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Kinetic studies on isotopic exchange between neodymium ion and its diethylenetriaminepentaacetic acid complex
J. inorg,nucl.Chem.,1970,Vol.32, pp. 1287to 1293. PergamonPress. Printedin Great Britain
KINETIC STUDIES ON ISOTOPIC EXCHANGE BETWEEN NEODYMIUM ION ITS DIETHYLEN ETRIAMIN EPENTAACETIC COMPLEX
AND ACID
T. ASANO, S. O K A D A and S. T A N I G U C H I Department of Chemistry, Radiation Center of Osaka Prefecture, Shinke-cho, Sakai, Osaka, Japan
(Received 27 June 1969)
Abstract-An isotopic exchange reaction between neodymium ion and its DTPA complex in aqueous solution was studied over the concentration range of l × 10-4M-1 × 10-3M of each reactant and pH range of 5.5-7.0. The rate was found to be proportional to [NdY] 1"°, [Nd3+]°'3-1"° and [H+] 2"°-°'3 and was expressed by: R M min -t = k,[NdY][Nd ~+] + k2[NdY][H+][Nd 3+] + k4[NdY][H+] 2 + ks[NdY][H+]3 where kl, k2, lq and ks are 0.35M -1 min -1, 3-4 × 105M-2 min 1, 1.1 × 10SM 2 min-~ and 1.4 × 1013M-:~ rain-1 at 25°C in 0-01M ammonium acetate buffer solution. A monoprotonation process cannot be observed. In acid solution the exchange reaction proceeds by a protonation and bimolecular collision processes. In neutral solution the bimolecular collision process is predominant. Although dependence of the rate on the hydrogen ion concentration is also observed in neutral solution, it is not attributed to the protonation process but to the bimolecular collision process in which hydrogen ions participate. INTRODUCTION
WE HAVEbeen studying theft-decay effects of the chelate compound 149NdDTPA in aqueous solution paying attention to the bond rupture of the complex[l]. The decay effects were found to be closely related to an isotopic exchange reaction. For better understanding of the fl-decay effects, therefore, knowledge of the isotopic exchange reaction is essential. Although isotopic exchange reactions of metal polyaminocarboxylate chelate compounds have been studied by many workers[2-9], systematic studies over a wide pH range have scarcely been reported. Rate equations in which the hydrogen ion concentration appears are only a first step because: (1) it cannot be determined whether protonation of the complex or dissociation of the protonated complex determines the rate, and (2) measurements of the acid formation constant of the protonated chelate (MHnY) are generally incomplete. 1. 2. 3. 4. 5. 6. 7. 8. 9.
Unpublished work. S. S. Jones and F. A. Long, J. phys. Chem. 56, 25 (1952). C. M. Cook, Jr. and F. A. Long, J. Am. chem. Soc. 80, 33 (1958). R.H. Betts, O. F. Dahlinger and D. M. Munro, Radioisotopes in Scientific Research, Proc. Intern. Conf., Paris, 1957. Vol. 2, p. 326. Pergamon Press, New York (1958). M. Tsuchimoto, Bull. chem. Soc.Japan 38,478 (1965). M. Tsuchimoto and K. Saito, J. inorg, nucL Chem. 27,849 (1965). S.S. Krishnan and R. E. Jervis, J. inorg, nucl. Chem. 29, 87 (1967). R. E. Jervis and S. S. Krishnan, J. inorg, nucl. Chem. 29, 97 (1967). P. Glentworth, B. Wiseall, C. L. Wright and A. J. Mahmood, J. inorg, nucl. Chem. 30, 967 (1968). 1287
1288
T. ASANO, S. O K A D A and S. T A N I G U C H I
