(aldehydes and aldehydic esters) and periodate-permanganate cleavage (esters and diesters) of a catalytically reduced sample of methyl linolenate. Data from five similar comparisons have been treated statistically, and no significant difference was detectable at the 95% level between the results obtained from periodate-permanganate cleavage and those from either of the ozonide procedures. Percentage recovery of aldehydes with the corresponding aldehydic esters from various mixed monoene samples was individually computed for both direct injection and MRA ozonide procedures. The standard deviation for direct ozonide injection was 1.67y0 with 95% confi. MRA, dence limits of ~ k 2 . 0 7 7 ~ For
the standard deviation was 1.82% with 95% confidence limits of =k2.26%. Fklative variation for individual components derived from the MRA procedure was 11.0% for aldehydes and 17% for aldehydic esters. ACKNOWLEDGMENT
Mass spectrometric identifications of ozonide fragments were supplied by E. Selke. LITERATURE CITED
( 1 ) Blumer, M., Thomas, D. W., Science 147 (3662), 1148 (1965). ( 2 ) Bonner, W. A., J. Chem. Educ. 30, 452 (1953).
(3) Davison, V. L., Dutton, H. J. Abstracts of Papers, 87a, 39th Fall keet-
ing, Am. Oil Chemists' SOC., Cincinnati, Ohio, October 1965. (4) Kitahara, K., Yakugahu Zasshi 80,
1628 (1960). (5) Nickell, E. C., Privett, 0. S., Lipids 1(3), 166 (1966). ( 6 ) Fbhrschneider, L., 2. Anal. C h a . 170, 256 (1959). RECEIVEDfor review May 11, 1966. Accepted July 5, 1966. Presented at 39th Fall Meeting of the American Oil
Chemists' Society, Cincinnati, Ohio, October 1965. The Northern Laboratory is headquarters of the Northern Utilization Research and Development Division, Agricultural Research Service, U. S. Department of Agriculture. The mention of firm names or trade products does not imply that they are recommended by the Department of Agriculture over other firms or similar products not mentioned.
Exchange Equilibrium through Ion Exchange Membranes An a 1ytica I A ppI icatio ns W. J. BLAEDEL and T. J. HAUPERT Chemistry Department, University o f Wisconsin, Madison, Wis.
b The high selectivity of modern ion exchange membranes is illustrated, and potential analytical applications to extraction and concentration of ionic substances are outlined. The distribution of cations at cation exchange equilibrium is described theoretically and verified experimentally. Extraction of cations through a cation membrane is favored by high ionic strength and by anionic complexers in the extractant solution. One-stage batch extractions can be made to exhibit losses below 1%. With simple apparatus, 1 00-fold enrichment in concentration is achievable experimentally. Limitations are stated.
S
THE INTRODUCTION of ion exchange membranes, their properties have been studied extensively, both theoretically and experimentally. Work through 1961 is summarized by Helfferich (4). More recently a review has been written by Krishnaswamy (6) which covers major advances in the period 1960-63. Except for electrodialysis, there have not been many applications of ion exchange membranes to practical analytical problems. They have been used as bridging or isolation media in electrochemical cells (a), in coulometric titrations (6),as supports in electrochromatography (S), and for the pctentiometric determination of ion activities based on the measurement of membrane potentials ( 7 ) .
