KINETICS OF ION EXCHAXGE IN CHELATING RESIN
Nov., 1963
For air Pot = 0.25Pfir2. For blood constituents J C N ~ is not a function of pressure, therefore
_ _ - constant X k , JO,
(11)
JN2
Scholander’s paste was about 10% plasma,* 4 0.10, and the flux measurement was made a t room teimperature, about 25”, and in the absence of carbon dioxide. For these conditions the pH may rise to about 8 and the coefficient of P in eq. 5 is then about -0.25. A plot of the theoretical ICm from eq. 4 and 8 for these conditions is shown by the solid lines in Fig. 2 for DE = 2.0 X lo-’ cm.2/sec., and by the dotted lines for D E = 2.0 X cm.2/seo. The effect of the increase in the coefficient of P in, eq. 5 can be seen by comparing the dashed curves in Fig. 1 with the solid curves in Fig. 2 . The increase in the coefficient does not greatly change the position of the curve on the vertical scale but daes cause the peak t o be sharper and the flat portion to be longer. For coefficients much larger than 0.25 the curve will tend to become flat over most of the pressure rangewith a sharp spike a t about 15 mm. Scholander’s experimental data can be compared to our theoretical curves in Fig. 2 by matching theory and experiment a t 140 mm. oxygen pressure to give the lower dashed curve in Fig. 2. All that can lbe said is that there is qualitative agreement. If we assume that in Scholander’s data the cell membrane does not hinder movement of oxygen, we can match his data at 140 mm. to our theoretical curve for cells without membrane. Scholander’s data are then E=
(8) P. F. Scholander, private communication.
2263
shown as the upper dashed curve in Fig. 2. Again there is qualitative agreement so that it is not possible from this treatment to evaluate quantitatively the effect of cell membrane on oxygen movement througlh the cell. There appears, however, to be somewhat better agreement between the experimental and theoretical curves when the theory includes a cell membrane, giving evidence that there is some effect due to the membrane. Figure 3 shows tlie dimensionless flux parameter J+L/P,DAa as a function of mean oxygen pressure, when the oxygen pressure gradient is 10 mm., for the dispersed system as calculated from eq. 4 and compares this curve with our previous resulh2 The flux parameter calculated here from integration of the MeredithTobias dispersion equation falls as it should between the curves for alternate layers of hemoglobin and plasma in series and in para,llel. One of the parameters of whole blood not yet well1 known is D E , the diffusion coefficieiit of oxyhemoglobin in the hemoglobin solution found in the red blood cell. The comparison of Scholander’s experimental data to theory using both DE = 2.0 X lo-’ and 2.0 X cme2/sec.as shown in Fig. 2 does not permit a choice of DE for whole blood. Additional diffusion data on whole blood, preferably a direct measurement of DE:, are needed. Acknowledgment.-This study was supported by a U. S. Public Health Service Grant, No. H 6796, and the Miller Institute for Basic Research in Science. The authors wish to thank Dr. T. D. 1Iueller for programming eq. 4 and 8 for evaluation on a digital computer.
ICINETICS OF ION EXCHANGE IN THE CHELATING RESIX BIO-CHELEX 100. 1 . THE EXCHAKGE O F THE ALKALINE EARTH IOSS B Y CARLA H E I T X E l + ~ ~ 7 1 R G V I A S SD
GEORGE ?\IARKOVITS
Department of Inorganic and Analytical Chemistry, Hebrew University, Jerusalem, Israel Received February 15, 196s The exchange of the cations Ca, Sr, and M g on the chelating resin Bio-chelex 100 in the hydrogen form wad studied. The slow step which determines the rate of exchange of these ions is diffusion through the resin particle. The diffusion coefficientEi a t two temperatures and the activation energies for the various cations were calculai ed.
