Nov., 1959
TEMPERATURE DEPENDENCE OF SOMECATION-EXCHANGE EQUILIBRIA
1901
TEMPERATURE DEPENDENCE OF SOME CATION EXCHANGE EQUILIBRIA IN THE RANGE 0 TO 800°1 BY KURTA. KRAUS AND RICHARD J. RARIDON~ Contribution f r o m the Oak Ridge National Laboratory, Chemistry Division, Oak Ridge, Tenn. Received M a y 1 1 , 1969
The temperature dependence of a number of cation-exchange equilibria (tracers of Na+, K + , Rb+, Cs+, Be++, Ba++, Co++, Zn++, La+a, Eu+S us. H + ; tracers of K f , R b f , Cs+ and Ba++ us. N a + ) was studied in dilute aqueous electrolyte solutions. The temperature range was 0 to 150’ for exchanges with the H+-form of the resin and 0 to 200” for those with the Na+-form. The upper temperature limits were impose_d by the stability of the resin (H+-form) a2d the “safe” operating range of the equipment (Na+-form). Apparent heat_(A H ’ ) , entropy ( A T ’ ) and heat capacity ( A & ’ ) changes were computed for the ion-exchange equilibria. I n all cases AC,,‘ was positive; in a few cases it was quite large (up to 20 cal./deg/ equiv.). Good agreement between calculated and observed selectivity coefficients could be obtained by assuming ACp’ to be constant which leads to a linear variation of A B ’ with temperature T,. and of A T ’ with log 7’. In many cases A P ’ becomes zero in or near the temperature Lange studied (minima in the selectivity coefficient us. temperature curves); this appears to be one reason why values of A H ‘ for ion-exchange reactions are often small. 0.1 to 10 curies per g. of element). The stated radiochemical purities were greater than 98%, except for Nag4 and K24 which were stated t o be more than 95% pure. No further purifications were carried out. The radiochemical purity of the shorter lived isotopes was checked by following the decay rates. Samples of Na*4, K42,Rbso and La140were each counted for several half-life periods, with no appreciable deviations from the accepted values for the half-lives. 4. Solutions.-An approximately 1 M stock solution of HClO, was prepared from C.P. reagents and standardized by the usual methods. A stock 1 ill NaClOa solution, prepared from the salt, was standardized by a cation-exchange technique. A known volume of the solution was passed through a column of Dowex-50 in the H+-form. The capacity of the bed was in excess of that needed to replace the N a + ions of the solution by H + ions from the resin. The concentration of E a + (and hence of NaCIOa)could thus be established by acid-base titration of the effluent. Conversions from molarity ( A t ) to molality ( m ) were made using appropriRte density values from the literature. 5 . Procedure.-Resin samples (air-dried) were uniformly loaded with the “trace” metal; the resin was agitated with appropriate solutions of the radioactive tracers in a supporting electrolyte whose cation was the same as that on the resin ( H + or Na+). The electrolyte concentration 1. Method.-The method which was described earlier,a of the solutions was chosen so that most of the tracer would involves passage of eluting solution over a uniformly loaded be adsorbed in a few hours. From analysis of the solution bed of exchanger, analysis of the efRuent and computation before and after agitation the amount of adsorbed tracer of the distribution coefficients ( D )with the known initial was determined. Concentration of the trace ion in the composition of the bed. Metal analyses were carried out resin, mg(,),was calculated as amount/kg. of dry resin. radiometrically and concentrations of the supporting elec- The usual weight of resin loaded into the column was ca. trolyte determined by standard titrations. 0.5 g., with a total capacity of ca. 2 meq. The average 2. Resin.-The measurements were carried out with amount of activity used was 0.1 millicuries (me.). Since Dowex-50 X 12 ( W ) of mesh size 200 to 325. Capacity all traces had specific activity larger than 100 mc./g., the (4.67 moles/kg. dry H+-form resin) was determined by ti- tracer contributed lo00 5
By fitting (“least squares”21) the experimental data to eq. 16, the parameters (a,p, K ( ) listed in Table I1 were obtained. The solid lines in Figs. 1 to 3 represent the curves computed from these parameters. The deviations between observed and calculated values of K’ (see also Table I) appear to be within experimental error except in a few cases a t the extremes of the temperature range. For this reason, the first point in the K+-Na+ exchange series was not included in the least square (21) The “least square” fitting was carried out with the O R N L digital computer, the ORACLE: we are indebted to Dr. Milton Lietake for providing the code and assisting in the computations.
