Page 224 - Vogel's TEXTBOOK OF QUANTITATIVE CHEMICAL ANALYSIS

7 ION EXCHANGE

Amount of solute on resin Amount of solute in solution
Kd = -
Weight of resin, g Volume of solution, mL
The distribution coefficient can be determined by batch experiments in which
a small known quantity of resin is shaken with a solution containing a known
concentration of the solute, followed by analysis of the two phases after
equilibrium has been attained. The separation factor, cc, is used as a measure
of the chromatographic separation possible and is given by the equation,

where K,, and Kdl are the distribution coefficients of the two constituents. The
greater the deviation of cc from unity the easier will be the separation. For
normal laboratory practice, a useful guide is that quantitative separation should
be achieved if cc is above 1.2 or less than 0.8.
An important relationship exists between the weight distribution coefficient
and the volume of eluant (Vmax) required to reach the maximum concentration
of an eluted ion in the effluent. This is given by the equation:
Vmax = Kd VO + VO
where Vo is the volume of liquid in the interstices between the individual resin
beads. If the latter are spheres of uniform size and close-packed in the column,
Vo is approximately 0.4 of the total bed volume, Vb. The void fraction Vol Vb of
the column may, however, be determined experimentally or calculated from
density data.
The volume distribution coefficient is also a useful parameter for chromato-
graphie calculations and is defined as
Amount of ion in 1 mL of resin bed
Du =
Amount of ion in 1 mL of interstitial volume
It is related to the weight distribution coefficient by

where 8 is the void fraction of the settled column.
It is also related to Vmax by the equation
Vmax = Vb(Du + 8)
It should be remembered that the relationships given above are strictly
applicable only when the loading of the column is less than 5 per cent of its
capacit y.
The application of these parameters may be illustrated by the following
example.
Example. A mixture of ca 0.05 mmole each of chloride and bromide ions is to
be separated on an anion exchange column of length lOcm and 1 cm2
cross-section, using 0.035 M potassium nitrate as the eluant. The distribution
coefficients (Kd) for the chloride and bromide ions respectively are 29 and 65.
65
Separation factor cc = - = 2.24
29
This value indicates that a satisfactory separation could be achieved, and this