340
J A C K SCHUBERT
JXCIi SCIICI3ERTClinton Luboratoites. Oak Radye, T'eunfTsee and ?'fie .4tyonrir Smtzorcal L a b r i / u t o r y , Ch?rnyo, Illinois Receared August $0,1947 INTRODUCTION
'
Realization of the fact that it is not necessary to have knowledge concerning the exact mass-action lan- or adsorption equation which fits ion-exchange data has led t o the use of ion exchangers for purposes other than the usual recovery, concentration, and purification operations reviewed by Sussman and Mindler (13). One bypasses the necessity for such information in most cases by devising the experiment so as to measure relative effects. It is the purpose of this paper to present the concepts and methods n-hich enable one to employ ion exchangers, apecifically cation exchangers, for the qualitative and quantitative determination of many physical-chemical properties. The experimental results obtained by applying the equations and concepts developed here will be given in subsequent papers. Many of the resulting applications are quite unique, inasmuch as they require only radiochemical concentrations, that is, about lo-'' mole of an element. Thus the dissociation constants of complexes such as strontium tartrate have been measured (12) when the concentration of Sr++ was about lo-" mole per liter. Briefly, the applications for which we have used ion exchangers include: ( a ) the determination of the dissociation constants of complex ions, ( b ) the rapid detection and evaluation of the relative complex-forming properties of organic salts, (c) measurements of the activity coefficient of tracer substances in the presence of large concentrations of a foreign electrolyte, ( d ) the detection and study of radiocolloids, (e) the qualitative determination of the state of tt radioelement in solution, and (f) the determination of the valence and relative basicity of a cationic radioelement. Because the bulk of the experimental \vork has been done with the acidresistant and high-capacity synthetic resin cation exchangers (7), the discussion will be restricted to these types of cation exchangers. The methods discussed here are uniquely applicable for studying the properties of radiochemical concentrations of riibstarices when large amounts of fnreign 1 The specific inaterial discussed here \\as derived from part of the studies made and reported by the writer as a member of the .lrgonne Sational Laboratory, Chicago, Illinois, and the Clinton Laboratories, Oak Ridge, Tennessee, and is based OII n o r k performed under Manhattan District Contract Ko. R-5405-Eng-39. 2 Present address: Department of Physiological Chemistry, I-niversity of Minnesota, Minneapolis 14, Minnesota.
ION EXCHANGERS IX DETERMINATION
OF PHYSICAL PROPERTIES. I
341
electrolytes are present. Hov-ever, the procedures are usef111as n-ell in studies involving macroscopic concentrations. GENERAL PROPERTIES O F CATION EXCHANGERS
X cation exchanger may generally be considered to be a porous salt containing an insoluble anion and exchangeable cations. The cations undergo exchange on acid groups such as phenolic, sulfonic, and carboxyl groups ( i ) . Experimentally, it has been found that with resin particles of 60--100 mesh: ( I ) -it any given pH the adsorption of a given cation will decrease as the concentration of foreign cations is increased (2). (2) S o significant adsorption of anions or neutral substances in true solution takes place (2, 12). (3) The adsorptive capacity of the adsorbent for a given cation increases with increasing pH.3 This phenomenon has been known t o occur with carbonaceous exchangers (8) and has been shown to occur with the synthetic amberlite resins as well (12). ( 4 ) The adsorption reaches a reproducibly constant value in about 2 to 4 hr. (2). ( 6 ) The affinity of a cation for the adsorbent increases with increasing valence; thus, the monovalent, divalent, and trivalent cations, for example, form separate groups. Some overlapping may occur, but this rule serves as a good first approximation (2). Proceeding from the above observations, we can now present the methods for applying ion exchangers to specific problems. MEASUREMENT O F DISSOCIATION CONSTANTS O F COMPLEX IONS RAVING ZERO OR K E T XEGATIVE CHARGE
A complex ion is considered to be formed when a chemical bond exists between an ion and an atom or group of atoms or other ions so that the forces acting between them lead to the formation of an aggregate with sufficient stability to make it convenient for the chemist to consider it as an independent species (9). In general, the equilibrium for the complex ion, IZLX;, may he written (4) :
and from the law of mass action:
K e shall use brackets, [ 1, to represent thermodynamic activities, and parentheses, ( ), to represent stoichiometric cioncentrations. Tn the latter case we define K , as 3 This is not the case with the synthetic cation-exchange resin, Doweu 50 (W. C. Bauinan and J. Eichhorn: J. ilm. Chem. SOC.69, 2830 (194711, since it contains nuclear sulfonic acid groups as the sole ion-active group.
