1614
0. D. BONNER AND LINDALou SMITH
tive in producing low contact angles (0 to 10") on metal surfaces."7 The values of kcor as a function off or of hmax which are listed in col. 5 of Table I1 indicate a downward trend with a leveling off a t higher values of hm,,. A reason may be a simplification made in the treatment of Fig. lB, where it was assumed that the surface whose radius of curvature was r' maintained the same curvature when it reached water level. However, this is not the case, since the surface gradually merges with the water level and does not abruptly intersect it. This gradual merger with the water level causes an increase in r' which produces an error in the calculation of k. The efbut apfect is considerable a t lower values of h,,, parently can be neglected when hma, is greater than about 2 cm. (where r' is about 5 em). For this reason the most reliable value of k is taken as 6.3 X 10'' c.g.s. which recurs a t higher values of hmax. A dimensional analysis of eq. 3 shows that k must have the units MT-' which are the dimensions of a surface fluidity.8 The original assumption about the transfer rate shows that k is equal to the flux of molecules through a unit resistance and under a unit surface pressure difference. Flow measurements were made with cetyl alcohol to determine the value of k, since surface viscosity data were available for this substance and possible correlations could be investigated. It is also known that the two branches of the surface pressure ( P ) - area isotherm exhibit a different flow behavior. At low pressures the flow of the monolayer is Newtonian; while a t higher pressure, it is non-Newtonian. The calculation of k ordinarily can be made to only about 10% due to the precision with which the quantities in eq. 3 can be determined. The calculation of k for this case was further complicated because log ( y o - y ) / y vs. time and P vs. surface concentration were not linear. Cetyl alcohol forms a condensed type monolayer which collapses at higher surface pressures forming a solid f h . (7) D. J. Trevoy and H. Johnson,Jr., Abstraots of Papers presented at Miami, Florida, April 7-12, 1957, Div. of Colloid Chemistry of A.C.S.
Vol. 61
Occasionally, the solid which sometimes formed during spreading, clogged the surface channel and prevented the flow of monolayer, thereby adding to the difficulties. For these reasons only qualitative results will be given: They are (1) k is not constant but decreases linearly with increasing P in the range of 5-24 dynes cm.-l. (2) There are two distinct sections in the k vs. P curve both of which are linear, the lower pressure section having the greater slope. (3) The value of k for the higher pressure section varies with the surface pressure range chosen; k being higher for greater T. These observations when compared with the known properties of cetyl alcohol show that k decreases with P while surface viscosity increases with T. There are two distinct regions in the behavior of both properties which correspond to the regions in the equilibrium curve. Also the variation of the k values with the P range chosen (for higher pressure section) may be related to the fact that this film is non-Newtonian and that the shear rates change with pressure differences. These observations, although they are stated qualitatively, do show that k may be related to the surface fluidity in the case of cetyl alcohol. It is difficult to relate k (originally a proportionality constant) to a single film property, because the expression used to explain the experimental results is much simpler than the actual situation. The mechanism assumes that the flow occurs in a two-dimensionalsystem, while it was shown by the experiments with dyes, that the flow really occurs in a three-dimensional system. Also no attempt has been made to describe the flow in the surface channel but only to consider the flux through it. The k may, therefore, contain several quantities which arise from treating the complicated situation as a very simple one. I n short, the k may be related to the flow properties of films, but a t this time it is possible to confirm only the general behavior described above. In any event k can be thought of as the flux of molecules through a unit resistance (as defined above) under a unit surface pressure difference. ( 8 ) M. Joly,
I
t
I
J. CoZl. Sci., 11, 519 (1956).
THE EFFECT OF TEMPERATURE ON ION-EXCHANGE EQUILIBRIA. I. THE SODIUM-HYDROGEN AND CUPRIC-HYDROGEN EXCHANGES BY 0. D. BONNER AND LINDALou SMITH^ Department of Chemistry, University of South Carolina, Columbia, South Carolina Received June 27, 1967
Ion-exchange reactions between sodium and hydrogen and betwezn cupric and hydrogen ion on sulfonic acid type (Dowex The equilibrium constant, K F is greater than unity 50) resins have been studied over the temperature range 0 to 97.5 over this entire temperature range, and decreases with increasing temperature. The equilibrium constant h'2 is also greater than unity over this entire temperature range but increases with increasing temperature. This produces negative values of AH0 and AS0 for the former exchange reaction and positive values of these thermodynamic functions for the latter. The variation of the equilibrium constants with temperature is believed to be caused primarily by the change of activity coefficients of the ions in the resin phase.
