and Standard Free Energy of Transfer Effect of Temperature on Equilibrium Partitioning Using Linear Free Energy Relationships (LFERs) to Predict and/or to Evaluate Partition Constants and/or Partition Coefficients Box 3.2 Partition Constants, Partition Coefficients, and Distribution Ratios -A Few Comments on Nomenclature Concluding Remarks... 

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