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Transfer of Sb(III) in an equilibrated extraction system
J. inorg,nucl.Chem.. 1970.Vol.32. pp. 3673to 3676. PergamonPress. Printedin Great Britain
TRANSFER
OF Sb(llI) IN EXTRACTION
AN EQUILIBRATED SYSTEM
K. JUZNI(~ and S. F E D I N A Institute "Jo2ef Stefan", Ljubljana, Yugoslavia
(Received25 February 1970) Abstract--Self-diffusion and interfacial transfer of antimony(Ill) species in an equilibrated liquidliquid extraction system have been measured at various temperatures. The absolute viscosities of the solutions in the systems were also determined. From the data the effective radii of the diffusing species and the free energies of activation of transfer across the interface were calculated, INTRODUCTION
THE LITERATURE contains few references [1-4] to transfer processes comprising the diffusion of extractable species in two phases and their transfer across a liquid-liquid interface in a static extraction system in chemical equilibrium. The data for such processes give valuable information about the effective size of species and about the chemical reaction accompanying transfer across an interface. Panicle radii can be calculated from diffusion and viscosity data using the equation given by Glasstone et al.[5]. Similar equations given by Stokes and Einstein yield more reasonable values when compared with those obtained by other methods. Radioactive tracer techniques for studying interfacial resistance in a especially-designed cell were first utilised by Tung and Drickamer[1]; the capillary technique[6] was later also used for measuring interfacial resistance, and proved to be experimentally very simple. The precision of both methods depends on the magnitude of the interfacial resistance. If this is small in comparison with the rate of liquid diffusion the results become correspondingly inaccurate. EXPERIMENTAL
Materials Antimony(Ill) chloride and hydrochloric acid (analytical grade) and m-xylene (puriss) were obtained from Riedel de Haen Co. Tri-n-octyl phosphine oxide (TOPO) from Eastman Kodak Organic Chemicals was used without further purification. Tracer Sb-124 was obtained by irradiating antimony(I I I) chloride in the Triga reactor in Ljubljana.
Procedure Equilibrated extraction systems were prepared by shaking equal volumes of aqueous and organic solutions for 2 hr in a thermostated shaker at selected temperature. The solutions used were 0.0686 M antimony(I 1I) chloride in 4 M HCI and 0-0686 M TOPO in m-xylene. Smaller quantities of systems of I. 2. 3. 4. 5. 6.
L. H. Tung and H. G. Drickamer, J. chem. Phys. 20, 10, 13 (1952). P. L. Auer and E. W. Murbach, J. chem. Phys. 22, 1054 (1954). 1. H. Sinfelt and H. G. Drickamer, J. chem. Phys. 23, 1095 (1955). T. Hahn, J. Am. chem. Soc. 79, 4625 (1957). K. H. Stern and E. S. Amis, Chem. Rev. 59, 1 (1959), K. Ju2ni~, J. inorg, nucl. Chem. 30, 2270 (1968). 3673
3674
K. JUZNI(~ and S. F E D I N A
the same compositions as above, but labelled with radioisotope, were prepared separately in the same way. Physical measurements Self-diffusion coefficients were determined with the capillary technique introduced by Anderson [7]. The capillaries were 3 cm long and 0-5 mm i.d. Three of them filled with radioactive organic and aqueous phases, respectively, were suspended vertically in 50m! of the corresponding inactive solution which was stirred by a magnetic stirrer. The experiments were performed in two tightlyclosed vessels. In all cases the time of diffusion was sufficiently long to satisfy the condition Dr~12 > 0"2. The diffusion coefficients were calculated from the following approximate equation [8] M 8 ( zr2Dt~ - - ~ ~ exp M o 7r" ~---~ /
(1)
where Mo is the initial amount of radioisotope in capillary, M the amount after time t, D the diffusion coefficient and I the length of capillary. The interfacial transfer coefficients were determined by a modified capillary technique [6], which differs from the above method in that the capillaries filled with the radioactive organic phase were placed in inactive aqueous solutions, so that the liquid-liquid interface was formed at their open ends. Diffusion from the capillaries was allowed to proceed for an appropriate time such that the condition pZDt/I 2 > 0-5 was fulfilled. The interracial transfer coefficients were calculated from the equations [6] M
