Indian Journal of ChemistryVol. 30A, April 1991, pp. 322-327

Changes in thermodynamic parameters in the exchange of alkalineearth metals with sodium ions in Dowex-50Wx 8 and

Amberlyst-15 resins in aqueous medium

R S D Toteja, B L Jangida* & M Sundaresan

Analytical Chemistry Division, Bhabha Atomic Research Centre, Bombay 400 085

Received 29 May 1990; accepted 31 July 1990

Standard free energy, ~ GO, enthalpy, ~ HO and entropy, ~SO, changes have been evaluated forMg2+INa ", Ca2+ INa +, Sr2+INa ", Ba2+ INa + exchange systems on strong polystyrenesulfonic (PSS) ac-id type cation exchange resins, Dowex-50Wx 8 and Amberlyst-15 (macroreticular) in dilute aqueous so-lutions from equilibrium ionic distribution and heat of exchange measurements calorimetrically at 298K.The alkaline earth metals are preferred by both the resins and the preference increases from magnesiumthrough barium. The selectivity is lower for all the metals on Amberlyst-15 resin. The exchanges takeplace with absorption of heat. The endothermicity is more on Amberlyst-15 and it decreases with in-creasing size of the metal ion on both the exchangers. The uptake of divalent ions is governed by increasein entropy. The difference in entropies of hydration of alkaline earth metal and sodium ions is consideredto be a major factor responsible for increase in standard entropy. The lower selectivity of alkaline earthmetals on Amberlyst-15 is attributed to decrease in the hydration numbers of the cations in the resinsince it imbibes more water than Dowex-50Wx 8.

Considerable amount of work has been done onion-exchange equilibria involving organic cation ex-change resins but very less work has been reportedon enthalpy changes involving heterovalent ions.Further, no systematic study has been made on thedependence of the heat of exchange of unequallycharged cations on the ionic composition of the ex-changer. Boyd et al. 1 reported for the first time sucha dependence for Zn2+ /Na + exchange reaction. La-ter Jangida and Sundaresan? reported this type ofdependence for Al3+ IH+ exchange system. Recen-tly, Boyd ' has reported the changes in the thermod-ynamic properties for the heterovalent ion exchangereaction of lanthanum with sodium ions. The pre-sent work is a part of an on-going programme in ourlaboratory on the thermodynamics of heterovalentcation exchange reactions, and presents the equilib-rium and thermochemical measurements on strongpolystyrenesulphonate (PSS) type resins, Dowex-50Wx 8 (8% DVB nominally crosslinked gel type)and Amberlyst-15 (macroreticular type of unknowncross-linking). The standard free energy change,/). GO and the enthalpy change, sn» were estimatedfor four heterovalent cation exchange systems,Mg2+ INa+, Ca2+ /Na+, Srl+ INa+ and Ba2+/Na+on these two resins and the entropy changes, /).Sowere derived.

It is important to note that Bonner and cowork-ers"? reported equilibrium constants for several ca-

322

tion exchange systems involving uni-, bi- and tri-va-lent ions on various crosslinked Dowex-50 resins.But the activity coefficient ratios were not deter-mined for most of the ion pairs. Flett and Meares!"estimated activity coefficient ratios by using thetheory of mixed electrolytes and calculated the ther-modynamic equilibrium constant (K) and hence freeenergy changes, by combining the data of Bonnerand coworkers"? and the activity coefficient ratios.However, there was an error" in the calculation ofK and the results reported by them 10 need re-evalu-ation. This has been explained later in the text.

