Ion release as influenced by the mode of exchange

ION RELEASE AS INFLUENCED OF EXCHANGE Lambert Wiklander Institute

of Pedology, Received

April

Royal

and Erik Nilsson

Agricultural

6, 1963;

BY THE MODE

revised

College, December

Uppsala,

Sweden

1, 1953

ABSTRACT In this paper a simple theory of the continuous ion exchange supposed to occur in natural systems is discussed and some experimental data are presented. The release of adsorbed ions is calculated and compared with the corresponding release from the batch exchange of static systems. The experimental results were found to support the theory.

Ion exchange in natural systems, e.g., biological systems and soils, is generally a more or less continuous process of low rate which often fails to produce a final equilibrium state. Reactions of this type we find, for example, in the desorption of cations from soil colloids as part of the uptake of nutrients by plants. The replacing agent is primarily the hydrogen ions of carbonic acid slowly produced by the plant roots and living organisms. The capacity of the replacing hydrogen ions per unit time must obviously be low. Because of the nutrient absorption, caused both by the migration of ions and the flow of water from the soil into the roots, the concentration of replaced ions in solution is kept low. As a consequence of this mechanism the exchange will be slow and continuous. Part of the reactions involved in the loss of nutrients by leaching also belong to this type of exchange, since the sinking water contains carbonic acid and other electrolytes, leading to an ion exchange. The uptake and leaching of nutrients have a disturbing effect on the distribution of the diffusible ions in the soil. As a matter of fact the active roots are far from being in contact with the whole soil surface, and the leaching water in many soils moves mainly in fissures, cracks, root holes, and other interstices. Because of these conditions, an ion diffusion, intimately associated with ion exchange, takes place, the latter being continuous and of low rate. This process may be pictured as a repeated batch exchange taking place in an infinite number of steps, the amount of ions exchanged in each step being infinitesimal, owing to a low activity of the replacing ion. Further, the 223

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LAMBERT

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ERIK

NILSSON

concentration in the solution of the ions replaced from the solid phase is often low, owing to a more or less complete removal of the ions from the exchange system or by some sort of inactivation (e.g., complex formation) rendering the ions unable to take part, in the equilibrium. An exchange of this kind consequently requires a special theoretical and experimental treatment. The theory as presented here followed as a logical consequence of an investigation concerning the influence of the proportions of the exchanging ions and of the exchange of minute quantities on the ion distribution (1). It was briefly discussed in connection with a study of the release of plant nutrients in soil (2). In a recent paper (3) this exchange was further studied and given the name continuous inJinitesima1 ion exchange’ to distinguish it from other categories of exchange such as the batch type and the dynamic exchange, taking place in static systems and columns, respectively. In the continuous exchange we are interested in how far the exchange will proceed in a certain time, that is, the amount of ions released or the change in the composition of the adsorbed ions in this time. In the batch exchange, on the other hand, we study the ion distribution after a more or less momentary exchange caused by addition of electrolytes or by mixing exchangers of different composition. THEORETICAL

A simple mathematical expression of the continuous exchange may be derived in the following way. We assume an exchanger saturated with the ions A and B of the same valence, the total amount of the ions being AT and Br moles. By addition of a third ion, R moles of the adsorbed ions are replaced. As has been shown in several papers from this Institute, ion-exchange reactions may be described by means of the Donnan equilibrium. The resulting distribution of the ions A and B between exchanger (e) and intermicellar solution (s) after the replacement can therefore be expressed as follows :

(4s __ = (4 -2 @>a (B>e

PI

where ( ) means activity of the respective ions. Using the well-known relationship

(A) = SAMI, fA being activity coefficient of A and [ ] concentration,

we obtain

bl 1 In

the

following

for

the

sake

of brevity

called

only

continuous

eschange.