53706
1
L
in
os
01
0 I
l l l l l t l
L
I
I t ,
IO
100 TIME, MINUTES Figure 1. Diffusion of sodium and iodide ions through a cation exchange membrane (AMF C103) Different rets of points denote replicate experiments
INCE
Currently available membranes are homogeneous, chemically inert, highly permselective, and have good mechanical properties. Water leakage is negligible, even at heads of several feet. These highly improved characteristics of modern ion exchange membranes will permit a variety of additional analytical uses. I n this paper, experimental data are given to illustrate and demonstrate their potentialities in the separation, extraction, and concentration of ionic species. THEORY
Qualitative. The outstanding property of ion exchange membranes is their permselectivity-a term that denotes the difference in diffusibility
between ions of opposite charge. Through the mechanism of the Donnan equilibrium, ions of the same charge type as the fixed ionic groups (Le., co-ions or nonexchangeable ions) are excluded from the membrane phase, and they exist in relatively low concentration compared to the exchangeable counterions which have a charge opposite to the charge on the fixed groups. Because of their low concentration in the membrane phase, co-ions diffuse much more slowly than counterions through the membrane phase. Ample data exist in the literature that illustrate the permselectivity of membranes, but for the purposes of this paper, an idea of the high permselectivity is given in Figure 1 which shows the rates of transport of radioNa*' and r a d i 0 - 1 ~ ~through ~ a cation exchange membrane (AMF C-103) from a solution containing 0.2M NaI on one side of the membrane into a 0.05M NaI solution on the other side. It is apparent that Na ion exchange equilibrium is reached within 1 to 2 hours, whereas I ion exchange is still far from equilibrium even after 24 hours. During the first hour or two, Na ion is transported several hundred times faster than I ion. Because electroneutrality must be maintained, the rate at which an electrolyte may diffuse through a membrane is limited by the low rate of diffusion of the co-ion. Electrolytes may therefore exist at different concentrations on opposite sides of a membrane for days VOL 38, NO. 10, SEPTEMBER 1966
e
1305
without chemical equilibrium being reached , while a counterion equilibrium may be reached within a few hours. Figure 2 illustrates these two equilibrium states. It is the large disparity in the rates of attainment of these two equilib rium states that permits use of ion exchange membranes for analytical purposes. (Note that at cation exchange equilibrium in Figure 2, 99% of the potassium hasmoved from compartment 2 to compartment l!) This effect has been known for a long time and has recently been described quantitatively by Sutcliffe (8) to help explain the migration of ions from low to high concentrations in plants. The quantitative treatment based on the Donnan equilibrium is well known (f), and the results are the same as those of the following section. Quantitative. The heterogeneous equilibrium that represents the exchange between a cation B z B in the membrane phase with a cation A z A in the aqueous phase is: zBA'A
+
Z
ZAZB
B
~
+
A ZAB'B
(1)
A and B represent the two cations present in each solution, the z's represent the valences of the ions denoted by the subscripts, and the bars represent species in the membrane phase. The thermodynamic equilibrium constant for the above exchange reaction has been defined by HellTerich (4):
The a's represent activities of the species denoted by the subscripts. If a system consists of two solutions (1 and 2) of different compositions sep arated by a cation exchange membrane, then at cation exchange equilibrium, the equilibrium condition exists at both surfaces, and dA,lZB ' aB.lzA
. dB.1'~
aA,:B
-
6A,ZzB ' aA.z'B
as.:'
. dB.z'~
(3)
If there is cation exchange equilibrium within the system, then there can be no net cation migration and no cation concentration gradients within the membrane, and the activities of species A and B must be uniform throughout the membrane phase. dA.l
=
dA.2
(4)
dB.1
= alia
(5)
Combination of Equations 3-5 gives an expression relating the compositions of the two solution phases that are in cation exchange equilibrium on the two sides of the membrane.
1306
0
ANALYTICAL CHEMISTRY
Figure 2. Ion exchange equilibrium and chemical equilibrium Cancentratiam computed for equal volumes of salutiw in compartments 1 and 2. Dotted line represents a cation exchange membrane
The activities in Equation 6 can be approximated by molarities (C's) and single ionic activity coefficients (y's).
