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Investigation of some kinetic parameters for M2+H+ exchanges on zirconium(IV) tungstophosphate — a cation exchanger
ELSEVIER
Reactive & Functional Polymers 32 (1997) 67-74
REACTIVE & FUNCTIONAL POLYMERS
Investigation of some kinetic parameters for M*+-H+ exchanges on zirconium(IV) tungstophosphate - a cation exchanger A.P. Gupta *, Pradeep K. Varshney Department of Applied Chemistry & Polymer Technology, Delhi College of Engineering, K. Gate, Delhi-l 10006, India
Accepted 19 August 1996
Abstract The kinetics and mechanism for the ion-exchange processes Mg’+-H +, Ca2+-H+, S?+-H+, Ba?+-H+, Zn*+-H+, Cd*+-Hf, and Pb*+-H+ at 25°C. 33‘C, 4X, 65°C (&l°C) temperatures on zirconium(IV) tungstophosphate were’ studied using approximated Nemst-Planck equation under the particle diffusion controlled phenomenon. Some1 physical parameters, i.e. fractional attainment of equilibrium Ucr,. self diffusion coefficients (D,), energy of activation (E,) and entropy of activation (AS*) have been estimated. These investigations reveal that the equilibrium is attained faster at higher temperature probably due to availability of thermally enlarged matrix of zirconium(W) tungstophosphate cation exchanger. Keywords:
Zirconium(IV) tungstophosphate; M*+-Ht exchanges; Kinetic parameters, i.e. D,, E, and AS*
1. Introduction The inorganic ion-exchange materials based on polyvalent metals have been established now an excellent recognition in various disciplines, i.e. metal ion separation, preconcentration, catalysis, environmental studies, medical science (kidney dialysis), ion-selective electrodes preparations, heterogeneous solid-state membrane formation and in ion-exchange fibre preparation, etc. To discharge the functioning in all above mentioned disciplines the ion-exchange process is main. To become aware about the process, the investigations of some kinetic parameters such as diffusion coefficient, energy of activation and entropy of activation, etc., are very much essential. It is noteworthy that these parameters tell us * Corresponding author. Fax: +91 (1 I) 2964038.
about the mechanism, rate determining step and rate law obeyed by ion-exchange process. Earlier studies [l-l l] of kinetic behaviour were based on Bt criterion [ 121 which is not very useful for a true ion-exchange process :because of different effective diffusion coefficienti and different mobilities [13] of the exchanging ,ions are involved. Nernst-Planck [ 14,151 equations provide more appropriate values for the various kinetic parameters. Involving Nernst-Planck equation, Varshney et al., have published theirfindings [ 16-221 on a number of ion-exchange materials. Mishra has investigated energy and entropy of activation as a linear function of ionic mobihties and radii for the exchange of alkaline earth metal ions on zirconium(IV) phosphoantimonate [23]. This paper deals with the investigation of some kinetic parameters for Mg*+--H* Ca*+H+, S?+-H+, Ba*+-H’, Zn*+-H+, Cd‘2+ -H+,
l381-5148/97/$17.00 Copyright 0 1997 Elsevier Science B.V. All rights reserved. PII S1381-5148(96)00071-S
68
A.P Gupra, P.K.
Varshney /Reactive & Functional Polymers 32 (1997) 67-74
and Pb2+-H+ ion-exchange process at different temperatures, i.e. 25°C 33”C, 45°C 65“C, (&l”C) on zirconium(IV) tungstophosphate [24,25]. 2. Experimental 2. I. Reagents Zirconium oxy chloride (made in Germany), sodium tungstate (Ranbaxy), ammonium sodium hydrogen ortho phosphate (B.D.H) and ortho phosphoric acid (CDH) were used for the synthesis of ion exchanger. All other chemicals were of AnalaR grade.
