Journal of Nuclear and Radiochemical Sciences, Vol. 7, No. 2, pp. 21-27, 2006

Modeling the Sorption Kinetics of Cesium and Strontium Ions on Zeolite A
K. M. Abd El-Rahman,*, a M. R. El-Sourougy,a N. M. Abdel-Monem,b and I. M. Ismailba

Hot Laboratory Center, Atomic Energy Authority, P.O. 13759, Cairo, Egypt
Chemical Engineering Department, Faculty of Engineering, Cairo University, Giza, EgyptbReceived: December 12, 2005; In Final Form: August 21, 2006
Zeolite A was chemically synthesized and characterized using X-ray diffraction, X-ray fluorescence, and thermal
analysis. The sorptive removal of cesium and strontium ions from aqueous waste solution using synthetic zeolite
A was investigated. Experiments were carried out as a function of pH, solute concentration, and temperature(298–333 K). Analysis of the respective rate data in accordance with three kinetic models revealed that the intraparticle diffusion was the rate determining step for the sorption of both studied ions. Values of the pseudo firstorder and pseudo second order rate constants and the particle diffusion coefficients were determined from thegraphical representation of the proposed models. Activation energy and thermodynamic parameters of free energy(∆ G*), enthalpy (∆ H*), and entropy (∆ S*) of activation for each sorption process were calculated from the linearized form of Arrhenius equation.

1. Introduction
The treatment of aqueous radioactive waste solutions requires
the concentration of dissolved metal ions followed by recovery
or secure disposal.1 Radionuclides of cesium and strontium,
because of their greater yield in the nuclear fission process andlonger half-lives, are among the most hazardous radionuclides
in the nuclear waste effluents for the environment.2 Different
techniques such as chemical precipitation, ion exchange, andevaporation are used for the treatment of aqueous waste solutions containing these ions. Ion exchange seems to be an attractive method because of its simplicity, selectivity, and efficiency.3
Synthetic aluminosilicate zeolites act as an efficient porous
exchange media and its cation exchange properties are widelyused for agriculture, nuclear industry, detergent industry, andenvironmental protection.4-7 The potential applications of zeolites and other selective ion exchangers have been well documented by Dyer. 8 These materials possess high exchange
capacity, element selectivity and specificity, and good resistantproperties to radiation and heat.9-10 The aim of this work is to
examine the efficiency as a cation exchanger of the preparedzeolite A for the removal of cesium and strontium ions fromwaste solutions. The effect of various parameters such as intial
metal concentration, contact time, and temperatures are examined. The kinetics of an exchange reaction is also evaluatedusing the light of current known models and the relevant
parameters were determined.
2. Experimental
2.1. Chemicals and reagents. All the reagents used wereof AR (Analytical Reagent) grade chemicals. Stock solutionsof the test reagents were prepared by dissolving CsCl,
SrCl2·6H2O, CaCl2, and MgCl2· 6H2O in distilled water.
2.2. Preparation and characterization of zeolite A. The
zeolite A having aluminosilicate structure was synthesized bymixing the aqueous solutions of NaAlO2, Na2O SiO2, and NaOH.11
Sodium aluminate (13.5 g) and sodium hydroxide (25 g) are dissolved in 300 mL of water, then stirred and boiled. The alumi*Corresponding author. E-mail: km_abdelrahman@yahoo.com

