The temperature dependence of the exchange enthalpy of calcium and sodium ions on polymethacrylic and polyacrylic cationites

1723

ISSN 0036-0244, Russian Journal of Physical Chemistry A, 2007, Vol. 81, No. 11, pp. 1723–1727. © Pleiades Publishing, Ltd., 2007.Original Russian Text © V.A. Ivanov, O.T. Gavlina, E.A. Ilyukhina, V.I. Gorshkov, 2007, published in Zhurnal Fizicheskoi Khimii, 2007, Vol. 81, No. 11, pp. 1927–1931.

INTRODUCTION

The influence of temperature on ion exchange equi-libria and selectivity of ion exchangers has been studiedin detail, first for sulfo acid cationites and stronglybasic anionites and, during the past 15 years, also com-plex-forming ionites. Fairly abundant data have beencollected in monographs [1, 2] for ionites of the firstgroup and in [3, 4] for ionites of the second group. Tem-perature effects on the enthalpy of ion exchange on ion-ites, however, remain virtually unstudied.

The influence of temperature (up to 473 K) on theenthalpy of exchange of various ions from dilute solu-tions, in which one of the ions was a microcomponent,on a polystyrene-type sulfocationite with 12% divinyl-benzene (DVB) was studied in [5]. The enthalpies werecalculated in that work from the temperature depen-dences of corrected equilibrium coefficients at fixedsolution compositions. The physical meaning of thevalues obtained this way was not completely clear. Inaddition, according to the authors of [5], the valueswere obtained with large errors. The conclusion wasnevertheless drawn that the enthalpies of exchange ofsingly and doubly charged ions estimated this wayincreased as the temperature grew.

The differential enthalpy of exchange of sodium andcalcium ions on KB-4 polymethacrylic cationite calcu-lated from the corrected experimental equilibrium coef-ficients at fixed ion exchanger compositions was foundto increase as the temperature grew [6]. However, inthat work also, only a tendency toward an increase inthe enthalpy was claimed because of large measure-ment errors.

In this work, the influence of temperature on theexchange of calcium and sodium ions on polyacrylicand polymethacrylic cationites was studied using a

more accurate procedure suggested in [7] for determin-ing the differential enthalpy of ion exchange on selec-tive ionites. The procedure was based on the determina-tion of the composition of solutions in equilibrium sys-tems at two temperatures without analyzing the ionitephase.

EXPERIMENTAL

Objects of Study and the Preparation of Ionites

We studied gel carboxyl polymethacrylic cationitesKB-4P2 and KB-4 with 2.5 and 6% DVB, respectively,KB-2e4 gel polyacrylic cationite cross-linked by trieth-ylene glycol dimethacrylate (4%), and Purolite C104macroporous polyacrylic cationite (unfortunately, thecontent of the cross-linking agent (DVB) was not spec-ified for Purolite by the manufacturer).

All the ionites were regenerated before measure-ments. For this purpose, a 0.5 N solution of HCl takenin a twofold excess with respect to the exchange capac-ity was passed through a portion of an ionite in a col-umn, the ionite was washed with water, and a 0.5 Nsolution of NaOH taken in a twofold excess withrespect to the capacity was passed through it. As aresult, the Na form of the ionite was obtained. Next, toremove excess alkali from the intergrain space, the col-umn was washed with a small amount of distilled wateror a 2.5 N solution of NaCl with pH

~ 8–9

taken in anapproximately twofold excess compared with the vol-ume of the ionite in the column.