0
20
CO
60
Time (min
2.2. Apparatus A temperature-controlled incubator shaker having a variation of f 1°C was used during equilibrium studies. 2.3. Synthesis of zirconium(ZV) tungstophosphate Zirconium(IV) tungstophosphate was prepared by mixing solutions of 0.1 M sodium tungstate, 0.1 M ammonium sodium hydrogen ortho phosphate (or 0.1 M ortho phosphoric acid) and 0.1 M zirconium oxy chloride at room temperature in the different ratios. Hydrochloric acid (cont.) or ammonia was added to the precipitate to bring desired pH value and then it was heated to boil just. The precipitate was allowed to stand for 24 h. in the mother liquor and was then decanted and washed with distilled water and filtered by suction; it was then dried at 50°C. This dried product broken into small granules when it was immersed in water and these granules were converted into H+ form placing it in 3 M HNOs for 2 days. Finally, the exchanger was washed with demineralized water in order to remove the excess of acid and was again dried at 50°C. 2.4. Determination of infinite time of exchange The infinite time of exchange is the time necessary to obtain equilibrium in an ion-exchange
80
100
I20
)F
Fig. 1. A plot of UcT)versus I (time) for Mtzf-H+ exchanges on zirconium(W) tungstophosphate at 33 (&lT)
process. The ion-exchange rate becomes independent of time after this interval. Fig. 1 shows that 30 minutes are required for the establishment of equilibrium at room temperature, i.e. 33 f 1°C for Mg 2+-H+. Similar behaviour has been observed for Ca2+-H+, S3+-H+, Ba2+-H+, Zn2+H+, Cd*+-H+, and Pb2+-H+ exchanges. Therefore, half an hour has been assumed to be infinite time of exchange for the system. 2.5. Kinetic measurements The sample was grounded and sieved to obtain different particle sizes (25-30, 50-70, 70-100, 100-150 mesh sizes). Out of them the particles of mean radii * 125 pm (50-70 mesh size) were used to evaluate various kinetic parameters. The rate of exchange was determined by the limited bath technique by taking 20-ml fractions of 0.02-M metal ion solutions (Mg2+, Ca2+, St+, Ba*+, Zn2+, Cd2+, and Pb*+) which were shaken with 200 mg of the exchanger in H+ form in several stoppered conical flasks at different temperatures, i.e. 25°C 33°C 45°C 65°C (&l°C) for different time intervals (0.5, 1, 2, 3, 4 minutes). The supematant liquid was removed immediately and the determinations were made as usual by
A.P. Gupta, I? K. Varshney /Reactive & Functional Polymers 32 (I 997) 67-74 Table 1 r values for Mgzf-Hf. Ca2+-Hf, Sr*+-H+, Ba*+-H+, Zn2+H+, Cd*+-H+ and Pb*+-H’ exchanges on zirconium(IV) tungstophosphate at different temperatures after various time intervals. Time (min)
33°C
45°C
65°C
Mg*+-H+ 0.5 1 2 3 4
0.012 0.031 0.058 0.087 0.132
0.020 0.041 0.073 0.132 0.157
0.031 0.057 0.132 0.177 0.230
0.041 0.073 0.150 0.208 0.281
Ca*+-H+ 0.5 1 2 3 4
0.020 0.041 0.070 0.111 0.142
0.020 0.048 0.094 0.130 0.167
0.031 0.064 0.111 0.174 0.224
0.041 0.083 0.150 0.234 0.304
2 3 4
0.012 0.019 0.046 0.069 0.106
0.019 0.041 0.082 0.120 0.148
0.020 0.063 0.111 0.174 0.224
0.033 0.069 0.142 0.196 0.267
Ba*+-H+ 0.5 1 2 3 4
0.204 0.042 0.074 0.108 0.142
0.032 0.053 0.090 0.136 0.177
0.034 0.061 0.108 0.155 0.209
0.042 0.083 0.155 0.218 0.294
Zn*+--Hf 0.5 1 2 3 4
0.011 0.021 0.027 0.050 0.072
0.015 0.025 0.050 0.086 0.111
0.021 0.027 0.072 0.111 0.148
0.027 0.057 0.131 0.167 0.234
Cd2+-H+ 0.5 1 2 3 4
0.011 0.012 0.020 0.03 1 0.043
0.012 0.020 0.031 0.050 0.072
0.020 0.043 0.072 0.111 0.137
0.03 1 0.058 0.111 0.156 0.216
0.021 0.030 0.062 0.099 0.122
0.024 0.051 0.099 0.149 0.192
0.036 0.071 0.140 0.227 0.286
0.040 0.08 1 0.170 0.262 0.357
1
The results are expressed in terms of fractional attainment of equilibrium .!Ics) with time t according to the equation U(r) = the amount of exchange at time t
Pb*+-H+ 0.5 1 2 3 4
2.6. Analytical procedures
5 values at 25°C
Sr*+-H+ 0.5
69
EDTA (M/100) titrations. Each set was repeated three times and the mean values were taken for calculations.