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JACK SCHUBERT
The constant K , is the "instability" constant of the complex ion, because it is a measure of its tendency to dissociate into simple ions. We shall refer to K, and/or K , as the "dissociation constant" of a complex ion. Two well-known physical methods which have been used for the determination of complex ions are solubility and E.N.F. measurements. Additionally, the "frog's heart" method ( 5 ) has been used t o measure the dissociation constants of the calcium, strontium, and magnesium citrate complexes, and is based on the observation that the amplitude of contraction of the ventricle of the isolated frog's heart is a function of calcium-ion concentration. With a given weight and volume of solution, the adsorption isotherm of a tracer cation, If'", has been found to be linear over a very wide range of concentrations of the tracer, i.e.,
MR, Fa
=
constant
= Xo =
per cent adsorbed x volume of solution (100 - per cent adsorbed) X g. exchanger
(4)
where R is the anionic part of the exchanger. The procedure for the determination of the dissociation constant of a complex ion involves the determination of the per cent adsorption of the cation in a solution of known and constant ionic strength in the absence of a specific complesforming agent, and in the presence of the same. Since one measures relaticc adsorptions, no need exists for knowledge concerning the formulation of the base-exchange reaction per se. I n addition, as shown later, the absolute value of the dissociation constant can be determined when the adsorption is measured a t two different concentrations of complex-forming agent, independent of information as to the nature of the adsorption equilibria in the total absence of the specific complex-forming agent. We shall assume the following conditions to exist in deriving the equation from cation-exchange equilibria for determining the dissociation constant of the complex ion, A4&, where c 5 0: (1) The complex-forming ions are "swamped" by excess neutral salt; the ionic strength remains nearly constant. (2) The concentration of JI'" is negligible as compared to that of the complex-forming anion, -2-*;actually, 11'" is present in radiochemical concentrations mole per liter). (3) All pairs of solutions n-hich are compared have the same pH, volume of solution, and weight of adsorbent. (4) The exchanger used has been previously saturated with the cation component of the bulk electrolyte. ( 5 ) S o adsorption of the complex-forming anion or of the complex ion takes place. The symbols to be employed in the discussion are as follon-s: a = per cent of 31'" irhich has been adsorbed by the exchanger at equilibrium n-hen the complex-forming anion, is present
ION EXCHANGERS I X DETERMIXATION O F PHYSICAL PROPERTIES. I
a. = same as a when ,Ipb is absent s = per cent of 11'" which remains in solution at equilibrium when is present (actuallys = 100 - a) so = same as s when X bis absent (so = 100 - a,,) Xo = %/so, i.e., slope of adsorption isotherm
343
A-b
( A - ~ ) = concentration of complex-forming anion in moles per liter (11'") = concentration of the cation x-hich is bound in the complex ion, expressed in CY, 8, or y counts per minute per milliliter (MA;) = concentration of the complex ion expressed in terms of the counts per minute per milliliter of ;\I+" which are bound in the complex, or (11zA4;)= s - ao/Xo, as will be evident from the subsequent discussion (MR,)= concentration of adsorbent for given conditions a t equilibrium expressed in counts per minute per milliliter of 11'" From equation 4 n-e have
(X+") = -1IR,/Xo Substituting the value of l I + a from equation 6 into equation 3 we find
k'--(?rfRc)Z(A-b) z/ c X ; ( x ! -4;) I t is seen that (M&) is equal to the total counts remaining in solution a t equilibrium less the counts of AI-', the value of the latter being simply (MR,)/Xo. Hence, equation 6 is conveniently espreqsed as (counts ;\I+" absorbed)" (A-b)y counts M f aabsorbed] total counts, AI+",remaining in solution .