Ionites in the mixed Ca, Na form with the requiredfraction of calcium were prepared following two proce-dures. First, a portion of the volume of the cationiteobtained in the Na form was placed in a column 0.8–1 cm in diameter and converted into the Ca form bypassing a 0.5 N solution of

Caël

2

taken in excess at a

CHEMICAL THERMODYNAMICS AND THERMOCHEMISTRY

The Temperature Dependence of the Exchange Enthalpy of Calcium and Sodium Ions on Polymethacrylic and Polyacrylic Cationites

V. A. Ivanov, O. T. Gavlina, E. A. Ilyukhina, and V. I. Gorshkov

Faculty of Chemistry, Moscow State University, Leninskie gory, Moscow, 119992 Russiae-mail: [email protected]

Received July 6, 2006

Abstract

—The influence of temperature on the exchange of calcium and sodium ions from solutions of 2.3–2.8 g-equiv/l concentrations on KB-2e4 gel polyacrylic cationite, KB-4P2 and KB-4 gel polymethacrylic cat-ionites, and Purolite C104 polyacrylic cationite was studied over the temperature range 273–400 K. It wasshown that, simultaneously with a substantial increase in selectivity with respect to calcium ions, the differen-tial enthalpy of the ion exchange reaction increased linearly on all polyacrylic and polymethacrylic cationitesas the temperature grew.

DOI:

10.1134/S0036024407110015

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RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A

Vol. 81

No. 11

2007

IVANOV et al.

rate of 1–2 ml/min. The column was then washed witha small amount of water. Portions of ionites in the Naand Ca form were loaded into a flask using a smallamount of a 2.5 N solution of NaCl and mixed for a dayuntil equal ionic compositions of separate grains wereestablished.

According to the second procedure, a mixed solu-tion of NaCl and

Caël

2

taken in excess was passedthrough an ionite in the Na form at a certain tempera-ture until equilibrium was established.

Methods for Determining the Enthalpy of Ion Exchange

Ion exchange equilibria on carboxyl ionites werestudied in such a way that main composition changesoccurred in solution, whereas the composition of theionite changed insignificantly, as the temperature of theionite–solution system increased. The enthalpy of ionexchange was therefore calculated exclusively on thebasis of the analytic data on solution compositions inequilibrium systems at two temperatures [7].

Static method.

A mixed 2.3–2.8 N solution of NaCland

Caël

2

(150–300 ml) was added into a flask with asuspension (

~200

ml) of an ionite in the mixed Ca, Naform of a certain composition. The solution approxi-mately corresponded to equilibrium with the ionite of agiven composition at temperature

T

1

. The flask wasplaced into a thermostat at temperature

T

1

, and the sus-pension was periodically stirred. The concentration ofCa

2+

in the solution was determined by complexono-metric titration to check whether or not the system wasat equilibrium.

Temperature was then increased to

T

2

(by 10–25 K),the system was again equilibrated, and the equilibrium

solution was analyzed. The time of equilibrationdepended on temperature and varied from 3 h at 298 Kto several minutes at high temperatures (atomic absorp-tion spectroscopy was used to construct the kineticcurves shown in Fig. 1). After equilibration, the con-centration of

Na

+

was determined by emission flamephotometry.

In some of the experiments performed this way, thetemperature was above 373 K. The flask was thentightly closed by a Teflon lid with a rubber gasket and aTeflon capillary with a valve whose one end wasimmersed into the solution inside the flask. Pressure inthe flask increased as equilibrium water vapor pressurewas established. Because of an increase in pressure,solution flowed through the capillary when samples foranalyses were taken.

An ionite was then rapidly transferred from the flaskinto a column, solution from the intergrain space wasremoved using a water-jet pump, and a 0.5 N solutionof HCl taken in excess was passed through the column.The filtrate was analyzed to determine the amounts ofthe calcium and sodium ions displaced.

The swelling ability of polymethacrylic and poly-acrylic cationites decreases somewhat as the tempera-ture increases (the volume of the ionites changes by asmuch as 18–20% as the temperature increases from 293to 363 K [8]), and the solution becomes diluted withwater from the ion exchanger phase. However, at asmall (on the order of 20 K) difference between thetemperatures

T

1

and

T

2

, changes in solution concentra-tions are very small.

Dynamic method.