ION

RELEASE

where CY*,~is the equilibrium

AND

MODE

OF

225

EXCHANGE

quotient, related to the activity

factors by

01A.Bis assumed to be constant. Because A and B have the same valence and are present in the same liquid phase, their concentrations may be substituted with the corresponding moles (A, , A, , B, , B,), and the equilibrium is thus independent of the volume of the intermicellar and micellar solutions. Using the equations : A, = A, + A, BT = Bs + Be R

=A,+B,

Eq. [2] is transformed into the following only dependent variable :

AS

expression, cont,aining A, as the

= aa,B(R - As)

AT - A,

BT-

R-l-

A,’

[31

If the exchange is very small, that is, R << AT + BT , and the conditions are fulfilled as stated below, it follows that A, -CCAT and (R - A,) << B, . Equation [3] may thus be reduced to:

A, -=

~A,B@

AT

-

A,)

[41

BT

or after transformation:

AA, =

CU,B.AT BT + cu,~.Ar

. AR,

151

where AA, and AR mean the released amounts. The validity of [4] and [5] requires, however, that (YA,B be not very large (w,, not >> 1) if the mole fraction of A is very small, that is, AT:B, -+ 0, and that aA,B be not very small (c%,B not << 1) if the mole fraction of B is very small, that is, BT: AT--to. If the exchange is a real continuous infinitesimal reaction, the conditions being AR -+ dR and AA, t CIA, , the exchange may be best described by the differential quotient -dA, dAs dRorxr The total amounts A, and B, of Eq. [5] have then to be substituted

with

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LAMBERT

WIKLANDER

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ERIK

tilLSSON

the corresponding variables A, and B, . The resulting differential reads -dA, = cu.B.Ae.dR Be + CYA,B~

equation b31

whereA,=AT-AgandB,=Br-RfA,. For integration [6] is combined with the last two equations and can then be written aA,B. A,.dR -dA, = 171 %4,E’A, - A, + AT + BT - R and after transformation -d-&[--A, which gives

+ AT + BT - R] = a.i,B.Ae.dR

+ cxd,B-Ae.dAe

-dA, - dR d-4 A, =QA’RAT+BT-&-R* Equation

@I

[S] can be integrated directly; thus In A, =

In (AT + BT - A, - R) + C

(YA,B

PI

when R = 0, A, = AT, and C = In AT - %,B In BT. By substitution of C in [9] we obtain A ln’=~A,BlnAT+BT-AC-R, AT

BT

or since A, = AT - A,: AT

-

=

A,

A*

BP -I- A, - R aA*B ( ) * BT

DOI

From Eq. [lo] the release of the ion A by a continuous exchange can be calculated as a function of the total release R. From the relation R = A, + B, the release of the ion B is obtained. Equation [lo] can also be written in a form more convenient for calculation of the exchange isotherm. Thus, A, -= AT

B, - IxAmB 0 BT ’

Taking the logarithms of the function, log A, = log AT + aA, B log B, -- , BT

WI

ION

RELEASE

AND

MODE

OF

EXCHANGE

227

gives an equation of the first degree with Q!as the slope of the line. However, it must be kept in mind that the straight-line relationship is valid only as long as (Yis a constant. By several experiments it has been established that (Y has a tendency to vary with great changes in the ion proportion. The degree of this variation is dependent on the nature of the ions and the exchanger. It is of interest to note that in previous experiments (3) a proved to be rather constant for exchange performed as small successive replacements, supposed to resemble the continuous exchange. The relationship between 01,the relative release of A and B that is, A,:AT B,:B/ and the total release R has been discussed previously (1, 3). The relationship proved to be:

if A has a lower adsorption affinity than B, and A,:& aA.B 6 B,:BT

< 1 =

if the opposite is true and

In Figure 1 exchange isotherms are given for the continuous exchange as well as for the batch type of exchange, the former calculated from formula [ll] and the latter from the Donnan equilibrium. The relative adsorption affinities of the ions A and B are varied by assuming a! to be equal to 0.25, 1, and 4. Mole fraction of A is assumed to be 0.01. From the figure the following conclusions can be drawn: 1. The desorption curves of the batch exchange are symmetric, whereas those of the continuous exchange are asymmetric. 2. When (YA,B= 1, that is, the adsorption affinity of A and B being the same, the release is independent of the type of exchange and is proportional to the total release. 3. When CYA,B= 0.25 (or more generally a A, B < l), A being more firmly adsorbed than B, the continuous exchange releases less of A but more of B than does the batch exchange. 4. When ffA,B = 4 (Or more generally BA,B >l), A being more weakly adsorbed than B, the continuous exchange releases more of A but less of B than does the batch exchange. 5. The continuous exchange compared with the batch exchange therefore

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NILSSON

FIG. 1. Influence of the mode of exchange on the release of an ion A, combined with an ion B of the same valence, the equilibrium quotient (o1A.B) assumed to be 0.25, 1, and 4 and the replacement (R) of A + B to vary from 0 to 100%. B.E. and C.I.E. signify batch exchange and continuous exchange, respectively. A, means amount of A replaced and AT total amount adsorbed originally. Mole fraction of A = 0.01.