2 sin 2p
2Dt
M0 = p p+s,npcosp, exp( -p 7 ) and cot p p
D al
(3)
where p = kl, k being a constant in the solution of the diffusion equation, a the interracial transfer coefficient, and the other terms have the same meaning as in Equation (1). To solve Equations (2) and (3) ratios of M/Mo were plotted against p in radians according to Equation (2) and a value of p was selected which made the ratio M / M o equal to that observed experimentally. This was then used in Equation (3) to calculate a. The viscosities of the solutions in the extraction systems were determined with Ubbelohde's suspended meniscus viscometer. Using double-distilled water of known viscosity to determine the characteristics of the viscometer, viscosities of the solutions were calculated from the measured flow-times and densities according to the equation [9] d°
rK
1-~,/
r"
(4)
where r/is the absolute viscosity of the liquid, d" the density of air, d" the liquid density, r the flow time; K and L are constants and n was taken as unity. Densities were determined with a 100ml pycknometer. All the above measurements were performed at temperatures of 25 °, 35 °, 45 ° and 55°C constant within ± 0-02oc. RESULTS
AND
DISCUSSION
Values of the self-diffusion coefficients (D) and of the interfacial transfer c o e f f i c i e n t s ( a ) a t v a r i o u s t e m p e r a t u r e s a r e g i v e n i n T a b l e 1. E a c h v a l u e r e p r e s e n t s the arithmetricai mean of three results obtained from parallel measurements in a single run. Deviations from the mean of the diffusion coefficients were within 7. J. S. Anderson and K. Saddington, J. chem. Soc. 381 (1949). 8. J. H. Wang, J . A m . chem. Soc. 74, 1182 (1952). 9. L. Korson, W. D. Hansen and F. J. Millero, J. phys. Chem. 73, 1,34 (1969).
Transfer of Sb(l I 1)
3675
_+_1 per cent, while those of the tranffer coefficients varied up to ___30 per cent. Table 1 also shows the distribution coefficients (K,,°), i.e. the ratios of the concentrations of antimony in the organic and aqueous phases after equilibrium had been attained. Table 1. Diffusion and interfacial transfer coefficients of antimony(Ill) species T °C
K,,"
25 35 45 55
2.3 2.1 2.0 1.8
10~D, cm2/s Aqueous Organic 104c~,cm/s 7.55 9.13 10.9 13.1
4.85 5.85 6.85 8.17
0.7 I-5 1.8 3.2
Arrhenius plots for diffusion and interfacial transfer, constructed by plotting log D and log a respectively against 1[ T gave the following linear relationships. log D, = -- 3410/2.3 R T - 2.62 for diffusion in the aqueous phase, log Do = - 3240/2-3 R T -- 2-92 for diffusion in the organic phase, and log a = - 9080/2.3 R T + 2-55 for interfacial transfer. Our results for densities and flow times in the viscometer for both phases, togethei with the calculated absolute viscosities at different temperatures, are listed in Table 2. The effective radii (r) of the antimony species have been calculated from the Stokes-Einstein relation r --- kT/6zr'oD. This equation was derived for the motion Table 2. Flow times in viscometer, densities and viscosities of the phases in the extraction systems T °C
Dest. water
Aqueous
y(s)
25 35 45 55
245.4 199.7 167,4 144.0
289.6 243.7 208.7 183"2
Organic 207.4 185"8 169,7 158.0
d"(g/cm:q Aqueous Organic 1.0647 1.0609 1.0562 1-0515
"0(cp) Aqueous Organic
0.8679 0-8597 0.8506 0.8415
1.133 0.948 0.806 0.700
0.646 0-575 0.520 (1"477
of relatively large spherical particles through a continuum of viscosity ~ [10], and its applicability in a case such as ours has been discussed by several authors [ 11, 12]; it has been established that only the numerical factor might be erroneous. Values of the radii obtained are given in Table 3. The effective radius of the Sb species in the aqueous phase remain nearly constant as the temperature increases over the given temperature range. Constant values of quantity k T / D ~ have also been found by other workers in several other cases, e.g. for water[ 13]. In the organic phase a slight decrease in the radius is observed. This may be 10, 1 I, 12, 13,
R. H. Stokes, Trans. Faraday Soc. 49, 886 (1953). .1. C. M. Li and Pin Chang, J. chem. Phys. 23, 518 (1955). H. Watts, B. J. Alder and J. H. Hildebrand, J. chem. Phys. 23,659 (1955). J. H. Wang, J. A m. chem. Soc. 737, 510 ( 1951).