nate solution is added, with vigorous stirring, to the hot solutionof sodium metasilicate (14.2 g in 200 mL water) in a 1 L beaker.
The entire mixture was heated with stirring at about 90 ˚C for 2
hours until the suspension settled quickly when stirring was
stopped. The suspension is then filtered and the solid washedmany times with bidistilled water and dried overnight in an ovenat 110 ˚C.12
The inorganic product was sieved to obtain particles lessthan the size 0.25 mm. The crystallinity and chemical composition of the prepared material were investigated using X-ray
diffraction (XRD), X-ray fluorescence (XRF), and thermal
analysis. Also, the total surface area of zeolite A was measured by means of NOVA 3200 Series, Quantachrome Inc.,
USA using nitrogen adsorption method at 77 K, and applicationof the Brunauer, Emmett, and Teller (BET) method.
2.3. Kinetics studies. The effect of solution pH on uptakeof the two ions by zeolite A was studied at room temperature
to understand a maximum removal effeciency. For these investigations, a series of 50 mL test tubes were employed. Eachtest tube was filled with 10 mL of a 100 mg/L metal ion solution and adjusted to the desired pH from 2.0 to 8.0 by pH meter.
The pH of the solution was adjusted using dilute solution ofhydrochloric acid or sodium hydroxide. A known amount ofzeolite A (10 mg) was added into each test tube. The tubes
were shaked for 24 hours to attain an equilibrium. The
obtained suspension was centrifuged to separate the solid fromthe liquid phase. The obtained clear liquid phases were diluted
to an appropriate concentration range for the elemental analysis by atomic absorption spectroscopy.
In the experiments of the kinetic investigation, 10 mg of zeolite A was contacted with 10 mL solution containing known
concentration of cesium and strontium ions. Kinetic studies
were carried out with the different initial concentrations (50,100, and 150 mg/L). The temperature of the system was kept
the constant values (298, 313, and 333 K) by the thermostat
shaker during the exchange process. In the specified timeintervals, the suspension was separated from the liquid phase.
The concentration of the metal ions in the liquid phases were
measured by atomic absorption spectroscopy. The amountsorbed at time t, qt (mg/g), was determined as follows(c – c )V
qt = 0 t ,(1)W© 2006 The Japan Society of Nuclear and Radiochemical Sciences
Published on Web 11/15/2006

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RahmanJ. Nucl. Radiochem. Sci., Vol. 7, No. 2, 2006

Intensity (kcps)

2.0

1.5

1.0

∆T
0.5

0.0
10

20

30

40

50

60

70

80

2θ angle (deg)Figure 1. X-ray diffraction pattern of prepared zeolite A.

Temperature / ˚CTABLE 1: The strongest three peaks in XRD pattern ofsynthesized zeolite A
Peak
No.
9
8
10

2θ angle(deg)
27.05729.77723.997

Spacing(d/Å)

Crystallinity(I/Io)

Intensity(kcps)

12.29
8.71
7.11

100
69
35

1.945
1.938
1.832

Figure 2. Differential thermal analysis for prepared zeolite A.
TGA

Temp (˚C)

4.00

800.00600.00mg
3.00

400.00200.00TABLE 2: Quantitative elemental analysis of preparedzeolite A using X-ray fluorescence spectroscopy

0.00

2.00
0.00

20.00

40.00

60.00

80.00

Time /minConcentration (%)
27.79
39.43
32.14
0.076
0.026
0.008
0.015

where co and ct are the liquid phase concentrations at the time
=0 and t, respectively (mg/L), V is the volume of the solution(L), and W is the weight of the solid used (g).
3. Results and discussion
3.1. Characterization of material. The powder XRD pattern of the prepared material is shown in Figure 1. The XRD
patterns revealed that the synthesized material exhibits crystalline pattern. The strongest three peaks in XRD patterns wered=12.29 Å at I/Io =100, d=8.71 Å at I/Io =69 and d=7.11 Å at I/
Io =35 as shown in Table 1. These values are characteristic forzeolite A as reported in the literature of structure Na2O Al2O3
1.85 SiO2 5.1 H2O.11,12
X-ray fluorescence is a suitable method that can be used forquantitative elemental analysis. Table 2 listed the results of theelemental analysis of the prepared zeolite A material. Silicon
to aluminum ratio (Si/Al) gives the expected zeolite type.
Based on Table 2 the prepared zeolite has Si/Al ratio of about
0.82 within the range of zeolite A reported in the literature, i.e.
0.7 to 1.2.12 Thermal analysis of the prepared material was carried out with a heating rate of 5 ˚C/min to determine the thermal behaviour of the prepared zeolite A. Differential thermal
analysis (DTA) is shown in Figure 2. The peak at 180 ˚C shows
endothermic reaction derived from loss of combined water.
Thermal gravimetric analysis for the 3.213 mg prepared zeolite
A in its sodium form was performed in the range from 25–800
˚C as shown in Figure 3. The total weight loss is 1.161 mg
equivalent to 36.134% of the initial weight of the sample. The
greater portion of weight loss occured before 16.70 min at 180
˚C and then the rest of weight loss occurred until 71.07 min.
The final loss occurs at 800 ˚C. This weight loss shows that all
combined water molecules was lost at this temperature. Results

Figure 3. Thermal gravimetric analysis for prepared zeolite A.