Examination of the Debye-Huckel law indicates that the activity coefficient ratio in Equation 7 tends toward unity, for ions of comparable size and charge or for solutions of comparable ionic strengths. If the activity coefficient ratio is approximated as unity,
The validity of Equation 8 is demonstrated in the experimental section of this paper. Equations 7 and 8 represent the exchange equilibrium concentrations of any two cationic species regardless of their relative initial concentrations in the two solutions. However, if the concentration of one species ( B ) is much less than that of the other ( A ) , then at cation exchange equilibrium there will be no significant redistribution of A from the initial distribution, and the distribution of B will be determined by the initial distribution of A in the system. I n other words, a species present at trace concentration will distribute itself between two solutions separated by an ion exchange membrane in a ratio set by the initial concentration ratio of the predominant electrolyte. Potential Applications in Separation and Concentration. The analytical potentialities inherent in Equation 8 are impressive. Thus, if a sample solution 1 containing cation B is contacted with an extractant solution 2 containing cation A at a much higher concentration, then B should migrate almost quantitatively into the extractant solution, but any anionic impurities in the sample solution should not migrate. I n principle] concentration may also be achieved. Thus, if a large volume of dilute sample solution 1 containing
cation B is contacted with a small volume of an extractant solution 2 containing A at a much higher concentration, there should be a many-fold concentration of B into the extractant. Through the use of complexing agents, extraction and concentration of a particular ion may be made even more efficient. Thus, if cation B in a sample solution is contacted through a cation exchange membrane with an extractant containing an anionic complexer that binds B into an anionic complex, then any B migrating into the extractant should be bound there as the anionic complex. The use of complexers to promote extraction might be particularly advantageous whenever high electrolyte concentrations in the extract are undesirable. It should be noted that the use of ion exchange membranes appears particularly suited for concentration and extraction during sample preparation, particularly for trace analysis. In contrast to other techniques such as liquid extraction, the cation exchange equilibrium distribution ratio set by Equation 8 is dependent only on the charge of the ions, and is independent of the properties of the membrane. Thus, for all ions of a given charge, the extent of extraction is the same, and the extract has the same relative composition as the original sample solution. EXPERIMENTAL
Verification of Equation 8 at Tracer Levels. Four systems were investigated that contained one electrolyte in the range 0.001-0.05M, while the other electrolyte, whose cation exchange equilibrium distribution was measured, was at radio-trace levels. Isotopic distributions were measured for C s l n in CsCl solutions and Zn" in ZnC& solutions. Distributions were a h found for C s l " in NaCl solutions and Zn65 in NaCl solutions. For these measurements, a cation exchange membrane (AMF C-103, American Machine and Foundry, Springdale, Conn.) of 2.86 sq. cm. cross-sectional area was sandwiched between two mirror-image 5.46m1. cavities milled in Plexiglas blocks (Rohm & Haas, Philadelphia, Pa.). Each cavity contained a small magnetic stirring bar and ports to permit introduction and sampling of the solution. In each case, the membrane was equilibrated with a 1M solution of the principal electrolyte, flushed with water, and then each chamber was rinsed several times with a t-acer-free solution of the principal electrolyte at the concentration which was to be used in the experiment. The chambers were then filled with solutions of the principal electrolyte and the respective tracer ion was added to the more concentrated solution. After cation exchange equilibrium had been attained, 100 pl. of each solution were withdrawn and counted using a scintillation detector
A
WI
I p'
I/
IO
