Chromatographic Separation by Ion Exchange R. F. BADDOUR AND R. D. HAWTHORN Massachusetts Znstitute of Technology, Cambridge, Mass.
I
F A solution containing a mixture of ions (a band solution) is made to flow into the top of an ion exchange column, the ions in solution will exchange with the ions in the column. If another solution is then passed into the column, the band ions will exchange with the ions in this eluting solution and thus be washed out of the column. The resin selectivity varies for the different ions, so that the ions are washed out in an order which is the reverse of the order of their selectivities. This provides a basis for ionic separations, and the technique is called ion exchange chromatography. The possibility of effecting the separation of ions chromatographically has been amply demonstrated. Quantitative predictions of the degree of separation have been presented for some very special cases (4, 9,l a ) , such as solutions dilute with respect to the ions t o be separated, no interference between band ions, and linear and/or irreversible exchange kinetics. This work is concerned with separations for which none of these simplifications are valid. Experimental measurements were made of the separation of potassium and hydrogen ions using a solution of sodium ions as eluent and packed beds of Dowex 50 as the exchanger. Variables were column height, equivalents of ions in the band, and proportions of ions in the band. Rate of solution flow, particle size of resin, and total concentration of ions were held constant. Results of work on elution of single bands ( 1 ) suggest that the eluent most favorable for separation of two ions would be one for which the resin's selectivity was intermediate between those for the two ions being separated. For this case, overlap occurs between the sharp edges of the two bands, which should result in a minimum of cross contamination. On this basis, sodium was selected as an eluent for mixtures of potassium and hydrogen. . Analytical techniques were readily available for solutions containing sodium, potassium, and hydrogen ions. I n addition, exchange rate and equilibrium data had been obtained previously for the sodium-hydrogen and sodium-potassium systems (6, IO). These data were used to make estimates of separation based on the use of equations developed for elution of single bands. METHOD OF CALCULATION
where subscripts R and S refer t o concentrations on the resin and in solution, respectively, of A, B, and D ions. Equations 1 and 2, together with conservation equations for ions B + and D+, which are identical in form with that used in derivation of the single-band elution equations ( 6 ) ,and appropriate boundary conditions for the concentrations of ions B + and D a t the top of the column and a t the head of the advancing band, form a complete mathematical description of the chromatographic exchange process ( 7 ) . Analytical solutions to this set would be of substantial value if rate and equilibrium constants for the ion pairs in the absence of the third ion could be used. Solutions to these equations have not been obtained, but a method of numerical integration has been outlined ( 7 ) . It was instructive to determine under what conditions these equations reduce to those for single bands. The solution in terms of dimensionless groups to the equation for a single band being eluted through an ion exchange column is ( I , 6, 8),for r # 1: +
(3)
(4)
After a study of the differential equations described above, the solution for single bands (Equation 3), and the experimental data for mixed-band elution, Equation 3 was used to calculate results for the mixed bands using the following methods. K-Band. The resin selectivity for potassium ion was greater than that of either hydrogen, the other band ion, or of sodium, the eluent. In using th; single-band equation, the inlet concentration for potassium, C K+, was taken to be its actual concentration in the band solution. This is equivalent to neglecting the effect of hydrogen on the potassium band. As this corresponds to the case of using eluting and band solutions with different concentrations, u and y in Equation 3 have the definitions (3, 6):
A major purpose of this work was t o develop a technique for estimating the chromatographic separation of ions using rate and equilibrium data obtained from two-ion systems. A series of differential equations was developed using techniques and nomenclature similar to that of Goldstein (6). For a bed initially saturated with ions A+, through which is passed a solution of ions B + and D+, followed by an eluting solution of ions A+, the rate expressions should be:
2517
u = c/co, y = kcoQ/V for y u = c / c & y = kcAQ/V
Y
(6)
(7)
H-Band. The resin selectivity for hydrogen ion was less than that of either potassium or sodium. I n using the single-band equation, the inlet concentration for hydrogen, c;+, was taken t o be the total concentration in the band solution, c l , but for the total milliequivalents of hydrogen, the true experimental value was used. This is equivalent to stating that the interaction effect of potassium on the hydrogen band is to concentrate the hydrogen to full solution strength a t the top of the column. When a slug of potassium-hydrogen solution ffows into the top of the column, the potassium exchanges almost exclusively for the sodium, and the resulting sodium-hydrogen mixture flows down the column where hydrogen is deposited. When potassium from additional band
INDUSTRIAL AND ENGINEERING CHEMISTRY
2518
solution reaches this point, the potassium will displace hydrogen, increasing the hydrogen ion concentration to above its initial value. This concentration effect is enhanced by the fact that potassium tends to concentrate a t the top of the column and the hydrogen flows through this portion with little dispersion. The net effect of these factors is apparently such that this calculation technique is reasonable. 0.15
0 10 U
D 05
0
0 4
0 1
u 0 2
0 1
0 40
SO
60
70
80
90
100
I10
120
130
Y
Figure 1.
