Liquid partitioning coefficient

Where FCl is the solute gas-liquid partition coefficient, r is the tendency of the solvent to interact through k- and n-electron pairs (Lewis basicity), s the contribution from dipole-dipole and dipole-induced dipole interactions (in molecular solvents), a is the hydrogen bond basicity of the solvent, b is its hydrogen bond acidity and I is how well the solvent will separate members of a homologous series, with contributions from solvent cavity formation and dispersion interactions. 

Solution The phase in which reaction occurs will be denoted by the subscript /, and the other phase wiU be denoted by the subscript g. Henry s law constant will be replaced by a liquid-liquid partition coefficient, but will still be denoted by Kh- Then the system is governed by Equations (11.29) and (11.30) with = —kai and ( ) = 0. The initial conditions are... 

The P scale of solvent polarity is based on a combination of gas-liquid partition coefficients reported by Rohrschneider [43]. 

L. A. Predicfion of the solubility, activity coefficient and liquid/liquid partition coefficient of organic compounds. QSAR Comb. Sci. 2004, 23, 709-720. 

Figure 11. The clinopyroxene-liquid partition coefficient for 4+ ions entering the M2-site shown as a function of the ionic radins of the trace cation. Changes in clinopyroxene composition along a solid solntion lead to small changes in the dimensions of M2 (ro Jw 2>), which can lead in turn to changes in the relative fractionation between 4+ ions of similar ioiuc radii, such as and Th" (shown as vertical lines). We contrast the partitioning behavior of a diopside-rich clinopyroxene = 1 044 A) and a...

The net retention volume and the specific retention volume, defined in Table 1.1, are important parameters for determining physicochemical constants from gas chromatographic data [9,10,32]. The free energy, enthalpy, and. entropy of nixing or solution, and the infinite dilution solute activity coefficients can be determined from retention measurements. Measurements are usually made at infinite dilution (Henry s law region) in which the value of the activity coefficient (also the gas-liquid partition coefficient) can be assumed to have a constant value. At infinite dilution the solute molecules are not sufficiently close to exert any mutual attractions, and the environment of each may be considered to consist entirely of solvent molecules. The activity... 

The gas-liquid partition coefficient is evaluated froa the specific retention volune using equation (1.6)... 

The gas-liquid partition coefficient is relate to the capacity factor by equation (1.11). 

Where is the initial analyte concentration in the liquid phase, C( the concentration of analyte in the gas phase, K the gas-liquid partition coefficient for the analyte at the analysis temperature, V, the volume of liquid phase, and V, the volume of gas phase (318-321,324,325). From equation (8.3) it can be seen that the concentration of the analyte in the headspace above a liquid in equilibrium with a vapor phase will depend on the volume ratio of the geis and liquid phases and the compound-specific partition coefficient which, in turn, is matrix dependent. The sensitivity 1 of the headspace sampling method can be increased in some instances adjusting the pH, salting out or raising the... 

Ettre, L.S., Welter, C., Kolb, B. (1993) Determination of gas-liquid partition coefficients by automatic equilibrium headspace-gas chromatography utilizing the phase ratio variation method. Chromatographia 35, 73-84. 

Figure 4.7 Assumed probability density function for the degree of melting F (top). Resulting probability density functions for the reduced solid concentration of element i upon fractional melting (middle) and batch melting (bottom) for different solid-liquid partition coefficients D,.

The Uj and w, deviates are normal deviates, the deviates vf are log-normal. See text for the description of the computed random variables K represents mineral-liquid partition coefficients, F the fraction of residual melt, x the fraction of a mineral in the cumulate, D bulk solid-liquid partition coefficients. 

Figure 4.11 Monte-Carlo simulation (100 trials) of error propagation for La/Yb fractionation in residual melts by clinopyroxene-garnet removal from a basaltic parent magma (see text for parameter description and distributions used). Top mineral-liquid partition coefficients for La and Yb. Bottom variations of the La/Yb ratio as a function of the fraction F of residual melt.

Figure 8.19 Evolution of the liquid concentration at the interface with a solid growing at the constant rate v from a solution initially at C0. K is the solid-liquid partition coefficient. Steady-state takes longer to establish for incompatible elements.

Table 9.1. Mineral-liquid partition coefficients used for the forward modeling of batch-melting.

In equation (9.2.2), Dt is the bulk solid-liquid partition coefficient... 

Assumed source concentrations C0 for four arbitrary elements (column 2), mineral 1-liquid and mineral 2-liquid partition coefficients (columns 3 and 4), residual solid-liquid bulk partition coefficients calculated from mineral abundances listed in Table 9.2. Concentration units are arbitrary. 

The best way to convince ourselves that this rather convoluted technique works well is to build a synthetic example that we invert in a second stage. We use four elements (m = 4, elj to el4), five lavas (s = 5) for which we assume the melt fraction and residual mineral abundances listed in Table 9.2, and two non-sterile residual minerals (Mini and Min2) whose partition coefficients are listed in Table 9.3. The assumed source composition is listed in Table 9.3 which also shows the assumed bulk solid-liquid partition coefficients for each lava. 

Since we know the source composition, partition coefficients and phase abundances in molten sources, we can calculate the synthetic melt and mineral concentrations using equation (9.2.2). The five 4x3 matrices Ak can be built the first column of Table 9.4 is made of the melt concentrations ( lavas ). Mineral concentrations in the next two columns are computed from melt concentrations using the appropriate mineral liquid partition coefficients. High precision is needed to ensure accurate inversion. 

From equation (9.2.12), the bulk solid-liquid partition coefficients Dj° are... 

Figure 9.6 Comparison of the equilibrium [equation (9.2.2)] and fractional melting [equation (9.3.15)] models for a bulk solid-liquid partition coefficient Dt of 0.1 (top) and 2 (bottom). Although the concentrations predicted by the two models diverge rapidly for incompatible elements in instantaneous melts, they remain virtually identical for compatible elements.

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