Materials and MethodsDowex-50Wx 8 (J.T. Baker) and Amberlyst-If

(Rohm and Haas) resins were reagent grade prepar-ations with 100-200 and 20-25 mesh sizes respect-ively. The resins were converted into sodium, mag-nesium, calcium, strontium and barium forms, airdried and stored. Their moisture contents were de-termined after drying at 383K in a vacuum oven andthe exchange capacities were determined by theconventional method. The isopiestic method wasused for determining the equivalent water contentsof the fully swollen resins at unit water activity. Thecapacities on dry basis and equivalent water con-tents are presented in Table 1.Equilibrium procedure

Air-dried resin (Na" form) (0.5g) was equilibrat-'J

TOTEJA et al.: lHERMODYNAMICS OF EXCHANGE OF Al.KAlJNE EARTII METALS WITH SODIUM IN OOWEX- 50WX8

Table I-Capacities and equivalent water contents ofDowex-50Wx 8 and Amberlyst- 15

Resin Dowex-50Wx 8 Amberlyst-15form --------

Capacity n,meq/g dry (mole of

resin H20 equiv)11.6411.1111.6011.5411.2711.23

Capacitymeq/gdry

resin

n,(mole of

Hp/equiv)

10.808.728.277.887.495.77

4.844.264.274.233.833.25

HRNaRMgRCaRSrRBaR

4.954.524.864.494.273.82

ed with the total electrolyte mixture (50ml) contain-ing 0.1 N NaCl and 0.1 NMCl2 (where M wasMg2+, Ca2+, Sr2+ or Ba2+). The volumes of NaCland MCl2 were adjusted so as to give the desiredequivalent fraction of M2+ in the resin after equili-bration.

The equilibrated solution was analysed' for M2+ions only by EDTA titration at pH 10 using EBT asan indicator. A known amount of magnesium wasadded while titrating Ca2+, Sr2+ or Ba2+ ions to geta sharper end point.

The equilibrium compositions of the resin and so-lution phases were obtained from the amount of res-in taken, its capacity, the concentration of M2+ ionat equilibrium and the initial composition of the so-lution. The concentrations of M2+ and Na" in theresin phase were calculated by difference.

Calorimetric measurementsThe isoperibol calorimeter set-up, described else-

where.':'? was used with some modifications. Thedewar flask was enclosed in a thick ( - 5 mm) cylin-drical brass vessel complete with a flange and an 0ring and nuts and bolts arrangement to make thevessel water tight. It was immersed completely be-low the surface of water in the thermostat for a bet-ter control of temperature. A potentiometric strip-chart recorder, Omniscribe (0 to 5 V) (Digital Elec-tronics, Bombay) was used for recording imbalancein the Wheatstone bridge potential. A digital d.c.source (Zenith Electronics, model DPML 200) wasused to supply a constant voltage (upto 6 V) to theheater. A digital electronic quartz timer (APLAB)having a range from 1 ms to 999.9 s and time baseaccuracy of ± 0.1 was used to measure the time ofpassage of current through the heater.

The procedure followed for the measurement ofheat of exchange was the same as described earlier-.The electrolyte mixture (100 mI) filled in the dewar

flask consisted of 0.1 NNaCI and 0.1 NMCl2 as thecase may be. The electrolyte solution in the. calor-imeter was analysed for M2+ ions after attamme~tof equilibrium. The equivalent fraction and the mil-liequivalents of M2+ ions in the exchanger corre-sponding to the measured heat exchange were cal-culated.

Treatment of Experimental Data

Evaluation of 6. GOThe standard state reaction for the M2+!Na + ex-

change system in the resin has been described byBoyd et al) and is represented by Eq. (1).

2NaR (a = 1, equil with 0.1 N NaCl)+ MCl2 (aq, a = 1) = MR2 (a = 1, equil with0.1 NMCI2)+2NaCI (aq, a= 1) ... (1)

The thermodynamic equilibrium c0o:>tant, ~ for theabove reaction was estimated followmg Games andThomas" equation (2) (contributions from the sol-vent terms were neglected)

lnK=-l+LlnKcdNM ... (2)

where

... (3)

In Eq. (3) s; is the experimental stoichiome.tricconcentration product, N Mand N Naare the equiva-lent fractions of the resinates, MR2 and NaR in theexchanger, mM and mNa are the molalities of MCl2and NaCI respectively in solution, YMand YNaarethe respective activity coefficients of M2+ and Na +ions in the electrolyte mixture and Y± MCI,andY± NCIare the mean molal activity coefficients forthe saaltsMCl2 and NaCl respectively in the aqueouselectrolyte mixture.

