IONE:XCHANGE ON THE MINERALCLINOPTILOLITE
Table V gives 19Fchemical shifts relative to (C2Hs)20.BF3= 0 for the addition compounds studied. The numbers are average values measured a t -30 to -50". Although the chemical shifts vary with composition and temperature, even if the extreme values were used, the order of the compounds would not be changed. With the exception of THFaBF3 in which the cyclic nature of the compound reduces the shielding, the order follows the strength of the addition compounds. The n.m.r. kinetic studies of mixtures of (CzH5)20, BF3,and three ethers and (C2Hs)2Sin which the organicboron trifluoride ratios are greater than 1 are in accord with a two-path BF3exchange mechanism. The direct exchange between two addition compounds is a
531
Table V :
19F Chemical Shifts" of BF3 Addition Compounds
Chemical ahift, Compound
p.p.m.
(CH3)zO.BFa
+5.3 +2.7
THF.BF3
0.0 -1.3 -19.5
(CzHs)zO.BFa
CJ360CH3 .BF3 (C&)zS.BFs
+ shifts are upfield (greater shielding). slower process of higher activation energy than the path involving BF3transfer to a free ether.
Ion Exchange on the Mineral Clinoptilolite
by Darryl G. Howeryl and Henry C. Thomas Department of Chemistry, University of North Carolina, Chapel Hill,North Carolina
(Received August 51, 1964)
Cation-exchange equilibria on the zeolitic mineral clinoptilolite have been investigated for the pairs of ions Na+-Cs+, Na+-NH4+, and NH4+-Cs+ a t 30 and 70" using column techniques with radioactive tracers. The standard values of AF and AH are shown to obey the triangle rule with discrepancies of only about 0.1 kcal./mole. The system is discussed in terms of the excess thermodynamic functions.
The cation-exchange properties of the zeolitic mineral clinoptilolite have been the subject of several recent inv e s t i g a t i o n ~ . ~The ~ ~ individuality of the mineral has been established by M ~ m p t o n . It ~ is considered to be an altered pyroclastic. Further alteration results in its conversion to the clay mineral hectorite. Clinoptilolite is being used quite extensively as a selective sorbent for certain radionuclides5; its behavior as an ion exchanger is of considerable interest for both practical and theoretical reasons. We here give an account of the equilibria reached by this material with solutions of the chlorides of sodium, ammonium, and cesium, in pairs. The measurements have been made a t two
temperatures, so that a fairly complete thermodynamic treatment can be given. (1) This paper is based on the dissertation submitted by D. G. Howery to the faculty of the University of North Carolina in partial fulfillment of the requirements for the degree of Doctor of Philosophy. The work was supported by the U. S. Atomic Energy Commission under Contract No. AT-(40-1)-2130. (2) L. L. Ames, Jr., Am. Mineralogist, 45, 689 (1960); 46, 1120 (1961); 47, 1067, 1310, 1317 (1962). (3) G. R. Frysinger, Nature, 194, 351 (1962). (4) F. A. Mumpton, Am. Minerdogist, 45, 351 (1960). (5) D. K. Jamison, et al., Ed., "The Use of Inorganic Exchange Materials for Radioactive Waste Treatment," U. S. Atomic Energy Commission, TID-7644 (1963).
