Fraction of association

What fraction of cocaine has reacted with water We can formulate a for a base, called the fraction of association ... 

Terms to Understand acid dissociation constant, K.d fraction of association, a pK weak base... 

Fig. 3.47. Variation of 0, the fraction of associated ions, with a, the distance of closest approach (i.e., the ion size parameter).

Consider KCl and take a to be the sum of the ionic radii. Use data from tables to get these. Thus, one can calculate d of the Bjerrum theory over a reasonable concentration range and, using appropriate tables, obtain the value of the fraction of associated ions. Now recalculate the values of log/. for KCl for 0.1 to 2 Af solutions from the full Debye-Hlickel theory involving allowance for ion size and hydration — but now also taking into account 0. In this approach, Cq(1 - 0) is the concentration of the ions that count in the expressions. (See Appendix 3.6.) Does this accounting for 0 improve the fit ... 

The Fraction of Association.—If equation (72) is integrated between r = o, where a is the effective mean diameter of the ions, or their distance of closest approach, and r = the result should give the number, which will be less than unity, of oppositely charged ions that may be regarded as associated with a given ion. In other words, this quantity is equal to the fraction of association (d) of the strong electrolyte into ion-pairs thus... 

The values of Q(b) as defined above have been tabulated for various values of b from 1 to 80, and so by means of equation (76) it is possible to estimate the extent of association of a uni-univalent electrolyte consisting of ions of any required mean diameter a, at a concentration c in a medium of dielectric constant D, It will be seen from equation (76) that in general d increases as b increases, i.e., d increases as the mean diameter a of the ions and the dielectric constant of the solvent decrease. The values for the fraction of association of a uni-univalent electrolyte in water at 18 have been calculated by Bjerrum for various concentrations for four assumed ionic diameters the results are recorded in Table XXXVII. The extent of association is seen to increase markedly with decceasing ionic diameter and increasing concentration. The values are... 

Paraffins can be present in crude oil as molecular paraffins as well as associated molecules. The fraction of associated or molecular paraffins in crude oil depends on many factors. However, one of the more important factors is... 

To compare both treatments it is useful to calculate the distribution of associated ions around the central one as predicted by Bjerrum s distribution function (5.3.5). We may inquire at which distance dfrom the central ion does a given fraction of associated ions exist, on the average. This fraction will be f(d) f l) and from eqn. 5.3.5... 

F%. 64. Temperature dependence of the fraction of associated monomeric units for solutions of i-PMMA ( ----) and s-PMMA (------)... 

Fig. 65. Schematically shown temperature dependence of the fraction of associated monomeric units (p) and of turbidity (t) for s-PMMA (s = 0.91 in butyl acetate on molecular scale the process is very fast subsequent aggregation needs more time. Reproduced from Adv Colloid Int Sci [Ref. 212] by the courtesy of the authors and of Elsevier Science-NL, Sara Burger-hartstraat 25,1055 KV Amsterdam, The Netherlands...

Generally it is possible to use concentrations disregarding activities. If Q is sufficiently lipophilic to be effectively present only in the organic phase and if side factors a)-c) are also ignored, then the fractions of associated with X and Y may be readily calculated In many cases, satisfactory predictions for reactions under PTC conditions can be obtained in this way, at least from the preparative point of view. It should however be taken into account that side processes cannot always be neglected. Brandstrom reported a number of examples and quantitative evaluations of this matter... 

Fig. 3. Plots of the Dolal fraction of associated species P. in ApU vs temperature (I) 63 inM 2 solution (2) 5.7 nM solution.

The fraction of associated functional groups is p = l-Cog/(c/) [p is also known as the degree of conversion or the extent of reaction in the case of irreversible association of functional groups). Using eqns [60]-[62] leads to the degree of conversion at the gelation point ... 

The closed association model means that above the CMC, added molecules go into micelles. The fraction of unassociated molecules and of micelles are plotted together in Fig. 4.18. Further information on calculating the fraction of associated molecules can be found in Section 6.4.5, where the one-dimensional self-assembly (of cylindrical micelles for example) is considered. 

The closed association model of micellization can be used to obtain the fraction of molecules in micelles as a function of total amphiphile concentration. Using concepts from Section 6.4.5 derive expressions for the fractions of associated and unassociated molecules and hence obtain plots similar to those in Fig. 4.18. 

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