3676
K. JUZNI(~ and S. F E D I N A Table 3. Radii of antimony(liD species and free energies of activation of transfer across the interface T °C 25 35 45 55
lOSt, cm Aqueous Organic 2'55 2'60 2'67 2"62
6"97 6"70 6"54 6"17
AG~ (cal/mole)
13260 13260 13600 13670
ascribed to the diminution of factors which contribute to the value of the effective radius, viz. actual radius of the particle and its interactions with its surroundings. Free energies of activation (AG $) of transfer across the liquid-liquid interface were calculated from the equation of absolute rate theory [3, 14], of the form a = lkT/h exp ( - A G $ / R T ) , where k is Boltzmann's constant, h Planck's constant, T the absolute temperature, R the gas constant and I the distance between two equilibrium positions in the liquid. An approximate value of 6.10 -8 cm was obtained for / from ( V / N ) '/3 for m-xylene, where V is the molar volume and N Avogadro's number. The values of A G$ are given in Table 3. They are practically independent of temperature and are relatively large compared with those for diffusion in either the organic or aqueous phase (4990 cal/mole and 4010 cal/mole at 25°C). An analogous behaviour was observed in studying the transfer of sulphur in an extraction system [3]. 14. Glasstone, Laidler and Eyring, Theory of Rate Processes. McGraw-Hill, New York (1941).
TRANSFER
OF Sb(llI) IN EXTRACTION
AN EQUILIBRATED SYSTEM
K. JUZNI(~ and S. F E D I N A Institute "Jo2ef Stefan", Ljubljana, Yugoslavia
(Received25 February 1970) Abstract--Self-diffusion and interfacial transfer of antimony(Ill) species in an equilibrated liquidliquid extraction system have been measured at various temperatures. The absolute viscosities of the solutions in the systems were also determined. From the data the effective radii of the diffusing species and the free energies of activation of transfer across the interface were calculated, INTRODUCTION
THE LITERATURE contains few references [1-4] to transfer processes comprising the diffusion of extractable species in two phases and their transfer across a liquid-liquid interface in a static extraction system in chemical equilibrium. The data for such processes give valuable information about the effective size of species and about the chemical reaction accompanying transfer across an interface. Panicle radii can be calculated from diffusion and viscosity data using the equation given by Glasstone et al.[5]. Similar equations given by Stokes and Einstein yield more reasonable values when compared with those obtained by other methods. Radioactive tracer techniques for studying interfacial resistance in a especially-designed cell were first utilised by Tung and Drickamer[1]; the capillary technique[6] was later also used for measuring interfacial resistance, and proved to be experimentally very simple. The precision of both methods depends on the magnitude of the interfacial resistance. If this is small in comparison with the rate of liquid diffusion the results become correspondingly inaccurate. EXPERIMENTAL
Materials Antimony(Ill) chloride and hydrochloric acid (analytical grade) and m-xylene (puriss) were obtained from Riedel de Haen Co. Tri-n-octyl phosphine oxide (TOPO) from Eastman Kodak Organic Chemicals was used without further purification. Tracer Sb-124 was obtained by irradiating antimony(I I I) chloride in the Triga reactor in Ljubljana.