Activity coefficient of MCh. and NaCl mixtureThe activity coefficient ratio, Y~NaC/Y~MCI,vari-

ed with the relative concentration of NaCI and MCl2in external solution since the ionic strength changedfrom 0.1 to 0.13. The method suggested by Boyd etall for the sodium-zinc nitrate aqueous mixture hasbeen used for the calculation of log [y : NaCl!Y;MCI,].

Thus B = 2BNaCI- BMCI,The values of BNaCi = 0.005, BMgCl)= 0.2295,BCacll= 0.1605, BSrCl,= 0.1418 and BBsCI,= 0.0975were calculated as per the Eqs (5) and (6) of Boyd et

323

INDIAN J CHEM, SEC. A, APRIL 1991

al' using the literature" values of y ~NaCIandy ~Mel,for 0.1 m pure NaCI and MCl2 solutions res-pectively. The B-values were then obtained from theabove and are as follows:

Mixture1. MgCl2 + NaCI2. CaCl2 + NaCl3. SrCl2 + NaCI4. BaCl2 + NaCl

B0.21950.15050.13180.0875

The log [y : NaC/Y ; MCI,]values were calculated foreach set of experiment from a knowledge of the con-cent rations of NaCI and MCl2 at equilibrium. Thisratio varied from 0.1972 to 0.2193 for Mg2+/Na";from 0.2042 to 0.2261 for Ca2+ /Na "; from 0.2059to 0.2279 for Sr2+ /Na + and from 0.2103 to 0.2320for Ba2 + /Na + system.

The validity of the above method was verified bycomparing the data with the published work. Plat-ford'" has reported the activity coefficients for a ter-nary system, H20-NaCI-MgCl2 at 298K. Consider-ing a case of a mixed electrolyte at a total ionicstrength of unity (/-l = 1) where mNaCI = 0.4 andmMgCl2= 0.2 the reported values for log Y ± NaCIandlog Y±MgCI2are -0.173 and -0.326 respectively inthe mixed electrolyte thus giving log [y: NaC/Y; MgClJ= 0.280 which compares well with the valueof 0.297 calculated by the above method by obtain-ing the BNaCIand BMgCl2values at 1 N pure electro-lytes of NaCl and MgCl2 respectively. The agree-ment can be considered satisfactory since the com-parison has been done for an electrolyte mixture ofhigh (/-l = 1) concentration while the equations (5)and (6) used by Boyd et all are best suited for dilutesolutions.

The log K, values were obtained from Eq. (3) andwere plotted versus the equivalent fraction NM(Figs1 and 2). The curves were extrapolated on bothsides to NM= 0 and NM= 1 and the areas underthem were determined graphically.

The thermodynamic equilibrium constant wascalculated using Eq. (2) and 1'1GO was obtained fromthe expression (4 )

1'1GO (kJ/equiv.) = - 1- RT In K ... (4)

Evaluation of 1'1HOThe quantity I'1Ho is defined as the standard en-

thalpy change which accompanies the completeconversion of homoionic exchanger NaR to MR2,each in their respective standard states. To findI'1Ho, the integral enthalpy of exchange per equiva-lent, 1'1H, for the complete reaction must be derivedfrom the experimental heats corrected for the en-

324

2·0 Be

o I I , ! ! I I I I

o 0,' 0·2 0-3 0'4 0·5 0·6 0·7 008 o-s ',0NM2+

Fig.1-M2+ /Na" exchange on Dowex-50Wx 8 (aqueous)

Be Dz.o

Sr

... Co

"r"0

M

a I I I I

OQ·' 0·2 0'3 Q-4 0·5 0·6 0·' 0·8 osNM2+

Fig. 2-M2+ INa+ exchange on Amberlyst-15 (aqueous)

thalpy changes which occur in an electrolyte solu-tion. Thus

... (5)

where ¢JLis the apparent molar heat content. The1'1H of total exchange was determined by numericalintegration of the composition dependent differen-tial heat of exchange, (01'1HI oN M)'