the amount of exchange at infinite time t
(1)
and the corresponding values [23] wure calculated by solving the Nemst-Planck equation [14,15]. These values for different metal ion (M*+-H+) exchanges are given in Tabke 1 at different temperatures. 3. Results and discussion Kinetic parameters have been made under the particle diffusion controlled phenomenon for the exchange of Mg*+-Hf Ca*+-H+, S@-H+, Ba*+-H+, Zn*+-H+, Cd2;--H+, and PbF+-H+. The particle diffusion controlled phenomenon is favoured by a high metal ion concentratmn, relatively a large particle size of the exchanker and a vigorous shaking of the exchanging mixture at a particular constant temperature. A study of the concentration effect on the rate of exchange is proportional to the metal ion concentration at and above 0.02 M, when the rate of excHange is independent of the concentration of the metal ion in the solution (it confirms the particle diffusion controlled phenomenon). Below this concentration the film diffusion is more prominent. Plot of Ucsj versus t (time in minutes) for a@ metal ions are given in Fig. 2, which indicates that the fractional attainment of equilibrium is fa$ter at a higher temperature suggesting that the mobility of the ions increases with an increase in temperature. The uptake decreases with time. The present system may be considered to follow the ‘infinite solution volume’ [ 131 condition because CV >> c v where C and c ;are the metal ion concentrations in the solution and the exchanger phase, respectively, V and v are the volumes of these two phases. The Nemst+Planck equation can be solved with some additional as-
”
a2
04
2
3
0
4
2+
Zn
08
06
1.0 -
05.
2
Time (min
1
3
4
exchanges
Pt?+
I
0
02
0.4
0.6
OB
10
on zirconium(N)
1 _______)
Fig. 2. Plots of .!/(,J versus t (time) for different M 2+-H+
0.51
.
9
0
1
2
tungstophosphate
0.5
l!!!!!?
0.6
08
3
at different
4
C:
temperatures
(&IT).
A.f? Gupta, PK. Varshney/Reactive & Functional Polymers 32 (1997) 67-74
sumptions [ 131 which are valid for inorganic ion exchangers as the swelling charges and the specific interactions are not significant in this case. As a result we obtain a coupled interdiffusion coefficients DAB,the value of which depends on the relative concentrations of the counter ions A and B in the exchanger phase (CA and Ca). For CA << En the interdiffusion coefficient assumes the value b)~, A being the counter ion initially present in the exchanger phase. Since in the present study the exchanger is taken in the H+ form, DA may be replaced by &. The numerical results can be expressed by the explicit approximation: Ucs) =
(
1 - exp [n*(f;(a)r
+
+ f3W3)])
f2bb2 l’*
(2)
where t is the half time of exchange = &t/r:; a! is the mobility rate = fin/&; r, is the particle radius; and & is the interdiffusion coefficient of metal ion. Under the condition 1 5 a ( 20 and the charge ratio Zn/ZM = l/2 (where Zn is the H+ form of the exchanger and ZM is the exchanging metal ion) which are fulfilled in the present case, the three functions ft (a), &(a) and fs(a) can be expressed [ 131 as fl((Y) = -
1 0.64 + 0.36~~~.~~*
(2a)
f*(U)
1 0.96 - 2 .0 .o!“.4635
(2b)
=
f3(cz) =
-
-
1 0.27 + 0 .09 .a’,14
Table 2 Slopes of r versus t plots for different metal ions at different temperatures on zirconium(W) tungstophosphate Migrating ion Mg2+ Ca*+ S?+ Ba2+ Zn2+ Cd2+ Pb2+
S (SK’) x 104 25 “C
33OC
45°C
65°C
5.0 6.0 4.33 6.0 3.0 1.67 5.0
6.66 7.33 6.0 7.67 4.67 3.0 8.0
9.66 9.0 9.0 8.67 6.33 6.0 11.67
11.7 12.6 11.3 11.33 9.61 9.0 14.67
for M2+-H+ exchanges at a metal ion concentration of 0.02 M. The results are shown in Fig. 3. The slopes (S) of various t versus t plots for all metal ions are given in Table 2. The S values are related to & as
s=DH The values of - log & obtained by using the Eq. 3 were plotted against l/T. Straight lines are obtained for all the metal ions studied and are shown in Fig. 4 justifying the validity’of the Arrhenius equation &
= D,exp
A solution for Eq. 2 for each value of U(r) gives a corresponding value of t by graphical method. Table 1 shows the various t values for divalent metal ions at 25”C, 33”C, 45°C and 65°C (*l’(Y). While the slope values of the t versus t plots are given in Table 2. These are the straight lines passing through the origin, confirming the particle diffusion controlled phenomenon
--$ (
>
The energy of activation (E,) and the pre-exponential constant (Do) were then estimated from these plots using the value of & at 273 K. The entropy of activation (AS*) was then calculated by substituting [13] Do in Eq. 5, Do = 2.72d2y
(2c)
71
AS
1
exp [ R where d is the ionic jump distance [26] taken as 5 A; K is the Boltzman constant; h is the Planck’s constant; and T is the temperature taken as 273 K. The values of diffusion coefficient (Qo), energy of activation (E,) and entropy of activation (AS*) thus obtained are summarised in Table 3. The kinetic studies of zirconium(IV) tungstophosphate for different metal ions indicate that
72
Al? Gupta, PK. Varshney/Reactive & Functional Polymers 32 (1997) 67-74
3
n
N
A.P Gupta, l?K. Varshney /Reactive & Functional Polymers 32 (1997) 67-74
73
11.4 II.6 -
118 -
11.8 -
I I I I 65 65 33 25
120,
cl
66
$+Ud
(‘K)
65
33
25
0
.-)
Fig. 4. Plots of - log I)A versus l/ T (“K) for M *+-H+ exchanges on zirconium(IV) tungstophosphate.