found to be 1.54, while the square root of the ratio of the zinc tracer activities '~) (assumed equal to ( C Z , J C Z ~ , ~ ) ~was found to be 1.51, in excellent agreement with Equation 8. Experimental Achievement of Concentration. T o demonstrate the use of ion exchange membranes as concentrating devices, a cylindrical cell was designed to fit into the well of the scintillation counter. A rod of Teflon (l/z-inch diameter, 31/r-inches long) was cut longitudinally in half. A hemicylindrical cavity was milled into each half to give a trough-like inch shell-one 3 inches long and in depth, and the other 3 inches long and '/I6 inch in depth. The shells of Teflon were then press-fitted into similar but larger, thicker, and more rigid shells made from Plexiglas (Rohm & Haas, Philadelphia, Pa.). Two platinum tubes (0.OWinch 0.d.) were press-fitted through slightly undersized holes bored into the end of each cavity, to serve as entrance and exit ports for the passage of solutions through the cavity. The cell was assembled with a cation exchange membrane (AMF C103) sandwiched between the two cavities. Bands of 1/4-inch 0.d. gum rubber tubing were used to hold the halves of the cell together. Silastic sealant (Dow-Corning Corp., Midland, Mich.) applied to the edges of the membrane and permitted to harden before assembly served as a gasket. To demonstrate the degree of concentration obtainable by the transport mechanism of Equation 8, the assembled cell, with inlet and outlet tubes attached, was inserted into the well of the scintillation counter. The smal-
1
-
.=&NaI, NaZ4-.05 M I
I
NaX I
100
TIME, MINUTES
lo00
Figure 3. Time required for achievement of cation exchange equilibrium (AMF C103 Membrane) Dashed horizontal liner denote cation exchange equilibrium
(Model DS5, Nuclear Chicago Corp., Des Plaines, Ill.) in conjunction with a recording spectrometer (Model 1820A), a radiation analyzer (Model 1810), and a count rate meter (Model 162013). Results are shown in Table I, which contains all data accumulated without rejection of extrema1 values. For the two cases of selfdiffusion (CS~" in CsCl and Zn65 in ZnClz) the activity coefficient ratio in Equation 7 is unity, and the theoretical and experimental tracer distributions should be identical. The selfdiffusion rases therefore permit estimates of the accuracy and precision of the measurements. Thus, the median differences are -1.2% (for the Cs system) and 1.O% (for the Zn system), indicating no systematic error in measurement of the tracer distributions. On the other hand, the relative root mean square differences between the experimental and theoretical distributions are 2.8% (for the Cs system) and 3.9y0 (for the Zn system), which are estimates of the precision of the measurements. For the diffusion of Cs'" in NaCl and of Zn65 in NaC1, the median differences (-0.5 and +1.7%, respectively) between the theoretical and experimental distributions, as well as the root mean square differences (1.8 and 2.7'%, respectively), are within experimental error, which supports the validity of Equation 8 at the tracer level. It is unexpected that the activity coefficient ratios do not differ from unity by more than a few per cent for any of the systems in Table I. Systems with electrolyte concentrations much over a few tenths molar were not investigated because the Donnan exclusion breaks down, giving deviations from Equations 7 and 8. Fragmentary work was done on the time required to reach cation exchange equilibrium for experiments like those of Table I . The results shown in Figure 3 indicate that achievement of cation exchange equilibrium is about 10-fold slower for Zn transport than for Cs transport. But it is interesting to note that approximately the same length of time (about 2 hours) was required for all of the monovalent systems
+
to reach cation exchange equilibrium despite differences in the amount of material that had to be transported. A more complete study of the rate of transport of ions through ion exchange membranes is under way. Verification of Equation 8 for Macroconcentrations. A solution contain-
ing 0.05M NaCl and 0.01M ZnCl, was equilibrated with a solution containing 0.05M NaCl and 0.05M ZnClr plus tracer NaZ4and Zn65, using the same cell and membrane described previously. After 24 hours, 100 pl. of each solution were withdrawn and counted at the photopeaks of Na24 and Zn65. The ratio of the sodium tracer activities in the two compartr .,~) ments (assumed equal to C N ~ , ~ / C Nwas ~~~
Table 1.
~
Distribution of Tracer Ions at Ion Exchange Equilibrium
Equilibrium distributions Bulk electrolyte AC1z.a CsCl (2.4
CA,*
0.05
0.05
Theor. 1
= 1)
NaCl (2.4
Molarities CA.1
(CA.I/ c,,~).B'z.*
1)
0.20 0.05 0.50 0.05 0.05
0.05 0.01 0.05 100.05
4 5 10 50 1
0.20
0.05
4
0.05 0.50 0.05 0.05
0.01 0.05 lo-' 0.05
5 10 50 1
0.20
0.05
4
0.05 0.50
0.01 0.05
5 10
0.05 0.05 0.20 0.05
lo-' 0.05
50
0.50
0.05
0.05 0.01
1 16
25 100
Difference
%
C B . ~ / C B . P (exp. -
Exptl.
theor.)
1.01 1.04 0.958 3.94 4.94 10.2 48.2 0.998 1.03 0.994 4.10 3.94 5.02 9.73 49.3 1.01 1.09 1.06 4.04 3.92 4.06 4.90 10.0
+.lo
-2.0 +1.5 -2.0 0.0
10.5
+5.0
49.3 1.01 16.7 25.6 98.5
-1.4 +1.0
VOL 38, NO. 10, SEPTEMBER 1966
$4.0 -4.2 -1.5 -1.2 +2.0 -3.6 -0.2 f3.0 -0.6 +2.5 -1.5 +0.4 -2.7 -1.4 +1.0 +9.0 +6.0 +1.0
+4.4
+2.4 -1.5
e
1307
Table II.
