THE STABILITY OF A COMPLEX ION A Laboratory Experiment in Radiochemistry and Ion Exchange PAUL KRUGER and JACK SCHUBERT University of Chicago, Chicago, Illinois, and Argonne National Laboratory, Lemont, Illinois
Tm experiment described in this paper is designed for
the cation exchanger according to the following equation:
a laborat,ory course in advauced physical chemistry.
I t introduces the student to three important aspects of physical chemistry; (1) the determination of the composition and stability of a complex ion in solution; (2) the use of synthetic organic ion exchangers; and (3) simple radiochemical terhnique. The experiment consists in the measurement of the distribution of carrier-free' radioactive stontium between a buffered solution containing varying concentrations of ritric acid and a cation exchanee resin immersed in the solution. The stability quotient of the complex ion formed between Sr++ aud the citrate ion, Cit3-, is calculat,ed from differences in the uptake of Sr++ by the cat,iou exchanger from solutions of various citrate concent ratio^^^. The measurements are made under sirnulated physiological conditions, i. e . , a PH of 7.25 and ionic strengt,h of 0.16. Practically all of the citric acid is present. as a trivalent ion when the p H is greater than 7.0. The theoretical and experimental aspects of ion exchange technique as applied to complex ion have already been discussed ( 1 , 2 ) .
Srt+
+ n rit3-
-
Sr(Cit),.3-3*
(3
The formation quotient, Kf,for reartion (3) is:
The distribution coefficient, Kd,is defined as the ratio of concentration of strontium in the resiu phase to that in the external solution, thus: % Sr in exchanger volume of solution (ml.) (5) mass of exchanger (mg.) Kd = % Sr in solution .
-
In the absence of Cit3-, thedistribution coefficient, ], is designated as Kdo,is equal to [ s ~ R z ] / [ s ~ + +which c o n ~ t a n because t the ratio [ N a + l ' / [ N a ~ ]in ~ equatioll (') is constant. We can now obtain expressions for [ST++]and [Sr (Cit),'-"l in terms of cation exchange equilibria by siubstitution into equation (4). The term Kdorepresents the distribution coefficient of strontium wheu CitJ- is absent while Kd represeuts the distribution coTHEORY efficient when Cit3- is ~ r e s m t . All ~ other conditions The reart,ion between a cation exchange resin in the such as pH, ionic strength, etc., remain constant. It sodium form and strontium ion in a solution buffered is also assumed here that only one complex ion is present and that the complex ion itself is not retained by the wit,h a sodium salt can be written: cation exchanger. Thus we have
.
~
Srt+
+ 2NaR
-
SrFh
+ 2Na+
(1)
in which R represents the insoluble anionic part of the cation exrhange resin with an assumed charge of - 1. The concentration of Sr++ is negligible in comparison with that of Na+, heuce no appreciable change in Na+ concentration in either the solution or resin phases occurs a t any time. The equilibrium quotient, K,, for reaction (1) is given by the following mass action expression: K,
=
ISrR.1 [Na+Ia [Sr j [NaR12
and therefore
[Srn.] [Sri+] = --
(7)
K.iO
and [Sr(Citj,,"-J"]
=
[sfid IS&] - [Sr++] = K*
lid
- ISrRi -
(8)
KdO
10,
I*,
++
conwnin whirh the bracketed terms represent trations. The addition of Cit3- to the solution reduces the concentration of Sr++ and reduces the uptake of Sr++ by
'
~~~
A carrier-free radioactive element is one which does not have weighable or visihle amounts oi inactive isotopes of that clement sasoeiated with it.
Substitution of the expressions for [Sri+J and [Sr(Cit),Z-3'l as given in equations (7) and (8) into equation (4) for K, leads to K, =
( R O I K d- 1 [Cit3-in
(9)
1 In the general ease there are as many t e r m in the equation for the distribution coefficient as there are molecular species containing the cation under studs.