Volume 69, Number B
February 1966
DARRYL G. HOWERY AND HENRYC. THOMAS
532
The complexities of ion exchange between solutions and silicate minerals of open structure6 are so varied that little is to be gained by attempting more than a formal thermodynamic treatment of the data, such as that given by Gaines and tho ma^.^ This treatment implies that the free energy function of the solid exchanger will be simplest if compositions are given as equivalent fractions when ions of different charge types are involved. Thus the chemical potential associated with the ion A in a zeolite combination with ion B, (A,B)Z, is written paS =
+
,UA"(T) RT In NA~A
(1)
where N A is the equivalent fraction of A in (A,B). For the solution we write as usual PA' = PA"
+ RT In
+ BZ = B + + AZ
KB* = ( ~ B T B ) ( N A =~ KcB AA)&
(4)
lnfB =
NA
In
KcBA
4-[
NB
In
1 N ~ In KcBA
dNB
(6)
(7) For brevity, we refer to the stoichiometric equilibrium The Journal of Physical Chemistry
AFmx
(8)
=
Of
AF, - AFmid
the solid phase activity coefficients are not equal to unity unless the exchanging ions have like charge. Thus for A+ competing with B+2,we have
NA = nA/(nA
dNB ( 5 )
+ nB In NB
It is to be noted that while the excess free energy such a solid is certainly zero
fB
The evaluation of the thermodynamic equilibrium constant and of the solid phase activity coefficients results from an appropriate integration of the GibbeDuhem equation for the solid phase. In general this requires a knowledge of solvent uptake and solvent activity as well as of the co-ion concentration in the exchanger phase. The activity coefficientsfA, fB are made definite by some convenient, arbitrary, selection of standard states for the solid, which also h e s the meaning of K Band ~ of the standard free energy. We take the standard states as the pure monoion solids and the usual solute standard states for the solution. Since it has been shown that clinoptilolite sorbs no anion and since we coniine our attention to solutions sufficiently dilute so that the water activity changes inappreciably with composition, the Gibbs-Duhem equation together with eq. 4 gives the following rules for computing the activity coefficients and the value of K B ~ 1nfA = -NB In K,B'
AFd
- = nA In NA RT
(3)
gives the usual equilibrium constant expression (mA?'A) ( N B f B )
NA, NB
(2)
WLA~A
The condition for equilibrium in the exchange reaction, written here for singly charged ions
A+
quotient multiplied by the activity coefficient ratio for the solution phase as the rational equilibrium quotient, Kc. Most of the interesting detail of the behavior of the exchanger is reflected in the activity coefficients; we may use them to calculate the various excess thermodynamic functions. For this purpose, when ions of different charges are to be considered, we must broaden somewhat the usual definition on the basis of which the excess quantities are calculated. We define an ideal mixed solid as one in which the free energy with respect to appropriate amounts of pure monoion solids, n A and n B moles, is given in terms of the equivalent fractions
+ 2 n ~ )NB ;
+
2 n ~ / ( n ~2 % ~ )
=
and 1n fA = N B / ~In; f B
=
-NA
but
+
AFX = RT(nA I n f ~ nnB In fB) is identically zero for our ideal solid. The temperature coefficientsof the activity coefficients at k e d solid composition lead directly to the heat of mixing
and hence to the excess entropy of the solid T A S , ~= AH^
- AF,~
(10) If complete exchange studies on three ions, A+, B+, C+, in pairs are made, the self-consistency of the work can be assessed by the "triangle rule" applied to the standard free energies and enthalpies of the exchange (6) An excellent account of these, with many references t o the original literature, is given in F. Helfferioh, "Ion Exchange,"McGraw-Hill Book Co., Inc., New York, N. Y.,1962,pp. 185-193. (7) G.L. Gaines and H. C. Thomas, J. chm.Phys., 21,714 (1953).