Experimental effects of band interference Comparison with calculated curves
In the calculation technique the single-band equations are used, making a separate assumption for each of the two ions being separated, concerning the manner in which the other ion interferes with it. For the potassium ion, the assumption is made that the effect of interference of the hydrogen ion on it is negligible. For the hydrogen ion, it is assumed that the potassium ion acts to concentrate it to the strength of the total band ion solution a t the top of the column. EXPERIMENTAL PROCEDURE
The Dowex 50 cation resin and the column used are identical with those which have been described (6). The average diameter of the resin beads in the sodium form and in the presence of distilled water was 0.0446 cm. The column was 1.5 om. in diameter and either 27 or 54 cm. high. The eluting solution was O . 1 N sodium chloride and the band solutions were mixed solutions of potassium chloride and hydrochloric acid, such that the normality with respect to chloride ion was 0.1. To make a run, the velocity was first adjusted to an effluent flow rate of 0.450 cc. per second with the eluting solution flowing -through the column. The two-way stopcock a t the top of the mdumn was switched to admit band solution a t the same flow rate until the desired volume had been pafised through. The stopcock was switched back t o admit eluting solution. Samples were taken according to a predetermiqed schedule. On the average 10-cc. or 20-cc. samples were taken after each 100 cc. of eluent. A 10-cc. portion of the sample was titrated to determine hydrogen ion concentration, and, when appropriate, a separate portion was diluted and potassium was determined by the lithium inkrnal standard method using a Baird Associates Model DB-2 flame photometer. The total milliequivalents of resin in the column and the voids volume were determined experimentally. Rate and ?equilibriumconstants were determined experimen-
Vol. 47, No. 12
tally for the potassium-hydrogen system, using a previously described procedure (6). The values of rate and equilibrium constants used in calculating elutriation curves are listed in Table I. The rate constants are for a particle Reynolds number of 1.26. CALCULATED AND EXPERIMENTAL RESULTS
Comparisons of the elutriation curves predicted by the methods described above with the experimental data are shown in Figures 1, 2, and 3. In this series of experiments column height was varied twofold, band width was varied 6.5-fold, and the ratio of potassium to hydrogen ion in the band solution was varied ninefold. Band Interference. Figure 1, A , compares the predicted curve with the experimental data for the case in which 10 meq. of potassium were passed through the column a t two different inlet concentrations of potassium. If there is negligible interference of hydrogen with the potassium band, then plots of u versus y, as defined in Equation 7 , should coincide tor the two runs. As shown in the figure, there is good agreement between the two sets of experimental data and between these data and the calculated curve. This result and those for the other runs shown in Figures 2 and 3 indicate that the assumption of negligible effect of hydrogen on the potassium band is valid over the range investigated. When similar runs are compared for bands containing 20 meq of hydrogen ion, the results shown in Figure 1, R, were obtained. The agreement between runs is considerably poorer than was the case for potassium. Agreement between the calculated curve and data points is also poor for the run with the higher proportion of potassium in the band solution. Fairly good agreement is obtained between the calculated curve and the points for run 2, however, in which the band contained initially 50% hydrogen ion, compared with 25% hydrogen for run 5. Good agreement is obtained for the other runs shown in Figures 2 and 3, in which the initial concentration of hydrogen ion in the band is 50 or 75% of the total. Thus, the assumption of a concentration effect of potassium on the hydrogen ion in the band seems to give good calculated results unless the ratio of hydrogen ion to potassium falls too low, in this case 1 to 3. The lack of agreement is such that the calculated curve indicates less cross contamination than was actually measured. Table I. Summary of Rate and Equilibrium Constants for 0.1N Chloride Solutions s5+,% k Na+ - H + (5) K + - Nrt+ ( 1 0 , 1 1 ) K + - H+ a K + = 50%.
0.33 0.22 0.40
50
1 50 1 50 2 ooa
75 K
85
1 40 1.65
1:io
..
..
