RICHARD XI. WALLACE
2418
a concentration of 5 mmoles/l. Under these conditions, direct photolysis is inappre~iable.~The yield of Hz = 1.1 pmoles/l./flash was independent of pH from 2.7 to neutral, again in contrast to the similar radiolysis results. lt appears that about one-third of the hydrogen atoms are scavenged by the methanol. From Fig. 2 this would indicate that [methanol]/ [HI was 2500. This corresponds to a concentration 2 X M hydrogen atoms/flash compared to 3 X M estimated from the formic acid system. Somewhat different behavior was observed in the formic acid system. Here a higher yield of hydrogen was obtained a t pH 2.7 than a t neutral pH. A possible explanation has been provided by the work of Matheson, et a1.,'6 who find that some ions produce eaq- on photolysis. We did not observe this increased hydrogen yield in the photolysis of the sulfate ions methanol. MI However, the addition of formate ions [4 X may liberate eaq- leading to a higher hydrogen atom yield via reaction 3. The aerated formate solutions showed an increased yield of hydrogen peroxide at this
+
concentration. The rate of reaction of hydrogen atoms with formate ion is 100 times that of their reaction with methanol"; hence, [HCOO-] = 4 X M is equivalent to 4 X low2M methanol. Using Fig. 2 we may calculate that the formate should capture 60% of the hydrogen atoms and produce 1.80 X M hydrogen/flash. The measured value was 1.75, in very good agreement with that calculated. The rates of reaction of the reducing species in the photolysis of aqueous solutions from pH 7 to pH 2.7 and in the radiolysis of acidic solutions are very similar. We have, therefore, interpreted our results with both radiations in terms of one species, namely the hydrogen atom. Acknowledgment. We wish to thank W. Mulac and J. Cooper for helping in this work, and M r . B. E. Clifft, who operated the linear accelerator. (16) M. Matheson, W. Mulac, and J. Rabani, J . Phys. Chem., 67, 2613 (1963). (17) G. Czapaki, J. Rabani, and G. Stein, Trans. Faraday ~ o c . ,58, 1 (1962).
Determinations of Charges on Ions in Solutions by Donnan Membrane E quilibriuml
by Richard M. Wallace Savannah River Laboratory, E. I . d u Pont de Nemoura & Co., A i k e n , South Carolina
(Received April 9, 196'4)
A method was developed for determining the charge of cations dissolved in perchloric acid solutions by measuring the concentrations of the ions on opposite sides of a permselective membrane in solutions of varying acidity. The method was applied to Na+, Mg2+,Ca2+, SrZ+, UO22f, Ala+, La3+,Th4+,and Ru(1V). The results agreed with the accepted values of the charge except for Ru(IV), on which a charge of +4 was found rather than + 2 which had previously been reported.
Introduction It is frequently necessary to determine the charges of ions in solution. Methods for charge determinations have been developed by Strickland2" and Cady and Connick2bbased on variations of the distribution of an The Journal of Physical Chemistry
ion between an ion-exchange resin and an aqueous Phase, expressed as a fUmtion of the aqueous Phase concentration of an ion of known charge. Trofinov, Stepanova, and Grinbergas4developed a method based on changes in the distribution of pairs of ions between
DETERMINATIONS OF (2HARGES
ON
IONS BY DONNAN MrEMBRANE EQUILIBRIUM
a single aqueous phase and different ion-exchange resins, expressed as a function of the specific volume and capacity of the resin. The first method requires assumptions of constant activity coefficients in the resin phase and constant or known activity coefficients in the aqueous phase. The first assumption is nearly valid for small fractional loading of the resin with the ion of unknown charge, which often requires that the resin be equilibrated with fairly concentrated solutions of the ion of known charge, where estimations of the activity coefficients are uncertain. The second method avoids concern about the activity coefficients in the aqueous phase but still requires one to assume constant activity coefficients in the resin phase. It also involves more work, since it is necessary to determine the specific volume and capacity of the resin in addition to the distribution of ions. A method of charge determination was developed based on Donnan membrane equilibrium across permselective (ion-exchange) membranes. The chief advantages of this method are that it avoids any concern about the activity coefficients of ions in the resin phase and enables measurements to be made in dilute aqueous solutions where adequate corrections for activity coefficients can be made by the Debye-Hiickel equation. Basis of Method. If two solutions of electrolytes are separated by a membrane permeable to cations but impermeable to anions and solvent, the total electrolyte concentrations expressed in equivalents per unit maw of solvent must remain constant, due to the immobility of the anions and solvent, but the various cations that are present will be redistributed between the two phases until equilibrium is established. Conditions for equilibrium in such a system are given by several authors“-’ and can be summarized by the equation
where A ~ and R A ~ are L the activities of the ith cation of right and left sides of the membrane, respectively, Z iis the charge of the cation, and K is a constant for all cations in the system that depends only on the nature of the two solutions. If the equilibrium distribution of a cation C of charge 2 is measured between two acid solutions of different concentrations, eq. 1becomes
where AH^ and AHLrefer to the activities of the univalent hydrogen ion on the right and left sides of the membrane.