Table 3 D,, & and AS’ values for the exchange of H+ with some metal ions on zirconium(IV) tungstophosphate Metal ion exchanging with Hf
Diffusion coefficient (LX,) (m2 s-t)
Energy of activation (I&) (KJ mole-‘)
Entropy of activation (AS*) (J deg-’ mol-t)
Mg2+ Ca*+ s12+ Ba2+ Zn2+ Cd*+ Pb2+
4.169 x 4.570 x 8.318 x 2.754 x 7.586 x 5.012 x 1.995 x
9.935 9.932 12.1274 15.366 12.758 19.027 14.008
-
lo-” 10-m lo-lo 1O-9 lo-” 1O-9 10-s
equilibrium is attained faster at a higher temperature as shown in Fig. 2 probably because of higher diffusion rate of ions through the thermally enlarged matrix. The particle diffusion phenomenon is evident from the straight lines passing through the origin for the t versus t plots as shown in Fig. 3. Negative values of the entropy of activation suggest the greater degree of order achieved during the forward ion-exchange [M2+H+] processes shown in Fig. 5A and positive values of energy of activation (Fig. 5B) facilitates the forward ion exchange. AS* and E, (Fig. 5A and B) values reveal the linear relationship with ionic radius, hydrated ionic radius and ionic mobilities.
75.969 75.205 70.225 60.281 70.991 55.289 62.950
Acknowledgements Authors are thankful to Prof. P.B. S arma, Principal, and Prof. R. Chandra, Head of D”epartment of Applied Chemistry and Polymer 1Technology, Delhi College of Engineering, for &-Oviding research facilities. We are also thankful~to Dr. G.L. Verma and Dr. R.C. Sharma, Department of Applied Chemistry and Polymer Tech&logy, for their valuable suggestions and encouragement during the course of this work. One iof us, Pradeep K. Varshney, thanks Delhi College of Engineering for financial help as HRD-JRI?.
A.l? Gupta, PK. Varshney/Reactive & Functional Polymers 32 (1997) 67-74
74
1
-50
7 -60 F 5 E -70 ‘i g -80
.
z. -90 h a -100
. A-i . I\ -I I
1
2
3
1
2
3
A
I
10
20
30
GD
50
60
1.0
2.0
3.0
4.0
5.0
60
I
0
B
Ionic Radius
Hydmted
( A’ 1
Ionic Radios
( A’ 1
I
I
70
80
1
70
80
bnic Mobility
( In2“Of1 Sk-l) x log
Fig. 5. Variation of & and AS* with ionic radii, hydrated ionic radii and ionic mobilities of alkaline earth metals on zirconium(IV) tungstophosphate.
References HI A.L. Ruvarac and V. Vesely, J. Inorg. Nucl. Chem., 32 (1970) 3939. PI A. Clearfield and AS. Medina, J. Inorg. Nucl. Chem., 32 (1970) 2775. [31 G. Alberti, R. Bertrami, M. Caseola, U. Costantino and J.P. Gupta, J. Inorg. Nucl. Chem., 38 (1976) 843. r41 J.P. Rawat and P.S. Thind, J. Phys. Chem., 80 (1976) 1384. [51 R.G. Herman and Clearheld, J. Inorg. Nucl. Chem., 38 (1976) 853. [61 J. Mathew and S.N. Tandon, Can. J. Chem., 55 (1977) 3875. [71 J.I? Rawat and SK. Singh, J. Inorg. Nucl. Chem., 40 (1978) 897 PI 1.P Saraswat, S.K. Srivastava and A.K. Sharma, Can. J. Chem., 57 (1979) 1214. [91 N.J. Singh and S.N. Tandon, Ind. J. Chem., 19A (1980) 416. DOI N.J. Singh, J. Mathew and S.N. Tandon, J. Phys. Chem., 84 (1980) 21. r111 KG. Varshney and A. Premadas, Ind. J. Chem., 20A (1981) 841. WI G.E. Boyd, A.W. Adamson and L.S. Myers, J. Amm. Chem.