1
;:+ :/
Zn‘+
2.4
2.8
I
l
l
445 125 405
I
3.6
3.2
($) I
103 I
I
85 65 45 25 TEMPERATURE (“C.).
I I
52
Fig. 2.-Temperature dependence of cation-exchangeequilibria (metal tracers on Dowex-50 X 12, H + form). 13L L‘i2 -
+
”
-
5 io-
;
9-
8-
g
7-
1
+ v
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KURTA. KRAUSAND RICHARD J. RARIDON
1906
Vol. 63
TABLE111 THERMODYNAMIC FUNCTIONS OF CATION-EXCHANGE EQUILIBRIA Temperature ("C.) Exchange
Na-H
Function
0
25
-RT In K '
-0.244 -1.34 -4.0 -1.004 -2.42 -5.2 -1.161 -3.07 -7.0 -1.419 -3.79 -8.7 -0.377 0.47 3.1 -1.050 -1.52 -1.7 -0.311 -0.13 0.7 -0.236 -0.15 0.3 -0.929 0.08 3.7 -0.884 0.43 4.8 -0.497 -0.93 -1.6 -0.618 -1.07 -1.7 -0.825 -1.38 -2.1 -0.763 -0.05 2.6
-0.154 -1.11 -3.2 -0.887 -2.14 -4.2 -0.999 -2.79 -6 0 -1.219 -3.40 -7.3 -0.461 0 62 3.6 -1.026 -1.09 -0.2 -0.338 0.10 1.5 -0.255 0.10 1.2 -1.044 0.57 5.4 -1,024 0.86 6.3 -0.458 -0.90 -1.5 -0.577 -1.06 -1.6 -0,775 -1.36 -2.0 -0,840 0.22 3.5
AR' AS' K-H
-RT In K' Aif'
AS' Rb-H
-RT In K'
AR' As
CS-H
-RT In Ii AI71
AS' Be-H
-RT In K'
AB' AS'
Ba-H
-RT In K'
AR' AS'
CO-H
-RT In K'
AB' AS' Zn-H
-RT In K '
AR' AS'
La-H
-RT In K'
AR' AS' Eu-H
-RT In K'
AB' AS' K-Ne
-RT In K'
AB' AS' Rb-Na
-RT In K'
AR' AS' Cs-Na
-RT In K '
AR' AS'
50
-0.083 -0.88 -2.5 -0.794 -1.85 -3.3 -0.860 -2.51 -5 1 -1.052 -3.02 -6.1 -0.557 0 76 4.1 -1.038 -0.66 1.2 -0.384 0.33 2.2 -0.295 0.35 2.0 -1.199 1.06 7.0 -1.200 1.29 7.7 -0.422 -0.87 -1.4 -0.537 -1.05 -1.6 -0.726 --I .34 -1.9 -0.939 0.48 4.4
-RT In Ii' AR, AS' function, AC; is constant, AH' a linear function of Ba-Na
75
100
125
150
175
200
-0.031 -0.64 -1.8 -0.723 -1.57 -2.4 -0.743 -2.22 -4.2 -0.914 -2.63 -4.9 -0.665 0.90 4.5 -1.084 -0.22 2.5 -0.448 0.55 2.9 -0.354 0.60 2.8 -1.392 1.55 8.4 -1.409 1.73 9.0 -0.388 -0.85 -1.3 -0.497 -1.04 -1.6 -0.679 -1.32 -1.8 -1.059 0.75 5.2
0.005 -0.41 -1.1 -0.673 -1.28 -1.6 -0.647 -1.94 -3.5 -0.805 -2.24 -3.8 -0.782 1.05 4.9 -1.161 0.21 3.7 -0.528 0.78 3.5 -0.432 0.85 3.4 -1.620 2.04 9.8 -1.640 2.16 10.2 -0.356 -0.82 -1.2 -0.459 -1.03 -1.5 -0.634 -1.30 -1.8 -1.199 1.02 5.9
0.025 -0.18 -0.5 -0.642 -1.00 -0 9 -0.570 -1.66 -2.7 -0.722 -1.85 -2.8 -0.910 1.19 5.3 -1.267 0.64 4.8 -0.623 1.01 4.1 -0.526 1.11 4.1 -1.881 2.52 11.1 -1.919 2.59 11.3 -0.326 -0.79 -1.2 -0.421 -1.02 -1.5 -0.590 -1.28 -1.7 - 1.356 1.29 6.6
0.031 0.06 0.1 -0.628 -0.71 -0.2 -0.510 -1.37 -2.0 -0.663 -1.46 -1.9 -1.046 I .33 5.6 -1.400 1.07 5.8 -0.732 1.23 4.6 -0.637 1.36 4.7 -2.173 3.01 12.3 -2.215 3.02 12.4 -0.298 -0.76 -1.1 -0.383 -1.01 -1.5 -0.548 -1.25 -1.7 -1.530 1.55 7.3
0.022 0.29 0.6 -0.631 -0.43 0.5 -0.467 -1.09 -1.4 -0.627 -1.08 -1 0 -1.190 1.48 5.9 -1.558 1.50 6.8 -0.855 1.46 5.2 -0.762 1.61 5.3 -2.493 3.50 13.4 -2.537 3.45 13.4 -0.271 -0.73 -1.0 -0.346 -1.00 -1.5 -0.507 -1.23 -1.6 -1.720 1.82 7.9
0.001 0.52 1.1 -0.651 -0 14 1.1 -0.440 -0.81 -0.8 -0.612 -0.69 -0.2 -1 343 1.62 6.3 -1.741 1.93 7.8 -0.990 1.69 5.7 -0.901 1.86 5.8 -2.841 3.99 14.4 -2.883 3.89 14.3 -0.246 -0.71 -1 .o -0.310 -0.99 -1.4 -0.467 -1.21 -1.6 -1.925 2.09 8.5