Introduction The chelating resin Bio-chelex 100 consists of a crosslinked polystyrene matrix with irninodiacetic acid, R-X(CH2COOE[)2, as the functional group. In some preliminary experiments it was found that in acid solutions the resin can act as an anion exchanger a t tlie nitrogen atom and thus may enable the study of chloro complexes. Sorption of copper chloride was studied a t various concentratioiis of hydrochloric acid. It was shown that CuClb2- was sorbed rapidly a t high concentrations olf acid,l but very slowly in the a,bsence of hydrochloric acid, i.e., in weak acid and neutral solutions. It therefore appears that the sorption of copper proceeds by two different exchange reactions, the one an anion-exchange reaction in concentrated acid solutions and the other a very slow exchange by (1) G. Markovits and C. Hsitner-U’irguin, unpublished results.
chelation. To explain these results, the kinetics of tlie exchange on the hydrogen form of the resin were studied. The cations used in this study were the alkaline earths which are known to give weak complexes with iminodiacetate in solution, and copper, which gives a ver,y strong complex with the same anion. A kinetic study on the similar Dowex A-1 resin was effected b,y Turse and Rieman.2 These authors worked with the sodium form of the resin, concluding that the slow step is the chemical exchange reaction for cations giving a chelate with the resin, while when nonchelatiiig cat,ions such as the alkaline ions were used, the slow step is diffusion through the particle. Schwarz3 studied the kinetics of isotope exchange on the same Dowex A-1, S a form resin for the sodium and zinc ions in (2) R.Turse and W. Rieman, 111, J. Phys. Chem., 66, 1821 (1961). (3) A. Schaarz, Thesis, Israel Institute of Technology, Haifa, 1962.
2264
c.4RLA
HEITNER-WIRGUIN ASD GEORGE RIARKOVITS
buffered solutions. He also concluded that in the case of sodium the slow step is the diffusion within the resin particles, while in the case of zinc the chemical exchange reaction is the rate-determining step. It is interesting to note that Schtvarz3and Turse and Rieman2concluded that the rate-determining step is the chemical reaction for zinc and copper, although they could not obtain a linear plot for log (1 - F ) us. t. Since the water content of the resin in the hydrogen and sodium form is different (resin volume4 of S a + , 1.00; H+, 0.45), the kinetics of the exchange reactions on these two resin forms need not be identical. Experimental The resin used was Chelex 100 prepared by Bio-Rad Laboratories (analytical grade of the resin Dowex A-1) supplied in 50100 mesh particles in the sodium form. The resin was converted t o the hydrogen form by hydrochloric acid and washed with water until the effluents were free of chloride ions. The capacity of the resin was determined by passing a sodium sulfate solution through samples of 0.25-0.50 g. of the resin. The hydrogen ions thus liberated were titrated with NaOH with phenolphthalein as indicator. This method gives one hydrogen ion per iminodiacetic group and the capacity found was 2.27 rt 0.02 meq. H+/g. of an air-dried resin. The latter was analysed for nitrogen, and the following percentages were found: (a) for the hydrogen form 3.51; (b) for the sodium form 4.44. These results agree well with the determined hydrogen capacity of the resin. The capacity of the resin as an anion exchanger was determined by equilibrium experiments with a series of solutions containing various concentrations of sulfuric acid. The sulfate concentration was determined from the equilibrium solutions, gravimetrically as BaS04. The equilibrium capacity found was solution). about 0.4 meq. of S042-/g. of resin (in a 0.05 M Rates of exchange were determined in a modification of the limited bath technique.6 Chloride salt solutions (50 ml., 1 M ) of the cation or 250 ml. (0.01 M ) were shaken in a thermostat until the desired temperature was reached, then 0.5 g. of Chelex 100 in the hydrogen form was added. After a given time the solutions were rapidly filtered with suction through a sintered glass funnel. On these solutions, separated at different intervals of time from various experiments, the necessary analyses were carried out to determine the extent of exchange. During these experiments the solutions were stirred vigorously (not less than 1200 r.p.m.) Analytical Procedures.-The cations calcium, strontium, and magnesium were determined by titrations with MgEDTA using Eriochrome black as indicator .6 Copper was determined complexometrically also, using the P S N i n d i ~ a t o r . ~ Potentiometric titrations were carried out to ascertain that for every cation sorbed, two hydrogen ions were released. For control purposes, the cation determinations were carried out both on the solutions and on the resin (eluting the cation with nitric acid). Particle Size of Resin.-The Chelex 100 was passed through appropriate sieves and two fractions could be separated. The radius of the particles in each fraction was determined by measuring the diameter of 100 beads on a micrometer microscope. These measurements were made on dry particles as well as on particles which had been immersed for 24 hr. in the appropriate electrolyte solution (concentration 1 &I). -4s had been expected from the swelling data given by Dowex4 (H+, 0.45; Ca, 0.53), there were practically no changes in the size of the immersed particles, and the mean diameter measured was within the experimental error (about 4-5%).