100
80

Uptake, %Element
Na
Al
Si
Ca
Ti
Mn
Fe

60
40

Sr
Cs

20
0
0

2

4

6

8

10

pH
Figure 4. Effect of pH on the uptake percentage of cesium and strontium ions on zeolite A.

from thermal analysis mostly agreed with those reported by
Yu et al.13
Based on the XRD and the thermogravimetric results, theoxide chemical composition of the synthetic zeolite A can be
expressed via the formula: Na2O Al2O3 1.85 SiO2 5.1 H2O. The
theoretical cation exchange capacity (CEC) of synthetic zeolite
A in Na + form equals to 5.45 meq/g on the basis of the chemical formula. The BET surface area measured of the zeolite A
in sodium form after the thermal treatment for two hours at 473
K was 634.52 m2 /g.
3.2. Effect of pH. In order to investigate dependence of
maximum removal efficiency on pH, experiments were conducted in the pH range 2 to 8 and the results are depicted in
Figure 4. The recovery (%) of the metal ions by the preparedzeolite A increases gradually with an increase in pH value. In
the subsequent studies, experiments were performed in thesolution pH value of 6 to avoid any possible hydroxide precepitation.15
3.3. Effect of initial concentration. The effect of initial concentration were investigated on a sorption process at a fixed temperature. The experiments were performed at the initialModeling the Sorption kinetics of Cesium and Strontium ions on Zeolite A

80

150

50 ppm100 ppm
150 ppm

(a)

23

(a)

60

qt /mg g-1

120

qt /mg g-1

J. Nucl. Radiochem. Sci., Vol. 7, No. 2, 2006

90
60

40

298 K
313 K
333 K

20

30
0

0

0

20

40

60

80

0

100

20

40

60

80

100

Time / minTime / min
200

120

50 ppm100 ppm
150 ppm

(b)
160

(b)
100

qt /mg g-1

qt /mg g-1

80

120
80

60

40

20

0

0

0

50

100

150

Time / min

298 K
313 K
333 K

40

0

20

40

60

80

100

120

140

Time / minFigure 5. Effect of initial concentration on the amount sorbed of (a)Cs + and (b) Sr2+ from aqueous solutions onto zeolite A.

Figure 6. The rate of uptake of (a) Cs + and (b) Sr2+ from aqueous
solutions onto zeolite A.

concentrations of 50, 100, and 150 mg/L at 298 K for both the ionsas shown in Figure 5. It is clear that the sorption amount of theions increases with increasing the initial concentration, and theamount of sorbed strontium ion is grater than that of cesium ion.
These results illustrate that the increase in uptake capacity of thezeolite A with increasing of Cs + and Sr2+ concentration may be
due to higher probability of collision between the two ions andadsorbent particles.16
3.4. Kinetic studies. Preliminary investigations on anadsorption rate of the studied ions by the zeolite A indicatedthat the process is quite rapid and typically 60–80% adsorptionof the equilibrium value for each ion occured within 30 min.
The initial rapid sorption takes place in the initial stage (0–30
min) and then gradually increases slowly to reach an equilibrium value in approximately 90–120 min.
The amounts of both cesium and strontium ions exchanged
at the different time intervals, for the fixed concentration of
100 mg/L and at (298, 313, and 333 K), are plotted in Figure 6.
The data showed that the amount of the sorbed Cs + and Sr 2+
increases with the increase in temperature. This indicate an
endothermic nature of the process and the required time toreach equilibrium remained practically unaffected. Also, theamount recovery of each ion from the solution increases withtime, and attained equilibrium with 90 min for cesium and 120
min for strontium. The equilibrium time was independent of
the initial metal ion concentration in this study. The recovery
amount versus time curves are monotonously increasing to an
equilibrium, suggesting that the metal ions might cover on thesurface area of the adsorbent.
Most sorption processes take place by a multistep mecha-