small values of A n ' near room temperature is not necessarily significant. For the alkali metal-Na + reactions, however, curvature of plots of log K' vs. 1/T is very small, T',in hence extremely large, and the low values of AH' appear characteristic. Further, for these reactions the pattern of selectivities (K < Rb < Cs) persists from 0 to 200" and is reflected in a similarly regular pattern for the enthalpy and entropy changes. For these reactions the excess free energy change in kcal. is considerably smaller than AI? and further, AS' for these reactions is approximately the same. Hence the Tmin = -2.303T@/a = -801.70/a (20) relative selectivities for these systems seem to be Values of Tminare included in Table 11. A sur- primarily determined by the changes in heat conprisingly large number of ion-eschnnge equilibria tent. We are hesitant to make other generalizaiions have Tmin in or near the range 0 to 200" and hence the fact that so many ion-exchange equilibria have regarding the comparative values of AF', AH' or
T and AS' a linegr function of_log T . Representative values of AH' (kcal.], AS' (e.u.) as well as of the excess free energy AF' = - RT In K' (kcal.), computed a t 25" temperature intervals for the various ion-exchange equilibria, are listed in Table 111. At a temperature T = Trnin, AH' becomes zero and the curves such as in Figs. 1 to 3 have minima. This temperature may be computed by rearranging eq. 17 to
Nov., 1959
TEMPERATURE DEPENDENCE OF SOME CATION-EXCHANGE EQUILIBRIA
AS' of the various ion-exchange reactions. Thus, while near room temperature AH' for the alkali metal-H + exchange reactions becomes increasingly negative as the atomic number of the alkali metal increases, this simple relationship does not hold a t high temperatures. A similarly smooth relationship between AS' and atomic number of the alkali metals near room temperature is destroyed at high temperature. For these reasons of course some of the many previously proposed generalizations are also untenable. Thus for example, Boyd and co-workersg state that "ions of smaller hydration displace those of higher hydration or entropy, so that an over-all entropy decrease occurs." While it is true that frequently AS' is negative this is by no means universally correct and indeed AS' is a temperature dependent function, which in some cases changes sign in the temperature range studied. Detailed comparison of our values of AH' and does not AS' with those previously appear fruitful a t this time. There is clearly qualitative agreement between our results a t the lower temperatures and those described in the literature and not much more than qualitative agreement could in general be expected. Some authors have used different resins (e.g., phenolformaldehyde) or resins of different (or unspecified) cross-linking. Further, most data were obtained a t substantial loading rather than the tracer loading used here. In those cases where data in the literature pertain to, or can be extrapolated to "zero loading," agreement is gratifying. The calorimgtric data of Cruickshank and Meares18 give AH' = -1.25, -2.05, and -0.73 kcal. for the Na+-H+, K+-H+ and K+-Na+ systems at 25" which may be compared with our values of -1.11, -2.14 and -0.90 kcal., respectively; they find AS' = -3.02, -4.57 and -1.31 e.u. for these systems, while we find -3.2, -4.2 and -1.5 e.u. Similarly agreement is good between the data reported here and those of Plane and Krausi3 for the Zn++-H+ exchange for which we find AH' = 0.10 kcal. a t 25" while the earlier work gives 0.15 f 0.15. Interestingly Plane and Kraus find for the Cd++-H+ exchange reaction AH' = 1.4 kcal. which, if confirmed, would imply that even relatively similar transition elements may show large differences in the heats of adsorption. Extrapolation of the data-of Bonner and Smith" to zero loading yields AH' = -0.3 kcal. a t 0" and 1.1 kcal. a t 100" for the Cu++-H+ reaction in good agreement with our values of -0.13 and 0.78 kcal. for the Co++-H+ reaction a t these temperatures. However, agreement is poor for the Na+-H+ reaction where one computes from Bonner and Smith -4.4 and -1.0 kcal. at 0 and loo", respectively, while we find - 1.34 and -0.41 kcal. Description of the temperature dependence of the equilibria has been in terms of a constant heat