Procedure Equilibrated extraction systems were prepared by shaking equal volumes of aqueous and organic solutions for 2 hr in a thermostated shaker at selected temperature. The solutions used were 0.0686 M antimony(I 1I) chloride in 4 M HCI and 0-0686 M TOPO in m-xylene. Smaller quantities of systems of I. 2. 3. 4. 5. 6.
L. H. Tung and H. G. Drickamer, J. chem. Phys. 20, 10, 13 (1952). P. L. Auer and E. W. Murbach, J. chem. Phys. 22, 1054 (1954). 1. H. Sinfelt and H. G. Drickamer, J. chem. Phys. 23, 1095 (1955). T. Hahn, J. Am. chem. Soc. 79, 4625 (1957). K. H. Stern and E. S. Amis, Chem. Rev. 59, 1 (1959), K. Ju2ni~, J. inorg, nucl. Chem. 30, 2270 (1968). 3673
3674
K. JUZNI(~ and S. F E D I N A
the same compositions as above, but labelled with radioisotope, were prepared separately in the same way. Physical measurements Self-diffusion coefficients were determined with the capillary technique introduced by Anderson [7]. The capillaries were 3 cm long and 0-5 mm i.d. Three of them filled with radioactive organic and aqueous phases, respectively, were suspended vertically in 50m! of the corresponding inactive solution which was stirred by a magnetic stirrer. The experiments were performed in two tightlyclosed vessels. In all cases the time of diffusion was sufficiently long to satisfy the condition Dr~12 > 0"2. The diffusion coefficients were calculated from the following approximate equation [8] M 8 ( zr2Dt~ - - ~ ~ exp M o 7r" ~---~ /
(1)
where Mo is the initial amount of radioisotope in capillary, M the amount after time t, D the diffusion coefficient and I the length of capillary. The interfacial transfer coefficients were determined by a modified capillary technique [6], which differs from the above method in that the capillaries filled with the radioactive organic phase were placed in inactive aqueous solutions, so that the liquid-liquid interface was formed at their open ends. Diffusion from the capillaries was allowed to proceed for an appropriate time such that the condition pZDt/I 2 > 0-5 was fulfilled. The interracial transfer coefficients were calculated from the equations [6] M
2 sin 2p
2Dt
M0 = p p+s,npcosp, exp( -p 7 ) and cot p p
D al
(3)
where p = kl, k being a constant in the solution of the diffusion equation, a the interracial transfer coefficient, and the other terms have the same meaning as in Equation (1). To solve Equations (2) and (3) ratios of M/Mo were plotted against p in radians according to Equation (2) and a value of p was selected which made the ratio M / M o equal to that observed experimentally. This was then used in Equation (3) to calculate a. The viscosities of the solutions in the extraction systems were determined with Ubbelohde's suspended meniscus viscometer. Using double-distilled water of known viscosity to determine the characteristics of the viscometer, viscosities of the solutions were calculated from the measured flow-times and densities according to the equation [9] d°
rK
1-~,/
r"
(4)
where r/is the absolute viscosity of the liquid, d" the density of air, d" the liquid density, r the flow time; K and L are constants and n was taken as unity. Densities were determined with a 100ml pycknometer. All the above measurements were performed at temperatures of 25 °, 35 °, 45 ° and 55°C constant within ± 0-02oc. RESULTS
AND
DISCUSSION
Values of the self-diffusion coefficients (D) and of the interfacial transfer c o e f f i c i e n t s ( a ) a t v a r i o u s t e m p e r a t u r e s a r e g i v e n i n T a b l e 1. E a c h v a l u e r e p r e s e n t s the arithmetricai mean of three results obtained from parallel measurements in a single run. Deviations from the mean of the diffusion coefficients were within 7. J. S. Anderson and K. Saddington, J. chem. Soc. 381 (1949). 8. J. H. Wang, J . A m . chem. Soc. 74, 1182 (1952). 9. L. Korson, W. D. Hansen and F. J. Millero, J. phys. Chem. 73, 1,34 (1969).