Concentration Achievable with Cation Exchange Membrane
Volume ratio, Total tracer donor/ Tracer concentration activity, c.p.m. accep ratio, acceptor/donor Donor Acceptor tor Theor. Exptl.b
Solution composition Donor Acceptor 0.01MNaC1, 0.10MNaCl 1100 3650 3.38 1W 10.2 1 0 - 4 ~csci, csis7 0 . 0 2 M NaC1, 0.01M EDTA, 310 13197 2.82 Very high 120 lO-dM ZnClz, Zn”, 0 . 8 M NHa, 0.8M NHa, 0.1M NHiCl 0.1M NHiCl Calculated from ratio of principal electrolyte concentrations and Equation 8. b Calculated from the total activity ratio and volume ratio. 0
ler cavity was filled with 0.10M NaCl and then closed off by means of a screw clamp. This quiescent solution served as the acceptor for the radiotracer. Through the larger cavity, a solution containing 0.01M NaCl and lO-‘M CsCl with Csln tracer was pumped a t a rate of 0.7 ml./minute by means of a peristaltic pump (model 500-1200, Harvard Apparatus Co., Dover, Mass.). The flowing solution, called the donor solution, was pulsed to effect stirring. The uptake of Csln was followed as a function of time, using the recorder of the y-ray spectrometer. The record was taken until a steady counting rate was achieved, after which the relative activities of the solutions in each compartment were found by difference by successively flushing each compartment with water and measuring the residual activity. To find the tracer distribution ratios at cation exchange equilibrium, the total counting rate in each compartment was divided by the compartment volume. Results are shown in Table 11. The same procedure was used for demonstrating the concentration of Zn(I1) with EDTA as a complexing agent. In this case, the flowing donor solution contained 0.02M NaCl, 0.8M NH,, 0.1M NHaC1, and 10-4M ZnClz with Zn65 tracer while the auiescent acceptor solution contained 0.8M “1, O.1M NH4C1. and 0.01M EDTA (disodium salt). Results are also shown in Table 11. Quantitative Extraction with Complexers. The effectiveness of complexation for the quantitative extraction of Zn tracer was found using a cell similar to that used for the dekrmination of the equilibrium distributions. The volumes of the donor and acceptor compartments were 8.7 and 5.6 ml., respectively, and the interfacial area was about 11 sq. cm. The compartments were separated with a cation exchange membrane (AMF C-103). The sample solution containing ZnClz tagged with Zn65 was placed in the donor compartment and the extractant containing excess EDTA
1308
ANALYTICAL CHEMISTRY
was placed in the acceptor compartment. Both solutions were duffered with 0.8M NHrO.lM NHdC1. Samples of 100 pl. were withdrawn from the donor solution for counting a t various times. Three extraction experiments with differing ZnClz and EDTA concentrations were performed, with results as shown in Figure 4. The precision of these measurements, especially a t long times, was limited by the low residual activity in the donor compartment. It is notable that the relative rate of extraction was independent of the ZnClz and EDTA concentrations over the ranges studied, and that only about 0.3% of the Zn remained unextracted after 3 hours in all cases.
-1.0
IO
1000
Figure 4. Extraction of Zn(ll) tracer with EDTA 0 1 O-‘M
ZnCIz, Z n k 0 . 0 0 5 M EDTA Zne5-0.005M EDTA Zna6-2 X 1 O-’M EDTA
0 10-%4 ZnCI,, A 1 0-6M ZnCI,,
branes was done with materials that were much less selective and less homogeneous than modern materials, and some of the results do not apply quantitatively to modern membranes. A reinvestigation is in order. ACKNOWLEDGMENT
DISCUSSION
Even though the theory has been verified, and good yields and high concentration enrichment have been obtained experimentally, it should be pointed out that the purpose of this work has simply been to indicate the analytical potentialities of ion exchange membranes for extraction and concentration. From the standpoint of practical analytical use, the equipment leaves much to be desired. The design of superior equipment must await the availability of membranes in a greater variety of forms; tubing, for example, would permit more efficient countercurrent extraction than the presently available sheets. There are also two fundamental limitations to the use of ion exchange membranes. First, the Donnan exclusion breaks down at high ionic strengths and the permselectivity decreases. Second, the design of practical equipment is critically dependent upon the rate of diffusion of substances through the membranes. Factors that affect the rate of diffusion have been clearly defined (4), but much of the past work on the rate of diffusion through ion exchange mem-
100
TIME, MINUTES
The authors thank Robert Schmelzer for his helpful advice and aid in constructing the cells used in this work and also Mary Lathrop for her technical assistance. LITERATURE CITED
(1) Berg, E. W., “Physical and Chemical Methods of Separation,” p. 183, McGrew-Hill, New York, 1963. (2) Blaedel, W. J., Evenson, M. A., Znorg. Chem. 5, 944 (1966). (3) Caplan, S. R., J . Electrochem. SOC. inR. 577 ---I -. . I I Q P , ~). \----
(4) Helfferich, F:; “Ion Exchange,” pp. 156, 339-420, 345-66, McGraw-Hill, New Ynrk. - -. . . 1962. - -.
(5)’Ho, P. P. L., Marsh, M. M., ANAL. CHEM.35, 618 (1963). (6) Krishnaswamy, N., J . Sci. Znd. Res. ( I n d i a ) 24(5), 244 (1965). (7) Parsons, J. s., ANAL.CHEM. 30, 1262 (1958). (81 Sutcliffe? J. F., “Mineral Salts Ab-
sorption in Plants,” Pergamon Press, New York, 1962. RECEIVEDfor review May 19, 1966. Accepted June 24, 1966. Work supported by U. s. Atomic Energy Commission Grant No. AT(11-1)-1082. Presented in part at First Great Lakes Regional Meeting, ACS, Chicago, Ill., June 1966.
