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Diffusion of bromide, iodide and thallium ions at various temperatures
Appl. Rndinr. ht. Vol. 37. No. I, pp. 37-39, hr. J. Radiul. Appt. Instrum., Part A Printed m Great Britain
1986
0883-2889/86 $3.00 + 0.00 Pergamon Press Ltd
Diffusion of Bromide, Iodide and Thallium Ions at Various Temperatures S. F. PATIL, Department
N. G. ADHYAPAK
of Chemistry,
University
of Poona,
and S. S. JOSH1 Pune 411 007, India
(Received 15 April 1985; in revised form 30 May 1985)
Self-diffusion of bromide, iodide and thallium ions has been studied in NH,Br, NaI and Tl,SO, respectively over a temperature range of 25%50°C using agar gel medium. Activation energy for the process of diffusion in the above systems is computed from the experimental and theoretical diffusion coefficient data obtained by the zone-diffusion technique and Onsager’s equation respectively. A comparison of theoretical and experimental activation energies shows a good agreement in the cases of iodide and thallium ions while the experimental activation energy is found to be lower than theoretical in the case of bromide ions.
Introduction
Experimental
Survey of the literature shows that a large amount of data is available on the diffusion coefficient of various ions and electrolytes but in almost all cases the work is done at 25”C, and there are only a few reports(‘m3) on the measurement of activation energy for the process of diffusion. This is mainly due to the experimental difficulties encountered in the measurements of diffusion coefficients at higher temperatures. The chief difficulty to be overcome in the accurate determination of diffusion coefficients in aqueous solution is mixing due to convection and streaming flow. Hence, all the methods try to create conditions under which the above effects are reduced to a minimum. A number of such precision methods(“6J have been developed. However, these methods have not been ued very often for the measurement of diffusion coefficients at higher temperatures due to the complexity involved in the techniques. The abovementioned errors and difficulties are reduced to a minimum by immobilizing the system in gel medium, as has been pointed out by several workers.(7m9’ The agar gel by virtue of its structure is capable of holding about 98% water in a practically immobilized and semi-rigid state, eliminating the direct streaming and convectional flow of the solution and providing an ideal medium for the study of diffusion. The present paper reports the activation energy values for the self-diffusion of Brr, I- and Tl+ ions in NH,Br, NaI and Tl,SO, respectively over the temperature range of 25-50°C using a simple technique of zone-diffusion which enables measurements at higher temperatures without any difficulty.
The self-diffusion of Br- in NH,Br labelled with 82Br (t,,, = 36 h), I- in NaI labelled with “‘I (tlf2 = 8.04 d) and Tl+ in T&SO, labelled with *04T1 (I,,* = 3.9 y) was studied in 1.5% agar gel using the zone-diffusion technique. (lo) The diffusion coefficients were measured in the temperature range of 25-5O’C at 0.1 M concentration for Br- and I- ions and at 0.01 M concentration in case of Tl+ ions, due to the low solubility of T1,S04. The central zone of the diffusion column contains the labelled electrolyte of the desired concentration and gel columns on either side contain the unlabelled electrolyte of the same concentration. The details of the experimental procedure and calculations of diffusion coefficient are reported in our previous paper.(“)
Results and Discussion The variation of diffusion coefficient with temperature in various systems is presented in Table 1 and the corresponding Arrhenius plots are shown in Fig. 1. Each value of diffusion coefficient reported in the present work is an average of four independent measurements with an accuracy of f0.2%. Table 1 also includes theoretical values of D, in NaI, which are shown in parentheses along with the experimental values. It is obvious from the Table 1 and Fig. 1 that the diffusion coefficient increases with temperature in each system. As the diffusion coefficients are measured in agar gel medium, one has to take into consideration the effect of temperature on the agar 37
38
S.
Table
I.
of
Variation
F.