Sot., 69 (1947) 2836. H31 F. Helfenich, Ion Exchange. McGraw Hill Book Co., New York, N.Y., 1962. u41 W. Nemst, Z. Physik. Chem., 2 (1888) 613; 4 (1889) 129. [I51 M. Planck, Ann. Pays. Chem., 39 (1890) 161. WI K.G. Varshney, S. Agrawal and K. Varshney, Acta Chim. Hung., 116 (1984) 69. [I71 K.G. Varshney and S. Rani, Ind. J. Chem., 22A (1983) 657. [181 K.G. Varshney, S. Agrawal and K. Agrawal, Coll. Surf., 13 (1985) 341. iI91 K.G. Varshney and S. Rani, Reactive Polym., 3 (1985) 231. WI K.G. Varshney, A.A. Khan and S. Rani, Coll. Surf., 25 (1987) 131. WI K.G. Varshney, U. Sharma, S. Anwar and A.A. Khan, Ind. J. Chem., 23A (1984) 152. WI K.G. Varshney, A. Gupta and K.C. Singhal, Coll. Surf., 82 (1994) 37-48. [231 A.K. Mishra, J. Ind. Chem. Sot., (1995) 777-781. v41 A.P. Gupta and Pradeep K. Varshney, Synth. React. Inorg. Met.-Org. Chem., USA, communicated. P51 A.P. Gupta and Pradeep K. Varshney, React. Funct. Polym., 31 (1996) 111-116. Ml R.M. Barrer, R.F. Bertholomew and L.V.C. Rees, Phys. Chem. Solids., 21 (1961) 12.
Reactive & Functional Polymers 32 (1997) 67-74
REACTIVE & FUNCTIONAL POLYMERS
Investigation of some kinetic parameters for M*+-H+ exchanges on zirconium(IV) tungstophosphate - a cation exchanger A.P. Gupta *, Pradeep K. Varshney Department of Applied Chemistry & Polymer Technology, Delhi College of Engineering, K. Gate, Delhi-l 10006, India
Accepted 19 August 1996
Abstract The kinetics and mechanism for the ion-exchange processes Mg’+-H +, Ca2+-H+, S?+-H+, Ba?+-H+, Zn*+-H+, Cd*+-Hf, and Pb*+-H+ at 25°C. 33‘C, 4X, 65°C (&l°C) temperatures on zirconium(IV) tungstophosphate were’ studied using approximated Nemst-Planck equation under the particle diffusion controlled phenomenon. Some1 physical parameters, i.e. fractional attainment of equilibrium Ucr,. self diffusion coefficients (D,), energy of activation (E,) and entropy of activation (AS*) have been estimated. These investigations reveal that the equilibrium is attained faster at higher temperature probably due to availability of thermally enlarged matrix of zirconium(W) tungstophosphate cation exchanger. Keywords:
Zirconium(IV) tungstophosphate; M*+-Ht exchanges; Kinetic parameters, i.e. D,, E, and AS*
1. Introduction The inorganic ion-exchange materials based on polyvalent metals have been established now an excellent recognition in various disciplines, i.e. metal ion separation, preconcentration, catalysis, environmental studies, medical science (kidney dialysis), ion-selective electrodes preparations, heterogeneous solid-state membrane formation and in ion-exchange fibre preparation, etc. To discharge the functioning in all above mentioned disciplines the ion-exchange process is main. To become aware about the process, the investigations of some kinetic parameters such as diffusion coefficient, energy of activation and entropy of activation, etc., are very much essential. It is noteworthy that these parameters tell us * Corresponding author. Fax: +91 (1 I) 2964038.
about the mechanism, rate determining step and rate law obeyed by ion-exchange process. Earlier studies [l-l l] of kinetic behaviour were based on Bt criterion [ 121 which is not very useful for a true ion-exchange process :because of different effective diffusion coefficienti and different mobilities [13] of the exchanging ,ions are involved. Nernst-Planck [ 14,151 equations provide more appropriate values for the various kinetic parameters. Involving Nernst-Planck equation, Varshney et al., have published theirfindings [ 16-221 on a number of ion-exchange materials. Mishra has investigated energy and entropy of activation as a linear function of ionic mobihties and radii for the exchange of alkaline earth metal ions on zirconium(IV) phosphoantimonate [23]. This paper deals with the investigation of some kinetic parameters for Mg*+--H* Ca*+H+, S?+-H+, Ba*+-H’, Zn*+-H+, Cd‘2+ -H+,
l381-5148/97/$17.00 Copyright 0 1997 Elsevier Science B.V. All rights reserved. PII S1381-5148(96)00071-S
68
A.P Gupra, P.K.