In the present paper, we attempt to obtain further information about the isotopic exchange reaction of the neodymium D T P A chelate compound over a wide pH region, although a complete elucidation of our empirical rate equation has not yet been attained. EXPERIMENTAL Materials. Radioactive 147Nd (Tit2 = 11.1 d) was produced by pile neutron irradiation of commercail neodymium oxide and was used as tracer. Neodymium D T P A complex solution was prepared by adding an equivalent amount of neodymium nitrate solution to Na2DTPA stock solution. The latter solution was prepared by dissolving one equivalent of D T P A (Diethylenetriaminepentaacetic acid) in two equivalent of sodium hydroxide solution and standardized by titration against standard copper ion solution by using PAN (1-(2pyridylazo)-2 naphthol) indicator. Procedure. A solution of neodymium nitrate labeled with 147Nd was mixed with the neodymium D T P A complex solution. Each solution was made up in 0.01M ammonium acetate buffer solution. The pH of the solution was adjusted by addition of either ammonium hydroxide or acetic acid to an accuracy of---0.05. The reaction mixture was thermostated to the 25---0. I°C. At appropriate time an aliquot was passed through a Dowex 50 X-8 cation exchange column. The radioactivity of the eluate was measured by a scintillation counter with a well-type NaI(TI) crystal. RESULTS
The exchange reaction between neodymium ion and its D T P A complex was studied over a concentration range of 1 × 10-4M-1 × 10-3M of each reactant and a pH range of 5-5-7.0. The results were plotted using Mackay's formula[10],
In(l--F)=
Rt(a+b) ab
where F is fractional exchange obtained at time t, and a and b represent the molar concentration of neodymium ion and its D T P A complex, respectively. Representative results at four pH values are shown in Fig. 1. An apparent zero time exchange of about 10 per cent was observed. Therefore, the fractional exchange was corrected by the method of Prestwood and Wahl[11]. The rate was calculated from the half time of the exchange. The exchange reaction was found to be first order with respect to the neodymium D T P A complex concentration over the whole range of pH studied. Dependence of the rate on the neodymium ion concentration is shown in Fig. 2. Even at pH 5.5 some dependence on the neodymium ion concentration is observed. The order with respect to the neodymium ion concentration changes from one at pH 7.0 to 6.5, to 0.6 at pH 6.0 and 0.3 at pH 5.5, respectively. The order also increases slowly with increasing neodymium ion concentration. The dependence of the rate on the hydrogen ion concentration is shown in Fig. 3. The order with respect to the hydrogen ion concentration increases with decreasing pH value. In the same pH range the order with respect to the hydrogen ion concentration also increases with decreasing neodymium ion concentration. For the curve D the 10. O. E. Myers and R. J. Prestwood, Radioactivity Applied to Chemistry (Edited by A. C. Wahl and N. A. Bonner), 2nd Edn., p. 7. Wiley, New York (1958). 11. R.J. Prestwood and A. C. Wahl, J. Am. chem. Soc. 71, 7177 (1949).
Kinetic studies on isotopic exchange
1289
1.0 '9
'7
I
pH = 7 . 0
H = ...='5 h •3
2
4
pH = 6 . 0 6
8
,
10
,
12
14
16
Time,hr
Fig. I. Semi-logarithmic plot of ( 1 - F) against time at various pHs: [NdDTPA] = 2× 10-3M; [Nd 34] = 5 × 10-4M.
pH = 5"5
D ~ o/
p.=
6
o
..J I
.'.2
4:0
3:8
~6
~'4
3:2
~0
-- Log [Nd3*3
Fig. 2. Dependence of rate on neodymium ion concentration: [NdDTPA] = 2× 10-3M. (Plots represent experimental results and lines represent results calculated using the rate equation).
k i n e t i c order i n c r e a s e s f r o m 0.3th to s e c o n d with d e c r e a s i n g p H v a l u e from 7.0 to 5.5. DISCUSSION T h e rate e q u a t i o n d e r i v e d f r o m the e x p e r i m e n t a l results is R M m i n -1 = k l [ N d Y ] [ N d 3+] + k 2 [ N d Y ] [ H + ] [ N d 3+] + k 3 [ N d Y ] [ H +] + I q [ N d Y ] [ H + ] 2 + k s [ N d Y ] [ H + ] 3.