24 19
When eq. 2 is written in terms of concentrations and activity coefficients, and the logarithms of both sides are taken and rearranged, it becomes
where C and H are the equilibrium concentrations of the cation C and the hydrogen ion, respectively, and the symbols R and L have their previous meaning. The quantity 0 is a collection of activity coefficients defined as
P=(z)z(E) where Y is an activity coefficient in terms of concentrations, and the subscripts refer to the ion and side of the membrane to which the activity coefficients belong. Equation 3 shows that if can be evaluated, the charge on an unknown ion can be calculated from the distribution of an ion between acid solutions of different concentration. The equation is of course applicable to the distribution of ions between solutions of any univalent cation. The quantity 2’ is the charge one would calculate if the activity coefficientswere assumed to be unity. p can be estimated by assuming that the activity coefficient Y z of an ion of charge 2 is related to that of an ion of unit charge Y1 in the same medium by the expression
Y,
=
YIZe
(4)
which is equivalent to assuming that the size parameter il in the Debye-Huckels expression shown below is the same for all ions, and that differences between the mole fraction and molarity bases can be ignored.
(1) The information contained in this article was developed during the course of work under Contract AT(07-2)-1 with the U. S.Atomic Energy Commission. (2) (it) J. D. H. Strickland, Nature, 169, 620 (1952); (b) H. H. Cady and R. E. Connick, J . Am. Chem. SOC.,80, 2646 (1958). (3) A. M. Trofinov and L. N. Stepanova, Radiolchimya, 1, 403 (1969). (4) A. A. Grinberg, A. M. Trofinov, and L. N. Stepanova, ibid., 2 , 78 (1960). ( 5 ) F. G. Donnan, Chem. Rev., 1, 73 (1924) (6) K. Sollner, et al., in “Ion Transport Across Membranes,” H. T. Clarke, Ed., Academic Press, New York, N. Y., 1954, pp. 144-188. (7) F. Helfferich, “Ion Exchange,” McGraw-Hill Book Co., Inc., New York, N. Y., 1962, p. 372 ff. (8) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” Butterworths Scientific Publications, London, 1955, p. 228.
Volume 68, Number 9 September, 1964
RICHARD M ,WALLACE
2420
where Ii is the activity coefficient of an ion of charge Zi on the mole fraction basis. A and R are constants and p is the ionic strength. It was further assumed that the activity coefficient of the hydrogen ion is a function of ionic strength only, and is equal to the mean activity coefficient of the salt-free acid solution at the ionic strength of the salt-containing solution. These assumptions are justified because j3 is essentially a correction factor and is not required to great accuracy. While variations of d between ions might cause a variation of 20% in B at ionic strength as high as 0.2, such variations will usually be smaller, and the effect of charge will far surpass that of the size parameter. The other assumptions will not produce errors as large as those involved with the size parameters. On the basis of the assumptions, eq. 3 can be written
necessary that the system come to equilibrium with respect to the transfer of cations long before it does with respect to the other constituents. This condition has been found to occur in practice, but because of osmosis and slight anion leaks and the lack of perfect selectivity, solutions must be analyzed for all relevant components after equilibration. Permselective membranes are composed of ionexchange resins and possess the properties of these resins as well as that of permselectivity. Such properties are sometimes troublesome, especially when working with highly charged ions in dilute acid solutions, for these cations are frequently absorbed so strongly by the memhrane that they become undetectable in solution. It is usually possible to circumvent this problem by nearly saturating the membrane with such ions before equilibration. Saturation of the membrane does not interfere with the method because the state of the membrane is unimportant as long as it retains the property of permselectivity.