AH= t (aI'1HlaNM)dNM ... (6)

The chord area technique" was applied for derivingthe dependence of (a 1'1HI aN M)on the equivalentfraction, NM in which the measured heats of partialexchange per equivalent were plotted as chords. Asmooth curve defining (aI'1HliJN.M) as a function ofNMwas drawn through the mid-points of the chords(Figs 3 and 4 where only midpoints have been plot-ted) such that the area above and below any givenchord was equal. The area under the curve withinthe limits as per Eq. (5) was determined to obtainI'1Hvalue.

The ¢JLvalues were obtained from literature'? andthe I'1;L values for Mg2+/Na '. Ca2+ /Na +, Sr2+INa + and Ba2+ /Na + exchange systems were calcu-

TOTEJA et aL: THERMODYNAMICS OF EXCHANGE OF ALKALINE EARTII METALS WITH SODIUM IN OOWEX- SOWX8

1'000 r,

1200A

A.!""';OOO r,C

> C·5l:' 800

"7 ,4 I4g4.. 600cCa:i

>< V SrIXIIa... 400 X

X.X200

00 01 0·2 0·3 0-4 0·5 06 0·7 ~ C).g 1·0

N",2+

Fig. 3- Heats of panial exchange of M2 + /Na + system as a func-tionofNM2+ onDowex-50Wx 8 (aqueous)

lated as 640, 586, 531, 515 J/equiv respectively byobtaining e., values for 0.1 Nsolutions.

Results and DiscussionThe reliability of the equilibrium data was tested

by conducting the equilibrium measurements forfour exchange systems under investigation on Do-wex-50 x 8 resin in duplicate. The duplicate resultsagreed within ± 5%. .. . .

The dependence of log K, on ioruc composmon(loading) of the resins is shown in Figs 1 and 2where log K; increased with the equivalent fractionof the preferred ion for all the exchange systems ex-cept for Sr2+ /Na + system on Arnberlyst-15 where adecrease was observed at higher loading.

As mentioned earlier, Flett and Meares'? haveobtained equilibrium data of Bonner and cowork-ers" - 9 and substituted them for K, in their Eq. (13)(see ref. 10) to calculate K which was not correct!'.While the latter have used mole fraction of the resin-ate in their equation for the calculation of equilibri-um constant, the former have used Gaines and Tho-mas'! equation where equivalent fraction of the re-sinate has been used. For the counter ions of thesame charge the moie fraction and equivalent frac-tion become equal but in the case of heterovalentsystem it is not so. The equation using mole fractionscale for the calculation of K differs from that basedon equivalent fraction by a factor which is ~qual. tothe difference in the valences of the counter Ions m-volved. Jangida 18 has explained this effectively by anillustrative example. Thus K values calculated byFlett and Meares 10 are in error b~ a factor of(ZB - Z A) and in turn the free energy change, !!J.G'(cal/equiv) is in error by a factor of - RT(~ - ZA)/ZAZf!'

The dependence of the differential heat at.ex-change, !!J.Hon NMis shown in Figs 3 and 4. !!J.Hfor

2800

o Ca

2400 9 Sr

x Ba

~200.oT>·3<T•3

T~ 1600!!!<i ~ ~"1:1:<l

1200

800 9

400

Xxx x

.0.2 .0.8 1.0.0.4 .0.6

N2+-M

Fig. 4- Heats of partial exchange of M2 + /Na + system as a func-tion ofN" .. on Amberlyst-IS (aqueous)

Dowex-50 X 8 resin (Fig. 3) did not change withcomposition of resin except for Mg2+/Na + systemwhere a maximum was observed and then a de-crease at higher loadings. In the case of Arnberlyst-15 resin (F.ig. 4) !!J.H increased continuously withcomposition for Mg2+ /Na + system but it remainedconstant for the rest three systems upto NM~ 0.8and then increased at higher loadings.