.
Although the ion-exchange .process has been studied by many investigations a t room tempera(1) These results were developed under a project sponsored by the United States Atomio Energy Commission.
ture, very little information is available on the thermodynamics of ion-exchange on a sulfonate styrene-divinylbenzene resin at temperatures Other than 25". I n earlier work with sulfonated phenol-
I
Dec., 1957
SODIUM-HYDROGEN AND CUPRIC-HYDROGEN EXCHANGE
formaldehyde resins Boyd, et aLY2noted that AH for the ion-exchange process at room temperature should be small. Free energy, enthalpy and entropy data also have been reported3p4for several exchange systems on resins of this type. Cosgrove and Stricliland4 have reported values of AFo = -460 .tal., AHo = -1450 cal. and ASo = -1.0 e.u. for the potassium-hydrogen exchange on a sulfonated styrene-DVB exchanger of unspecified DVB content and at an unspecified loading (% potassium ion). Dicke16 has noted that the equilibrium quotients for exchanges involving the alkali metal and hydrogen ions decrease with increasing temperature over the range 0 to 75". These quotients were calculated, however, for only one unspecified resin composition at each temperature; ie., the composition resulting from the mixing of a sample of the pure resin in one ionic form with a pure solution of the other cationic chloride. Gregore has reported the results of a similar series of investigations over the temperature range 5 to 60". He also measured the equilibrium quotients for only one resin composition a t each temperature, but in this instance the resin composition was reported. In 1952, N. T. Coleman' noted that AH for the Ca-K exchange is positive, indicating that a very large positive entropy may occur when a divalent cation replaces a univalent one. It is believed that because of the interest in separations of ions a t elevated temperatures, which allows one-to take advantage of the more rapid rate of exchange, the investigation of the thermodynamics of the ion-exchange process should be profitable. This paper is the first of a series in which exchanges between various types of ions will be studied over the temperature range 0 to 97.5". These investigations were concerned with exchanges involving a univalent alkali metal ion, a divalent transition element ion and hydrogen ion. Experimental (a) Cupric-Hydrogen Exchange .-The methods of equilibration and separation of aqueous and resin phases a t room temperature have been described previously.8 The ionic strength of the cupric nitrate-nitric acid solutions was maintained at approximately 0.1. A modification of this batch procedure was also used for the exchanges at 0". The flasks were shaken for at least six hours in an ice-bath. The aqueous phase was then removed by suction through a fritted disc while the flasks remained in the ice-water bath. At elevated temperatures the temperature was controlled by equilibration of the resin and solutions in a jacketed vessel through which were refluxed vapors of appropriate liquids. Liquids which were used and their boiling points are as follows: cyclopentane, 50"; carbon tetrachloride, 77.5'; n-heptane, 98". The temperature of the aqueousresin exchange system was some 0.5' lower than that of the organic liquids a t the two higher temperatures. After equilibration the resin and aqueous phases were separated a t the temperature of the experiment. The resin was then removed from the apparatus, washed with distilled water and eluted with potassium nitrate solu(2) G . E. Boyd. J. Schubert and A. W. Adamson, J . A m . Cfiem. Soc., 69, 2818 (1947). (3) T. R. E. Kressman and J. A. Kitchmer, J. Chem. Soc., 1198
(1949). (4) J. D.CoRgrove and J. D. H.Strickland, ibid., 1845 (1950). ( 5 ) G. Dickel and L. Nieciecki, 2. Elektrocfiam., 59, 913 (1955). (6) H.P.Gregor and J. I. Bregman, J. Colloid Sci., 6,323 (1951). (7) N. T.Coleman, Soil Sei., 74, 115 (1952). ( 8 ) 0.D. Bonner and F. L. Livingston, THISJOURNAL, 60, 530 (1956).
