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Self-diffusion of 131I− and 110Ag+ in microconcentrations: Their mutual interaction at high dilution
J. inorg,nucl.Chem., 1972.Vol.34, pp. 2543-2549. PergamonPress. Printedin GreatBritain
SELF-DIFFUSION O F 1all- A N D l]°Ag+ I N MICROCONCENTRATIONS: THEIR MUTUAL INTERACTION AT HIGH DILUTION F. K E P A K and J. KI~IVA Nuclear Research Institute of the Czechoslovak Academy of Sciences, ReL Czechoslovakia (First received 17 September 1971 ; in revised form 8 December 1971) Abstract-The self-diffusion of 10-aM and 10-~M I- or Ag + ions and the effect o f A g ÷ ions in concentrations of 10 -9 to 10-SM on the self-diffusion of 10-SM and 10-eM I - in aqueous solution has been studied. The presence of silver ions influenced the self-diffusion of iodide ions and from its course the gradual formation of trace amounts of Agl sol has been inferred.
INTRODUCTION
IN EARLIER communications[I-3] the dependence of the self-diffusion of 85Sr and several radionuclides (l°eRu, J44Ce, 14rpm, 154Eu, 59Fe and 5ZMn), which form colloidal hydroxides, on the ionic strength and pH of the solution has been studied. The formation of trace amounts of colloidal hydroxides of corresponding elements can be deduced from the variation of the self-diffusion coefficient as a function of pH as well as the adsorption of 89Sr on Fe(III) and Mn(IV) hydroxides from the course of its self-diffusion in the presence of trace amounts of these hydroxides. In this work attention is paid to the self-diffusion of the microconcentrations of the I- and Ag ÷ ions, which can form a sol or crystallic ionic precipitate of AgI, which is an insoluble substance of another type than hydroxides mentioned in earlier communications[I-3]. The physicochemical properties of the sol and crystallic precipitate of silver iodide are described in a number of papers [4-1 1]. The precipitation kinetics from the solutions and the solid phase formation by nucleation is treated by Doremus[12], Nancollas and Purdie [1 3], and in mono1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 1 I. 12. 13.
F. Kepfikand J. Kfivfi, J. inorg, nucl. Chem. 32, 719 (1970). F. Kepfik and J. K~iv~t,J. inorg, nucl. Chem. 33, 1741 (1971). F. Kepfik andJ. Kfivfi, J. inorg, nucl. Chem.34, 185 (1972). J. Th. G. Overbeek, In Colloid Science (Edited by H. K. Kruyt) Vol. 1, pp. 75, 159, 307, 331,332. Elsevier, Amsterdam (1952). J. Lyklema and J. Th. G. Overbeek, J. colloid Sci. 16, 595 (! 961). J. Lyklema, Dis. Faraday Soc. 42, 81 (1966). J. Lyklema, Adv. colloid interface Sci. 2, 65 (1968). M. Mirnik and P. Pravdir, Croat. Chem.Acta 30, 213 (1958). M. Mirnik and R. Despotovi~, Kolloid Z. and Z. Polym. 180, 51 (1962). M. Mirnik, KolloidZ. and Z. Polym. 205, 97 (1965). M. Mirnik, Ion Exchange Theory o f Coagulation, IRB Preprint No. 1 (69). R. H. Doremus, J. phys. Chem. 62, 1068 (1958). G. H. Nancollas and N. Purdie, Q. Rev. 18, 1 (1964). 2543
2544
F. KEP,~K and J. KR.IV,/~
graphics by Nielsen [14], Walton [15], and Dunning [16]. In our conditions the Iand Ag ÷ ions were highly diluted and the agglomerates of the AgI sol produced, which were characterized by a variation of the self-diffusion coefficient, were at a certain stage of equilibrium. We used again the method of an open end capillary to determine the self-diffusion coefficient. The self-diffusion coefficient of the iodide ion alone was determined by this method also in other communications [17-20]. The Equation given previously[l] was used for the calculation of the selfdiffusion coefficient: __c = 8_ o~
1
Co 7r2 = (2n+1) 2
exp (- (2n+l)2&Dt~
4h"
]
(1)
where D= Co = C= h= t=
self-diffusion coefficient, cm2/sec initial concentration of the ion diffusing in the capillary concentration of the ion diffusing in the capillary after a time t capillary height, cm self-diffusion time, sec.