1290
T. ASANO, S. O K A D A and S. T A N I G U C H I
/
I
7
/
~
Z
/
7
'
Slope=2
S pe 03
7:0
'
gs
'
--
Log I'H+]
go
5:5
Fig. 3. Dependence of rate on hydrogen ion concentration: [NdDTPA] = 2 × 10-ZM; I-1, [Nd 3+] = 1 x 10-3M; ©, [Nd a+] = 5 × 10-4M; A, [Nd a+] = 2 × 10-4M; O, [Nda+l --1 × 10-4M. (Plots represent experimental results and lines represent results calculated using the rate equation).
The D T P A ligand is abbreviated as Y hereafter. A plot of R/[NdY] vs. [Nd a+] should be linear at the constant pH value. This linear relation is shown in Fig. 4, where the intercept of curve D is nearly zero. The slopes of the lines in Fig. 4 which correspond to kl + ks[H+], are plotted against the hydrogen ion concentration and shown in Fig. 5. From the slope of the line in Fig. 5, rate constant kl and k2 were determined to be 0.35M -1 min -1 and 3.4 × 105M-2 min -1, respectively. From the values of the intercepts in Fig. 4, rate constant lq and k5 were calculated to be 1.1 x 10aM -2 min -1 and 1-4 x 101ZM-z rain -1, respectively. The contribution of the diprotonation process to the exchange reaction is so great that the ka value, the rate constant of monoprotonation process, could not be determined. A B,C,D
n
25""10
A
=23. 8 ~.211- 61
~19" 4
c
X
17-2 i
15 " 0(
2
i
i
4
I
I
6
I
I
8
I
I
I0
rNdS+]X104 M Fig. 4. R/[NdDTPA] vs. [Nd 3+] at various pHs: [NdDT PA] = 2× 10-3M; I-q, pH = 5-5; O, pH = 6.0; A, pH = 6.5; O, pH = 7.0.
Kinetic studies on isotopic exchange
1291
15 13
E11 0 X
~9 + 7 5
3
o:s
i:0
1:5
2-'o
2:5
3:o
[H+3XIO ~ M
Fig. 5. kl + I%[H+] vs. [H ÷] for the results obtained in Fig. 4.
Glentworth et al. also reported that the monoprotonation process could not be observed in the C e D T P A system[9]. The values of these rate constants are plausible in comparison with the corresponding ones obtained in other systems [9, 12]. Consequently, the following rate equation describes the results: R M rain -1 = 0.35[NdY][Nd 3+] + 3.4 × 10~[NdY][H+][Nd 3+] + 1.1 × 108[NdY][H+]2 + 1.4 × 1013[NdY][H+] 3. Comparison of the calculated values with the experimental values are shown in Figs. 2 and 3, where the lines represent the results calculated using the rate equation. The calculated values are in satisfactory agreement with the experimental values. A probable substitution process to interpret the first and second terms of the rate equation may be a simple bimolecular collision process (simultaneous rupture mechanism). Such a substitution process can also be explained by the step-wise dissociation mechanism which was considered preferable to the simultaneous rupture mechanism[13]. For the third and fourth terms, two reaction mechanisms can be considered: those are (1) unimolecular decomposition of the protonated complex (SE1)[3, 7, 8] and (2) acid-induced dissociation of complex (SE2)[2, 9]. If we can evaluate each value of the acid formation constants, some speculation about the protonation processes, SE 1 and SE2, will be possible. However, such a speculation is impossible, because the acid formation constants of multiprotonated complexes which behave as strong acids cannot be determined [14]. Krishnan and Jervis[7, 8] tried to explain the protonation process by using 12. T. Asano, S. Okada, K. Sakamoto, S. Taniguchi and Y. Kobayashi, J. inorg, nucl. Chem. 31, 2127 (1969). 13. F. Basolo and R. G. Pearson, Mechanisms of Inorganic Reactions, p. 200. Wiley, London ( 1958). 14. T. Moeller and L. C. Thompson, J. inorg, nucl. Chem. 24,499 (1962).