1907
capacity change Ac:, Unfortunately AC; is the least accurately known of the thermodynamic properties discussed since it is obtained by an implied double differentiation. I n spite of the large temperature range covered and the generally close agreement between calculated and observed values, AC,,' is probably not known to better than *0.5 cal./degree and frequently is uncertain by 1 cal./ degree. It is thus surprising that in the one example where comparison with the literature is feasible, agreement is very close. Surls and Choppin20 studied temperature dependence of adsorption of some lanthanides and actinides and found AC; = 18.2 cal./equiv./degree22 for Pmfa which is intermediate between our values of 19.5 for La+a and 17.3 for Eu+3, as one might expect from the relative position of these lanthanides. Since Surls and Choppin used a 4y0 DVB resin and we a 12y0 resin, this agreement may be fortuitous; otherwise it would imply a remarkable insensitivity of AC,,' to cross-linking. Examination of Table I1 shows that AC,,' for trace metal-H+ exchange reactions is large and there is a trend of increasing A€',,' with increasing radius of the metal ion. Values of A€,/ for exchanges involving the sodium form of the resin are substantially smaller than those for the hydrogen form resin. The difference amounts to 7 to 11 cal./deg./equiv. which presumably reflects possible partial association of the hydrogen ions with the sulfonate groups of the network. In conclusion, we might mention that one of the main objectives of this study was delineation of some of the problems which one might encounter in ion-exchange processes a t temperatures far from room temperature. Since the enthalpy changes for so many typical, though uncomplicated, ionexchange reactions is small a t room temperature and remains small a t high temperature one may conclude that ion-exchange behavior a t high temperature should not differ drastically from that at room temperature. For chromatographic separations, however, some allowance has to be made for possible reversals of selectivity with temperature. In the present study cations were selected for which there was little likelihood of hydrolytic reactions and the anion (Clod-) was chosen to decrease the probability of complications from complexing reactions. One may anticipate that heats of hydrolysis and of complexing are usually large and positive. Hence such reactions may become important a t high temperatures and for these systems large changes in ion-exchange behavior with temperature are to be expected. Conversely, the techniques described should prove useful for elucidation of these reactions a t high temperatures. Acknow1egment.-The authors are greatly indebted to Mr. Frederick Nelson for valuable advice.
*
(22) Their valuea are given on a per mole basis. They were divided by three to convert t o the per equiv. basis used here.