196
APRIL, 1993
197
stant weight at l10°C.3 One gram of resin is required for each experiment. Enough resin in quantity sufficient for several years should be prepared and stored. Reagents. Three solutions are employed: (I) a buffer solution containing Xa+ at a concentration of 0.16 M and the radioactive strontium, (2) a 0.16 M NaCl solution, and (3) a 0.05333 M sodium citrate solution. Freshly boiled distilled water is used in all soluA plot of log (KdO/Kd- 1) versus log [CitS-1, which tions. A universal Veronal%uffer (4) is employed. It concan he conveniently made on log-log paper, should be a straight line with slope n. The value of K,is obtainable tains no anions which react with alkaline earth cations to form insoluble compounds or appreciable amounts of from any point on the straight line. complex ions. The buffer (pH = 7.25) is prepared rts Equat,ion (9) can further be arranged into follows: 19.428 g. sodium acetate (NaC2H4Oa.3H2O) and 29.428 g. sodium diethylbarbiturate are dissolved in about a liter of freshly boiled distilled water. In addiA plot of l/Kd versus [Cit3-] for proper values of n tion 400 ml. of 8.5 per cent NaCl solution, 1100 ml. of should be a straight line which can be extrapolated to 0 . 1 M HC1,200 ml. of analytical reagent grade formalin [Cita-] = 0 to give the value l/KdO. This procedure as a preservative, and the carrier-free tracer Srso are affords a convenient method for confirming the experi- added5 and the solution is diluted to five liters. The buffer solution should be kept in a refrigerator if possimentally determined value of KdO. ble. The NaC1 solution consists of 9.53 g. solid NaC1 disAPPARATUS AND MATERIALS solved in enough water to make one liter. Cation Ezchanger. Any of the commercially availFor the citrate solution 15.685 g. Na citrate.2H20 able sulfonated polystyrene cation exchange resins can (M.W. = 294.12) are dissolved in enough water to make be used. These resins are particularly useful because one liter. It should he prepared fresh before each extheir capacity is independent of pH over a wide range periment, otherwise the concentration may change be(pH 2-13). Air-dried Dowex-50, consisting of par- cause of bacterial action. ticles in the size range between U. S. Standard sieves, Canting Equipmat. Any device which call detect Nos. 100-140, is recommended. The size of the resin beta particles can be used for the detection and measparticle is not an important factor because the equi- urement of SrS0. I t is desirable but not necessary to librium distribution of the cation exchange reaction is have sufficient activity so that each ml. of the solution independent of resin particle size. containing the radioactive strontium will have an The resin is conditioned by several washings, alter- activity ahout 100 times that of the background of the nately with solutions of 5 per cent NaCl and 5 per cent detecting instrument. The results cited below were obHCI. During the conditioning process a considerable tained with an Eck and Krebs counter. The samples quantity of "fines" are removed. This is accomplished must be placed in a reproducible position beneath the by stirring the resin sample in a large beaker filled with tube. The samples should be counted long enough to conditioning solution. Most of the resin is allowed to give from 1000total counts (3 per cent probable error) to settle, whereupon the liquid containing the 6nes is de- 10,000 total counts (1 per cent probable error). canted. This operation, when repeated several times, removes most of the "fines." hence in carwine: - - out the PROCEDURE equilibrium experiments, the resin settles quickly allowSolutions in 12 numbered flasks are prepared as ing the supernatant solution to be drawn off free of shown in Table 1. The flasks may he shaken either resin. After saturation with excess NaC1, the resin is mechanically for at least 2 hours or intermittently by equilibrated with excess 0.16 M NaCl solution. The hand during a morning or afternoon. Tivo aliqnots (the supernatant solution in contact with the resin is ad- volume depending on the level of the radioactivity) are justed to pH 7.2-7.3 with dilute NaOH solution. After withdrawn with a pipet from the supernatant solution the mixture has been stirred for an hour the pH of the in each flask. and transferred to 24 numbered 10-ml. supernatant liquid is tested, and readjusted, until no Moisture determinations are preferably conducted by drying chanze in DH. determined with a Beckman elass electrode, after stirring. ~h~ resin is filtered in & vacuum oven a t 44(t80n or over phosphorus pentoxide in a vacuum desiccator. Oven drying a t llO°C. may not give a through a Biichner funnel, and rapidly washed free of weight ior different kinds oi resins. adhering salt solution with distilled water. The Vemnd is a reziatered tmdr name for 5.5-diethvlbarbitu~ic washed resin is spread in a thin layer on a tray and air- acid. %r8' can be used ii of sufficiently high specific activity, thus are conducted with air-dried dried, All eliminating the necessity for allowing time for radioactive equiresin. Analysis showed that the &dried resin con- librium to be attained, Sr90 is inthe tained 3.86 milhuivalents of sodium Per gram and ,,,,i,,-f~~ state, is longer lived, and gives the student additional 12.5 per cent moisture as determined by drying to con- radiochemical experience. The concentration of Cita- is known, and Kdoand Kd are determined by measuring the fraction of tracer strontium remaining in the solution phases at equilibrium. Equation (9) can be rewritten:
-
-
ilaee
-
JOURNAL OF CHEMICAL EDUCATION TYPICAL RESULTS
Groups of students (two to a group) obtained the values shown in Table 2 for the formation quotient of Nar Cil NaCl Wt. Strontium solutim, solutia, strontium citrate after allowing 7 to 9 days for radiosolution. Flask wain. ml. ml. ml. No. mg. chemical equilibrium. The values given in the literature for measurements 1 0 25 75 0 n 25 75 o made under the same conditions are 2.82 to 2.88 (2). Slightly lower results than those in Table 2 with somewhat less scattering will be observed if the samples are allowed to age the full two weeks. Corrections such as those due to complex formation by the buffer anions can be made (2). Additionally, the equations can be modified so as to calculate Kr for positively charged complexes (2, 6) and for a series of consecutive complexes such as MA, MA2, MA3, e t ~(6). . The effectsof temperature and ionic strength on the strontium citrate flabbottomed porcelain dishes. Care should he exercised to insure that no resin particles are transferred. complex have been determined by the ion exchange To ensure a uniform deposit of salts, the solution should method (1). cover the bottom of the dish; additional water may be DISCUSSION added if necessary. If desirable, measurements with the radioisotopes of The aliquots may he dried with an infrared bulb or hot plate or be allowed to evaporate a t room tempera- Ca, Ba, or Ra with various organic acids can he made in ture. Before the counting, a t least 2 weeks should be place of the strontium citrate system. The weights of allowed for reestablishment of the equilibrium between resin and the range in concentration of the acids would have to be modified. Another interesting variation radioactive SrgOand its daughter YS0. The average activity of aliquots (1) and (2) give the would he the calculation of K, in systems of lower pH original [Sr++] which is added to each flask, and in which the citric acid is not completely dissociated the average activity of aliquots (3) and (4) measure the into Cita-. An example of the latter situation involving [Sr++] in solution after equilibrium is reached with calcium complexes with citric acid is available (7). Other topics of interest which relate to the experithe resin. From this KdO can be calculated. ments described here are the effect of variable tracer concentrations on Kd (S),the equilibrium theories of ion exchange (S), and anion exchange studies of halide The activity of the last aliquots measure complex ions of transition elements (10). Some of these topics, such as the limitations of the mass action expres[Sr++ + Sr(Cit).'-"I sion of equation (2), can be profitably adapted for use for varying citrate concentration, giving the necessary in other student experiments in ion exchange. data for the determination of Kr and n by themethods described. The accuracy of the experiment should be determined and expressed in terms of the probable error The encouragement and cooperation of Professor T. in K,. Reasonable estimates of the individual probable F. Young is gratefully acknowledged. errors of the techniques and instruments used may be substituted into the equation (5): LITERATURE CITED Recommended Compositions of the Solutions
mdioaty, radwwtivity
A
.-
A eoncentralions -- - T "I?.)
conrmtratlons
(13)
The main errors listed should include the statistical error of counting, the error in failure to obtain similar counting geometry, the error in not reaching equilibrium between S P and Yo,and volumetric errors. Errors no greater than 5 per cent should be obtained. TABLE 2 Typical Results @mp 1 A
2 3 4 5
log KI 2.94 2.89 2.87 2.87 2.77
.
(1) SCEUBERT, J., E. R. RUSSELL, AND L. S. MYERS,JR., J. Biol. Chem., 185, 387 (1950); SCEUBERT, J., J. Phys. C h . , 56, 113 (1952): (2). SCHWERT. J.. AND A. LINDENBAUM. J. Am. C h a . Soe..74, . . 3529 (1952j. W. C., AND J. EICHHORN, iW., 69, 2330 (1947). (3) BAUMAN, (4) MICHAELJS, L., Biochem. Z., 234, 139 (1931). J. J., "Laboratory Methods of Physical Chemistry," (5) JASPER, Houghtan-Mifflin Co., New York, 1938, p. 8. (6) FRoNAEns, S., Aefa Chem. Scand., 5, 859 (1951). (7) Muus, J., m n H. LEBEL,Danske Vidask. Selak. Math.-fys. Medd., 13, No. 19 (1936). J., in "Ion Exchange," edited by F. C. NACHOD, (8) SCHUBERT, Academic Press, Inc., New York, 1949, pp. 177-8; TOHPKINS, E. R., AND S. W. MAYER,J. Am. C h m . Soc., 60. -., -2R50 -- - 110471. . .. .,. (9) Born, G. E., Ann. Rev. Phys. C h a . , 2 , 309 (1951). J. Am. Chem. Sac., 73, (10) KUUS, K. A., AND G. E. MOORE, 9 (1951); ibid., 73, 13 (1951); ibid., 73, 2900 (1951).
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