Theoretical self-diffusion coefficient was calculated from the Relation [3]: x,
Dfl = 2-661 X 10- 7 2 Z~
(2)
where Dfl = theoretical self-diffusion coefficient of the ion j, cm2lsec h~ = limiting equivalent conductivity of the ion j, cm 2 x l1-1 × gequiv. -1, zj = valency of the ionj. The standard error 8 of the measurement of the self-diffusion coefficient was calculated from the formula [3]:
./
8 = ~ l p ( p - - 1)
(3)
the symbols having following meaning: 8 = standard error, A = deviation of the determined value from the mean value, p = number of all measurements. 14. A. E. Nielsen, Kinetics of Precipitation, pp. 1, 11, 29, 40, 66. Pergamon Press, Oxford (1964). 15. A. G. Walton, The Formation and Properties of Precipitates, pp. l, 44. Interscience, New York (1967); Nucleation (Edited by A. G. Zettlemoyer), p. 225. Marcel Dekker, New York (1969). 16. W. J. Dunning, In Nucleation (Edited by A. G. Zetflemoyer) p. 1. Marcel Dekker, New York (1969). 17. J. H. Wang andJ. W. Kennedy, J.Am. chem. Soc. 72, 2080 (1950). 18. R. Mills and J. W. Kennedy, J. Am. chem. Soc. 75, 5695 (1953). 19. V. V. Goncharov, V. G. Markova and V. I. Yashkichev, Radiokhim. 10, 575 (1968). 20, T. Williams and C. B. Monk, Trans. Faraday Soc. 57, 447 (1961).
Self-diffusion of 131I-and H6Ag+
2545
EXPERIMENTAL Apparatus The measurement of the self-diffusion coefficient was carried out simultaneously in five capillaries. Otherwise the measuring apparatus was the same as that given in previous communications[I-3]. The capillaries were dipped into 500 ml of inactive solution, which had the same composition and pH as the solution in the capillaries except the radioactive isotope which was only in the capillaries. The average capillary length was 3-537 cm, volume 0.030 ml and radius 0.052 cm. Solutions Chemicals AnalaR grade and triple distilled water were used for the preparation of the solutions. The radioisotopes J3JI (NaI) and 11°Ag(AgNO3) used were carrier-free and were made in the Nuclear Research Institute of the Czechoslovak Academy of Sciences at Re=~.(Czechoslovakia). The selfdiffusion of the I- ion alone labelled with 13q and Ag + labelled with H°Ag was carded out in 10-SM and 10-6M NaI or AgNO3 solutions respectively. In addition to the self-diffusion of individual ions the self-diffusion of the iodide ion in both concentrations mentioned in the presence of 10-gM, 10-SM, 10-rM, 10-6M and 10-SM Ag ÷ ion was carried out. The pH value of the solutions was 7'3, except the self-diffusion of Ag + alone where it was adjusted to 7-0 or 3-0. The ion c strength/z of the solutions was 0.01 (NaNO3). Procedure The procedure was similar to that given previously[I-3]. The self-diffusion time was 95 hr, temperature 25-0.02°C. The inner capillary surface was hydrophobized[2, 3] to avoid the surface adsorption of the radioisotope or to reduce it to minimum during the self-diffusion. The Agl sol was prepared in such a way that always two equivalent volumes of inactive (250 ml) or radioactive (25 ml) sodium iodide and silver nitrate solutions of double concentrations with respect to the concentration required after mutual mixing were mixed. The silver nitrate solution was slowly added to the radioactive sodium iodide solution under continuous stirring. The resulting solution remained for 30 min under stirring so that the precipitation reaction could take place in the whole volume of the solution in the case of exceeding AgI solubility product and occasional local supersaturation could be compensated. Then the self-diffusion was measured. In addition to capillaries for self-diffusion the radioactive solution was also present in "standard" capillaries of the same size, which, however, were not used for self-diffusion but they served for occasional correction for radioisotope adsorption on capillary walls during the self-diffusion. The self-diffusion coefficient D was calculated by means of the Equation (1), the concentrations Co and C being replaced by the radioactivity/0 of the solution before the self-diffusion in the "standard" capillary and by the radioactivity I in the capillary after the self-diffusion. The calculation was carded out on the G IER computer and as many terms of the Equation (1) were included into the calculation so that the ratio of the last term to all preceding terms included into the calculation was < 10-6.