A cationite in the

Na

+

form wasplaced into two temperature-controlled columns nos. 1and 2 (suspension volumes were of about 40 and20 ml). A mixed 2.3–2.8 N solution of NaCl and

Caël

2

taken in excess was passed through the columns at atemperature corresponding to the lower temperature ofmeasurements

T

1

. The composition of the solution cor-responded to equilibrium with the ionite containing thegiven fraction of calcium at the temperature

T

1

. Afterequilibrium was established in both columns, the tem-perature in column no. 1 was increased to the highertemperature of measurements

T

2

. The same workingsolution was passed through it, and filtrate sampleswere taken at the exit of the column. The compositionof the equilibrium solution at

T

2

was determined fromthe first elution curve points with approximately equalconcentrations of calcium (Fig. 2).

The solution at equilibrium at

T

1

was removed fromcolumn no. 2 using a water-jet pump, and a 0.5 N solu-tion of HCl was then passed through it until metal cat-ions were completely displaced from the ionite. The fil-trate was analyzed for Ca

2+

and

Na

+

to determine thecomposition of the ionite.

The equilibrium coefficients and differentialenthalpy of exchange of Ca

2+

and

Na

+

ions were calcu-

500300100

τ

,

min

0.08

0.06

0.04

0.02

0

c

Ca

,

g-equiv/l

1

2

34

5

Fig. 1.

Changes in the concentration of calcium ions in solu-tion in a static system comprising the KB-4P2 poly-methacrylic cationite in the mixed Ca, Na form (the fractionof calcium is 0.46) and a 2.4 N mixed solution of NaCl and

Caël

2

as the temperature increases (

1

) from 293 to 313 K,(

2

) from 293 to 333 K, (

3

) from 293 to 333 K, (

4

) from 333to 353 K, and (

5

) from 353 to 364 K.


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2007

THE TEMPERATURE DEPENDENCE OF THE EXCHANGE OF CALCIUM 1725

lated by the equations [6, 7]

(1)

(2)

Here,

y

Ca

and

y

Na

are the equivalent fractions of calciumand sodium in the ionite,

c

Ca

and

c

Na

are the molar con-centrations of calcium and sodium ions in solution, and

and

f

±

NaCl

are the molar concentrations of thesalts in solution. Molar concentrations and activitycoefficients were used because (1) and (2) were derivedfor a solution of the concentration 1 mol/l as the stan-dard state in equations for the chemical potentials ofions [9]. The calculated value, however, has thedimension of kJ/g-equiv according to the equation forthe ion exchange reaction to which (1) and (2) corre-spond. When (2) is used to calculate enthalpies, weobtain the same results if concentrations are measuredin g-equiv/l, because (2) contains the ratio of concentra-tions.

We used the mean molal activity coefficients ofNaCl and

Caël

2

instead of the molar activity coeffi-cients of the salts in equilibrium solutions

f

±

. The molalactivity coefficients were found according to the empir-ical equations

(3)

(4)

These equations were obtained in [6] for mixed2.5 molal solutions of NaCl and

Caël

2

when the con-centration of

Caël

2

was low. The use of molal activitycoefficients

γ

±

was caused by the absence of data onactivity coefficients on the molar concentration scale

f

±

.It was found in [6] that the difference between

and did not exceed 3% forthe solutions under consideration.