nism comprising (i) diffusion across the liquid film surrounding the solid particles (a process controlled by an external masstransfer coefficient), (ii) diffusion within the particle itself
assuming a pore diffusion mechanism (intraparticle diffusion),and (iii) physical or chemical adsorption at a site.
To describe the changes in the sorption of metal ions withtime, several kinetic models were tested. The rate constant ofeach metal ion for removal reaction from the solution by zeolite
A was determined using pseudo first order and pseudo second
order rate models. The Lagergren first order rate expression is
written as17
log (q e – q t ) = log q e –

kl
t,
2.303

(2)

where qe and qt are the amount of an ion sorbed onto the zeolite
A at equilibrium and at time t, respectively (mgg-1) and k1 is therate constant of pseudo first order equation (min-1). The slopes
and intercept of the plots of log (qe - qt) versus t, as shown in
Figure 7, were used to determine the first order rate constant k1.
It was observed that the sorption of both the ions followed theLagergren equation over the range within 30 min and the values of the first order rate constants almost did significantly notchange with temperature as listed in Table 3. A cosiderable
deviation between the experimental and calculated qe values
occurred (see Table 3), this confirms that it is not appropriate
to use Lagergren kinetic model to predict the sorption kineticsof the studied ions on the zeolite A for the entire sorption
period. Also, in the most cases in the literature, the pseudo
first order equation of Lagergren does not fit well with thewhole range of contact time and is generally applicable over

24

RahmanJ. Nucl. Radiochem. Sci., Vol. 7, No. 2, 2006
2

1.5

-1

t/qt /min g mg

1.5

log (qe - qt )

(a)

298 K
313 K
333 K

(a)

1

0.5

1.2
0.9
0.6

298 K
313 K
333 K

0.3
0

0
0

10

20

30

40

50

0

60

20

40

80

100

Time / minTime / min
2

2

(b)
t/qt /min g mg

1.5

-1

298 K
313 K
333 K

(b)
log (qe - qt )

60

1

0.5

0
0

10

20

30

40

50

1.5

1

298 K
313 K
333 K

0.5

0

60

0

50

Time / min

100

150

Time / min+2+

Figure 7. Lagergren plots for the sorption of (a) Cs and (b) Sr ionsfrom aqueous solutions onto zeolite A.

Figure 8. Pseudo second order kinetic plots for the sorption of (a)Cs + and (b) Sr2+ ions from aqueous solutions onto zeolite A.

TABLE 3: Pseudo first order rate constants of Lagergren plots for Cs + and Sr2+ ions sorbed onto zeolite A
qeexp /mg g-1

Temp, K
298
313
333

qecal /mg g-1

k1 /min-1

R2

Cs+

Sr2+

Cs+

Sr2+

Cs+

Sr2+

Cs+

Sr2+

69.0
71.7
73.8

90.7
93.8
97.3

59.74
58.29
55.20

69.77
54.33
45.54

0.06470.07210.07710.0716
0.06910.0704

0.977
0.975
0.968

0.968
0.985
0.976

TABLE 4: The calculated parameters of the pseudo second order kinetic models
qe /mg g-1

Temp, K
298
313
333

h /mg g-1 min-1

k2 /g mg-1 min-1

R2

Cs+

Sr2+

Cs+

Sr2+

Cs+

Sr2+

Cs+

Sr2+

76.92
77.52
78.13

95.15
96.15
99.01

8.881
12.01815.99718.32329.02840.0940.00150.00200.00260.00200.00310.0041

0.993
0.991
0.995

0.998
0.996
0.993

the initial stage (20 to 30 min) of the sorption process.17,18
The pseudo second order rate model is expressed as17-19
t
1
1
=
+
t,
2
qt
k2 qe
qe