IONE~XCHANGE ON THE MINERAL CLINOPTILOLITE
reactions. In terms of the equilibrium constants we must have KB* X KcB = KC* (11)
Experimental The equilibrium column method was used to determine the ionic uptake of the mineral. I n this procedure the exchanger is brought to equilibrium by extended treatment with a solution of given composition carrying an isotopic tracer for one (or possibily more) of the ions present. The uptake of the mineral for the traced ion is determined by exhaustive elution with any convenient “‘dead”solution. The method depends on a knowledge of the free volume of the column, which is simply determined from its increase in weight on Wing. This procedure amounts to a definition of the free volume and is satisfactory for reasonably high uptake by the mineral. Great care is necessary in the near trace regions of composition, when the measured uptake must be given by the difference of two nearly equal numbers. The sample of mineral used in these studies was kindly given to us by the Geochemical and Geophysical Research Unit, Hanford Laboratories Operation (Richland, Wash.). Because of variability in the composition of the mineral, we have carried out all of our experiments on this single sample. We are indebted to Dr. Peter A. Howell of the Tonawanda Laboratories of the Linde Company for optical and X-ray examination of this material. He has concluded that the major crystalline component is clinoptilolite with about 10% montmorillonite and quartz. A considerable quantity was crushed and sieved, the 30-140 mesh material being retained. This sample was exhaustively eluted, over an extended period of time, with 1 N NaCl until no trace of calcium or magnesium could be detected in the washings. This “sodium-based” zeolite was then freed of fines by swirling and decanting with water. After air-drying, the 30-80 mesh fraction was stored in a tightly stoppered bottle. Samples of this material were decomposed with HF-H2SO( and, after evaporation, taken up in dilute HC1. The solution from 0.1 g. of zeolite was shown to contain less calcium than corresponds to 0.01%; in the sample. We have used this very timeconsuming method for freeing the mineral of calcite because acid treatment has been shown to attack the aluminosilicate network and we wished to examine the mineral in as nearly its natural form as possible. Our results therefore cannot be expected to agree exactly with data obtained by others, e.g., Ames12who have used acid-treated material. Temperature control in the ion-exchange columns was maintained by pumping water from a thermostat through preheater jackets on the input lines just above
533
the columns and through jackets around the columns themselves. Previous experience with the equipment has shown that temperatures in the ion-exchanger bed are accurate to f0.1’ at 30’ and to f0.5’ at 70’. Due to the long periods necessary to reach equilibrium, several experimental factors were varied according to the relative concentrations of the input solutions. The various experimental conditions are summarized in Table I. It seems most probable that in some of the earlier work3 equilibrium was in many cases not reached. Table I : Experimental Conditions CA
CA Y C B
Weight of zeolite Saturation time Saturation volume Flow rate Elution time Elution volume Eluent Column dimensions
>> CB or >> CA
CB
0 . 5 g. 0.05 g. 1 day 7 days 0.7 1. 3.8 1. 0 . 6 ml./min. 1 . 5 days 0 . 5 1. 0 . 3 AT XaC1 8 X 0.85 cm.
Measurements of radioactivity were made on a singlechannel y-ray scintillation spectrometer using the usual NaI(T1) crystal. Samples for counting were 4 ml. portions of the solutions carefully pipetted into uniform plastic tubes. Each determination was based on three independent samples for each of which 50,00090,000 counts were taken. To check for complete elution, material from the columns was dried and counted directly. No significant “fixation” was detected with any of the ions here reported. Carrier-free Cs134and NaZ2were used as tracers. All solutions of the salts were prepared by weight from analytical grade reagents, using the manufacturer’s assay. Our cesium chloride was the “optical grade” stated by A. D. Mackay, Inc., to be 99.9+% pure. The pH of all solutions used was in the range of 5.2 f 0.2.
Results The cation-exchange capacities (c.e.c.) , based on four determinations for each ion, are, for Na+, 2.046 f 0.017mequiv./g., and, for Cs+, 2.039 f 0.011 mequiv./g. The c.e.c. for N&+ is inferred to be the same from an experiment in which a sodium zeolite lost 1.97 mequiv./ g. when treated with 0.02 N NHdC1. Elution chromatograms demonstrated that the selectivity sequence is Cs > NH4 >> Na. Volume 69, A-umber 2
Februarv 1966
DARRYL G. HOWERY AND HENRY C. THOMAS
534
When a sodium-based column is treated with solutions containing Na+*-Csf or Na+*-NHd+, the activity of the effluent iimt approaches then exceeds the activity of the influent. After a period depending on the relative input concentration, the activity of the effluent finally levels off at the influent value. These chromatographic "humps" indicated the need for the very long saturation times mentioned earlier. The uptake of the NH4+ion in mixtures has been obtained only by difference. Determinations in the Na+Cs+ system reveal that, although the c.e.c. values for Na+ and Cs+ separately are identical within experimental error, the total uptake in the mixed systems is always less. This is demonstrated in Table 11, where independently measured uptakes for the two ions are given together with their sums, which we would expect to be the same as the single-ion c.e.c.