RESULTS AND DISCUSSION T h e v a l u e s o f self-diffusion coefficients D, p H , the d a t a o n the e x c e e d i n g o f t h e s o l u b i l i t y p r o d u c t o f A g I a n d the signs o f the A g I s o l u t i o n charge are g i v e n in T a b l e 1. T h e v a l u e s o f s t a n d a r d e r r o r s for i n d i v i d u a l D v a l u e s are i n c l u d e d in the T a b l e 1. T h e d e p e n d e n c e o f the self-diffusion coefficient o n the c o n c e n t r a t i o n o f silver ions is p l o t t e d i n Fig. 1. A s m a y b e s e e n f r o m T a b l e 1 a n d Fig. 1 the c o u r s e o f the self-diffusion o f 1311- is different w i t h i n c r e a s i n g c o n c e n t r a t i o n o f silver i o n s for b o t h c o n c e n t r a t i o n s o f iodide ions. I t m a y b e a s s u m e d t h a t the s l o w i n g d o w n o f the self-diffusion o f 1311- in the p r e s e n c e o f A g ÷ i o n s i n d i c a t e s g r a d u a l f o r m a t i o n o f silver iodide sol. S t a b l e A g I colloid m a y b e a s s u m e d in the m e d i u m o f 0 . 0 1 M N a N O 3 [ 4 ] . T h e s o l u b i l i t y p r o d u c t o f A g I is v e r y l o w (1-5 × 10-16), the p r e c i p i t a t i o n o f A g O H or AgCI from trace chloride concentrations cannot be expected since their
F. K E P A K and J. K I ~ I V A
2546
Table 1. V a l u e s o f p H , self-diffusion coefficient, exceeding o f solubility product, and charge sign o f A g I
Cf
CAg+
pH
10-s 10-s 10-s 10-s 10-s 10-s 10-6 10-6 10-6 10-° 10-6 10-6 0
0 10-9 10-a 10-r 10-6 10-5 0 10-9 10-s 10-7 10-8 10-~ 10-8
7"3 7"3 7"3 7"3 7"3 7"3 7'3 7'3 7"3 7'3 7"3 7"3 7"0 7"0 3"0 3"0
0
10 - 6
0
10-s
0
10 -6
D × 102 I-(AgI) Ag +
sign o f A g I
multiple o f the exceeding o f A g I solubility product
+ + +
6.66 6.66 × 10 6.66 × 102
-
6.66 6"66 × 6.66 × 6.66 × 6.66 ×
16"20 8' 10 1 '93 2"29 1 "68 2" I0 16"10 16"00 13"10 11"40 4" 15 2"90
-
_+ +
10 102 102 102
5.07 5.36 15.70 16.90
C = ion concentration in M / 1 ; D = self-diffusion coefficient, cm2/sec. Standard error 8 o f the results:
8,%
DAg+,pH=3 3"0
DAg+,pH=7"0 11"1
DI 5"5
DAgI 15'5
2o
IO tO
_o x
c3
5
o
0
I
0
~l
0
I
I0 -e
r
I0- e
lO-r
I
lO-e
I
i0-5
C
Fig. 1. D e p e n d e n c e o f the serf-diffusion coefficient D on the concentration o f silver ions in the solution: D = self-diffusion coefficient, cm2/sec; c = silver ion concentration in M / I ; c u r v e (1) for 10-SM I-; c u r v e (2) for 10-SM I-.
Self-diffusion of 1311-and 11°Ag+
2547
solubility products are relatively high and they cannot influence, therefore, the formation of AgI sol. The concentration of impurity metal ions which could form colloid hydroxides in trace concentrations may be also considered as very low [21 ] and any essential effect of these hydroxides on the formation of AgI sol as little probable. The solubility product of AgI should be exceeded for the 10-~M concentration of I- ions at the 10-rM concentration of Ag + ions, for 10-6M concentrations of I- ions, already at the 10-gM concentration of Ag ÷ ions. Exceeding of solubility product, however, was not essential for the variation of the self-diffusion rate because the slowing-down of the self-diffusion did not correspond to these values of the Ag ÷ ion concentration. In the case of the 10-aM I- the AgI sol can be formed in the excess of Ag ÷ ions only so that it has positive charge, in the case of 10-6M I- the negative charge of the AgI sol changes to positive with increasing Ag ÷ concentration (Table 1). The self-diffusion is also different at exceeding of the solubility product by the same factor for both concentrations of iodide (10-aM I- with 10-rM to 10-SM Ag ÷, 10-6M I- with 10-aM to 10-7M Ag ÷, Table 1), the slowing-down of the self-diffusion with increasing Ag ÷ concentration being much slower for the 10-6M I- solution, to the contrary of the 10-SM I- solution, in which the slowing down of the self-diffusion occurs already before reaching the theoretical value of AgI solubility product. The small decrease in the self-diffusion coefficient at 10-6M I- with increasing Ag ÷ concentration to 10-TM would be possible to explain by stoichiometry, since in accord with solubility-product predictions most of the I- remains in solution and under this condition the value of the self-diffusion coefficient corresponds predominantly to I- ions. The self-diffusion rate fell rapidly for the 10-6M I- solution from concentrations higher than 10-TM Ag + thus when the Ag ÷ ion was in approximately equal or higher concentration with respect to I- ion and the sign of AgI changed to positive. The formation of a new phase is explained by the nucleation theory. The nucleation theory starts from an idea that in supersaturated solution there are not only the molecules A but also the embryos Ai, which are aggregates of A molecules. The Ai embryo loses or gains the A molecule and turns to A~+~ or A , embryos. The kinetic process in a supersaturated solution may be described in the following way [13, 16]: A+A
~A2
A z + A .~ A3
Ak-1 + A ~ Ak Ak + A .~ A k + 1
A i + A ~-- A~+I. The process of molecule attraction by embryos prevails and a critical nucleus A ~ is formed, which represents a new phase and there is a probability that this phase will grow up to macroscopic size. According to literature [ 15] homogeneous nucleation without any participation of impurities probably takes place with substances the solubility of which is lower than 10-6M and these substances 21. R. E. Thiers, Trace Analysis (Edited by J. Hoe and H. J. Koch) p. 641. Wiley, New York (1957).