tends to decrease the release of the more firmly adsorbed ions and to favor the release of the more weakly adsorbed ions. This effect is the more pronounced the greater the difference between the adsorption affinities of the ions, that is, the greater or the smaller the (Yvalue, and the more dissimilar the mole fractions of the adsorbed ions. An ion present in a high proportion may be only little or practically not at all affected. EXPERIMENTS

In our recent paper (3) some experimental results with the resinous cation exchanger Amberlite IR-100 saturated with either Li+ - K+, Na+ - K+, or Na+ - Cu2+ were presented to exemplify the ion-exchange theory discussed. In further experiments, discussed below, the same exchanger was saturated with Li+, K+, and Mg”+ in two different proportions: (1) 5 % Li+, 90 % K+, and 5 % Mg2+ and (2) 80 % Li+, 10 % K+, and 10 % Mg2+. The batch exchange was accomplished by addition of increasing amounts of hydrochloric acid to a set of identical systems of the respective ion proportions. No real continuous exchange experiment has been carried out. From the theory it appeared that the continuous and the batch exchange curves approach each other and finally coincide as the percentage replace-

ION

RELEASE

AND

MODE

OF

229

EXCHANGE

ments decrease. Utilizing this fact a quasi-method for the continuous exchange has been applied. In the experiments designed to resemble the conditions of the continuous exchange, small fractions of the adsorbed ions were successively replaced by addition of hydrochloric acid. Equilibrium having been established (two hours reaction time, shaking now and then), the free solution was thoroughly removed, new portion of acid added, etc. To increase the accuracy of the analyses successively replaced portions were combined, as given in the table, evaporated, and submitted to analysis. Li and K were determined by flame-photometer and Mg by the thiazol yellow method. The desorption curves of the “continuous” exchange were obtained by summation of the successively replaced quantities of the different ions and related to the sum of the released Li, K, and Mg. System I: Li+ 5%, Kf 90%, and Mg2+ 5 %. The results are given in Table I and Fig. 2. This experiment deals with a system containing a small amount of the weakly adsorbed Li and the firmly adsorbed Mg and a large amount of the moderately adsorbed K. System II: Lif 80 %, K+ 10 %, and Mg2+ 10 %. The results are given in Fig. 3. This system deals with an exchanger saturated with a large amount of the TABLE Replacement

of Lif,

4 grams of exchanger Mg.++ Two different second supposed HCl added, meq.

K+,

f ram

and Mgff

saturated with 0.25 types of experiment, to resemble continuous

0.077 0.13 0.18 0.22 0.23 0.24 0.245

K+

%, x

by Addition

of HCI

Mg*

Li+$K++Mg++

exchange

3.20 3.35 3.52 (4.45) 3.72 4.42 4.78 V’ontinuous”

5 x 0.1 10 x 0.1 10 x 0.1 20 x 0.1 10 x 0.15+ 10 x 0.20 20 x 0.30 15 x 0.40 2: rep&. = 100

IR-100

meq. Li+, 4.50 meq. K+, and 0.28 meq. the first being of batch type and the exchange. Solution volume 100 ml. Replaced, meq.

Li+

Batch 3 7 20 40 70 100

I Amberlite

0.55 1.14 1.89 2.79 3.41 3.76 4.09

Trace 0.0026 0.015 0.060 0.15 0.21 0.24

0.63 1.27 2.09 3.07 3.79 4.21 4.58

exchange

TOfd

T&d

T&d

0.063 0.12 0.16 0.21 0.24

0.43 0.91 1.31 1.90 2.61

Trace 0.0010 0.0019 0.0054 0.012

0.49 1.03 1.47 2.12 2.86

TOfd

0.25 0.25

3.30 3.70

0.013 0.023

3.57 3.97

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LAMBERT

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NILSSON

FIG. 2. Replacement of Li+, K+, and Mg++. Mole fractions small. Compare with Table I.