Transfer of Sb(l I 1)
3675
_+_1 per cent, while those of the tranffer coefficients varied up to ___30 per cent. Table 1 also shows the distribution coefficients (K,,°), i.e. the ratios of the concentrations of antimony in the organic and aqueous phases after equilibrium had been attained. Table 1. Diffusion and interfacial transfer coefficients of antimony(Ill) species T °C
K,,"
25 35 45 55
2.3 2.1 2.0 1.8
10~D, cm2/s Aqueous Organic 104c~,cm/s 7.55 9.13 10.9 13.1
4.85 5.85 6.85 8.17
0.7 I-5 1.8 3.2
Arrhenius plots for diffusion and interfacial transfer, constructed by plotting log D and log a respectively against 1[ T gave the following linear relationships. log D, = -- 3410/2.3 R T - 2.62 for diffusion in the aqueous phase, log Do = - 3240/2-3 R T -- 2-92 for diffusion in the organic phase, and log a = - 9080/2.3 R T + 2-55 for interfacial transfer. Our results for densities and flow times in the viscometer for both phases, togethei with the calculated absolute viscosities at different temperatures, are listed in Table 2. The effective radii (r) of the antimony species have been calculated from the Stokes-Einstein relation r --- kT/6zr'oD. This equation was derived for the motion Table 2. Flow times in viscometer, densities and viscosities of the phases in the extraction systems T °C
Dest. water
Aqueous
y(s)
25 35 45 55
245.4 199.7 167,4 144.0
289.6 243.7 208.7 183"2
Organic 207.4 185"8 169,7 158.0
d"(g/cm:q Aqueous Organic 1.0647 1.0609 1.0562 1-0515
"0(cp) Aqueous Organic
0.8679 0-8597 0.8506 0.8415
1.133 0.948 0.806 0.700
0.646 0-575 0.520 (1"477
of relatively large spherical particles through a continuum of viscosity ~ [10], and its applicability in a case such as ours has been discussed by several authors [ 11, 12]; it has been established that only the numerical factor might be erroneous. Values of the radii obtained are given in Table 3. The effective radius of the Sb species in the aqueous phase remain nearly constant as the temperature increases over the given temperature range. Constant values of quantity k T / D ~ have also been found by other workers in several other cases, e.g. for water[ 13]. In the organic phase a slight decrease in the radius is observed. This may be 10, 1 I, 12, 13,
R. H. Stokes, Trans. Faraday Soc. 49, 886 (1953). .1. C. M. Li and Pin Chang, J. chem. Phys. 23, 518 (1955). H. Watts, B. J. Alder and J. H. Hildebrand, J. chem. Phys. 23,659 (1955). J. H. Wang, J. A m. chem. Soc. 737, 510 ( 1951).
3676
K. JUZNI(~ and S. F E D I N A Table 3. Radii of antimony(liD species and free energies of activation of transfer across the interface T °C 25 35 45 55
lOSt, cm Aqueous Organic 2'55 2'60 2'67 2"62
6"97 6"70 6"54 6"17
AG~ (cal/mole)
13260 13260 13600 13670
ascribed to the diminution of factors which contribute to the value of the effective radius, viz. actual radius of the particle and its interactions with its surroundings. Free energies of activation (AG $) of transfer across the liquid-liquid interface were calculated from the equation of absolute rate theory [3, 14], of the form a = lkT/h exp ( - A G $ / R T ) , where k is Boltzmann's constant, h Planck's constant, T the absolute temperature, R the gas constant and I the distance between two equilibrium positions in the liquid. An approximate value of 6.10 -8 cm was obtained for / from ( V / N ) '/3 for m-xylene, where V is the molar volume and N Avogadro's number. The values of A G$ are given in Table 3. They are practically independent of temperature and are relatively large compared with those for diffusion in either the organic or aqueous phase (4990 cal/mole and 4010 cal/mole at 25°C). An analogous behaviour was observed in studying the transfer of sulphur in an extraction system [3]. 14. Glasstone, Laidler and Eyring, Theory of Rate Processes. McGraw-Hill, New York (1941).