If the simplification ot no interference of either band ion on the other were made, and Equations 6 and 7 used to define the dimensionless variables for the hydrogen band as well as for the potassium ion band, the predicted hydrogen band would overlap the potassium ion band to a greater extent and more cross contamination would be predicted. In all the cases studied, this simplification predicts more cross contamination than was observed experimentally and gives a much poorer estimate of the separation than the method presented here. Effect of Band Width. I n Figure 2, the data for runs 1, 3, 2, and 4 in the long column and for runs 6 and 7 in the short column show the effect of decreasing band width, holding other variables constant. For different band widths in either column, no change in the applicability or precision of the proposed prediction method is apparent. The agreement between experimental data and calculated curves is good for the entire range of band widths studied.
2519
INDUSTRIAL AND ENGINEERING CHEMISTRY
December 1955 O b
0 4
C c;
0 4
02 0 5
0 O d
01
0 9
03
C c;
C -
c,:
02
0 2
0 1
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0
0
0.3
0. e
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C:,
0.I
o U C L L I 4 - n J
0 IO00
/SO0
2000
2SOO
3000
Q
3500
4000
4500
5000
500
1000
1500
1 2000I
iw 2500
j 3000
I
I I
3500
I
4000
'
I
4500
Q,(cc.)
,fee.)
Figure 2.
0
Effect of changing band width and column height
Both series of runs indicate that the degree of separation, a8 measured by the lack of cross contamination, increases rapidly a8 band width is decreased. However, the improved separation of the band ions is in each case accompanied by a decreased maximum Concentration of each of the band ions and a greater fractional spread in each of the bands in the effluent. Thus, while the use of smaller bands increased the separation of band ions from each other, the resulting band solutions were more diluted by or contaminated with eluting ion. Effect of Column Height. The results for runs 6 and 2 and for runs 7 and 4 show the effect of doubling column height. The effects of increased column height are similar to those observed for decreased band width: (1) improved separation; (2) decreased maximum concentration of band ion and increased fractional spread of each band in the effluent; and (3) no change in the applicability of the method of calculation used. A comparison of run 3, in which 80 meq. of an equimolar band solution were passed through a column of 207 meq. of resin (a column utilization of 39%)) and run 6, in which 40 meq. of the same band solution were passed through a column of 104 meq. of resin, shows that simultaneous twofold increases of column height and band width result in bands less contaminated both with each other and with eluent. Runs 7 and 2 show the same result for 19% column utilization. The conclusion may be drawn from Figure 2 that the conditions favorable to good separation, accompanied by low band spread and dilution with eluting ion, would be use of a long column and high column utilization-that is, large bands. Effect of Band Proportions. Runs 5 and 8, shown in Figure 3, were made with band solutions initially containing potassiumhydrogen ion ratios of 1 to 3 and 3 to 1, respectively. The agreement between calculated curves and experimental data for the hydrogen band in run 5 and potassium band in run 8 ha8 been
discusbed. The agreement between data and calculations for the other two bands shown is good. Apparently, the assumption of the total concentration effect of potassium on the hydrogen band becomes better as the initial concentration of hydrogen approaches the total concentration more closely. No general conclusion regarding the effect of band proportions on degree of separation is obtained by examination of the plots. Effect of Rate and Equilibrium Constants. Because of uncertainties of the order of 10% in the values of rate and equilibrium constants, calculations were made to determine what effect a change of this magnitude would have on the calculated curves. A 10% change in rate constant had a small effect, in the range investigated, on either the shape or location of the band. On the basis of previous work with single bands, it would be predicted that sharper bands and therefore better separations would be obtained a t increased values of k / V , other things being the same. A similar change in the value of the equilibrium constant had a strong effect on both the shape and location of the calculated curves. Uncertainty about a proper value of K to use in calculations exists because K varies with proportions of the two ions present. The method finally adopted was to select a value of K corresponding to a concentration of band ion equal to about the peak concentration in the effluent band. This method of selecting an average K gave good results. In Figure 4, calculated curves are shown for two different values of KK+-NA+) one for a value corresponding to 50% potassium ion, the other to 15% (IO). The difference in results is great enough so that the importance of selecting a good average value of K is obvious. Values of K for the sodium-hydrogen system were estimated from a measured value for this resin a t 50% sodium ( 5 ) , and measured values for a similar resin over a range of proportiona, ( 2 ) ; the values used are listed in Table I.