Varshney /Reactive & Functional Polymers 32 (1997) 67-74
and Pb2+-H+ ion-exchange process at different temperatures, i.e. 25°C 33”C, 45°C 65“C, (&l”C) on zirconium(IV) tungstophosphate [24,25]. 2. Experimental 2. I. Reagents Zirconium oxy chloride (made in Germany), sodium tungstate (Ranbaxy), ammonium sodium hydrogen ortho phosphate (B.D.H) and ortho phosphoric acid (CDH) were used for the synthesis of ion exchanger. All other chemicals were of AnalaR grade.
0
20
CO
60
Time (min
2.2. Apparatus A temperature-controlled incubator shaker having a variation of f 1°C was used during equilibrium studies. 2.3. Synthesis of zirconium(ZV) tungstophosphate Zirconium(IV) tungstophosphate was prepared by mixing solutions of 0.1 M sodium tungstate, 0.1 M ammonium sodium hydrogen ortho phosphate (or 0.1 M ortho phosphoric acid) and 0.1 M zirconium oxy chloride at room temperature in the different ratios. Hydrochloric acid (cont.) or ammonia was added to the precipitate to bring desired pH value and then it was heated to boil just. The precipitate was allowed to stand for 24 h. in the mother liquor and was then decanted and washed with distilled water and filtered by suction; it was then dried at 50°C. This dried product broken into small granules when it was immersed in water and these granules were converted into H+ form placing it in 3 M HNOs for 2 days. Finally, the exchanger was washed with demineralized water in order to remove the excess of acid and was again dried at 50°C. 2.4. Determination of infinite time of exchange The infinite time of exchange is the time necessary to obtain equilibrium in an ion-exchange
80
100
I20
)F
Fig. 1. A plot of UcT)versus I (time) for Mtzf-H+ exchanges on zirconium(W) tungstophosphate at 33 (&lT)
process. The ion-exchange rate becomes independent of time after this interval. Fig. 1 shows that 30 minutes are required for the establishment of equilibrium at room temperature, i.e. 33 f 1°C for Mg 2+-H+. Similar behaviour has been observed for Ca2+-H+, S3+-H+, Ba2+-H+, Zn2+H+, Cd*+-H+, and Pb2+-H+ exchanges. Therefore, half an hour has been assumed to be infinite time of exchange for the system. 2.5. Kinetic measurements The sample was grounded and sieved to obtain different particle sizes (25-30, 50-70, 70-100, 100-150 mesh sizes). Out of them the particles of mean radii * 125 pm (50-70 mesh size) were used to evaluate various kinetic parameters. The rate of exchange was determined by the limited bath technique by taking 20-ml fractions of 0.02-M metal ion solutions (Mg2+, Ca2+, St+, Ba*+, Zn2+, Cd2+, and Pb*+) which were shaken with 200 mg of the exchanger in H+ form in several stoppered conical flasks at different temperatures, i.e. 25°C 33°C 45°C 65°C (&l°C) for different time intervals (0.5, 1, 2, 3, 4 minutes). The supematant liquid was removed immediately and the determinations were made as usual by
A.P. Gupta, I? K. Varshney /Reactive & Functional Polymers 32 (I 997) 67-74 Table 1 r values for Mgzf-Hf. Ca2+-Hf, Sr*+-H+, Ba*+-H+, Zn2+H+, Cd*+-H+ and Pb*+-H’ exchanges on zirconium(IV) tungstophosphate at different temperatures after various time intervals. Time (min)
33°C
45°C
65°C
Mg*+-H+ 0.5 1 2 3 4
0.012 0.031 0.058 0.087 0.132
0.020 0.041 0.073 0.132 0.157
0.031 0.057 0.132 0.177 0.230
0.041 0.073 0.150 0.208 0.281
Ca*+-H+ 0.5 1 2 3 4
0.020 0.041 0.070 0.111 0.142
0.020 0.048 0.094 0.130 0.167
0.031 0.064 0.111 0.174 0.224
0.041 0.083 0.150 0.234 0.304
2 3 4
0.012 0.019 0.046 0.069 0.106
0.019 0.041 0.082 0.120 0.148
0.020 0.063 0.111 0.174 0.224
0.033 0.069 0.142 0.196 0.267
Ba*+-H+ 0.5 1 2 3 4
0.204 0.042 0.074 0.108 0.142
0.032 0.053 0.090 0.136 0.177
0.034 0.061 0.108 0.155 0.209
0.042 0.083 0.155 0.218 0.294
Zn*+--Hf 0.5 1 2 3 4
0.011 0.021 0.027 0.050 0.072
0.015 0.025 0.050 0.086 0.111
0.021 0.027 0.072 0.111 0.148
0.027 0.057 0.131 0.167 0.234
Cd2+-H+ 0.5 1 2 3 4
0.011 0.012 0.020 0.03 1 0.043
0.012 0.020 0.031 0.050 0.072
0.020 0.043 0.072 0.111 0.137
0.03 1 0.058 0.111 0.156 0.216
0.021 0.030 0.062 0.099 0.122
0.024 0.051 0.099 0.149 0.192
0.036 0.071 0.140 0.227 0.286
0.040 0.08 1 0.170 0.262 0.357
1
The results are expressed in terms of fractional attainment of equilibrium .!Ics) with time t according to the equation U(r) = the amount of exchange at time t
Pb*+-H+ 0.5 1 2 3 4
2.6. Analytical procedures
5 values at 25°C
Sr*+-H+ 0.5
69
EDTA (M/100) titrations. Each set was repeated three times and the mean values were taken for calculations.