A further simplification of eq. 5 is possible under certain conditions. Perchloric acid was used as the medium for measuring the distribution of cations in the present study. It was found empirically that log y+ for perchloric acid was linear with the logarithm of its molality in the region 0.02 < m < 0.2 with a slope of -0.055. Consequently, if the concentration of the ion being studied is sufficiently small that it does not affect the ionic strength significantly, and if the measurements are made within the specified region (within their region y* is approximately equal to Y*), eq. 5 becomes Z = Z’ - 0.055Z(Z - 1) (6)
Experimental A diagram of one of the cells in which the membrane equilibrations were run is shown in Fig. 1. The cell
In practice, the distribution of cations must be meaawed between solutions of an acid containing a noncomplexing anion because the theory was developed with the premise that all activity effects were electrostatic in nature. For this reason, perchloric acid was chosen for the present work. It is also desirable to keep the ionic strength of the solutions as low as possible to stay within the limits of validity of the DebyeHiickel formula and to minimize the effects of variations in the size parameter. In the present work an attempt was made not to exceed an ionic strength of 0.1, although for certain cases it was expedient to go slightly higher. There are a few practical considerations related to the nature of actual membranes. Actual perniselective membranes are not perfectly selective and will pass anions and water as well as cations. This is not a sorious problem, however, for although the theory was developed for a perfect membrane, it is only
consisted of two 3 X 3 X 0.5 in. blocks of Teflon (Du Pont trademark for its fluorocarbon plastic), each containing a cylindrical cavity 2 in. in diameter and 0.375 in. deep, and a threaded filling passage leading from the cavity to the edge of the block. A 2.5-in. diameter circular cation-exchange membrane was placed between the two cavities and the blocks were bolted together. Stainless steel plates, 0.125 in. thick, at the back of each block prevented warping of the Teflon blocks. The volume of the cavity on each side of the membrane was approximately 20 ml.
Figure 1.
Membrane equilibration cell.
DETERMINATIONS OF CHARGES ON IONS BY DONNAN MEMBRANE EQUILIBRIUM
I n operation, 15 rnl. of solution was placed in the cavity on each side of the membrane, the threaded filling passages were sealed with plugs, and the assembly, with the membrane in a vertical plane, was rotated at 60-120 1r.p.m. about an axis through the center of the membrane and normal to its surface. This rotation of the membrane agitated the solutions and continually renewed the interfaces between the membrane and solutions. The initial device that was used in most of the present study for rotating the cells was able to hold six assemblies, but could be used at room temperature only. A more elaborate device was built later that permitted equilibrations to be made in s constant-tempersture bath. The design of these devices will be described in another report. The advantages of this method are that several equilibrations can be made simultaneously on the same apparatus and that equilibrium is achieved rapidly because of the large ratio of membrane area to solution volume. In preliminary tests to determine the integrity of the membranes and the cells, solutions containing 1 M HC10, were placed on one side of the membrane and pure water on the other. No detectable change in pH of the water wa13 found after the cells had been rotated for 2 hr. These tests demonstrated that the membranes did not leak and that the rate of transfer of anions was adequately slow. Osmosis was detectable during this peiriod but no attempt was made to measure its extent. Measurements were made of the distribution of Xa+, Mg2+, Ca 2 + , Sr2+, UOzz+, A13+, La3+, Th4+, and Ru(1V) between varying concentrations of perchloric acid. The procedure used with the alkaline earths and lanthanum was to place a 0.1 