Results and Discussion As the limited bath technique was used, the equations developed by Boyd, et a1.,6 and improved by Reichenberg8were used. (4) “Dor\ex Chelating Resin 4-1,” The Dow Chemical Co., 1959. ( 5 ) G E. Boyd, A . W. Adamson, and L. S. Myers, Jr., J. A m . Chem. Soc., 69, 2836 (1947). (6) (a) R. Pribil, “Complexonii in Chimia Analitica,” Edit. Tehn. Bucuresti, 1961, pp, 254-255; (b) W. Biedermann and G. Schwarzenbach, Chamaa (Aarau), 2, 25 (1948).
Vol. 67
The extent of reaction F is expressed as
F =
the amount of exchange at time t the amount of exchange a t infinite time
The rate of exchange can be determined by three different steps. (a) If the rate-determining step is diffusion through the ion-exchange particle, the following equations are valid.
F = 1 - -6 Z
exp(-n2Bt)
n2
79 n=l
where B = n2Dl/r2,r = radius of the spherical particle, and DI = effective diffusion coefficient. A linear plot of Bt us. t is obtained. Values of Bt for each F value are given by Reichenberg.8 (b) If the slow step is the diffusion through the liquid film at the resin particle boundary, then the equation reads log (1 - F )
=
-(R/2.303)L
where R is a constant defined bv the parameters of the film and the diffusion coefficients of -the ions through the liquid. (c) If the rate-determining step is controlled by mass action
S
log (1 - F )
___ ( t )
-2.303
where
8
=
KlmA+
kzmB+
It can be seen from the equations given in b and c that a plot of log (1 - F ) us. t will be a straight line, the slope giving the constant R or S. TaBLE 1 INFLUENCE OF CONCENTRATION O N THE EXTENT OF EXCHASGE OF
MgClz -F t , min.
5 10 15 20 45
1M
0.21 .28 .35 .40 .50
7
0.75 M
0.5 M
0.20 0.225 .29 .345 17’-0.38 .393 . . 42’-0.52
~----BX10~---7 1 J!f’ 0.75 M
8.60 8.00 8.72 8.45
7.72 8.61 8.40 8.30
0.51M
9.2 9.3 9.3 7.9
Although the equations given by Boyd6 were developed for the isotopic diffusion, it was later found by Dickel and Grimmeisssc that the particle diffusion equation is valid for ion exchange a t concentrations higher than 1 N , assuming that the composition of the external solution is constant (not time dependent) .8d In the present case, this condition is obeyed, since the ion uptake by the resin a t equilibria is very small in comparison with the total concentration (about 1 X g.-ion) of divalent ion from a total of 5 X g.-ion. As only a small part of the hydrogen ions on the resin are exchanged, the time dependent composition of the exchanger hardly changes either. (7) H. Fiaschka a n d H. Abdine, Chemiist-Analyst, 46,2 (1956). (8) (a) D. Reichenberg, J . Am. Chem. Soc., 76, 589 (1953); (b) D. E. Conway, J. H. G. Green, a n d D . Reichenberg, Trans. Faraday Soc., 50, 511 (1954); (e) G. Diokel a n d H. Grimmeiss, J . cham. phys., 65, 269 (1958); (d) G. Dickel a n d E. Hiibner, Kolloid-Z., 179, 60 (1961).
KINETICS OF 10sEXCHANGE IX CHELATING RESIN
Nov., 1963
TABLE I1 DIFFUSION COEFFlClESTS ASD EBEILGY O F ACTIVATION CALCULATED FOR Radius of 11
yarticlc, mm.
Mg2+
0 134 ,134 ,171 ,134
Ca2+ Ca2+ Sr2+
B , min, -1 30'
MClg 1 -?f ON
B , inin.-'
D ,cm.z/min.
D ,cm.g/min.