the amount of exchange at infinite time t
(1)
and the corresponding values [23] wure calculated by solving the Nemst-Planck equation [14,15]. These values for different metal ion (M*+-H+) exchanges are given in Tabke 1 at different temperatures. 3. Results and discussion Kinetic parameters have been made under the particle diffusion controlled phenomenon for the exchange of Mg*+-Hf Ca*+-H+, S@-H+, Ba*+-H+, Zn*+-H+, Cd2;--H+, and PbF+-H+. The particle diffusion controlled phenomenon is favoured by a high metal ion concentratmn, relatively a large particle size of the exchanker and a vigorous shaking of the exchanging mixture at a particular constant temperature. A study of the concentration effect on the rate of exchange is proportional to the metal ion concentration at and above 0.02 M, when the rate of excHange is independent of the concentration of the metal ion in the solution (it confirms the particle diffusion controlled phenomenon). Below this concentration the film diffusion is more prominent. Plot of Ucsj versus t (time in minutes) for a@ metal ions are given in Fig. 2, which indicates that the fractional attainment of equilibrium is fa$ter at a higher temperature suggesting that the mobility of the ions increases with an increase in temperature. The uptake decreases with time. The present system may be considered to follow the ‘infinite solution volume’ [ 131 condition because CV >> c v where C and c ;are the metal ion concentrations in the solution and the exchanger phase, respectively, V and v are the volumes of these two phases. The Nemst+Planck equation can be solved with some additional as-
”
a2
04
2
3
0
4
2+
Zn
08
06
1.0 -
05.
2
Time (min
1
3
4
exchanges
Pt?+
I
0
02
0.4
0.6
OB
10
on zirconium(N)
1 _______)
Fig. 2. Plots of .!/(,J versus t (time) for different M 2+-H+
0.51
.
9
0
1
2
tungstophosphate
0.5
l!!!!!?
0.6
08
3
at different
4
C:
temperatures
(&IT).
A.f? Gupta, PK. Varshney/Reactive & Functional Polymers 32 (1997) 67-74
sumptions [ 131 which are valid for inorganic ion exchangers as the swelling charges and the specific interactions are not significant in this case. As a result we obtain a coupled interdiffusion coefficients DAB,the value of which depends on the relative concentrations of the counter ions A and B in the exchanger phase (CA and Ca). For CA << En the interdiffusion coefficient assumes the value b)~, A being the counter ion initially present in the exchanger phase. Since in the present study the exchanger is taken in the H+ form, DA may be replaced by &. The numerical results can be expressed by the explicit approximation: Ucs) =
(
1 - exp [n*(f;(a)r
+
+ f3W3)])
f2bb2 l’*
(2)
where t is the half time of exchange = &t/r:; a! is the mobility rate = fin/&; r, is the particle radius; and & is the interdiffusion coefficient of metal ion. Under the condition 1 5 a ( 20 and the charge ratio Zn/ZM = l/2 (where Zn is the H+ form of the exchanger and ZM is the exchanging metal ion) which are fulfilled in the present case, the three functions ft (a), &(a) and fs(a) can be expressed [ 131 as fl((Y) = -
1 0.64 + 0.36~~~.~~*
(2a)
f*(U)
1 0.96 - 2 .0 .o!“.4635
(2b)
=
f3(cz) =
-
-
1 0.27 + 0 .09 .a’,14
Table 2 Slopes of r versus t plots for different metal ions at different temperatures on zirconium(W) tungstophosphate Migrating ion Mg2+ Ca*+ S?+ Ba2+ Zn2+ Cd2+ Pb2+
S (SK’) x 104 25 “C
33OC
45°C
65°C
5.0 6.0 4.33 6.0 3.0 1.67 5.0
6.66 7.33 6.0 7.67 4.67 3.0 8.0
9.66 9.0 9.0 8.67 6.33 6.0 11.67
11.7 12.6 11.3 11.33 9.61 9.0 14.67
for M2+-H+ exchanges at a metal ion concentration of 0.02 M. The results are shown in Fig. 3. The slopes (S) of various t versus t plots for all metal ions are given in Table 2. The S values are related to & as