PATIL
diffusion coet?icient
Br
I” NH,Br
wth
temperature
in different
25
2.1 I2
I.915
(1.876)
-
30
2.331
2.102
(2.096)
2.210 2.499
35
2.523
2.338
(2.329)
40
2.753
2.573
(2.572)
2 740
45
2.922
2.805
(2.831)
3.092
3.106
(3.102)
SO ‘)
E (kJ mol
12.9
* 0.5
15.550.5
gel. However, it has been shown that the obstruction effect caused by the agar gel is independent of temperature(‘.“.‘3) (25-50°C) which itself indicates that the gel structure is unaffected in the temperature range studied. Thus, the change of temperature only affects the process of diffusion. With increasing temperature, a larger fraction of the diffusing species acquires a requisite amount of energy in order to cross the potential energy barrier required for the process of diffusion, giving an increasing trend in the value of diffusion coefficient with temperature in agreement with the transition state theory of diffusion.(‘4’ The experimental activation energy for the diffusion of I- in NaI, Br- in NH,Br, and Tl’ in T&SO, is computed by least square fitting of the data presented in Fig. 1 and using the following Arrhenius equation: D = D,exp( - E/RT)
Br-in
M
I-
in NaI
(exptl
-
I-
in NaI
(fheoret.1
of different parameters required equation are taken from the
at 25°C:
D, ~10~5cm2s~‘=2.044-0.530~
NH4 Br
Fig.
I. Arrhenius
plots
3.3
K x IO3
for the self-diffusion
NH,Br, I- in NaI and Tl + in Tl?SO,.
of Br
’ = 2.286 - 0.599fi
D, /10m5cm’s
(3)
at 35°C:
D,~/lO~‘cm’s-’
= 2.541 - 0.670 fi
(4)
at 40°C:
D, /10m5cm* S-I = 2.809 - 0.747 XC
(5)
at 45 C:
D, /lo-‘cm*
s ’ = 3.093 - 0.828 ,/?
(6)
D, /lo-‘cm’
s
’ = 3.392 - 0.916 JC
(7)
at 50°C:
in NH,Br: = 1.755 - 0.404$!
at 18°C
(8)
D,, /IO ‘cm’ ss’ = 2.078 - 0.485 fi
at 25’C
(9)
D,,,jlO_ 5cmzs~’ = 1.707 - 0.851 3
at 18°C
(10)
D,,,/lo-‘cm’ss
at 25°C
(11)
for Tl+ in TI,SO
3.2
(2)
at 30°C:
D,, /10~5cm’ss’
(l/T)
in the litera-
The 0nsager-Gosting-Harned(‘5,‘81 equation for the diffusion of I- in NaI after appropriate substitution of the different parameters takes the following form at various temperatures.
for Br
3.1
0.2
In the cases of Br and Tl+ ions, due to the unavailability of the data required in the theoretical equations at various temperatures, the activation energy is determined by calculating the values of diffusion coefficients only at two different temperatures, and the theoretical equations in these systems are as follows:
, -4.4 M
3.419 I6 i
(16.1)
The values theoretical ture,“b.17’
(1)
These values are presented in Table 1 along with the standard deviation. The theoretical activation energy, on the other hand, in each system is determined from the corresponding theoretical diffusion coefficient values estimated on the basis of Onsager’s”” theory.
3.0
systems
l-l + in TI1:SO,“”
I in NaI D (IO qcm~S ‘)
TeIllP./SWteIll
r
et al
in
4
:
= 1.987 - 0.992 fi
The theoretical activation energy estimated from the diffusion coefficient data calculated on the basis of equations (l)-(11) is found to be 16.1, 17.9 and 15.7 kJ mol- ’ for the diffusion of II, Br and TI+ ions respectively while the corresponding experimental values are found to be 15.5 _t 0.5, 12.9 k 0.5 and 16.0 k 0.2 kJ mol ‘. A comparison of the former
Diffusion
of Br, I and Tl ions
and the latter values shows that they are in good agreement with the exception of NH,Br system, wherein the experimental value of activation energy is found to be less than the theoretical one.