2548
F. KEPAK and J. KI~IVA
exhibit colloidal behaviour. In our case the self-diffusion coefficient characterized the state of AgI molecule aggregates in a certain equilibrium stage. In 10-SM I- concentration a chemical interaction between I- and Ag + ions probably took place before reaching of the solubility product of AgI at the 10 -a and 10-SM concentrations of Ag + forming AgI molecule aggregates since the rate of the ~31I self-diffusion decreased in these conditions. The participation of trace impurity amounts on the initiation of the aggregation, however, cannot be excluded in this case. Further increase of Ag + concentration did not influence the self-diffusion rate of 10-SM 131I-, which suggests that a higher excess of precipitating ions does not lead to the formation of greater AgI aggregates. At 10-tM I- concentration and Ag + concentration 10-6M or higher the self-diffusion rate was still higher than at the 10-SM I- which suggests that the size of AgI aggregates was also smaller in the more concentrated solution of I- ions. It may be assumed on the basis of the kinetic conception of chemical equilibrium and Maxwell law of velocity distribution that quantitative reproducibility of common equilibria may be attained with 10e reacting molecules, which corresponds to 10-16g of reacting substance with an average molecular weight of 100 [22]. In our conditions the amount of reacting substance was much higher even at the lowest values of the microconcentrations of both ions so that the reproducibility of our system was guaranteed from thispoint of view. The radius of the critical nucleus is given as 18 :k for SrSO4, 22 A for BaSO~ [23]. Approximate size of the AgI molecule aggregates was 14.4 ~ for the lowest value of the self-diffusion coefficient D = 1.68 x 10-Semi/see, pH = 7.3 and viscosity ~ = 0.898 cP [3] calculated from the Stokes-Einstein relation [2] so that an agreement by order of magnitude is found with the values for SrSO4 and BaSO4. Evidently aggregates of AgIsol of very small dimensions were formed in our system, the growth to larger particles did not continue, crystallic phase was not formed. A quasi-equilibrium state was reached, which was characterized by the formation of aggregates of different dimensions up to critical size this distribution being relatively stable in the concentration range and time period investigated. The possibility of an effect of insignificant impurity concentrations on the formation of AgI sol below its solubility product cannot be excluded in our conditions. Theoretical self-diffusion coefficient calculated using the Relation[2] from limiting equivalent conductivities (XI- = 78-84 l~ -1 × g equiv. -1 × cm ~[24], XAg+= 61 "90 1-1-1g equiv. -~ × cm 2 [24]) is 2"095 × 10-5 cm2/sec for I- and 1.65 × 10-5 cm2! sec for Ag +. In the case o f A g + at pH --- 3 the experimentally measured value of D coincided with theoretical one within the error. At pH = 7.0 the determined selfdiffusion coefficient of Ag + is lower than theoretical value, the decrease of self-diffusion coefficient may be due to an interaction of Ag + with hydroxyl ions at this pH. The lower value of the self-diffusion coefficient of I- determined experimentally than theoretical one could be due to the oxidation of a part of Iions to I2 [25]. Is- could be formed by the reaction I2 + I- ~- I3- which diffuses 22. 23. 24. 25.
A.A. Benedetti-Pichler and J. R. Rachele, Ind. Engng Chem. analyt. Edn. 12, 233 (1940). A. W. Adamson, Physical Chemistry of Surfaces, p. 385, Interscience, New York (1967). Spravochnik Khimika, Vol. 3, 2nd Edn., pp. 709, 710, izd. Khimiya, Moscow-Leningrad. A. Ok~i~,Analytickd Chemic Kvalitativni (in Czech), pp. 507, 508. Academia, Prague (1966).
Self-diffusion ofl3q - and 11°Ag+
2549
probably more slowly than I- and decreases the value of the self-diffusion coefficient. Acknowledgement--The authors express their thanks to Dr. J. Hrub9 from the Nuclear Research Institute of the Czechoslovak Academy of Sciences, ~,e~ (Czechoslovakia), for his willingness in preparing and yielding the ~l°Ag radioisotope.