(3)

where k2 is the rate constant of pseudo second order equation(g mg-1 min-1).
The kinetic plots of t/qt versus t for Cs+ and Sr2+ sorption at
different temperatures are presented in Figure 8. The relation
is linear, and the correlation coefficient (R2), suggests a strong
correlation between the parameters and also explains that theion exchange process of each ion follows pseudo second orderkinetics. The product k2 qe2 is the initial sorption rate (h) represented as h = k2 qe2. From Table 4, it can be shown that the values of the initial sorption rate and rate constant were increased
with the increase in temperature. The correlation coefficientR2 has an extremely high value (>0.99), and its calculated equilibrium exchange capacity qe is consistent with the experimental data. These results explain that the pseudo second ordersorption mechanism is predominant and that the over all rate
constant of each ion exchange process appears to be controlled
by the chemical sorption process.18,19
Other simplified model is also tested because the above twoModeling the Sorption kinetics of Cesium and Strontium ions on Zeolite A

25

J. Nucl. Radiochem. Sci., Vol. 7, No. 2, 2006

4

-15.5

(a)

(a)

100 ppm

3

ln Di

Bt

-16
2

-16.5

298 K
313 K
333 K

1

-17
0.0028

0
0

20

40

0.003

60

0.00320.00340.0036

1/T

Time / min
4

-15.5

(b)

(b)

100 ppm

3

ln Di

Bt

-16
2

-16.5

298 K
313 K
333 K

1

-17
0.0028

0
0

20

40

60

0.003

0.00320.00340.0036

1/T

Time / minFigure 9. Bt versus time plots for the diffusion of (a) Cs + and (b) Sr2+
ions from aqueous solutions onto zeolite A.

Figure 10. Arrhenius plot for the sorption of (a) Cs + and (b) Sr2+ ionsfrom aqueous solutions onto zeolite A.

TABLE 5: Diffusion coefficient and thermodynamic parameters for the sorption of Cs + and Sr2+ onto zeolite A
Di × 1012 /m2 s-1

Metal ion
+

Cs
Sr2+

298 K

313 K

333 K

6.448
6.501

7.211
8.127

9.437
11.2908
Do ×2 10/m s-1Ea/kJ mol-1∆S*/J mol-1 K-1∆H*/kJ mol-1∆G*/kJ mol-1

2.438
12.50

9.06
13.05

-81.58-67.99

6.44
10.43

30.75
30.69

models equations cannot give definite mechanism. It is also
known that at an intensive stirring of the sorptive system, theintraparticle diffusion of the solute sorbed from the solution
into the sorbent pores could be a rate controlling mechanism.
In this study, a quantitative treatment of the data based on themodel suggested by Helfferich was applied.20 Various parameters were calculated using the following expressions as given
by Boyd et al.21
F(t) = 1 –

= 1–

6 ∞ 1
Σ exp(–Di π2 tn2 /ro2 ) ,π2 n=1 n2

(4)

6 ∞ 1
Σ exp(–n2 Bt) ,π2 n=1 n2

(5)

π2 Di
ro2

(6)

B=

,

where F is the fractional attainment of equilibrium at time t(F=qt /qe), B is the time constant, Di is the effective diffusion
coefficient of metal ion, and ro is the radius of the solid particle.
The Bt values in eq 5 for values of F were obtained from
Reichenberg’s table.22 The linearity test of Bt versus time plots
is employed to distinguish between film and particle diffusion

controlling sorption process. If the plot is a straight line passing
through the origin, then the sorption rate is governed by particle
diffusion mechanism otherwise it is governed by film diffusion.
Figure 9 depicts the Bt versus time plots for Cs+ and Sr2+ at different temperatures. The plots are linear and pass through theorigin for both the ions studied, indicating the sorption process
to be particle diffusion at all the studied temperatures. The values of Di calculated at different temperatures for Cs + and Sr2+
ions are presented in Table 5.
Plotting of ln D i versus 1/T (Figure 10) showed a straightline. This proves the validity of the Arrhenius equation:
ln Di = ln D0 – (E a / RT ) ,(7)

where, Do is a pre-exponential constant analogous to Arrhenius
frequency factor. The activation energies for both the ions, Ea,
were calculated from the slope of the straight lines in Figure 10
and the obtained values were presented in Table 5. Such a low
value of the activation energy for the sorption of each metal ion
indicates a chemical sorption process consisting of weak interaction between sorbent (zeolite A) and sorbate (Cs+ and/or Sr2+)
and illustrate that each sorption process has a low potential
energy. The Arrhenius equation would be also used to calcu-