Table 11: Total Uptake in the Na-Cs System a t 30" and = 0.02 N
Q
C(CS)/CO
0.00 .05
.10 .50 .75 .90 .95 1.00
m a
2.05 0.57 .45 .14 .099
.07 .04
PCS
PO
1.32 1.46 1.74 1.88 1.99 2.02 2.04
2.05 1.89 1.91 1.88 1.98 2.06 2.06 2.04
That this effect is not due to some hysteresis appears to be proven by an experiment in which a column previously used in a determination at c(Cs)/c, = 0.5 was switched to a solution at c/co = 0.1. The cesium uptake at C / Q = 0.1 was found to be 1.455 mequiv./g. A fresh (sodium-based) column equilibrated directly at c/co = 0.1 gave the nearly identical uptake, 1.457 mequiv./g. Furthermore, when a tagged sodium column was eluted with an untagged Cs-Na solution at c/co = 0.1, no residual activity was left on the column, implying that all the sites are equally available to both cesium and sodium. It appears to be highly improbablethat the variation of the total uptake with solution composition could be due to a large and variable sorption of negative ion. Direct experiment with solutions containing radioactive bromide shows that the zeolite either selectively sorbs water from these solutions or that the anion is repelled from the surfaces of the mineral. In addition we have found identical sodium capacities for both chloride and bromide solutions on two different samples of clinoptilolite. We are at a loss to explain the apparently variable The Journal of Physical Chemistry
capacity with the mixed solutions. It can, however, be demonstrated by direct calculation that the uncertainty in the c.e.c. of the clinoptilolite produces a generally negligible effect in the computed values of the thermodynamic functions descriptive of the system. We express concentrations and uptakes in terms of tbe selectively sorbed component; e.g., if the sorption of A is favored, with uptake P A N A
qA/(qA
+ qB)
=
q/qO = 1 - NB
(12)
The solutions used were a t a total concentration of 0.02 N throughout, so that we identify the molality and molarity of the ions. For reaction 3 in which it is supposed that A2 is favored
In the sodium-cesium system, for which the total u p take data are available, an attempt has been made to make the computations somewhat more self-consistent by using the appropriate total uptake value. For the sodium-ammonium and ammonium-cesium cases the single-ion c.e.c. has been used. In the sodium-cesium case, standard free energies calculated for go = 1.90 and for qo = 2.04 mequiv./g. differ by only 125 cal. (in 2400 cal.). From large scale plots, values of In KOwere read from which all the computations of the thermodynamic quantities have been made. The standard values of these are given in Table 111. Application of the triangle rule to these results demonstrates the self-consistency of the data. As is seen in Table 111, the disagreement between the observed and calculated values of AF' is no more than might be expected from experimental uncertainty. That the agreement for the enthalpies is equally good must be somewhat fortuitous; the temperature derivative of a free energy is a notoriously unreliable quantity. Table I11 : Standard Values of the Thermodynamic Functions a t 30" (cal./mole)
AF" AH'
Cs-Na
NHa-Na
CS-NHI
- 2420 - 2700
- 1290 -880
- 1020 - 1680
TAP -280 $410 -660 AF"(NH4-Na) AF"(Cs-NH4) = -2310, A = 110 cal./mole AH"(NH4-Na) -I- AHO(Cs-NH4) = -2560, A = 140 cal./mole
+
Deviations from ideality in the exchanger phase appear at once in the nonconstant values of KOand are reflected in the activity coefficients. These for an ideal
ION EXCHANGE ON THE MINERAL CLINOPTILOLITE
535
Table IV : Excess Thermodynamic Quantities at 30' N c s NE:,
- AFmX
0.00
0 13 29 54 130 182 181 102 63 33 0
I
.02 .05 * 10 .30 .50 .70 .90 .95 .98
1 .oo
Ca+-Na+ - AHmX
0
18 23 27 18
-5
- 187 41 55 -9 0
A&X
- AFmX
0.0
0 16 37 66 137 164 156 83 58 21 0
.o .o
.1 .4 .6 1.2 0.2
.o
.1 0
-
0