1615
0.40
0.20
0.00
-0.20
20 40 60 80 100 Mole % sodium resin. Fig. 1.-The variation of the equilibrium quotient for the sodium-hydrogen exchange on 16% DVB Dowex 50 with resin composition a t various temperature: A, 0"; B, 26"; C, 50"; D, 74.5"; E, 97.5'. 0
tion a t room temperature. In accorda.nce with the usual procedure, the analysis for both ions in each phase was performed. (b) Sodium-Hydrogen Exchange.-The control of the temperature for this exchange was accomplished in the same manner as for the cuprichydrogen exchange. The data which are reported for 74.5' were obtained by circulating water from a constant temperature bath through the jacket of the apparatus. This method of temperature control is less desirable than the method described previously. A column technique was used for these equilibrations. An excess of a solution containing the desired ratio of sodium chloride to hydrochloric acid at an ionic strength of 0.1 was slowly passed through a column containing the resin sample. The resin was thus finally in equilibrium with a solution of known composition and this necessitated the analysis of only the resin phase.
Discussion and Results The equilibrium data presented in Figs. 1 and 2 were obtained for the exchange reactions
+ NaCl = NaRes + HC1 and HRes + */&u(NO& = l/2Cu(Res)r + HNOa HRes
(1) (2)
on nominal 16% DVB Dowex 50 resins. The equilibrium quotients E
"aRd?Lac!i NERenmNaCl
(3)
and k =
N'/%u(Res)rm"Os NHRenml/aCu(NOi)r
(4)
are plotted as a function of resin composition at the various temperatures. The symbol N represents the mole fraction of the ion in question in the resin phase and m refers to molarity in the aqueous phase. Over the larger portion of the range of resin com-
1616
0. D. BONNER AND LINDALou SMITH
VOl. 6i
0.6(
0.5C 0.50
0.40
0.40 4
4
3 4
0.30
c;l
0.30 /
0.20
0.20
1
B
0.10
0.10 20 40 60 80 100 Equivalent % cupric resin. Fig. 2.-The variation of the equilibrium quotient for the cupric-hydrogen exchange on 16% DVB Dowex 50 with resin composition at various temperatures: A, 0'; B, 26"; C, 50"; D, 77"; E, 97.5'.
0
2.75 3.00 3.25 3.50 I ~ x T 103. Fig. 3.-Temperature dependence of equilibrium constants: A, cupric-hydrogen exchange; B, sodium-hydrogen exchange. 2.50
k2
positions, the equilibrium quotients and @l are greater than unity. At constant resin composition ikp generally decreases with increasing temperature while kp increases with increasing temperature. Equilibrium constants ~NaResfNaReal?2EClYeECl NaReafHResmNaClY*NaCi
I
I
(5)
and have been calculatedgJOfrom the equations log K =
lo1* log k
Y 'NsCl
dX
I
(7) 0.00
and log K =
E
log k
YaHNo' Y'/'Cu(NOa)r
dX
(8)
where X is the equivalent fraction of the preferred ion in the resin phase. This equation, of course, requires the standard state for the resin phase to be the pure swollen resin associated with only one cation. The external solution must be dilute enough that the water activity is essentially (9) W. J. Argersinger, A. W. Davidson and 0. D. Bonner, Trans. Kana. Acad. Sci., 68, 404 (1950). (10) E. Hogfeldt, E. Ekedahl and L. G . Sillen, Acta Chem. Scand., 4, 828 (1960). . .
I
d
I
I
I
1
J
I
20 40 60 80 100 Mole % sodium resin. Fig. 4.-The variation of the e uilibrium quotient for the sodium hydrogen exchange on 4 8 and 8% DVB Dowex 50 resins with resin compositionoat 26" and 74.5': A, 8% DVB, 26"; B, 8% DVB, 74.5 ; .C, 4% DVB, 26"; D, 4% DVB, 74.5'.