References 1. Patil S. F. and Adhyapak N. G. Int. J. Appl. Radiat. Isot. 32, 631 (1981). 2. Patil S. F. and Adhyapak N. G. J. Radioanal. Nucl. Chem. Lett. 93, 173 (1985). 3. Pathak B. K., Singh P. C. and Singh V. N. Acta cienc. Ind. 4, 231 (1981). 4. Anderson J. S. and Saddington K. J. Chem. Sot. S-381 (1949). 5. Northrop J. H. and Anson M. L. J. Gen. Physiol. 12, 543 (1929). 6. Harned H. S. and Nuttall R. L. J. Am. Chem. Sot. 69, 736 (1947); 71, 1460 (1949). 7. Arnikar H. J. Ann. Phys. 4, 1291 (1959).
39
8. Gupta R. P. and Prasad G. Z. Phrs. C’hem. (Neue F&e) 72, 255 (1970). 9. Cord& S. Tram Sot. Pharm. Mont&lier 15, 116 (1955). 10. Arnikar H. J., Patil S. F., Adhyapak N. G. and Potdar J. K. Z. Phys. Chem. (Neue F&v) 120, 51 (1980). 11. Patil S. F. and Joshi S. S. Proc. Radiat. Radiochem. Symp. RA 21-l (1982). 12. Patil S. F. and Adhyapak N. G. Ind. J. Chem. 20A, 1079 (1981). 13. Patil S. F. and Adhyapak N. G. Radiochim. Acta 30,239 (1982). 14. Eyring H. J. J. Chem. Phys. 4, 283 (1936). 15. Onsager L. Ann N. Y. Acad. Sci. 46, 241 (1945). 16. Parsons R. Handbook of Electrochemical Constants (Butterworths, London, 1959). 17. International Critical Tables of Numerical Data Physics, Chemistry and Technology Vol. VI (McGraw-Hill, New York, 1929). 18. Gosting L. J. and Harned H. S. J. Am. Chem. Sot. 73, 159 (1951).
1986
0883-2889/86 $3.00 + 0.00 Pergamon Press Ltd
Diffusion of Bromide, Iodide and Thallium Ions at Various Temperatures S. F. PATIL, Department
N. G. ADHYAPAK
of Chemistry,
University
of Poona,
and S. S. JOSH1 Pune 411 007, India
(Received 15 April 1985; in revised form 30 May 1985)
Self-diffusion of bromide, iodide and thallium ions has been studied in NH,Br, NaI and Tl,SO, respectively over a temperature range of 25%50°C using agar gel medium. Activation energy for the process of diffusion in the above systems is computed from the experimental and theoretical diffusion coefficient data obtained by the zone-diffusion technique and Onsager’s equation respectively. A comparison of theoretical and experimental activation energies shows a good agreement in the cases of iodide and thallium ions while the experimental activation energy is found to be lower than theoretical in the case of bromide ions.
Introduction
Experimental
Survey of the literature shows that a large amount of data is available on the diffusion coefficient of various ions and electrolytes but in almost all cases the work is done at 25”C, and there are only a few reports(‘m3) on the measurement of activation energy for the process of diffusion. This is mainly due to the experimental difficulties encountered in the measurements of diffusion coefficients at higher temperatures. The chief difficulty to be overcome in the accurate determination of diffusion coefficients in aqueous solution is mixing due to convection and streaming flow. Hence, all the methods try to create conditions under which the above effects are reduced to a minimum. A number of such precision methods(“6J have been developed. However, these methods have not been ued very often for the measurement of diffusion coefficients at higher temperatures due to the complexity involved in the techniques. The abovementioned errors and difficulties are reduced to a minimum by immobilizing the system in gel medium, as has been pointed out by several workers.(7m9’ The agar gel by virtue of its structure is capable of holding about 98% water in a practically immobilized and semi-rigid state, eliminating the direct streaming and convectional flow of the solution and providing an ideal medium for the study of diffusion. The present paper reports the activation energy values for the self-diffusion of Brr, I- and Tl+ ions in NH,Br, NaI and Tl,SO, respectively over the temperature range of 25-50°C using a simple technique of zone-diffusion which enables measurements at higher temperatures without any difficulty.