SELF-DIFFUSION O F 1all- A N D l]°Ag+ I N MICROCONCENTRATIONS: THEIR MUTUAL INTERACTION AT HIGH DILUTION F. K E P A K and J. KI~IVA Nuclear Research Institute of the Czechoslovak Academy of Sciences, ReL Czechoslovakia (First received 17 September 1971 ; in revised form 8 December 1971) Abstract-The self-diffusion of 10-aM and 10-~M I- or Ag + ions and the effect o f A g ÷ ions in concentrations of 10 -9 to 10-SM on the self-diffusion of 10-SM and 10-eM I - in aqueous solution has been studied. The presence of silver ions influenced the self-diffusion of iodide ions and from its course the gradual formation of trace amounts of Agl sol has been inferred.
INTRODUCTION
IN EARLIER communications[I-3] the dependence of the self-diffusion of 85Sr and several radionuclides (l°eRu, J44Ce, 14rpm, 154Eu, 59Fe and 5ZMn), which form colloidal hydroxides, on the ionic strength and pH of the solution has been studied. The formation of trace amounts of colloidal hydroxides of corresponding elements can be deduced from the variation of the self-diffusion coefficient as a function of pH as well as the adsorption of 89Sr on Fe(III) and Mn(IV) hydroxides from the course of its self-diffusion in the presence of trace amounts of these hydroxides. In this work attention is paid to the self-diffusion of the microconcentrations of the I- and Ag ÷ ions, which can form a sol or crystallic ionic precipitate of AgI, which is an insoluble substance of another type than hydroxides mentioned in earlier communications[I-3]. The physicochemical properties of the sol and crystallic precipitate of silver iodide are described in a number of papers [4-1 1]. The precipitation kinetics from the solutions and the solid phase formation by nucleation is treated by Doremus[12], Nancollas and Purdie [1 3], and in mono1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 1 I. 12. 13.
F. Kepfikand J. Kfivfi, J. inorg, nucl. Chem. 32, 719 (1970). F. Kepfik and J. K~iv~t,J. inorg, nucl. Chem. 33, 1741 (1971). F. Kepfik andJ. Kfivfi, J. inorg, nucl. Chem.34, 185 (1972). J. Th. G. Overbeek, In Colloid Science (Edited by H. K. Kruyt) Vol. 1, pp. 75, 159, 307, 331,332. Elsevier, Amsterdam (1952). J. Lyklema and J. Th. G. Overbeek, J. colloid Sci. 16, 595 (! 961). J. Lyklema, Dis. Faraday Soc. 42, 81 (1966). J. Lyklema, Adv. colloid interface Sci. 2, 65 (1968). M. Mirnik and P. Pravdir, Croat. Chem.Acta 30, 213 (1958). M. Mirnik and R. Despotovi~, Kolloid Z. and Z. Polym. 180, 51 (1962). M. Mirnik, KolloidZ. and Z. Polym. 205, 97 (1965). M. Mirnik, Ion Exchange Theory o f Coagulation, IRB Preprint No. 1 (69). R. H. Doremus, J. phys. Chem. 62, 1068 (1958). G. H. Nancollas and N. Purdie, Q. Rev. 18, 1 (1964). 2543
2544
F. KEP,~K and J. KR.IV,/~
graphics by Nielsen [14], Walton [15], and Dunning [16]. In our conditions the Iand Ag ÷ ions were highly diluted and the agglomerates of the AgI sol produced, which were characterized by a variation of the self-diffusion coefficient, were at a certain stage of equilibrium. We used again the method of an open end capillary to determine the self-diffusion coefficient. The self-diffusion coefficient of the iodide ion alone was determined by this method also in other communications [17-20]. The Equation given previously[l] was used for the calculation of the selfdiffusion coefficient: __c = 8_ o~
1
Co 7r2 = (2n+1) 2
exp (- (2n+l)2&Dt~
4h"
]
(1)
where D= Co = C= h= t=
self-diffusion coefficient, cm2/sec initial concentration of the ion diffusing in the capillary concentration of the ion diffusing in the capillary after a time t capillary height, cm self-diffusion time, sec.