The !!J.Ho values reported here for Dowex-50Wx 8 have been compared with those calculatedfrom the reported'P-" values using the triangularrule. The values obtained were 6.81, 4.74,3.74 and2.02 kJ/equiv for Mg2+ /Na ", Ca2+ /Na +, Sr2+/Na + and Ba2+ /Na + exchange systems respectively.All the !!J.Ho values for Dowex-50Wx 8 estimatedin the present work were lower than the calculatedones'P-'? except for Ca2+ /Na + system where the re-verse was observed. The differences could be due tothe fact that a different approach (dependence oncomposition) has been used in the present work forthe evaluation of !!J.Ho.

The four exchange reactions in both the resinswere endothermic and the endothermicity dec-reased from magnesium through barium. The endo-thermicity was higher for the macroreticular resin,Arnberlyst-15.

The endothermicity could be due to the fact that

INDIAN J CHEM, SEe. A, APRIL 1991

Table 2-Standard free energies, enthalpies, and entropies of ion exchange reactions at 298 K onDowex-50 X 8 and Amberlyst-15 in aqueous medium

Exchange Dowex-50Wx 8 Amberlyst-15system

-6GO 6Ho 65° -6Go 6HO 65°kJ/equiv kJ/equiv J/degiequiv kJ/equiv kJ/equiv J/equiv/deg

Mg2+-Na+ 1.54 5.66 24.2 0.77 8.21 30.1Ca2+-Na+ 2.09 4.89 23.5 2.15 6.16 27.9Sr2+-Na+ 2.84 3.54 21.4 2.46 4.69 24.0Ba2 +-Na + 3.95 1.52 18.4 3.44 1.99 18.2

the enthalpy change of an exchange reaction de-pends on the difference in energy of interactingcounter ions with resin functional groups and on rel-ative energy contributions due to the dehydrationsof a counter ion entering the resin and hydration of acounter ion originally present in the ion exchanger.The heats of hydrations of M2+ ions are more ex-othermic relative to that of Na + ions. The amount ofheat absorbed to remove M2+ ions from solution isonly partially compensated by the heat evolvedwhen two sodium ions enter the aqueous solution.This can be illustrated from the following hypotheti-cal exchange reaction.

2Na+ (g) + M2+ (aql=' M2+ (g)+ 2Na+ (g) ... (7)

The /).Ho values were calculated for the abovehypothetical reaction using the thermodynamic datafrom NBS Circular 20 500 and were found to be1113, 782, 636 and 494 kJ/mol for Mg2+/Na ",Ca2 +INa +, Sr2+/Na + and Ba2 + INa + systems re-spectively. These high values require complete de-hydration of the ions. Since /).HO obtained in Table2 were of the order of 3-17 kllmol only, partial de-hydration must have occurred during the exchangeprocess. This partial dehydration must be propor-tional to the heats of hydration of the ions so that en-dothermic reactions can be expected for M2+INa+exchange systems. The decreasing endothermicitywhile going from magnesium through barium wasalso evident from /).Ho calculated for Eq. (7).

The standard enthalpy changes opposed the ionexchange reactions studied in the present work. Itwas thus purely entropy effect which was responsi-ble for making /).GO negative.

It is significant to note that th::: relative magni-tudes of standard free energies of hydration" ofNa + and M2+ ions are such that a large positive/).GOof the hypothetical ion exchange reaction(Eq. 7) might be expected if these cations were com-pletely dehydrated on entering the exchanger. How-ever, the exchange systems reported in this workshowed small negative /)'Go (Table 2) indicating, as

326

suggested by Boyd et al;1 that a balance must haveoccurred between the net enthalpy change (to par-tially dehydrate M2+ ion and to fully hydrate twoNa + ions) and the net gain in entropy for the sameprocess. The water contents of the resinates (Table1) suggested that these ions retained their primaryhydration shells so the observed /).Ho and /).5°(shown in Table 2)) must have been governed by en-thalpy and entropy effects associated with secon-dary hydration shells. The gain in entropy on rem-oving this secondary water shell was thus sufficientto overcome the enthalpy change which opposedthe ion exchange reaction in the first place.

