Shedlovsky equation

In the foregoing discussion the Onsager equation has been used for the purpose of drawing a number of qualitative conclusions which are in agreement with experiment. The equation could also be used for quantitative purposes, but the results w ould be expected to be correct only in very dilute solutions. At appreciable concentrations additional terms must be included, as in the Shedlovsky equation, to represent more exactly the variation of conductance with concentration the general arguments presented above would, however, remain unchanged. 

Solubility of the compound. There must be some solubility. The pK of poorly soluble compounds must be measured in aqueous methanol solution. If several titrations are carried out with different ratios of methanobwater, the Yesuda-Shedlovsky equation can reveal the theoretical pK in purely aqueous solution. Similarly, for poorly soluble compounds, provided the log P is high enough, the compound may be determined by titration, by addition of the sample to the octanol first. The compound will then back partition into the aqueous layer. If this fails, then spectroscopic methods have to be employed as more dilute solutions may be used. 

In recent years, the extrapolation procedure developed separately by Yasuda and Shedlovsky has been reported [20,21,99] to provide pXa values from partially aqueous solutions that can sometimes closely approximate the values found in purely aqueous solutions. The Yasuda-Shedlovsky equation [Eq. (12)] can be used to correlate apparent pKg values in different solvent polarities (psl a) to approximate the aqueous pK value by extrapolation as a reciprocal function of the dielectric constant (e) of each of the cosolvent mixtures ... 

A plot of the Yasuda-Shedlovsky equation generally is a straight line. The fitted coefficients A and B are then used to estimate the pK value in a 100% aqueous solution, for which [H2O] = 55.5 molal and e = 78.3. Successful use of this approach in cosolvent mixtures requires a complex pH electrode calibration procedure [20]. 

NB As is well-known, this method of extrapolation often leads to errors due to the non-linearity of these plots, especially for amines at low alcohol percentages. It is a pity that the raw data (apparent pXa vs alcohol-water composition) was not available, so diat more recent procedures, such as the Yasuda-Shedlovsky equation, could be used in an attempt to extract more reliable pKa values. 

It is recognized that FHFP equation accounts for the concentration dependence of electrolyte solutions up to moderate concentrations and yields more reliable association constants than the Shedlovsky or Fuoss-Kraus equations. However, it was observed that the FHFP Equation (4.18), or the more simple Shedlovsky Equation (4.16), give similar fitting results, for some supercritical electrolyte solutions at low density (p < 0.3 g cm" ). The contribution of the electrophoretic effect to the concentration dependence of the molar conductivity is expected to be lower in supercritical water than in ambient water because of the much smaller viscosity and dielectric constant. Moreover, the higher-order terms in Equation (4.18) nearly cancel each other at moderate concentration in supercritical water (Ibuki et al., 2000). This could be the reason why differences among several conductivity equations vanish at supercritical conditions. 

Evers and Frank s value for is about a factor of 7 smaller than Kraus. The reasons for the discrepancy are probably due to (a) the sensitivity of the process of fitting the data to the Shedlovsky equation to small errors in conductance and (b) the neglect of process (34) by Kraus which is not justified for data with solutions of concentration > 10 M. Using their calculated values of Ag, ki, and Evers and Frank find very satisfactory agreement between their predicted conductances and experimental conductances at various concentrations less than 0.04M. Above this concentration, the agreement with experiment is not expected to be too good because of the onset of the process of metallic conduction which is predominant at higher concentrations. 

Drug dissociation constants are experimentally determined by manual or automated potentiometric titration or by spectrophotometric methods.40 Current methods allow determination of pXa values with drug concentrations as low as 10 to 100 pM. For highly insoluble compounds (concentration <1 to 10 pM), the Yesuda-Shedlovsky method41 is commonly used where organic cosolvents (i.e., methanol) are employed to improve solubility. The method takes three or more titrations at different cosolvent concentrations, and the result is then extrapolated to pure aqueous system. The dissociation constant can also be determined with less accuracy from the pH-solubility profile using the following modification of Henderson-Hasselbach equation ... 

Fuoss and Kraus [13] and Shedlovsky [14] improved Eq. (7.6) by taking the effect of ion-ion interactions on molar conductivities into account. Here, Fuoss and Kraus used the Debye-Huckel-Onsager limiting law [Eq. (7.1)] and Shedlovsky used the following semi-empirical equation ... 