In all experiments, the composition of ioniteschanged by as little as 0.5–2% as the temperatureincreased. In the dynamic experiment on KB-4P2,whose elution curve is shown in Fig. 2b, the fraction ofthe ionite volume in the dense suspension layer (0.63)and solution concentration (2.32 g-equiv/l) were takeninto account to find that the fraction of calcium in theionite changed as follows:

kyCa

1/2

yNa--------

cNa

cCa1/2

--------,=≈

∆Hn

= RT1T2

T2 T1–-----------------

cNa/cCa1/2( )T2

cNa/cCa1/2( )T1

--------------------------lnf NaCl±

2 / f CaCl2±3/2( )T2

f NaCl±2 / f CaCl2±

3/2( )T1

----------------------------------------ln+n

.

f CaCl2±

∆Hn

γ CaCl2±ln 2500/T– 54.5 8.21 T ,ln–+=

γ NaCl±ln 2100/T– 44.0 6.55 T .ln–+=


3/2 γ NaCl±2 /γ CaCl2±

3/2

yCa 313 K( ) y Ca 294 K( )0.63 0.0183 0.0125–( )

2.32-----------------------------------------------------+=

= 0.287 0.00158.+

This means that the equivalent composition of the ion-ite changed by only 0.55% as the temperatureincreased. Such a change in the ionite composition can-not be determined reliably by analytic methods. We canassume that the condition of a constant ionite composi-tion, which allows the differential enthalpy of ionexchange to be determined using the procedures sug-gested, was well fulfilled in our experiments.

The concentration of sodium ions in solution wasassumed to be constant in calculations by (2), because,in all experiments, this concentration changed by lessthan 1.5% as the temperature increased by 12–30 K.For instance, in the experiment considered above, theconcentration of sodium changed by only

(0.0058/2.32)

×

100%

= 0.25%. This change could not also be reliablyestablished by flame photometry.

RESULTS AND DISCUSSION

The temperature dependences of the equilibriumcoefficients of

Ca

2+

–Na

+

ion exchange on the gel poly-methacrylic and polyacrylic cationites studied areshown in Fig. 3. According to these data, the selectivityof cationites substantially increases as the temperaturegrows and continues to increase at temperatures above373 K. We found that the equilibrium coefficients forthe three types of weakly cross-linked gel cationites atvarious calcium ion fractions approximately fell on onedependence.

The temperature dependences of for exchangeof calcium and sodium ions on the gel and macroporous

∆Hn

600200

V

,

ml

0.03

0.02

0.01

c

Ca

,

g-equiv/l

(‡)

0.020

0.015

0.01030001000

V

,

ml

(b)

Fig. 2.

Elution curves in experiments performed to deter-mine the enthalpy of ion exchange on the KB-4P2 cationiteby the dynamic method (the fraction of calcium in the ionite(a) 0.51 and (b) 0.29, temperature intervals (a) 333–353 and(b) 294–313 K).

1726


Vol. 81

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2007

IVANOV et al.

polymethacrylic and polyacrylic cationites studied areshown in Figs. 4–6. The

T

2

–

T

1

temperature intervals towhich mean enthalpy values (symbols) correspond areshown by horizontal segments in these figures. The fig-ures also contain the

dependences on the mean temperature of the

T

2

–

T

1

intervals. These dependences reflect the contributionsof temperature effects on the activity coefficients of thesalts in solution to the value.

We see that the values obtained by the staticand dynamic methods agree with each other. The differ-ence between several experimental values at thesame temperature did not exceed 10%. The contribu-tions of the temperature effects on the activity coeffi-cients of the salts in solution ( ) to the val-ues are small. It follows that possible errors in estimatesof the temperature dependences of the activity coeffi-cients of the salts in solution cannot influence theresults obtained.

The enthalpy of exchange of calcium and sodiumions strongly increases, almost linearly, on all the ion-

∆Hn f ±( )RT1T2

T2 T1–-----------------


3/2( )T2


3/2( )T1

----------------------------------------lnn

=

∆Hn

∆Hn

∆Hn

∆Hn f ±( ) ∆Hn

420380340300

T

, K

120

80

40

0

k

~~

123456

Fig. 3.

Temperature dependences of the equilibrium coeffi-cient of exchange of calcium and sodium ions on the cation-ites (

1

–

3

)

KB-4, (

4

,

5

) KB-4P2, and (

6

) KB-2e4 at

y

Ca

=(

1

) 0.20–0.24, (

2

) 0.30–0.32, (

3

) 0.50–0.54, (

4

) 0.46–0.53,(

5

) 0.20–0.25, and (

6

) 0.52–0.56.