INDUSTRIAL AND ENGINEERING CHEMISTRY
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Vol. 47, No. 12
eluent is used for which the resin selectivity is intermediate between those of the two ions being separated. For this case, a method of calculation using equations developed for the elution of single bands of ions gives good results. NOMENCLATURE CH
+
crP+ Cd 01
G
concentration of band ion H + in effluent solution a t any instant, meq. per cc. = concentration of H + in band solution poured into the column, nieq. per cc. = concentration of eluting solution poured into the column, meq. per cc. = mathematical function (see Equations 4 and 5) =
J(s,y) = 1 -
0
e-u
Jo
e - 2 10 ( 2 d ~ ) c i qfunction occurring in
equation of single-band elutriation curve
0 6
~ B A
KBA
0 4
C -
Q
c;
OZ
QB
rE
0 0
500
IO00
1500
ZOO0
2500
3000
9500
4000
4500
+
r
Figure 3.
U
Effect of changing proportions of band ions
V
-X Applicability of Calculation Method. The results of the specific methods described above for applying the single-band equations t o the prediction of chromatographic separation have been compared here with experimental data for only one separation problem. In this case, the equilibrium constant for exchange of the ions being separated was 2.0, the eluting ion used was one for which the resin had selectivity intermediate between those for
X
Y YH
Y
A + ions on the resin, cc./(sec.)(meq.) equilibrium constant for exchange of B + ions in solution with A + ions on the resin, dimensionless = volume of liquid eluted from column minus voids volume of column, cc. = volume of band solution run into column, cc. =
=
~ / K E-+N A +
1/K time, seconds dimensionless group, e/%’ volumetric flow rate, cc. of liquid leaving the column per second = total resin in column, meq. = dimensionless group, k & / V = dimensionless group, product of k / V and total meq. of ions eluted from column = dimensionless grou , product of lc/V and total meq. of band ion, H+, airnitted to column = dimensionless group. Product of k / ’ and total meq. of band ion admitted to column = = = =
t QJcc 1
For dis-
cussion of evaluation, see ( 1, 6) = rate constant for exchange of B + ions in solution with
’
L I T E R A T U R E CITED
(1) Baddour, R. F., Goldstein, D. J., and Epstein, P., ISD. ENG. CHEM.,46, 2192-5 (1954). ( 2 ) Bonner, 0. D., Argersinger, 1%’. J., and Davidson, A. W., J . Am. Chem. Soc., 74, 1044-7 (1952). (3) Epstein, P., and Goldstein, D. J., M.S. thesis in chemical engineering, Massachusetts Institute of Technology, 1953. (4) Fujita, H., J . Phys. Chenz., 56, 949-53 (1952). (5) Gilliland, E. R., and Baddour, R. F., IWD. ENG.CHEM.,45, 330
15
a
10
0 05
0 30
40
50
60
80
70
90
100
110
120
Y
Figure 4.
Effect of equilibrium constant on predicted curve
the two band ions, and conditions were such that a rather complete separation was obtained. The agreement between predicted and experimental results was generally good. When curves calculated in a similar manner were compared with a single set of data taken by Tjiook (11) on the separation of sodium and hydrogen ion, using potassium as the eluting ion, agreement was poor with respect to both shapes and locations of the two bands. The calculation did predict very poor separation, which was obtained experimentally. On this basis, it is felt that the methods presented here may not be generally applicable to cases in which”the resin is either more or less selective for the eluting ion than’ for either of the band ions. With more experimental data, methods of using the single-band equations to predict satisfactorily separation in these cases might be developed. CONCLUSIONS
It has been determined experimentally that good separation of two ions is obtained using ion exchange chromatography if an
(1953). (6) Goldstein, S.,Proc. Roy. Soc., A219, 151-71 (1953). (7) Hawthorn, It. D., M.S. thesis in chemical engineering, LIassachusetts Institute of Technology, 1954. (8) Hiester, N. K., and Vermeulen, T., J . Chem. Phys., 16, 1087 (1948). (9) Player, S. W., and Tompkins, E. R., J . Am. Chem. Soc., 64, 2866-74 (1947). (10) Sujata, A. D., Ph.D. thesis in chemical engineering, University of Michigan, 1952. (11) Tjiook, T. K., unpublished work done under the Foreign Students’ Summer Project. Massachusetts Institute of Technology -~ (June to September 1953). (12) Vermeulen, T., and Hiester, K . K., IND.ENG.CHEM.,44, 636 (1952). RECEIVED for review March 9, 1955.
ACCEPTED July 27, 1955.
Correction In the article entitled, “Rate of Mass Transfer from Gas Stream to Porous Solid in Fluidized Beds” [C. T. Hsu and M. C. Molstad, IND.ENG.CHEM.,47, 1550 (1955)], Equation 11 on page 1557 should be