Theoretical self-diffusion coefficient was calculated from the Relation [3]: x,
Dfl = 2-661 X 10- 7 2 Z~
(2)
where Dfl = theoretical self-diffusion coefficient of the ion j, cm2lsec h~ = limiting equivalent conductivity of the ion j, cm 2 x l1-1 × gequiv. -1, zj = valency of the ionj. The standard error 8 of the measurement of the self-diffusion coefficient was calculated from the formula [3]:
./
8 = ~ l p ( p - - 1)
(3)
the symbols having following meaning: 8 = standard error, A = deviation of the determined value from the mean value, p = number of all measurements. 14. A. E. Nielsen, Kinetics of Precipitation, pp. 1, 11, 29, 40, 66. Pergamon Press, Oxford (1964). 15. A. G. Walton, The Formation and Properties of Precipitates, pp. l, 44. Interscience, New York (1967); Nucleation (Edited by A. G. Zettlemoyer), p. 225. Marcel Dekker, New York (1969). 16. W. J. Dunning, In Nucleation (Edited by A. G. Zetflemoyer) p. 1. Marcel Dekker, New York (1969). 17. J. H. Wang andJ. W. Kennedy, J.Am. chem. Soc. 72, 2080 (1950). 18. R. Mills and J. W. Kennedy, J. Am. chem. Soc. 75, 5695 (1953). 19. V. V. Goncharov, V. G. Markova and V. I. Yashkichev, Radiokhim. 10, 575 (1968). 20, T. Williams and C. B. Monk, Trans. Faraday Soc. 57, 447 (1961).
Self-diffusion of 131I-and H6Ag+
2545
EXPERIMENTAL Apparatus The measurement of the self-diffusion coefficient was carried out simultaneously in five capillaries. Otherwise the measuring apparatus was the same as that given in previous communications[I-3]. The capillaries were dipped into 500 ml of inactive solution, which had the same composition and pH as the solution in the capillaries except the radioactive isotope which was only in the capillaries. The average capillary length was 3-537 cm, volume 0.030 ml and radius 0.052 cm. Solutions Chemicals AnalaR grade and triple distilled water were used for the preparation of the solutions. The radioisotopes J3JI (NaI) and 11°Ag(AgNO3) used were carrier-free and were made in the Nuclear Research Institute of the Czechoslovak Academy of Sciences at Re=~.(Czechoslovakia). The selfdiffusion of the I- ion alone labelled with 13q and Ag + labelled with H°Ag was carded out in 10-SM and 10-6M NaI or AgNO3 solutions respectively. In addition to the self-diffusion of individual ions the self-diffusion of the iodide ion in both concentrations mentioned in the presence of 10-gM, 10-SM, 10-rM, 10-6M and 10-SM Ag ÷ ion was carried out. The pH value of the solutions was 7'3, except the self-diffusion of Ag + alone where it was adjusted to 7-0 or 3-0. The ion c strength/z of the solutions was 0.01 (NaNO3). Procedure The procedure was similar to that given previously[I-3]. The self-diffusion time was 95 hr, temperature 25-0.02°C. The inner capillary surface was hydrophobized[2, 3] to avoid the surface adsorption of the radioisotope or to reduce it to minimum during the self-diffusion. The Agl sol was prepared in such a way that always two equivalent volumes of inactive (250 ml) or radioactive (25 ml) sodium iodide and silver nitrate solutions of double concentrations with respect to the concentration required after mutual mixing were mixed. The silver nitrate solution was slowly added to the radioactive sodium iodide solution under continuous stirring. The resulting solution remained for 30 min under stirring so that the precipitation reaction could take place in the whole volume of the solution in the case of exceeding AgI solubility product and occasional local supersaturation could be compensated. Then the self-diffusion was measured. In addition to capillaries for self-diffusion the radioactive solution was also present in "standard" capillaries of the same size, which, however, were not used for self-diffusion but they served for occasional correction for radioisotope adsorption on capillary walls during the self-diffusion. The self-diffusion coefficient D was calculated by means of the Equation (1), the concentrations Co and C being replaced by the radioactivity/0 of the solution before the self-diffusion in the "standard" capillary and by the radioactivity I in the capillary after the self-diffusion. The calculation was carded out on the G IER computer and as many terms of the Equation (1) were included into the calculation so that the ratio of the last term to all preceding terms included into the calculation was < 10-6.