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RahmanJ. Nucl. Radiochem. Sci., Vol. 7, No. 2, 2006

TABLE 6: Kinetic parameters and normalized standard deviations for the sorption of Cs + and Sr2+ onto zeolite A
Cs+

Kinetic constants

Sr2+

298 K

313 K

333 K

298 K

313 K

333 K

Pseudo-first-order rate model
k1 /min-1
R2∆ q (%)

0.06470.977
10.2

0.07210.975
14.6

0.07710.968
11.5

0.07160.968
9.1

0.06910.985
8.2

0.0704
0.976
8.4

Pseudo-second-order model
k2 /g mg-1 min-1
R2∆ q (%)

0.00150.993
7.9

0.00200.991
6.5

0.00260.995
7.4

0.00200.997
6.19

0.0031
0.996
6.87

0.0041
0.993
8.87

6.448
0.993
5.7

7.211
0.995
5.4

9.437
0.987
4.5

6.501
0.992
2.3

8.127
0.987
1.6

11.2900.989
4.2

Helfferich model
Di × 1012 /m2 s-1
R2∆ q (%)

late D 0 which in turn is used for the calculation of activation
entropy, ∆S*, of the sorption process using 23
D0 = 2.72 (kTd 2 / h ) exp ∆ S* / R ,(8)where k is the Boltzmann constant, h is the Planks constant, dis the average distance between two successive positions, R is
the gas constant, and T is the absolute temperature. Assumingthat the value of d is equal to 5×10 -8 cm,23 the values of ∆S* forboth the ions were calculated and presented in Table 5. The
negative values of activation entropy obtained for the sorptionof both the ions normally reflect that no significant change
occurs in the internal structure of the zeolite solid matrix during the sorption of ions.23
The Gibbs free energy of activation, ∆G*, was calculated
from the well known equation: 24∆ G* = ∆ H* – T∆ S* = Ea – RT – T∆ S* ,(9)where ∆ H* is the activation enthalpy.
The estimated values of ∆ H*and ∆G*were presented in Table
5. The positive ∆ G* values suggest the existence of an energy
barrier and that the reaction is non-spontaneous process.24 The
positive values of ∆ H* indicate the endothermic nature for the
diffusion process.
In order to compare the validity of each model more efficiently, a normalized standard deviation, ∆ q is calculated using
the following equation25∆ q (%) =100×Σ [(q t exp – q t calc)/q t exp ]2
n –1

ing ion and (ii) a consequence of forming the ion hydration
shell and a reduction of the limitation for diffusion in the innerpart of the pore system caused by the effective size of ion.29

,

(10)

where the superscripts ‘exp’ and ‘calc’ mean the experimental
and calculated values respectively, and n is the number of measurements. Based on the ∆ q values, as given in Table 6, theuptake of both Cs+ and Sr2+ from aqueous solutions using zeolite A can be well described by the intraparticle diffusion
model given by Helfferich. A good correlation of the rate datain this model can support the mechanism. Previous workers
reported that the diffusion coefficient, Di, values in the rangeof 10 -11–10 -13 m2 /s for intraparticle diffusion is considered to be
the rate limiting step for the sorption of metal ions.26-28 As per
this, the rate controlling mechanism appears to be particle diffusion since the Di values are in the order of 10 -12 m 2 /s. The
increase in values of the kinetic parameters with increasing
temperature is mainly due to (i) the increase of the mobility of
the ion and a decrease in retarding forces acting on the diffus-

4. Conclusions
In this study, the kinetic sorption of cesium and strontium
ions were investigated and the following conclusions can beobtained.
1. The recovery of the metal ion was increases with theincrease in the initial concentration and the amount uptake ofstrontium is grater than that of cesium ions in all studied concentrations.
2. The amount of the sorbed cesium and strontium ionsincreases with the increase in temperature, indicating an endothermic nature of the process.
3. Analysis of the respective rate data in accordance with threekinetic models revealed that the intraparticle diffusion was therate limiting step for the sorption of cesium and strontium.
Also, the obtained kinetic data provide valuable information
about the exchange mechanisms.
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