50'
30'
SO0
x x
10-2
3.1 x 5 . 8 x lo-,
1.69 X
lo-,
9.6
8.43 1 49
THE EXCHdXGE O F
2265
>(:
Figure 1 represents the exchange of Ca, Sr, and Alg chlorides at two temperatures as a function of time. From the linearity of Bt 21s. t (Fig. 2) the slow step for these cases should be diffusion through the particle. To check these results, additional experiments were done in which the radius of the particle and the concentration of the solutions were changed From Fig. 2 it can be seen that the rate of exchange for calcium ions depends on the radius of the particle as can be expected for particle diff usion-controlled kinetics. I n Table I are represented the F and B values as a function of time for three different concentrations of IllgC1, solutione. These values are within the limits of experimental error and shorn clearly that the rate of exchange is not dependent upon the concentration in solution. It has already been shown by Conway, et d.,* that even in the case of diffusion kinetics there is a very small increase in the rate of exchange with a decrease in concentration. This is due to the fact that the concentration affects the radius Y of the swollen particles and probably also the diffusion coeHicieiit D1. Although in these experiments the conceiit rations chosen do not vary very much, the same tendency can be observed from the found F values. The calculated values of the diffusion coefficielits for three cations at two temperatures are presented in Table 11. The good accordance of the diffusion coefficients calculated from experiments with two different particle sizes should be noted. From the D values obtained at two temperatures, the energy of activation can be e ~ a l u a t e d . ~
1.15 x 2.72 x 2.77 x 3.17 x l'O
10-7 10-7 10-7 10-7
5.77 10.6 17
CHELEX
100
Ea, kcal./mole
Hydration no.
10-7 10-7
12.8 14.8
12 10
x 10-7
17.2
10
x x
/ -
0.8
4 .r
0.6
b
$
a
rn
sp.
0.4
0.2
20
40
80
GO
100
120
Time, min.
Fig. 1.-Rate of exchange adsorption of 1 M MClg solutions: 1, Sr 50"; 2, Ca 50'; 3, Mg 50"; 4, Ca 30'; 5, Sr 26'; 6, MI: 30'.
10
Time, min. 20
30
40
66
D1 D? ~- _ - - E, A In -
1 A-
R
T
From these results it can be seen thak the diffusion coefficients depend on the radius of the hydrated cation. The values found for the energy of activation for these reactions are unusually high compared with the values 5-10 kcal./mole obtained for the exchange of hydrogen by monovalent ions on strong cation exchangers.8.9 This may be due to the low swelling of the resin. Experiments done a t 0" showed that no exchange occurred under these conditions. A series of kinetic measurements was also carried out for the same exchange reactions a t low conceiitrations of the chloride salts, These reaults are summarized in Table TI1 by evaluation o€ the three rate constants a t different intervals of time. The values obtained for calcium show that it cannot be decided easily which step controls the exchange, since neither (9) T. R. E. Kressnien and J. A. Kitchener, Dzscusszons Fa~adayfloc., 4 , 90 (1949).
26
Sb
Time, min.
Fig. 2.-Plots of Bt us. time of 1 M MCl, solutions using Chelex ( T = 0.134 mm.): 1, Sr 50'; 2, Ca 50'; 3, Mg 50'; 4, Ca 30'; .5, Sr 26'; 6, Ca ( r = 0.171 mm.) 30"; 7, Mg 30'' (upper scale of time).
R. A. BOXHAM ASD T. IIJIMA
2266
TABLE I11 RATECONSTANTS FOR THE THREE TYPESOF KISETICS EVALUATED FROM DILUTED SOI,UTIOKS OF MC1, ( 3 X 10-8 M ) 30°--
----Mg*+
Min. 6 10
16 24 36 83
B X 102 min.-i 2.18 1.99 1.64 1.59 1.51 1.78
50O-7 R(8) X X 102 102 min.-i min.-i 8.60 9.20 9,60 8.00 9.25 5.41 Q,44 6.20 8,15 4.95
-----Mg%+
R(S) X 102
min.-' 3.11 2.40 1.56 1.09 1.20 1.02
Min. 3 5
7 10 15
-Cas*
30°--
B X 102 Min. min.-l 5 1.24 6 1.91 8 2.35 10 3.01 13 3.36 17 3.59 20 4.15
R(S) X 102 mine-' 2.60 2.90 2.86 3.01 2.90 2.76 2.84
B, R, nor X are true constants. In the case of magnesium, the results are much clearer, the B values being more constant than the R or X values. This relatiJ-e constancy is even better shomii at Z O O , and it may be assumed that the diffusion through the particle controls the exchange also in diluted solutions. (Homever, experiments with XgC1, done with two different particle sizes showed no clear proportionality between B values and the square of the radii or between R values and the first power of the particle radii.)