unchanged over the entire range of resin composition. I n the calculation of these equilibrium constants it has been necessary to ignore the activity c1 y2HNOa/ coefficient ratios y 2 ~ ~ ~ / y 2 N aand y * ' 2 ~ U ~as ~ 0data , ) 1 for these activitv coefficients are not available at all of the temperatures. Values of
I
Dec., 1957
EXCHANGE SODIUM-HYDROGEN AND CUPRIC-HYDROGEN
the ratio ')'2HCl/')'2NaC1 in pure 0.1 M solutions11 range from 1.056 a t 0" to 1.040 at 60". Activity coefficients of Cu(NO& solutions have been measured only a t 25" and the value of the ratio Y ~ H N O , / ~ ' / ' C ~ ( N O , )is , probably 1.2 to 1.3 a t this temperature. Since these dilute solutions will not deviate greatly from the ionic strength principle a t any temperature, the neglect of the activity coefficient ratio term should only introduce an almost constant error in the value of K . This will correspond to an almost constant error of RT In (activity coefficient ratio) in the values of AFO. There are two points of particular interest in these exchange systems. First, the plots of log K us. 1/T (Fig. 3) for these two exchanges have slopes of opposite sign. The resultant values of AH0 are negative, indicating an exothermic process, for the sodium-hydrogen exchange and positive, ;.e., endothermic, for the cupric-hydrogen exchange. The values of ASo (Tables I and 11)are negative a t all temperatures for the sodium-hydrogen exchange and positive a t all temperatures for the cuprichydrogen exchange. Secondly the values of AHo and AX0 for each exchange are seen to be relatively constant over the temperature range 50 t o 100' but to vary considerably near 0". The arithmetic signs of the values of these thermodynamic functions are in agreement with those of Cosgrove and Strickland4 and Coleman' for exchanges of ions of the same valence types. If one considers the ion-exchange reaction12 as a Donnan membrane type process, with the same standard state for the aqueous and resin phases, then for the sodium-hydrogen exchange
1617
are unavailable for solutions of nitric acid and cupric nitrate it seems reasonable to suppose that a similar situation should exist for this system. TABLEI SODIUM-HYDROGEN EXCHANQE DATAON 16% DVB DOWEX 50 Temp.,
OC. 0
26 50 74.5 97.5
AF@(d)
1.97 1.55 1.42 1.33 1.24
-369 -261 -227 -197 -160
AHO(ca1.)
ASo(e.u.)
-2434 - 787 - 686 - 677 - 668
-7.56 -1.76 -1.42 -1.38 -1.37
TABLE I1 CUPRIC-HYDROQEN EXCHANQE DATAON 16% DOWEX50 Temp., OC.
0
26 50 77 97.5
@
AFa(ca1.)
AHo(ca1.)
ASO(e.u.)
2.56 2.69 2.90 3.10 3.27
-511 -589 -683 -788 -872
183 476 604 613 622
2.54 3.56 3.98 4.00 4.03
If variations of the equilibrium quotient (and therefore of AFo) with temperature are associated with the resin phase rather than the solution phase then one must interpret the values obtained for ASo as also primarily due to effects in the resin phase. The sequence of "order" in the resin phase is, therefore, Na > H > Cu. This sequence follows that of the "distances of closest approach," &, given by Stokes and Robinson13for these cations with various anions. Their data do not include cupric ion but do include many other divalent (aHCl)sq = (aHC1)resin transition metal ions, all of which have values of & greater than those of sodium and hydrogen ion. and Since the positions of the sulfonate anion groups (@NaCl)aq (aNaC1)resin are fixed the smaller values of distances of closest the equilibrium constant K would necessarily be approach of anion and cation should correspond to unity and the equilibrium quotient lc would be greater '(order" in the resin phase. equal to the product of activity coefficient ratios A few exchange reactions also were carried out ( YaHC1/Y 'NaCl)resin and ( Y ~ N ~ C I / Y ~ H C I ) ~ ~ . using nominal 8% DVB and 4y0 DVB resins. Available data" indicate that activity coefficients The results of these exchanges are presented in of hydrochloric acid and sodium chloride in 0.1 m Fig. 4. It is noted that the effect of temperature solutions decrease very slowly with increasing decreases with decreasing DVB content of the temperature over the temperature range which resin. This would be expected since the equiwas studied. The ratio of these coefficients re- librium constant for all exchanges decreases as the mains almost constant. The variation in the DVB content decreases. The arithmetic signs equilibrium quotient with temperature must thus of AFO, AH0 and AS0 for the sodium-hydrogen exbe due to changes in the activity coefficients in the change system appear to be independent of the resin phase. Although activity coefficient data resin DVB content for these exchanges on 4,8 and l6Y0 DVB resins but the magnitude of these func(11) H. S. Harned and B. B. Owen, "The Phyeical Chemistry of tions increases with DVB content. Electrolytic Solutions," Reinhold Publ. Gorp., New York, N. Y., 1950, pp. 547, 557.
(12) 0. D. Bonner, TWSJOURNAL, 68, 318 (1954).
(13) R. H. Stokes and R. A. Robinson (1948).
d.Am. Chem. SOL, 70, 1870