RESULTS AND DISCUSSION T h e v a l u e s o f self-diffusion coefficients D, p H , the d a t a o n the e x c e e d i n g o f t h e s o l u b i l i t y p r o d u c t o f A g I a n d the signs o f the A g I s o l u t i o n charge are g i v e n in T a b l e 1. T h e v a l u e s o f s t a n d a r d e r r o r s for i n d i v i d u a l D v a l u e s are i n c l u d e d in the T a b l e 1. T h e d e p e n d e n c e o f the self-diffusion coefficient o n the c o n c e n t r a t i o n o f silver ions is p l o t t e d i n Fig. 1. A s m a y b e s e e n f r o m T a b l e 1 a n d Fig. 1 the c o u r s e o f the self-diffusion o f 1311- is different w i t h i n c r e a s i n g c o n c e n t r a t i o n o f silver i o n s for b o t h c o n c e n t r a t i o n s o f iodide ions. I t m a y b e a s s u m e d t h a t the s l o w i n g d o w n o f the self-diffusion o f 1311- in the p r e s e n c e o f A g ÷ i o n s i n d i c a t e s g r a d u a l f o r m a t i o n o f silver iodide sol. S t a b l e A g I colloid m a y b e a s s u m e d in the m e d i u m o f 0 . 0 1 M N a N O 3 [ 4 ] . T h e s o l u b i l i t y p r o d u c t o f A g I is v e r y l o w (1-5 × 10-16), the p r e c i p i t a t i o n o f A g O H or AgCI from trace chloride concentrations cannot be expected since their
F. K E P A K and J. K I ~ I V A
2546
Table 1. V a l u e s o f p H , self-diffusion coefficient, exceeding o f solubility product, and charge sign o f A g I
Cf
CAg+
pH
10-s 10-s 10-s 10-s 10-s 10-s 10-6 10-6 10-6 10-° 10-6 10-6 0
0 10-9 10-a 10-r 10-6 10-5 0 10-9 10-s 10-7 10-8 10-~ 10-8
7"3 7"3 7"3 7"3 7"3 7"3 7'3 7'3 7"3 7'3 7"3 7"3 7"0 7"0 3"0 3"0
0
10 - 6
0
10-s
0
10 -6
D × 102 I-(AgI) Ag +
sign o f A g I
multiple o f the exceeding o f A g I solubility product
+ + +
6.66 6.66 × 10 6.66 × 102
-
6.66 6"66 × 6.66 × 6.66 × 6.66 ×
16"20 8' 10 1 '93 2"29 1 "68 2" I0 16"10 16"00 13"10 11"40 4" 15 2"90
-
_+ +
10 102 102 102
5.07 5.36 15.70 16.90
C = ion concentration in M / 1 ; D = self-diffusion coefficient, cm2/sec. Standard error 8 o f the results:
8,%
DAg+,pH=3 3"0
DAg+,pH=7"0 11"1
DI 5"5
DAgI 15'5
2o
IO tO
_o x
c3
5
o
0
I
0
~l
0
I
I0 -e
r
I0- e
lO-r
I
lO-e
I
i0-5
C
Fig. 1. D e p e n d e n c e o f the serf-diffusion coefficient D on the concentration o f silver ions in the solution: D = self-diffusion coefficient, cm2/sec; c = silver ion concentration in M / I ; c u r v e (1) for 10-SM I-; c u r v e (2) for 10-SM I-.
Self-diffusion of 1311-and 11°Ag+
2547
solubility products are relatively high and they cannot influence, therefore, the formation of AgI sol. The concentration of impurity metal ions which could form colloid hydroxides in trace concentrations may be also considered as very low [21 ] and any essential effect of these hydroxides on the formation of AgI sol as little probable. The solubility product of AgI should be exceeded for the 10-~M concentration of I- ions at the 10-rM concentration of Ag + ions, for 10-6M concentrations of I- ions, already at the 10-gM concentration of Ag ÷ ions. Exceeding of solubility product, however, was not essential for the variation of the self-diffusion rate because the slowing-down of the self-diffusion did not correspond to these values of the Ag ÷ ion concentration. In the case of the 10-aM I- the AgI sol can be formed in the excess of Ag ÷ ions only so that it has positive charge, in the case of 10-6M I- the negative charge of the AgI sol changes to positive with increasing Ag ÷ concentration (Table 1). The self-diffusion is also different at exceeding of the solubility product by the same factor for both concentrations of iodide (10-aM I- with 10-rM to 10-SM Ag ÷, 10-6M I- with 10-aM to 10-7M Ag ÷, Table 1), the slowing-down of the self-diffusion with increasing Ag ÷ concentration being much slower for the 10-6M I- solution, to the contrary of the 10-SM I- solution, in which the slowing down of the self-diffusion occurs already before reaching the theoretical value of AgI solubility product. The small decrease in the self-diffusion coefficient at 10-6M I- with increasing Ag ÷ concentration to 10-TM would be possible to explain by stoichiometry, since in accord with solubility-product predictions most of the I- remains in solution and under this condition the value of the self-diffusion coefficient corresponds predominantly to I- ions. The self-diffusion rate fell rapidly for the 10-6M I- solution from concentrations higher than 10-TM Ag + thus when the Ag ÷ ion was in approximately equal or higher concentration with respect to I- ion and the sign of AgI changed to positive. The formation of a new phase is explained by the nucleation theory. The nucleation theory starts from an idea that in supersaturated solution there are not only the molecules A but also the embryos Ai, which are aggregates of A molecules. The Ai embryo loses or gains the A molecule and turns to A~+~ or A , embryos. The kinetic process in a supersaturated solution may be described in the following way [13, 16]: A+A
~A2
A z + A .~ A3
Ak-1 + A ~ Ak Ak + A .~ A k + 1
A i + A ~-- A~+I. The process of molecule attraction by embryos prevails and a critical nucleus A ~ is formed, which represents a new phase and there is a probability that this phase will grow up to macroscopic size. According to literature [ 15] homogeneous nucleation without any participation of impurities probably takes place with substances the solubility of which is lower than 10-6M and these substances 21. R. E. Thiers, Trace Analysis (Edited by J. Hoe and H. J. Koch) p. 641. Wiley, New York (1957).
