11.38

SECTION 11

TABLE 11.18 Relative Selectivity of Various Counter Anions

Relative

Relative

selectivity for

selectivity for

Counterion

Dowex 1-X8 resin

Dowex 2-X8 resin

OH

1.0

1.0

Benzenesulfonate

500

75

Salicylate

450

65

Citrate

220

23

175

17

I

Phenate

110

27

HSO

85

15

4

ClO

3

74

12

NO 3

65

8

Br

50

6

CN

28

3

HSO

27

3

3

BrO

3

27

3

NO 2

24

3

Cl

22

2.3

ClO

4

20

SCN

8.0

HCO

6.0

1.2

3

5.5

0.5

IO3

H PO2

5.0

0.5

4

Formate

4.6

0.5

Acetate

3.2

0.5

Propanoate

2.6

0.3

F

1.6

0.3

exchange behavior of a cation because they do not take account of

the influence of the aqueous

phase. More specific information about the behavior to be expected from a cation in a column elution

experiment is given by the equilibrium distribution coefficient

K

d .

The partitioning of the potassium ion between the resin and solution phases is described by the

concentration distribution ratio,

D c :

(D c )K

[K ]r

[K ]

Combining the equations for the selectivity coefficient and for

D

c :

(D c )K

kK/H

[H ]r

[H ]

PRACTICAL LABORATORY INFORMATION

11.39

concentration distribution ratios are inversely proportional to the solution concentration of the resin

counterion.

To

accomplish any separation of two cations (or two anions), one of these ions

must

be taken

up by the resin in distinct preference to the other. This preference is expressed by

the separation

factor (or relative retention),

K/Na, using K

and Na

as the example:

K/Na

(D c )K

kK/H

K

(D c )Na

kNa/H

K/Na

The more

deviates from unity for a given pair of ions, the easier it will be to separate them. If the

selectivity coefficient is unfavorable for the separation of two ions of the same charge, no variation

in

the concentration of H

(the eluant) will improve the separation.

The situation is entirely different if the exchange involves ions of different net charges. Now the

separation factor does depend on the eluant concentration. For example, the more dilute the coun-

terion concentration in the eluant, the more selective the exchange becomes for the ion of higher

charge.

In practice, it is more convenient to predict the behavior of an ion, for any chosen set of condi-

tions, by employing a much simpler distribution coefficient,

D

g , which is defined as the concentration

of

a

solute in

the resin phase divided by

its

concentration in

the

liquid

phase, or:

D g

concentration

of solute,

resin phase

concentration of solute, liquid phase

D g

% solute within exchanger

volume of solution

%

solute within

solution

mass of exchanger

D

g

remains constant over a wide range of resin to liquid ratios. In a relatively short time, by simple

equilibration of small known amounts of resin and solution followed by analysis of the phases, the

distribution of solutes may be followed under many different sets of experimental conditions. Var-

iables requiring investigation include the capacity and percent cross-linkage of resin,

the type of

resin itself, the temperature, and the concentration and pH of electrolyte in the equilibrating solution.

By comparing the ratio of the distribution coefficients for a pair of ions, a separation factor (or

relative retention) is

obtained for a specific experimental condition.

Instead of using

D g , separation data may be expressed in terms of a volume distribution coefficient

D v , which is defined as the amount of solution in the exchanger per cubic centimeter of resin bed

divided by the amount per cubic centimeter in the liquid phase. The relation between

D g and

D v is

given by:

D v D g

where

is the bed density of a column expressed in the units of mass of dry resin per cubic centimeter

of column. The bed density can be determined by adding a known weight of dry resin to a graduated

cylinder containing the eluting solution. After the resin has swelled to its maximum, a direct reading

of

the

settled

volume of resin is recorded.

Intelligent inspection of the relevant distribution coefficients will show whether a separation is

feasible and what the most favorable eluant concentration is likely to be. In the columnar mode, an

ion, even if not eluted, may move down the column a considerable distance and with the next eluant

may

appear in

the eluate

much earlier

than

indicated by the coefficient in

the

first eluant alone. A

11.40

SECTION

11

distribution coefficient value of 12 or lower is required to elute an ion completely from a column

containing about 10 g of dry resin using 250 to 300 mL of eluant. A larger volume of eluant is

required only when exceptionally strong tailing occurs. Ions may be eluted completely by 300 to

400 mL of eluant from a column of 10 g of dry resin at

D g values of around 20. The first traces of

an element will appear in the eluate at around 300 mL when its

D g

value is about 50 to 60.

Example

Shaking 50 mL of 0.001

M cesium salt solution with 1.0 g of a strong cation exchanger

in the H-form (with a capacity of 3.0 mequiv · g

1 ) removes the following amount of cesium. The

selectivity coefficient,

k Cs/H , is 2.56, thus:

[Cs ]r [H ]

2.56

[Cs ][H ]r

The maximum

amount of cesium which can enter the resin is 50 mL

0.001

M

0.050 equiv.

The minimum

value of [H

]r 3.00

0.05

2.95 mequiv, and the maximum value, assuming

complete exchange of cesium ion for hydrogen ion, is 0.001

M

. The

minimum

value of

the distri-

bution ratio is:

(2.56)(2.95)

[Cs ]r

(D c )Cs

7550

0.001

[Cs ]

Amount of Cs, resin phase

(7550)(1.0 g)

151

Amount of Cs, solution phase

50 mL

Thus, at equilibrium the 1.0 g of resin removed is:

100%

x

151

x

with all but 0.66% of cesium ions from solution. If the amount of resin were increased to 2.0 g, the

amount of cesium remaining in solution would decrease to 0.33%, half the former value. However,

if the depleted solution were decanted and placed in contact wit

h 1

g of

fresh resin, the

amount of

cesium remaining in solution would decrease to 0.004%. Two batch equilibrations would effectively

remove the

cesium from the

solution.