(7)
A0
or,
K,
=
(a)
(A-b)
~
A+
-
y
;]
When the experiment is performed in such a manner that an arbitrary, known concentration of A-* is aln-ays present, then one can calculate Xo from the adsorption results at two concentrations of LI-6q namely, AT6 and A F b . From equation 8 we have
Solving for Xo we find
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JACK SCHUBERT
An example of the data obtained by ion-exchange methods is furnished by the results (12) of a study of the dissociation constant of strontium tartrate. The experimental set-up consisted of 0.5 g. of air-dried cation-exchange resin converted to its ammonium salt and 50 ml. of a solution containing a known amount of tartaric acid, 0.2 molar in ammonium chloride and about lo-' mole of radiostrontium. The radiostrontium used was SrS9decaying as follows : SrS9--+PYS9 (stable) 53 d
At two different concentrations of tartaric acid the dissociation constants, K,, for the reaction: Sr Tar
Sr"
+ Tar--
were found to be 1.99 X and 2.04 X lo-', respectively. The average value, 2.02 X lo-* or pK, = 1.69, is in good agreement with that of Cannan and Kibrick (3), who found pK, = 1.65 from a study of hydrogen electrode titration curves of potassium chloride-strontium chloride mixtures a t an ionic strength of 0.2. The agreement between the two values is even closer when corrections for activity coefficients are considered. We may summarize the advantages of the ion-exchange method for the determination of the dissociation constants as follows: ( I ) Only tracer quantities of elements are necessary. ( 2 ) I t is workable over wide temperature and pH ranges. From the biochemical point of view this is important because one can measure the stability of a complex under physiologically important conditions. (3) It is both rapid and simple. Additionally, different cations can be worked with simultaneously in the same solution by the use of a tracer mixture followed by radiochemical analysis. (4) I t appears to be capable of good accuracy and precision. The method as such should serve as a valuable tool for the study of the solution thermodynamics of complex ions. For example, detailed studies of the variation of K , of strontium citrate with temperature and in, say, dioxane-water mixtures, would yield data of fundamental value. Furthermore, it would be of interest to apply the method to compounds of biological importance, e.g., metal proteinates. Paper I1 of this series will report (with ,J. TY. Richter) the results obtained from a study of the dissociation constants of metallic citrates and tartrates of strontium. RAPID DETECTION AND EVALUATION OF RELATIVE COMPLEX-FORMING PROPERTIES
Aside from the quantitative measurements of dissociation constants, ion exchange may be applied for rapidly testing the efficacy of complex-forming agents toward radioelements in a given solution. One can employ such a ratio of weight of adsorbent to volume of a given solution that the adsorption of a cationic radioelement is in the region of 50 per cent. The addition of equimolar concentrations of different reagents to individual solutions will serve as a means then of
ION EXCHAKGERS I S DETERMINATIOX O F PHYSICAL PROPERTIES. I
345
detecting complex-forming action and of determining qualitatively the relative strength of the different compleses formed. This procedure is of great use in devising schemes for chromatographic separations of inorganic elements. DETERMINATION O F ACTIVITY COEFFICIENTS
It has been shown (2) that the adsorption of mixtures of monovalent and divalent cations by a synthetic resin like Xmberlite IR-1 obeys the lan- of mass action ( a ) when the activities of the solid-phase components are expressed in terms of their mole fractions, ( b ) when the thermodynamic activities of the ions in the solutions are employed, and ( c ) when the anionic part of the adsorbent is taken to have an apparent charge of unity. These results agree with the equations developed by Yanselow (14) based on experimental work with inorganic zeolites. He was the first to point out the utility of ration exchange as a method for measuring activity coefficients and applied it to the barium-cadmium exchange reaction on bentonite (15). Consider a system containing a cation eschanger which is saturated with a cation M+"* and immersed in a solution containing the cations P+"z, etc. Vnder equilibrium conditions, the reaction is :
+
P+It2
&+ns
. .
+ ?AIR,
cPR,, i- dQR,,
+ ... eM+
'l
(10)
where R designates the insoluble anionic part of the exchanger. The thermodynamic expression of the equilibrium constant is :
For the reaction involving the monovalent cation A+ and the divalent cation
c++we may write:
C+
+ 2AR e CK, + 2h+
(12)
Thc cschange constant, ICa, becomes
where the quantities in parentheses are the concentrations in moles per liter and ya+ and yCT- are the activity coefficientsof cations A+ and C", respectively. If c'+ is present in radiochemical amounts in a solution of A+, then equation 13 hecomes
sinve (Mi) > > (C'Ib,. If is cwnrenient t o introduce K c , namely:
I foimd that ion exchange is a very rapid and simple method for characterizing the nature of radioelements in solution and for classifying qualitatively the chcniical nature of unknon-n radioisotopes. It shculd also be mentioned that the relative effects of comples-forming agents on a radioelement also serve as a means of placing the valence and basic'ity of an element. For example. the Th(IT? citrate complex forms one group, the rare earth citrate complexes fall in another group, etc. Within each group the behavior of each element relative to the other is related to the basicity (11). DISCUSSION
While the organic ion exchangers are very stable toward a great variety of reagents (2), it is important to recognize some of their limitations. In general, they are affected by nitric acid and should not be employed with solutions of nitric acid n-hich are stronger than 0.1 X. On the other hand, they are quite stable ton-ard even G JI solutions of hydrochloric or sulfuric acid. They undergo serious changes in solutions more alkaline than pH = 9. Anionic exrlimgers are, generally, more sensitive to temperature than the cation eschangers, becoming unqtable in the regions of 40°C. The organic cation exchangers, depending on the particular solution environment, appear to be stablc even at temperatures approaching 100°C. The inorganic cation exchangers such as the sodium aluminosilicates are not stable in acid solutions and function best in the pH region of -4.5-7. They have the further disadvantage of sometimes reacting with the heavy metals to form insoluble silicates which cannot be removed by ordinary cation-active reagents. Additionally, their adsorptive capacity is relatively low compared to the organic exchangers and varies with particle size. The extent to which the principles and methods described here can be applied t o the study of the complex-forming action of biological substances such as proteins and amino acids is a problem deserving of attention. By utilizing other phases of the behavior of ion exchangers it should be possible to extend their uses as a physicochemical tool. The kinetics of the adsorption process can probably be useful, for example, in establishing further criteria by which true ions and cdloids can bc distinguished from one another. SUMMARY
The exchange of vations bj- the synthetic resin cation exchangers is made the basis for numerous applications to physical-chemical problems. Many of these application$ require only radiochemical concentrations of an element. I t is shown hou- it i> possihle to measure quantities such as the dissociation constants of cbomplex ion. :inti activity mefficientz of electrolytes present in nearly zero r:oncentr:ttiori in thr pivwnw of macro.sc'opic concentrations of another electroIJ.tr. 111 d d i t i i ~ ~Ni , knon-ledge of the behavior of cation-exchange systems is utilized for i h c detrvtion and study of radiocolloids, the qualitative determination of the h t a t e of LI radioelement in iolution, and the determination of the vaIenw and l):isic*itJ- of c:itionir rdioelements.