M perchloric acid solution on one side of the membrane and a 0.01 M solution of the perchlorate salt of the test cation in varying concentrations of perchloric acid (0.01-0.1 M ) on the other side O F the membrane in each of the six cells. In a few inetances the salt was placed in the high acid side of the membrane so that equilibrium was approached frorn the other side. The cells were then rotated a t room temperature (25 f: lo)for about 20 hr. and the solution was analyzed for the appropriate cation and for hydrogen ion. A similar technique was used with sodium except that only trace concentrations of NaZ2were used in the study. A slightly differenttechnique was used with the other ions. They were first absorbed on the membrane from 0.1 M solutions of the salts in 0.01 M acid placed on both sides of the membrane. After agitation for 1 hr., the solutions were removed, the cells rinsed with
2421
water, and the desired concentrations of perchloric acid were placed in the cells. This procedure was followed in measurements on aluminum and uranyl ions because the perchlorate salts were not a t hand when the experiments were run, and because this procedure offered a convenient way to convert the nitrates to perchlorates. The same method was used for measurements on thorium and ruthenium(1V) because of the slow rate of transport of these ions through membranes and because equilibrium was achieved more rapidly by this technique. Rate studies with Na+, Ca2+, UOZ2+, and AI3+ indicated that equilibrium was substantially complete after 2 or 3 hr. The distribution of lanthanum ions was also found to be essentially complete after 20 and 45 hr., when allowance was made for osmosis and the distribution did not depend on which side of the membrane the ion was originally placed. It was inferred from these studies that 20 hr. would be sufficient time to achieve equilibrium for uni-, di-, and trivalent ions. Thorium did not reach equilibrium nearly as rapidly as the other ions. Measurement of the rate of transfer of thorium between two 0.1 M perchloric acid solutions, one of which was originally 2.5 X &if in thorium, across a membrane presaturated with thorium indicated that equilibration was only half-complete after 20 hr. and would be 99% complete after 130 hr. However, tests in which the membrane was first saturated with thorium and in which equilibrium was approached from the middle toward both ends indicated equilibration to be substantially complete after 40 hr., although small variations in calculated values of 2 suggested that results obtained after 120 hr. were inore reliable. Similar tests with ruthenium(1V) indicated that equilibrium was complete after 40 hr. In all equilibrat,ions the acid concentration on each side of the membrane changed, due primarily to osmosis. It was therefore necessary to determine acid concentration of all solutions after equilibration, and to assume that the ions under investigation were in equilibrium with solutions a t the time of sampling. Reagents and Materials. The membrane material used throughout these experiments, Ionac RIC 3142 cation-exchange membrane, was obtained from the Ionac Chemical GO. The membranes were in the sodium form when received but were converted to the hydrogen form prior to use. Solutions of lanthanum and thorium perchlorates were prepared by dissolving the oxide and carbonate of these elements, respectively, in stoichioinetric amounts of perchloric acid. All other solutions except those containing Ru(1V) were prepared from reagent grade salts in reagent grade perchloric acid. Volume 68, Number 0
September, 1964
RICHARD 34. WALLACE
2422