380340300

T

, K

16

8

0

∆

H

n ,

123456789

Fig. 4.

Temperature dependences of (

1

–

8

) and

(

9

) for exchange of calcium and sodium ions on

the KB-4 cationite. The fraction of calcium in the ionite

y

Ca

= (

1

) 0.30, (

2

) 0.38, (

3

) 0.50, (

4

) 0.24, (

5

) 0.32, (

6

) 0.37,(

7

) 0.5–0.54, and (

8

) 0.56. (

1–3

) Static measurements and(

4–8

) dynamic measurements.

∆Hn

∆Hn f ±( )

kJ/g-equiv

400360320

T

, K

20

10

0

∆ H n

,

12345

Fig. 5.


1

–

4

)

and

(

5


the KB-4P2 cationite. The fraction of calcium in the ionite

y

Ca

= (

1

) 0.42–0.46, (

2

) 0.23–0.24, (

3

) 0.25–0.29, and(

4

) 0.48–0.53. (

1

) Static measurements and (

2–4

) dynamicmeasurements.

∆Hn

∆Hn f ±( )

kJ/g-equiv


Vol. 81

No. 11

2007

THE TEMPERATURE DEPENDENCE OF THE EXCHANGE OF CALCIUM 1727

ites as the temperature grows. The ratio between theions in ionites does not influence substantially enthalpyvalues (Figs. 4 and 5). The differential enthalpies of ionexchange on weakly cross-linked KB-4P2, KB-4, andKB-2e gel cationites are fairly close to each other atequal temperatures (Figs. 4 and 5) and are somewhatlower on the Purolite C104 macroporous cationite(Fig. 6). This may be related to a considerably largercross-linking agent content characteristic of macroporouscationites. It should, in addition, be taken into account

that macroporous ionites are characterized by largenonexchange sorption contributions in systems withhigh-concentration solutions (nonexchange sorptioncontribution can be as large as 30–50% of the exchangecapacity for a 2.5 M solution of NaCl). This contribu-tion is much smaller for gel ionites (only 5–7% for theKB-4P2 cationite in the same solution) [10].

ACKNOWLEDGMENTS

This work was financially supported by the RussianFoundation for Basic Research (project no. 04-03-33020).

REFERENCES

1. F. G. Helfferich,

Ionenaustauscher

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Grundlagen,Struktur-Herstellung, Theorie

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Simple Ion-Exchange Equilibria

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, 205 (1998).4. V. I. Ivanov, V. I. Gorshkov, V. D. Timofeevskaya, and

N. V. Drozdova, in

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V. I. Gorshkov, Zh. Fiz. Khim.

74

(4), 734 (2000) [Russ.J. Phys. Chem.

74

(4), 641 (2000)].9. V. A. Ivanov, V. D. Timofeevskaya, and V. I. Gorshkov,

Zh. Fiz. Khim.

74

(4), 730 (2000) [Russ. J. Phys. Chem.

74

(4), 637 (2000)].10. V. A. Ivanov, V. D. Timofeevskaya, O. T. Gavlina, et al.,

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79

(8), 1494 (2005) [Russ. J. Phys. Chem.

79

(8), 1323 (2005)].

360320

T

, K

20

10

0

123

∆

H

n

,

Fig. 6.


1

,

2

) and

(

3


the (

1

) KB-2e4 and (

2

) Purolite C104 cationites. The frac-tion of calcium in the ionites

y

Ca

= (

1

) 0.52–0.56 and(

2

) 0.60–0.62. Dynamic measurements.

∆Hn

∆Hn f ±( )

kJ/g-equiv

Documents

The temperature dependence of the exchange enthalpy of calcium and sodium ions on polymethacrylic and polyacrylic cationites