FIG. 3. Replacement = 0.56 meq.

of Li+ and Mg*

of Li+, K+, and Mg++. Liz = 4.00, Kf,

being

= 0.50, and Mgi

ION

RELEASE

AND

MODE

OF

EXCHANGE

231

weakly adsorbed Li and a small amount of the moderately adsorbed K and the firmly adsorbed Mg. DISCUSSION

System I. The results are qualitatively in good accordance with the theory. Thus, there is a marked difference between the percentage replacements of Li and Mg, respectively, in the batch exchange and the “continuous” exchange. While the weakly adsorbed Li shows a greater desorption by the “continuous” exchange than by the batch exchange, the opposite is true of the firmly adsorbed Mg. At a total desorption of 70%, practically the entire amount of Li is released but only 6 % of Mg by the “continuous” exchange. The corresponding figures for the batch exchange are roughly 92 % of Li and 37 % of Mg. In addition to the effect of the mode of replacement, as discussed for ions of the same valence, the different concentration of the solutions, influencing the distribution of the mono- and bivalent ions (4), is also of importance in explaining the above results as to magnesium. As could be expected, the release of potassium, representing the major part of the adsorbed ions, is not affected by the type of exchange as far as can be disclosed by an experiment of this kind. The equilibrium quotient, aLi/K of the batch exchange has been calculated and proves to increase slowly with increasing degree of exchange (Table I). This experiment shows conclusively and in accordance with the theory that a desorption taking place successively and in small quantities, in comparison with a larger desorption, tends to conserve the firmly adsorbed ions at the expense of the weakly adsorbed ions. This effect increases with the difference in concentration and in adsorption affinity of the ions in question. It is greater for ions of different valence than for ions of the same valence and comes to a maximum if the desorption is a real continuous infinitesimal exchange. System II. Being the dominant ion, lithium behaves in this series the same way as potassium in the former, that is, no certain difference was found. On the other hand K and Mg, though being present at not less than lo%, show a greater desorption in the batch exchange than in the “continuous” exchange. This is explained by the higher adsorption affinity of K and Mg than of Li. The release of Mg in the “continuous” exchange is markedly small, reaching only about 3 % at a total release of 80 %. The corresponding figure in the batch exchange amounts to 20%. Owing to a higher degree of Mg saturation the difference between the Mg curves is less in system II than in system I. As a result of the greater competition between K and Mg than between Li and Mg, the Mg release in the batch as well as in the “continuous” exchange experiment is greater in system I than in system II.

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Though these studies were carried out with a synthetic exchanger, the conclusions arrived at may have important bearings on several natural reactions. According to Clark and Washington (quoted by Rankama and Sahama (5)) the contents of sodium and potassium in the lithosphere amount to 2.83 % and 2.58 %, respectively, giving a ratio of 1.1. In the sea, however, the corresponding ratio is 27.8. The greater losses of sodium compared to those of potassium by leaching and the accumulation of sodium in the sea may be explained partly by the fixation of dissolved potassium as lattice component of clay minerals and partly by the continuous exchange taking place. As a matter of fact sodium is more weakly adsorbed than potassium by the soil material, thus making possible a, dissimilar release of the two ions, strengthened by the continuous exchange. The loss of the important minor elements, present in the soil in very small quantities and being very firmly adsorbed, such as copper, cobalt, zinc, and molybdenum, may also be minimized by an ion exchange of the continuous type. In a recent survey, Tompkins (6) discusses factors determining the ion selectivity of exchange resins, without, however, including the mode of exchange. As made clear by our study, this must also be considered as a significant selectivity factor. Calculation of the equilibrium quotient of the mass action law and of the relative adsorption affinities of ions from exchange data has been carried out by several investigators during the last years. By the present theory and experiments evidences are brought about that such a procedure is valid only if the results obtained are applied to systems where the exchange is performed in the same way. Thus, equilibrium quotients gained by batch exchange may not be directly applicable to natural systems with ion exchange of the continuous type unless the batch exchange comprises only a small portion of the adsorbed ions. With the use of the ordinary replacement method for determination of the relative adsorption affinities of soil-adsorbed ions the percentage exchange should consequently be kept as small as possible. REFERENCES 1. 2. 3. 4. 5.

WIKLANDER, WIKLANDER, WIKLANDER, WIKLANDER, RANKAMA,

L., L., L., L.,

Acta Agr. Scud 1, 190 (1951). Trans. Intern. Sot. Soil Sci., Dublin, 1, 189 (1952). AND NILSSON, E., Acta Agr. Scand. 2, 197 (1952). Ann. Roy. Agr. CoZZ. Sweden (p. 107), 14, 1 (1947). AND SAHAMA, TH. G., “Geochemistry.” University of Chicago

K., Chicago, 1950. 6. TOMPKINS, E. R., Andyst

77, 970

(1952).

Press,