Ruthenium(1V) solutions were prepared by a method The first two columns in this table give the ionic similar to that described by Gortsema and C ~ b b l e . ~ strengths of solutions on each side of the membrane, According to this method, a solution of RuO4 (ca. 5 X calculated from the concentrations of acid and cation. M ) in 1 or 2 M HC104 was reduced to Ru(1V) The third contains the ratio of the hydrogen ion conwith HzOz. The Ru(1V) was absorbed on a cationcentration on the right side of the membrane to that on exchange resin (Dowex 50 W X8, 200-400 mesh) in the left, while the fourth column contains the the hydrogen form which was placed on a column and same ratio for the cation under investigation. The eluted with 0.25 M lanthanum perchlorate in 0.5 M HC10,. The first fraction collected was free of lanTable I : Determination of Charges on Ions thanum as indicated by its failure to give a precipitate with oxalic acid. The absorption spectrum of the 2’ z IrL PR HR/HL CR/~L Ru(1V) was nearly identical with that given by Cobble Na and Gortsema for monomeric Ru(1V). 0.0133 0.0819 6.17 6.38 1.02 1.02 Analyses. The NaZ2was determined with a well3.75 3.82 0.0231 0,0865 1.02 1.02 type y-scintillation spectrometer. A sufficient number 1.02 2.12 2.17 0.0419 0.0890 1.02 1.49 1.47 0.0616 0.0917 0.97 0.97 of counts were taken in each measurement to limit the 0.97 1.192 1.186 0.0789 0.0905 0.97 counting error to 0.3%. 1.000 0.995 ... ... 0,0980 0,0980 Concentrations of RIg, Ca, Sr, and La were deMga+ termined by complexometric titrations with EDTA.’Ol1’ 2.19 0,0342 0.1116 2 . 5 0 7.47 2.06 The hIg was determined directly with Erio T indicator. 2 . 0 1 4 . 5 3 2 . 1 6 0,1088 2.02 0.0445 The other ions wTere determined by substitution titra1.66 2.88 2.09 0.0566 0.1078 1.95 tions using the Mg-EDTA complex and Erio T indi1.46 2.25 1.93 2.07 0,1075 0.0661 cator. Titrations were carried out with 0.01 M EDTA 1.98 1.17 1.36 1.82 0.0884 0.1074 using a microburet. EDTA solutions were standard0.992 0.988 ... ... 0.1084 0.1074 ized with magnesium oxide and metallic zinc. PreLa3+ cision on these analyses was *0.5(%. 2.49 20.5 3.31 2.85 0.0393 0.1478 UOZ2+,A13+, Th4+, and Ru(1V) were determined 3.47 2.98 1.99 10.91 0.0512 0.1471 colorimetrically, UOz2+ as the thiocyanate complex,12 1.82 7.81 3.44 2.96 0.1492 0.0594 1.61 5.42 3.55 3.07 0.0700 0.1487 A1 as a complex with alumin0n,~3T h as a complex 3.19 1.45 3.91 3.69 0.1480 0,0809 with thorin,14 and Ru as the t e t r ~ x i d e . ~Ab1.34 3.08 3.80 3.49 0.1481 0,0908 sorption measurements were made with a Beckman Th4 + DU spectrophotometer. Reproducibility on these 4.49 3.83 0.1597 1.704 10.95 0.0910 analyses was ~ 1 except % for aluminum, where the 1.521 6.72 4.54 3.90 0.1632 0.1049 precision was f3%. Hydrogen ion was determined by 4.64 4.01 1.437 5.38 0.1659 0.1133 titration with sodium hydroxide to a methyl red end 4.67 4.07 1.359 4.20 0.1760 0.1273 point. No interference was incurred with the alkaline 4.44 3.74 0.1215 1.517 6.37 0.0787 1.379 4.07 4.37 3.70 0.1276 0,0916 earth elements, In cases where significant quantities of other cations were present, they were removed before Ru(1V) titration by passing the solutions through a column of 4.44 3.76 1.332 3.59 0.1431 0.1060 cation-exchange resin in the hydrogen form. Correc4.68 4.07 1.310 3.54 0.1854 0.1363 4.11 4.77 1.176 2.17 0.1365 0.1151 tions were made for the acid liberated by the absorption 4.12 4.76 1.491 6.70 0.1480 0.0983 of these ions, based on their concentration and known 4.83 4.20 1.254 2.98 0.1393 0.1105 charge per atom. +
Results and Discussion Table I gives a detailed summary of the results obtained with five of the ions studied, Na+, Mg2+, La3+, Th4+, and Ru(1V). The table indicates the dependence of the measured and calculated variables of ions of each different charge as the ratio of acid concentrations on the two sides of the membrane is varied. Rutheniuni(1V) is also included because it gave the only unexpected result in the series of experiments. The Jownal of Physical Chemistry
(9) F. P.Gortsema and J. W. Cobble, J . Am. Chem. Soc., 83, 4317 (1961). (10) G. Schwarzenbach, “Complexometric Titrations,” Methuen and Co., London, 1957. (11) H. A. Flaschka, “EDTA Titrations,” Pergamon Press, New York, N. Y., 1959. (12) F.D.Snell, C. T. Snell, and C. A. Snell, “Colorimetric Methods of Analysis,” 3rd Ed., Vol. 11-A, D. Van Nostrand Co., Princeton, N. J., 1959,p. 390. (13) F. D.Snell, et al., ibid., p. 175. (14) F. D.Snell, et al.. ibid., p. 515.