The ions are highly associated into ion pairs and due to this the Shedlovsky conductance equation is applicable. Thus, the experiments are easily analysed. An equation analogous to Eq. (41)... 

The apparent acid dissociation constants (p s)Ka) of two water-insoluble drugs, ibuprofen and quinine, were determined pH-metrically in ACN water, dimethyl-formamide water, DMSO water, 1,4-dioxane-water, ethanol water, ethylene glycol-water, methanol water, and tetrahydrofuran water mixtures. A glass electrode calibration procedure based on a four-parameter equation (pH = alpha-i- SpcH -i-jH[H+] -i-jOH[OH ]) was used to obtain pH readings based on the concentration scale (pcH). We have called this four-parameter method the Four-Plus technique. The Yasuda Shedlovsky extrapolation p s)K a + log [H2O] = A/epsllon -1- B) was used to derive acid dissociation constants in aqueous solution (pKa). It has been demonstrated that the pK a values extrapolated from such solvent-water mixtures are consistent with each other and with previously reported measurements. The suggested method has also been applied with success to determine the pKa values of two pyridine derivatives of pharmaceutical Interest. Spectrometric, ultraviolet (UV) ... 

Another method, also based on the assumption that Onsager s equation is the true limiting relation, depends upon Shedlovsky s equation, which for uni-univalent electrolytes takes the form... 

This equation was improved by Fuoss and Kram taking account of the interionic effects on conductance through the limiting law. On the other hand, Shedlovsky used the semiempirical equation. 

Evans, Zawoyski and Kay analysed data for R4N salts in acetone (AC) " with the Fuoss-Onsager equation. They found Ka decreases with cation size, and for the anions, association decreases in the order Bu4NBr(i = 264) > I-(143) NOg > CIO4 (80) > Pic-(17). This agrees with data for methylethylketone. The fact that association of Bu4NC104 in AC, benzonitrile, and methylethyl-ketone corresponds to = 4.85 A for the three solvents, indicates formation of contact ion pairs. Tetraalkylammonium halides in dimethyl-formamide (DMF) have small association constants when the data are evaluated with Shedlovsky s eqn. 5.4.10. When the data for Me4NPic in is assessed with Fuoss and Hsia s eqn. 5.2.31, a is 6.0 A. 

FIGURE FIO. Equivalent conductance of NaCI solutions at 25°C. Shedlovsky s equation (X +... 

Shedlovsky (Shedlovsky, 1938) proposed an improvement of this equation which takes into account the interionic effect on conductivity. 

The precision of the experimental data is a key issue in choosing a conductivity equation to fit the concentration dependence of the molar conductivity and, in the case of associated electrolytes, the association constant. Old meas-mements of conductivity, particularly those by Franck and co-workers in Germany and by Marshall and co-workers in ORNL (USA), having imcertainties aroimd 1% were fitted using the Shedlovsky or the Fuoss-Kraus equations, which allows the simultaneous determination of A° and K,. 

Shedlovsky observed that the value of Ao as calculated from Equation (4.24) was not constant, but showed almost linear variation with concentration. The linear extrapolation function... 

Shedlovsky found that for several salts the right-hand side of equation (C.22) varied linearly with c up to about 0.1 mol dm. His method of obtaining A" is therefore to plot experimental values in this form against c, and to extrapolate the straight line to c = 0. 

Very accurate values are available for the common ions in water at 298 K, based on the work of Macinnes, Shedlovsky and Longsworth. These authors measured transport numbers and conductivities of HCl, KCl, NaCl and LiCl over a range of concentration, thus obtaining values for the molar conductivity of the chloride ion in these solutions. These were extrapolated according to Shedlovsky s equation (see conductivity at infinite dilution) with the result shown in figure M.I. A very accurate value, A (C1") = 76.3412" cm moP is thus available for the chloride ion, and by subtraction of this from the A values of the four electrolytes, AT values for the four cations are obtained. Other transport number data are now unnecessary, as the molar conductivity of a cation can be found by subtraction from the A value of its chloride, or of an anion from A" for its sodium or potassium salt. Values for the commoner ions are given in table M.l. 

Even solution (c) may be too highly conducting to be suitable for a cell designed for very dilute solutions. In this case, calibration is based on interpolation from the very accurate measurements of Shedlovsky on more dilute aqueous KCl solutions at 25 °C. Up to a concentration c/moldm" = 0.001 these are represented by the equation... 

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