Molar distribution coefficient

The fact that X for both salts lies in the range 0.20-0.25 shows that water in the membrane is a less effective solvent for ions than is bulk water i.e. the low-dielectric-constant matrix polymer lies well within the range of the electrostatic fields around the ions. Our value of Xg, the molar distribution coefficient of sodium chloride between polymer and solution, is in good agreement with values obtained by direct measurement (1,5,10, 11,12). This is further evidence in favour of our theories and assumptions. 

Researchers used also the diflfusion coefficients of the products [35] and the molar distribution coefficient of the hydroxide [36] for the modification of the shrinking core model. 

The density of Bronstcd and Lewis acid sites was determined by IR spectroscopy (Nicolet 710) of adsorbed pyridine, after desorption at 250°C, using the molar extinction coefficients previously obtained by Emeis [11]. The acid strength distribution of selected zeolites was studied by NH3-TPD in an Autochem 2910 Equipment (Micromeritics) coupled to a quadrupole mass spectrometer. First, NH3 was adsorbed at 175°C until saturation and then desorbed by increasing the temperature up to 800°C at a heating rate of 10°C/min. 

For a non-homogeneous membrane,both the diffusivity and salt distribution coefficient may vary as a function of position across the membrane. However, the steady-state conditions require that the molar salt flux and the total volume flux remain constant throughout the membrane. Therefore, the integrated expression,... 

Gaussian curves (normal distribution functions) can sometimes be used to describe the shape of the overall envelope of the many vibrationally induced subbands that make up one electronic absorption band, e.g., for the absorption spectrum of the copper-containing blue protein of Pseudomonas (Fig. 23-8) Gaussian bands are appropriate. They permit resolution of the spectrum into components representing individual electronic transitions. Each transition is described by a peak position, height (molar extinction coefficient), and width (as measured at the halfheight, in cm-1). However, most absorption bands of organic compounds are not symmetric but are skewed... 

The slope of this line is the distribution coefficient (Kd), which is the ratio of the arsenic concentration on the adsorbent (Cads) to the concentration of the associated remaining arsenic in the aqueous solution (Csdn). With each linear adsorption isotherm, Kd has only one value. That is, a linear distribution indicates that the partitioning of arsenic between the adsorbent and the solution is constant over the given range of arsenic concentrations (Eby, 2004), 221. If both concentrations (Cads and Csoin) are in the same units (such as molal), Kd is unitless. However, if the adsorbed concentration is given in molal and the dissolved concentration is molar, then Kd has the units of liter/kilogram. 

Problem 5 If the distribution coefficient of benzoic acid between water and C(Ht is 0.304 at 20°C, calculate the number of moles of benzaic acid which may be extracted from 100 c.c. of 0.02 molar aqueous solution by 10 c.c. of C(fl6. 

The distribution coefficient Kj (Equation 2) is defined as the volume fraction of pores, in a stationary phase, which is effectively permeated by a solute of a given size. V0 is the interstitial volume of the porous medium, measured by the elution volume of a high molar mass solute that is totally excluded from the matrix pores. Ve is the elution volume of the product of interest. Vs represents the total solvent volume within the pores, available for small solutes. 

Intracrystalline Fe2+-Mg2+ distributions in natural and synthetic orthopyroxenes have been determined from intensities of absorption bands in their polarized spectra (Goldman and Rossman, 1977a Steffen et al., 1988). Molar extinction coefficients of crystal field bands centred at 10,500 to 11,000 cm-1 and 4,900 to 5,400 cm-1 originating from Fe2+ ions located in pyroxene M2 sites ( 5.5.4) enabled the iron contents to be estimated from the Beer-Lambert law equation, eq. (3.7). 

Here, Vi is the molar volume of the solute (as a measure of the size of the cavity to accommodate the solute i in the solvent), d is an empirical parameter which takes also account for polarizability n, a and / characterize respectively the acidity or basicity which in general represents the ability to form hydrogen bonds, and the C s are solvent characteristics independent of the solute. Meyer and Maurer [39] used this equation for 30 systems (371 substances, 947 experimental distribution coefficients) to evaluate generalized solvent Cj parameters. 

The distribution coefficients are corrected for the solvent molecular weight through multiplication by the molar volume of the solvent (vs) ... 

Kg is the experimental distribution coefficient and K g the corrected value. This correction is required, because any measure for the interactions that occur in certain solvents should be more related to the ratio of mole fractions than to the ratio of concentrations of the solute in the liquid phase and in the gas phase. We may assume the molar volume of the gas phase to be constant and hence irrelevant if our purpose is a classification of solvents. However, the molar volumes of solvents vary a great deal. The Kg values for n-octane in various hydrocarbon solvents vary up to a factor of 3.9 between cyclohexane and squalane [216]. The Kg values vary by a more realistic factor of 1.5 [214]. 

Since the equilibrium distribution coefficient Kassoc l is related to the overall energy change in Gibbs free energy AGassoc, for the separation process carried out at constant pressure P and constant molar volume V of the solvent, then the capacity factor K, also takes on the well-known fundamental thermodynamic dependency through the relationships ... 

The distribution coefficient of benzene, K2, between the pore and the fluid phases is defined as the ratio of the molar concentration of benzene in the pore phase, P2,p> to that in the fluid phase, p2,f, at infinite dilution in both phases. 

Applying this function into the mass-balance equation (2-33) and performing the same conversions [Eqs. (2-34)-(2-39)], the final equation for the analyte retention in binary eluent is obtained. In expression (2-67) the analyte distribution coefficient (Kp) is dependent on the eluent composition. The volume of the acetonitrile adsorbed phase is dependent on the acetonitrile adsorption isotherm, which could be measured separately. The actual volume of the acetonitrile adsorbed layer at any concentration of acetonitrile in the mobile phase could be calculated from equation (2-52) by multiplication of the total adsorbed amount of acetonitrile on its molar volume. Thus, the volume of the adsorbed acetonitrile phase (Vj) can be expressed as a function of the acetonitrile concentration in the mobile phase (V, (Cei)). Substituting these in equation (2-67) and using it as an analyte distribution function for the solution of mass balance equation, we obtain... 

Given in Table 5 are aU the calculated distribution coefficients. In these calculations butanoic acid has a calculated group contribution molar volume of 74.66 cm /mol (see Table 3). 

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