350
JACK SCHUBERT B S D J. W. RICHTER
REFEREXCES (1) BOYD,G. E , BROSI,A . R., CONS, E . , LESLIE,W.,.\ND SCHCBERT, J . : Unpublished work. (2) BOYD,G. E., SCHUBERT, J., ANI) hn.uisos. .I.W.:J . -4m. Chem. Soc. 69,2818 (1947). (3) CANNAS,R . K., . ~ N DKIBRICK,A . : J. Am. Chem. Soc. 60,2314 (1938). (4) GLASSTONE, S.: Physacal Chemistry, p . 955. D . Van Sostrand Company, Inc., S e w York (1940). (5) HASTINGS, A . B., ~ I C L E C F. S , C., EICHELBERGER, L . , HALL,J. L., ASU DACOSTA, E.: J. Biol. Chem. 107, 351 (1931). (6) JENKY, H . : J . Phys. Chem. 36, 2217 11932). (7) MYERS,R. J.: ‘(Synthetic Resin Ion Exchangers,” in Adoances in Colloid Science, T’ol. I. Interscience Publishers, Inc., S e w T o r k (1942). (8) SELSON, R . , ASU WALTOS,H. F.: J. Phys. Chem. 48, 406 (1911). (9) PAULING, L.: T h e Nature of the Chemzcal B o n d , 2nd edition, p. 3. Cornel1 Cniversity Press, Ithaca, Kew Y ork (1940). (10) SCHUBERT, J.: Unpublished work. (11) SCHUBERT, J., A N D REVINSON, D.: Unpublished work. (12) SCHCBERT, J., AND RICHTER,J . IT.: J. Phys. Colloid Chem. 62, 350 (1948). (13) SUSSXAN, S., ASD ~ I I S D L E R A ,. B.: Chem. Ind. 16, 789 (1945). (14) VANSELOW, A . P . : Soil Sci. 33, 95 (1932). A . P.: J. .4m. Chem. Sac. 64, 1307 (1932). (15) YANSELOW,
THE USE OF I O S EXCHASGERS FOR THE LlETER3IISXTIOS OF PHYSICAL-CHEhlIChL PROPERTIES OF SUBSTAXCES, PARTICULARLY R.IDIOTRhCERS, I S SOLCTIOS. I1
THEDISSOCIATIO?; CONSTASTS
O F STROXTIUM CITRATE AND STRONTIUM TARTRSTE’
JACK SCHCBERT2 A K D J. W. RICHTER3 Clinton Laboratories, Oak Ridge, Tennessee Receiced r l i ~ g u s 20, t 1947 INTRODCCTION
Cations of the alkaline earths readily form complex ions with the anions of carboxylic acids. The most commonly used methods for measuring the dissociation constants of these comples ions are the determination of solubility (7) and electrometric procedures (4,6). The dissociation constants of the citrate complexes of calcium, strontium, and magnesium have also been studied, using a 1 The specific material discussed here is derived from part of the studies reported in May 1945 by the authors and is based on work performed under Manhattan District Contract Eo. W-7405-Eng-39 a t the Clinton Laboratories, Oak Ridge, Tennessee. * Present address: Department of Physiological Chemistry, Cniversity of Minnesota, Minneapolis 14, Minnesota. 3 Present address: Department of Chemistry, University of Minnesota, Minneapolis 14, Minnesota.