The self-diffusion of Br- in NH,Br labelled with 82Br (t,,, = 36 h), I- in NaI labelled with “‘I (tlf2 = 8.04 d) and Tl+ in T&SO, labelled with *04T1 (I,,* = 3.9 y) was studied in 1.5% agar gel using the zone-diffusion technique. (lo) The diffusion coefficients were measured in the temperature range of 25-5O’C at 0.1 M concentration for Br- and I- ions and at 0.01 M concentration in case of Tl+ ions, due to the low solubility of T1,S04. The central zone of the diffusion column contains the labelled electrolyte of the desired concentration and gel columns on either side contain the unlabelled electrolyte of the same concentration. The details of the experimental procedure and calculations of diffusion coefficient are reported in our previous paper.(“)
Results and Discussion The variation of diffusion coefficient with temperature in various systems is presented in Table 1 and the corresponding Arrhenius plots are shown in Fig. 1. Each value of diffusion coefficient reported in the present work is an average of four independent measurements with an accuracy of f0.2%. Table 1 also includes theoretical values of D, in NaI, which are shown in parentheses along with the experimental values. It is obvious from the Table 1 and Fig. 1 that the diffusion coefficient increases with temperature in each system. As the diffusion coefficients are measured in agar gel medium, one has to take into consideration the effect of temperature on the agar 37
38
S.
Table
I.
of
Variation
F.
PATIL
diffusion coet?icient
Br
I” NH,Br
wth
temperature
in different
25
2.1 I2
I.915
(1.876)
-
30
2.331
2.102
(2.096)
2.210 2.499
35
2.523
2.338
(2.329)
40
2.753
2.573
(2.572)
2 740
45
2.922
2.805
(2.831)
3.092
3.106
(3.102)
SO ‘)
E (kJ mol
12.9
* 0.5
15.550.5
gel. However, it has been shown that the obstruction effect caused by the agar gel is independent of temperature(‘.“.‘3) (25-50°C) which itself indicates that the gel structure is unaffected in the temperature range studied. Thus, the change of temperature only affects the process of diffusion. With increasing temperature, a larger fraction of the diffusing species acquires a requisite amount of energy in order to cross the potential energy barrier required for the process of diffusion, giving an increasing trend in the value of diffusion coefficient with temperature in agreement with the transition state theory of diffusion.(‘4’ The experimental activation energy for the diffusion of I- in NaI, Br- in NH,Br, and Tl’ in T&SO, is computed by least square fitting of the data presented in Fig. 1 and using the following Arrhenius equation: D = D,exp( - E/RT)
Br-in
M
I-
in NaI
(exptl
-
I-
in NaI
(fheoret.1
of different parameters required equation are taken from the
at 25°C:
D, ~10~5cm2s~‘=2.044-0.530~
NH4 Br
Fig.
I. Arrhenius
plots
3.3
K x IO3
for the self-diffusion
NH,Br, I- in NaI and Tl + in Tl?SO,.
of Br
’ = 2.286 - 0.599fi
D, /10m5cm’s
(3)
at 35°C:
D,~/lO~‘cm’s-’
= 2.541 - 0.670 fi
(4)
at 40°C:
D, /10m5cm* S-I = 2.809 - 0.747 XC
(5)
at 45 C:
D, /lo-‘cm*
s ’ = 3.093 - 0.828 ,/?