s=DH The values of - log & obtained by using the Eq. 3 were plotted against l/T. Straight lines are obtained for all the metal ions studied and are shown in Fig. 4 justifying the validity’of the Arrhenius equation &
= D,exp
A solution for Eq. 2 for each value of U(r) gives a corresponding value of t by graphical method. Table 1 shows the various t values for divalent metal ions at 25”C, 33”C, 45°C and 65°C (*l’(Y). While the slope values of the t versus t plots are given in Table 2. These are the straight lines passing through the origin, confirming the particle diffusion controlled phenomenon
--$ (
>
The energy of activation (E,) and the pre-exponential constant (Do) were then estimated from these plots using the value of & at 273 K. The entropy of activation (AS*) was then calculated by substituting [13] Do in Eq. 5, Do = 2.72d2y
(2c)
71
AS
1
exp [ R where d is the ionic jump distance [26] taken as 5 A; K is the Boltzman constant; h is the Planck’s constant; and T is the temperature taken as 273 K. The values of diffusion coefficient (Qo), energy of activation (E,) and entropy of activation (AS*) thus obtained are summarised in Table 3. The kinetic studies of zirconium(IV) tungstophosphate for different metal ions indicate that
72
Al? Gupta, PK. Varshney/Reactive & Functional Polymers 32 (1997) 67-74
3
n
N
A.P Gupta, l?K. Varshney /Reactive & Functional Polymers 32 (1997) 67-74
73
11.4 II.6 -
118 -
11.8 -
I I I I 65 65 33 25
120,
cl
66
$+Ud
(‘K)
65
33
25
0
.-)
Fig. 4. Plots of - log I)A versus l/ T (“K) for M *+-H+ exchanges on zirconium(IV) tungstophosphate.
Table 3 D,, & and AS’ values for the exchange of H+ with some metal ions on zirconium(IV) tungstophosphate Metal ion exchanging with Hf
Diffusion coefficient (LX,) (m2 s-t)
Energy of activation (I&) (KJ mole-‘)
Entropy of activation (AS*) (J deg-’ mol-t)
Mg2+ Ca*+ s12+ Ba2+ Zn2+ Cd*+ Pb2+
4.169 x 4.570 x 8.318 x 2.754 x 7.586 x 5.012 x 1.995 x
9.935 9.932 12.1274 15.366 12.758 19.027 14.008
-
lo-” 10-m lo-lo 1O-9 lo-” 1O-9 10-s
equilibrium is attained faster at a higher temperature as shown in Fig. 2 probably because of higher diffusion rate of ions through the thermally enlarged matrix. The particle diffusion phenomenon is evident from the straight lines passing through the origin for the t versus t plots as shown in Fig. 3. Negative values of the entropy of activation suggest the greater degree of order achieved during the forward ion-exchange [M2+H+] processes shown in Fig. 5A and positive values of energy of activation (Fig. 5B) facilitates the forward ion exchange. AS* and E, (Fig. 5A and B) values reveal the linear relationship with ionic radius, hydrated ionic radius and ionic mobilities.
75.969 75.205 70.225 60.281 70.991 55.289 62.950
Acknowledgements Authors are thankful to Prof. P.B. S arma, Principal, and Prof. R. Chandra, Head of D”epartment of Applied Chemistry and Polymer 1Technology, Delhi College of Engineering, for &-Oviding research facilities. We are also thankful~to Dr. G.L. Verma and Dr. R.C. Sharma, Department of Applied Chemistry and Polymer Tech&logy, for their valuable suggestions and encouragement during the course of this work. One iof us, Pradeep K. Varshney, thanks Delhi College of Engineering for financial help as HRD-JRI?.
A.l? Gupta, PK. Varshney/Reactive & Functional Polymers 32 (1997) 67-74
74
1
-50
7 -60 F 5 E -70 ‘i g -80
.
z. -90 h a -100
. A-i . I\ -I I
1
2
3
1
2
3
A
I
10
20
30
GD
50
60
1.0
2.0
3.0
4.0
5.0
60
I
0
B
Ionic Radius
Hydmted
( A’ 1
Ionic Radios
( A’ 1
I
I
70
80
1
70
80
bnic Mobility
( In2“Of1 Sk-l) x log
Fig. 5. Variation of & and AS* with ionic radii, hydrated ionic radii and ionic mobilities of alkaline earth metals on zirconium(IV) tungstophosphate.
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