2548
F. KEPAK and J. KI~IVA
exhibit colloidal behaviour. In our case the self-diffusion coefficient characterized the state of AgI molecule aggregates in a certain equilibrium stage. In 10-SM I- concentration a chemical interaction between I- and Ag + ions probably took place before reaching of the solubility product of AgI at the 10 -a and 10-SM concentrations of Ag + forming AgI molecule aggregates since the rate of the ~31I self-diffusion decreased in these conditions. The participation of trace impurity amounts on the initiation of the aggregation, however, cannot be excluded in this case. Further increase of Ag + concentration did not influence the self-diffusion rate of 10-SM 131I-, which suggests that a higher excess of precipitating ions does not lead to the formation of greater AgI aggregates. At 10-tM I- concentration and Ag + concentration 10-6M or higher the self-diffusion rate was still higher than at the 10-SM I- which suggests that the size of AgI aggregates was also smaller in the more concentrated solution of I- ions. It may be assumed on the basis of the kinetic conception of chemical equilibrium and Maxwell law of velocity distribution that quantitative reproducibility of common equilibria may be attained with 10e reacting molecules, which corresponds to 10-16g of reacting substance with an average molecular weight of 100 [22]. In our conditions the amount of reacting substance was much higher even at the lowest values of the microconcentrations of both ions so that the reproducibility of our system was guaranteed from thispoint of view. The radius of the critical nucleus is given as 18 :k for SrSO4, 22 A for BaSO~ [23]. Approximate size of the AgI molecule aggregates was 14.4 ~ for the lowest value of the self-diffusion coefficient D = 1.68 x 10-Semi/see, pH = 7.3 and viscosity ~ = 0.898 cP [3] calculated from the Stokes-Einstein relation [2] so that an agreement by order of magnitude is found with the values for SrSO4 and BaSO4. Evidently aggregates of AgIsol of very small dimensions were formed in our system, the growth to larger particles did not continue, crystallic phase was not formed. A quasi-equilibrium state was reached, which was characterized by the formation of aggregates of different dimensions up to critical size this distribution being relatively stable in the concentration range and time period investigated. The possibility of an effect of insignificant impurity concentrations on the formation of AgI sol below its solubility product cannot be excluded in our conditions. Theoretical self-diffusion coefficient calculated using the Relation[2] from limiting equivalent conductivities (XI- = 78-84 l~ -1 × g equiv. -1 × cm ~[24], XAg+= 61 "90 1-1-1g equiv. -~ × cm 2 [24]) is 2"095 × 10-5 cm2/sec for I- and 1.65 × 10-5 cm2! sec for Ag +. In the case o f A g + at pH --- 3 the experimentally measured value of D coincided with theoretical one within the error. At pH = 7.0 the determined selfdiffusion coefficient of Ag + is lower than theoretical value, the decrease of self-diffusion coefficient may be due to an interaction of Ag + with hydroxyl ions at this pH. The lower value of the self-diffusion coefficient of I- determined experimentally than theoretical one could be due to the oxidation of a part of Iions to I2 [25]. Is- could be formed by the reaction I2 + I- ~- I3- which diffuses 22. 23. 24. 25.
A.A. Benedetti-Pichler and J. R. Rachele, Ind. Engng Chem. analyt. Edn. 12, 233 (1940). A. W. Adamson, Physical Chemistry of Surfaces, p. 385, Interscience, New York (1967). Spravochnik Khimika, Vol. 3, 2nd Edn., pp. 709, 710, izd. Khimiya, Moscow-Leningrad. A. Ok~i~,Analytickd Chemic Kvalitativni (in Czech), pp. 507, 508. Academia, Prague (1966).
Self-diffusion ofl3q - and 11°Ag+
2549
probably more slowly than I- and decreases the value of the self-diffusion coefficient. Acknowledgement--The authors express their thanks to Dr. J. Hrub9 from the Nuclear Research Institute of the Czechoslovak Academy of Sciences, ~,e~ (Czechoslovakia), for his willingness in preparing and yielding the ~l°Ag radioisotope.