(6)
D, /lo-‘cm’
s
’ = 3.392 - 0.916 JC
(7)
at 50°C:
in NH,Br: = 1.755 - 0.404$!
at 18°C
(8)
D,, /IO ‘cm’ ss’ = 2.078 - 0.485 fi
at 25’C
(9)
D,,,jlO_ 5cmzs~’ = 1.707 - 0.851 3
at 18°C
(10)
D,,,/lo-‘cm’ss
at 25°C
(11)
for Tl+ in TI,SO
3.2
(2)
at 30°C:
D,, /10~5cm’ss’
(l/T)
in the litera-
The 0nsager-Gosting-Harned(‘5,‘81 equation for the diffusion of I- in NaI after appropriate substitution of the different parameters takes the following form at various temperatures.
for Br
3.1
0.2
In the cases of Br and Tl+ ions, due to the unavailability of the data required in the theoretical equations at various temperatures, the activation energy is determined by calculating the values of diffusion coefficients only at two different temperatures, and the theoretical equations in these systems are as follows:
, -4.4 M
3.419 I6 i
(16.1)
The values theoretical ture,“b.17’
(1)
These values are presented in Table 1 along with the standard deviation. The theoretical activation energy, on the other hand, in each system is determined from the corresponding theoretical diffusion coefficient values estimated on the basis of Onsager’s”” theory.
3.0
systems
l-l + in TI1:SO,“”
I in NaI D (IO qcm~S ‘)
TeIllP./SWteIll
r
et al
in
4
:
= 1.987 - 0.992 fi
The theoretical activation energy estimated from the diffusion coefficient data calculated on the basis of equations (l)-(11) is found to be 16.1, 17.9 and 15.7 kJ mol- ’ for the diffusion of II, Br and TI+ ions respectively while the corresponding experimental values are found to be 15.5 _t 0.5, 12.9 k 0.5 and 16.0 k 0.2 kJ mol ‘. A comparison of the former
Diffusion
of Br, I and Tl ions
and the latter values shows that they are in good agreement with the exception of NH,Br system, wherein the experimental value of activation energy is found to be less than the theoretical one.
References 1. Patil S. F. and Adhyapak N. G. Int. J. Appl. Radiat. Isot. 32, 631 (1981). 2. Patil S. F. and Adhyapak N. G. J. Radioanal. Nucl. Chem. Lett. 93, 173 (1985). 3. Pathak B. K., Singh P. C. and Singh V. N. Acta cienc. Ind. 4, 231 (1981). 4. Anderson J. S. and Saddington K. J. Chem. Sot. S-381 (1949). 5. Northrop J. H. and Anson M. L. J. Gen. Physiol. 12, 543 (1929). 6. Harned H. S. and Nuttall R. L. J. Am. Chem. Sot. 69, 736 (1947); 71, 1460 (1949). 7. Arnikar H. J. Ann. Phys. 4, 1291 (1959).
39
8. Gupta R. P. and Prasad G. Z. Phrs. C’hem. (Neue F&e) 72, 255 (1970). 9. Cord& S. Tram Sot. Pharm. Mont&lier 15, 116 (1955). 10. Arnikar H. J., Patil S. F., Adhyapak N. G. and Potdar J. K. Z. Phys. Chem. (Neue F&v) 120, 51 (1980). 11. Patil S. F. and Joshi S. S. Proc. Radiat. Radiochem. Symp. RA 21-l (1982). 12. Patil S. F. and Adhyapak N. G. Ind. J. Chem. 20A, 1079 (1981). 13. Patil S. F. and Adhyapak N. G. Radiochim. Acta 30,239 (1982). 14. Eyring H. J. J. Chem. Phys. 4, 283 (1936). 15. Onsager L. Ann N. Y. Acad. Sci. 46, 241 (1945). 16. Parsons R. Handbook of Electrochemical Constants (Butterworths, London, 1959). 17. International Critical Tables of Numerical Data Physics, Chemistry and Technology Vol. VI (McGraw-Hill, New York, 1929). 18. Gosting L. J. and Harned H. S. J. Am. Chem. Sot. 73, 159 (1951).