The selective uptake of M2+ ions was accompan-ied by relatively large increase in standard entropychanges as is evident from Table 2. This suggestedthat extensive dehydration of M2+ ions must havetaken place when they entered the exchanger sincethe values approached the entropy increase for therelease of water by crystalline hydrates'? (i.e. ca 39.3llmol deg). The sizeable increase in entropy sug-gested that transfer of water molecules from the ex-changer to the dilute aqueous electrolyte mixture in-volved the release of bound water.

The measured values of /).5° are the net result oftwo factors-contributions due to increased hydra-tion of Na + ions when they enter aqueous phase andcontributions due to decreased hydration of M2+ions when they get exchanged. The contribution tothe net /).5° arising due to change in swelling, say inthe case of Dowex-50Wx 8, when Na " form of theresin is changed into M2+ form and the increasedconfigurational" entropy (5.9 Jzdeg/equiv) whentwo Na + ions are replaced by one doubly chargedM2+ ion may be considered small. Thus, increase in/).5° is largely contributed by the difference in theentropies of hydration of the exchanging ions.

The increase in /).5° could be explained due tohigher negative entropies of hydration of M2+ ionsas against that of the univalent Na + ions. The magni-tude of increase in entropy due to differences in hy-drations can be generalised if ~5° for the hypotheti-

TOTEJA et al.:THERMODYNAMICS OF EXCHANGE OF ALKAUNE EARTH METALS WITH SODIUM IN OOWEX- 50WX8

cal reaction (Eq. 7) can be calculated. In the absenceof entropy data on gaseous ions ~SO for Eq. 2 couldnot be calculated. The sodium and alkaline earthmetal ions were not completely dehydrated in theresinates as may be seen from the water contents ofthe ionic forms of the resins.

The selectivity of the alkaline earth metal ions wasfound to be less on Amberlyst-15 compared to thaton Dowex-50Wx 8. This may be due to the effect ofcrosslinking. Gupta" has interpreted the effect ofcrosslinking on the selectivity of alkali metals in 00-wex-50W resins in terms of various molecular inter-actions involved. A similar interpretation for the se-lectivity of alkaline earth metals cannot be given be-cause the hydration numbers for these cations in so-lution as well as resin phases are not available. How-ever, an attempt has been made to explain it quali-tatively.

The macroreticular Amberlyst-15 resin can beconsidered to behave like a low cross-linked ( < 8%OVB) resin compared to 00wex-50Wx 8 resinsince it imbibes more water (Table 1) due to its rigidstructure and large pore sizes. The alkaline earthmetals are able to form their hydration shells in themoderately crosslinked 00wex-50Wx 8 resinwhere the disturbing effects of the normal waterstructure as well as anions are absent. With decreasein crosslinking as in the case of Amberlyst-15, 00-wex-50W resin imbibes more water, and the hydra-tion shells of the preferred cations are destroyed toa greater extent by the normal water structureformed by the free water present in the resin. Whenalkaline earth metals are transferred from solutionto the resin phase, the change in hydration numbersin Amberlyst-15 will be less than that in Dowex-50Wx 8. Similarly, when Na " ions are transferredfrom resin to solution, the change in its hydrationnumber will be less in the former resin than that inthe latter. Therefore, the total change in hydrationnumbers due to the above two steps is less in Am-berlyst-15 than in Dowex- 50W x 8. When the hy-dration number of a cation increases a negative con-

tributiorr" or a positive contribution if it decreases,to ~ G would result. Thus the decrease in the hydra-tion numbers of the cation in Amberlyst-15 willhave positive contributions to ~Go (Table 2) caus-ing lower selectivities in the resin. The changes inhydration numbers account for the observed en-thalpy changes as well. There is a positive contribu-tion to ~Ho (Table 2) for Amberlyst-15 thus mak-ing them more endothermic than that for Dowex-50Wx8.

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327