Qualitatively, all three systems here examined exhibit similar behavior: the values of the Ko)s steadily decrease from the high value characteristic of the trace region for the selectively sorbed component to a lower value at the other extreme of composition. All the evidence at low proportion of either component points to definite limiting values of K,, Le., to Henry's law behavior. This is most clearly seen at the low cesium end of the cesium-sodium isotherm, where the data are most abundant. The situation at the cesium-rich end of the isotherm is less satisfactory. For purely experimental reasons it is most difficult to obtain reproducible data in this regio-ni It is also possible that an unobserved competition between cesium and hydrogen ion may here affect the results to some extent. The main features, but certainly not the details, of these results can be accounted for by either of two oversimplifications. We might suppose that the sites are all alike and that the difference of the binding energies of a pair of ions for a site is influenced only by the population of neighboring sites. For simplicity, we suppose that the entropy of an aggregate of loaded sites is given by the ideal mixing law, We thus assume that the sites are equally accessible to all ions and attempt to represent the solid as an analog of a regular solution, On this basis we have first approximation activity coefficients, for ions of like charge, of the forms W
+
ASmx
0 0 0
0
Discussion
W
- A Hmx 18 23 46 278 383 41 142 -96 -46
solid and equi-charge exchanges should have the constant value unity. A numerical summary of the nonideal behavior of clinoptilolite is given in Table IV in terms of the excess quantities for the imaginary molecular mixing at 30" of appropriate amounts of the monoion solids.
lnfA = - N B ' ; 1nfB = - N A 2 RT RT
NH4 +-Na
(14)
0.1 -0.5 -0.7 .4 .7 .5 .2 0
- AFmx
CS+-NHd +
- AHmx
ASmx
0 18 44 83 209 274 240 92 46 19 0
0 37 68 114 242 160 333 - 142 - 68 -27 0
0.0 -0.1 -0.1 -0.1 -0.1 .4 1.9 0.8 .4 .2 0
-
7
These lead to a linear variation of In K,B* with solid composition and to the well-known expression for the excess free energy of mixing AF," = W N A N B
(15)
There result the parabolic plots for AF," and AHm vs. N B , and if w is independent of the temperature, to a zero excess entropy. Inspection of Table IV shows that our systems indeed exhibit many of these characteristics. Since our values of A H , are very sensitive to experimental error, we might with some justice disregard the irregularities that appear in these quantities or ascribe them perhaps more reasonably to an insuEciently elaborate form for the activity coefficients, this latter being called for by the complex nature of In K,. Such qualitative agreement is an insufficient basis on which to draw conclusions as to the nature of the exchanger, as can be demonstrated by showing similar agreement with an entirely different model. Let us make an alternative extreme supposition and assume that the sites are so widely separated that interactions between them may be entirely neglected but that the binding energies vary from site to site. To get the simplest results, we suppose that the sites are distributed uniformly over a definite total energy range and that in any small range of energy there are the same number of sites and that in this group the entropy of mixing is approximately ideal. As is shown in the Appendix, this supposition produces in first approximation the following expression for the rational equilibrium quotient as a function of exchanger composition, y. (Here y is a mole fraction; the formula does not hold for unequal charge types.)
The quantities K z and K1 are determined by the limitVolume 60,Number 8 February 1066
DARRYL G. HOWERY AND HENRY C. THOMAS
636
ing values of K , at y = 0 and y = 1. The supposition as to the nature of the sites and their distribution in energy in effect predicts the whole course of K, in terms of the extreme sorption energies. The prediction is very rough when applied to clinoptilolite. As can be most easily seen by a numerical example for a special case, expression 16 for KOgives a plot of In KO vs. y scarcely distinguishable from the straight line between the intercepts at y = 0 and y = 1. Thus two extreme suppositions as to the nature of the exchanger predict nearly identical results for those thermodynamic functions immediately derivable from equilibrium data obtained at a single temperature. We can suggest no model which gives a convincing picture of the true nature of the exchange process in the zeolite mineral. Since we are in any case dealing with a somewhat heterogeneous material, better than rough agreement with any one model is not to be expected. It would be of interest to examine similarly highly purified natural or synthetic zeolites from the points of view here indicated.