DETERMINATIONS O F CHARGES ON IONS BY DONNAN MEMBRANE EQUILIBRIUM
fifth and sixth columns list Z’, the charge calculated without regard to activity effects, and 2, the charge calculated by eq. 5 . Activity coefficients of perchloric acid used in that equation were calculated from a formula given by Robinson and Baker.15 Table I1 contains average values of 2’ and of 2 for all of the ions calculated with both eq. 5 and 6, although eq. 6 is not strictly (applicable in all cases. The values cited for each ion are averaged over at least four measurements. Only those values were included for which the ratio of hydrogen ion concentration on the two sides of the membranes exceeded 1.5, except in the case of Ru(1V) and Th4+,where all of the data are included. Table I1 : Summary OF Results Ion
Na + Mg2+ Ca2 Sr2+ +
uozz+ A18 + LaS+
Th4 Ru(1V) +
Z’
Za
Zb
1 . 0 1 =t0.01c 2.13 =t0.05 2 . 1 4 f 0.05 2.16 f 0.02 2 . 1 5 f 0.02 3 . 5 1 zk0.10 3.44 It 0 . 1 1 4.53 0.12 4.70-t0.15
1 . 0 1 f 0.01c 1 . 9 9 f 0.06 2 . 0 1 f 0.05 2 . 0 3 f 0.01 2 . 0 4 f 0.02 3 . 1 3 ic 0 . 0 9 2 . 9 7 f 0.09 3.88 f 0.14 4.05 f 0.17
1.01 2.02 2.03 2.05 2.04 3.18 3.11 3.87 4.04
*
a Calculated from eq 5. are standard deviations.
b
Calculated from eq. 6.
c
Errors
An analysis of the propagation of errors shows that the error, uZ’, in 2’ is given by the following equation, if the relative error r in each individual concentration measurement is assumed to be the same.
Since the error in Z’ is inversely proportional to log it increases rapidly as H R / H ~ ,decreases to 1; values of 2’ determined a t higher values of this ratio are therefore imore reliable. Large values of the concentration ratio of hydrogen ions sometimes lead to experimental difkulties with highly charged ions because of the large difference in the concentration of
HR/HL,
2423
the cation under investigation on opposite sides of the membrane. It was therefore expedient to use rather small differences in hydrogen ion concentration when working with Th4+and Ru(1V). The concentrations of the cations under investigation were kept as small as possible, consistent with the analytical methods, so they would not have too large an effect on the ionic strength. The largest concentrations occurred with Mg, Ca, Sr, and La, where the maximum ratio of cation to hydrogen ion in any solution was 0.13; for the other ions this ratio was less than 0.03. The summary in Table I1 shows the method to be valid for determining the charges on ions in solution a t least up to charge +4. It also shows the necessity for making corrections for activity coefficients, especially when dealing with highly charged ions. The semiempirical eq. 6 gave almost the same value of 2 as eq. 5, and is probably adequate for most practical purposes. The value of Z for La calculated with eq. 6 showed the greatest discrepancy with the value of 2 calculated with eq. 5 because the high concentration and high charge made eq. 6 inapplicable. The results obtained with the singly, doubly, and triply charged ions agree with the generally accepted values of the charge on these ions. The charge of +4 for thorium agrees with the observation of Kraus and Holmberg ‘ 6 that Th4+ is the principal species present in acid perchlorate solutions. The results with Ru(IV), however, disagree with those of Gortsema and C ~ b b l ewho , ~ found the charge on that species in solution to be +2 by the method of Cady and Connick.2 The significance of the present result in terms of the structure of Ru(IV) in solution will be discussed in a future publication.
Acknowledgment. The author wishes to acknowledge the assistance of J. W. Crooks in the experimental work and R. H. Searle in the design and construction of equipment. (15) R. A. Robinson and 0. J. Baker, Trans. Proc. Rog. SOC. New Zealand, 7 6 , 250 (1946); Chem. Abstr., 41, 5000e (1947). (16) K. A. Kraus and R. W. Holmberg, J . Phys. Chem., 5 8 , 326 (1954).
Volume 68, Number 9
September, 1964