Yol. 67
From these results it can be concluded that in the case of the cations investigated, the rate-determining step is the diffusion through the particle. These results do not agree with those found for calcium and magnesium by Turse and Riemanb2 They found that the rate-controlling step is a second-order chemical reaction. The main difference between the present study and that of Turse and Riemaii2 consists in the fact that the latter worked with the sodium form of the resin, where swelling is more than twice as strong as in the hydrogen form used here. The rate of exchange in their case is therefore much higher. It is possible that under their experimental conditions the diffusion through the swollen particle is much quicker, and therefore the chemical reaction determines the rate of exchange. Experiments similar to those reported here were also carried out with copper solutions. The exchange of copper is much slower than that of the alkaline earths, which might be explained by the different extent of ionic or covalent bond in the different complexes. The results for the kinetics of copper exchange as well as a complete discussion ill be published separately.
THE THEORY OF ELECTRON SCATTERING FROM MOLECULES. 11. MOLECULAR HYDROGEN1* B Y R. A. BONHBM
AND
T. I I J I M S l b
Department of Chemistry, Indiana University, Bloomington, Indiana Received March 6 , 1963 Expressions for the differential cross sections for the total electron scattering (including all inelastic processes) and the elastic electron scattering from molecular hydrogen have been derived. The total molecular intensity has been computed with both the T a n g and Weinbaum molecular wave functions and the effect of the chemical bond on these calculations is discussed. The binding effects should contribute only small corrections to the usual interpretation of diffraction reeults for the case of H2unless extremely small angle scattering data were available.
The elastic differential scattering cross section for molecular hydrogen has been calculated by Massey, 2a Nassey and Nohr, 2b Roscoe, and McWeeiiy4 using the first Born approximation and neglecting polarization and exchange effects. Unfortunately, the results presented in the first paper are too general to be readily applicable to the discussion at hand, while the second pslper contains a number of small errors and is not sufficiently general to allow easy extension to other cases. The paper by McWeeiiy4 is coiiceriied only with the X-ray form factor of ai1 H atom in an Hz molecule in a fixed orientation in space. Also, Nassey and ;\lohr'szband Roscoe's3 evaluations of the main term containing the effect of chemical binding were not exact. We have calculated the total intensity of electrons scattered by molecules using the same approximations discussed previously and eniploying both the Wang wave function6 and the Weinbaum wave function.6 (1) (a) Contribution Number 1150 from t h e Chemical Laboratories of Indiana University; (b) the authors wish t o thank the United States Air Force Office of Scientific Research and the United States Atomic Energy Commission for their financial support. (2) (a) H. S. W. Massey, Proc. R o y . SOC.(London), 8129, 616 (1930); (b) H. S.If'. hIassey and C. B. 0. Mohr, zbzd., A136,258 (1932). (3) R. Roscoe, Phzl. Mag.,26, 32 (1938). (4) R. RlcWeeny, Acta C r y s t . , 6, 463 (1952). (5) S.C. Wang, P h y s . Rev., 31,579 (1928). ( 6 ) S. TVeinbaum, J . Chem. P h y s . , 1,593 (1933).
We have also succeeded in evaluating all but one of the necessary integrals in sirn.ple closed forins and it has been evaluated numerically. 1. General Theory The general theory of electron scattering from molecules has already been discussed7,*and so will only be recapitulated here. The total intensity of electrons scattered from a polyatoniic molecule can be expressed as
I
=
(4/a2r284)C gTJv, T
E j.Vv < + v r J 1'
N
SdQu
N
EC
n = l m=l
i=l
and
(7) T. Iijima, R. A. Bonham, and T. Ando, J . P h y s . Chem., 67, 1472 (1963). (8) L. 8 . Bartell, private communication.