Appendix It is possible to give a nearly complete account of the experimental results to be expected when exchange sorption of a pair of ions of like charge takes place on a surface of varying site energy if we suppose that the distribution of energy is linear between st lowest and a highest value and that there are no interactions between sites. That is, we suppose that between d e h i t e limits for any given range of energy there are to be found the same number of sites regardless of the value of the energy. At first sight, such a distribution seems highly artificial, but if one admits an upper and a lower bound for the energy, any continuous distribution could be imagined as pieced together out of linear segments. Thus an exchanger with a complex distribution of energies of sorption could be considered to be a heterogeneous material, each part of which is in equilibrium with every other part through the medium of the common solution with each part obeying a linear distribution law. The above ideas can be put into the following mathematical form: for a group of noninteracting sites all of the same energy, we have InK, = In-
y 1-x -= 1-y 2
-
- d T (Al) RT2
where we write y for the fraction of species 1on the surface and x for its fraction in solution. Here
- Ill0
(A21 is the partial enthalpy of species 1 on the surface with respect to its standard enthalpy in solution. Thus z 1= I71
The Journal of Physical Chemistry
- I;,is the enthalpy of exchange at compositions x, y. We have already supposed that these enthalpies are independent of composition; let us in addition suppose that they are independent of temperature. We can then write h-- y
1-x
1-y
-
2
AL RT
-
Now according to the above simplification of the nature of the surface, we suppose that we have for a surface of No sites ALm,
AL=
- ALmin No
N
+ ALmin
or, more simply, for 0 < 4' = N/No < 1 AL
-=A.$+B RT where the meanings of A and B are apparent. We note that for a group of sites of highest and lowest energies ALmax
K 2 = exp RT ALmin
K1 = exp RT
It is to be pointed out that KI, K2 are not values of KO for the entire surface. Now if there are dnl ions on the group of sites dN with energy A t B , we have 1 - 2 - eAE+B dnl dN - dnl x
+
We find y for the entire surface from this expression after integrating over .$ from 0 to 1, remembering that all groups of sites are in equilibrium with the same solution in which the fraction of ion 1is x
2
Because of our simple assumption as to the nature of the distribution of sites, we have here an expression which is easily evaluated. The result is the equation for the sorption isotherm of our surface
RT
y = l ALm,
- ALmin
1+-
In 1+-
-
,-ALmin/RT
X
- xe-ALm,,/RT X
ION EXCHANGE ON THE MINERAL CLINOPTILOLITE
1-x 1 1 x KI y = l - - In 1-x 1 Kz In - 1+-K2 K1 1+--
We may deduce at once some of the properties of KO for this surface. Thus lim
Y
- =
x,y--tox
lim KO=
K2
- Ki
1-x
lim - 2,g-11-y
- lim KO = z+l
Kz
Y
A direct integration of this expression has not been accomplished, but we can obtain the required result, as well as some illumination about the shape of the In KO vs. y curve, by putting the expression in the form
and KlKz - - In
This is also the standard free energy for the surface. It is of some interest to verify that we indeed get this value by the usual thermodynamic computation from In KOas deduced from the isotherm. Starting by solving the expression for the isotherm for (1 - x)/x, we find for KOexpressed as a function of
(A71
In K2 Ki
x-0
537
--
K2 Ki
- KI
(A8)
It is thus seen that the intercepts of a In KOus. y plot
lnK, =
In-
'
1 - Y
+ 1 n m 2 +
are indeed related to the limiting energiea of sorption, but in no very simple fashion. Because of the assumed variation of the exchange energy, it;is seen at once that the average exchange energy is S,l
AL dt = '/z (ALrnax
+
urnin)
(AS)
which corresponds to an average free energy of exchange given by
L1
In KOdy = In
-
Examination of this expression shows that if y -+ 1 y, the first and third terms simply change sign. Thus, the integral of these terms with respect to y over the whole range gives zero, and we verify that
s,' In
K, dy =
1/2
In K1K2
(A121
V o h m 69,Number 2 February 1966