1292
T. ASANO, S. O K A D A and S. T A N I G U C H I
Crystal Field Theory. This fails in the case of the rare earth complexes because o f insufficient information about crystal field effects of the 4 f e l e c t r o n orbitals. Consequently, the probable reaction processes are summarized as follows: 1. Bimolecular collision process N d Y 2 - + ,Nd~+ __, N d Y , N d + -..., Nd3++ , N d Y 2 NdHY-+
* N d 3+ ---) N d H Y * N d ~+ ~ Nd3++ * N d H Y - .
(1) (2)
2. Protonation process N d H Y - + H + "--* NdH~Y ~ Nd3++ H2Y 3-
(3)
N d H 2 Y + H + '-* N d H 3 Y + ~ Nd3++ H3Y 2-
(4)
H , Y ~5-"~- + *Nd 3+ - ~
* N d H n Y ~2-~-
(n = 2 or 3).
(5)
In these processes, one cannot determine whether the first or second step is ratedetermining. In ammonium acetate solution, the rare earth metal ions form acetate complex ions of the type M(Ac), t3-"~+ where n = 0,1,2, 3 or 4 [ 15, 16]. Glentworth e t al.[9] reported that reaction terms, dependent on hydrogen ion and metal ion concentrations in C e D T P A system, were affected remarkably by the change of an acetate ion concentration. T h e y suggested that the effects of the acetate ion concentration were due to the formation of the acetate complex ions. T h e s e effects in the present system would be great because of weak ionic strength such as c a . 0.01. Therefore, in view of the acetate ion effects the rate equation and reaction schemes described above should be overall ones under the conditions so far studied.
56
6-0
6~
~0
5.5
pH
6-5
60
~0
pH
Fig. 6. Contribution of elementary reaction rate terms with pHs for [Nd a+] = 1 x 10-4M (I) and 1 × 10-3M (II): Curve A, kl[NdY][Nda+]; Curve B, Iq[NdY][H+][Nda+]; Curve C, Iq[NdY][H+]~; Curve D, Iq[NdY][H+] a. 15. A. Sonesson, Acta chem. scand. 12, 165 (1958). 16. R. S. Kolat and J. E. Powell, lnorg. Chem. 1, 293 (1962).
Kinetic studies on isotopic exchange
1293
It becomes clear that the four elementary reaction processes (1), (2), (3) and (4) compete with each other in the exchange reaction. Evidently from the rate equation, the contribution of each elementary reaction to the overall reaction is affected by the concentration of neodymium ion and pH, but not by the concentration of complex ion. The percentage contributions of each elementary reaction at different pH values are shown in Fig. 6. Figures 6(I) and (II) show the distribution at constant neodymium ion concentrations of 1 x 10-4M and 1 × 10-:~M, respectively. In the pH range of 5.5-6.0, the protonation process is predominant at low concentration of neodymium ion, and the contribution of the bimolecular collision process becomes greater with increasing neodymium ion concentration. In the pH range of 6.5-7.0, the bimolecular collision process is predominant. The dependence of the rate on the hydrogen ion concentration observed at pH 7.0-6.5 (see Fig. 3) is not to be attributed to a protonation process but to a bimolecular collision process in which hydrogen ions participate. Acknowledgement-The authors wish to express their gratitude to Dr. J. Tsurugi (Chairman of Department of Chemistry of this Institute) for his continuing guidance and encouragement.
KINETIC STUDIES ON ISOTOPIC EXCHANGE BETWEEN NEODYMIUM ION ITS DIETHYLEN ETRIAMIN EPENTAACETIC COMPLEX
AND ACID
T. ASANO, S. O K A D A and S. T A N I G U C H I Department of Chemistry, Radiation Center of Osaka Prefecture, Shinke-cho, Sakai, Osaka, Japan
(Received 27 June 1969)
Abstract-An isotopic exchange reaction between neodymium ion and its DTPA complex in aqueous solution was studied over the concentration range of l × 10-4M-1 × 10-3M of each reactant and pH range of 5.5-7.0. The rate was found to be proportional to [NdY] 1"°, [Nd3+]°'3-1"° and [H+] 2"°-°'3 and was expressed by: R M min -t = k,[NdY][Nd ~+] + k2[NdY][H+][Nd 3+] + k4[NdY][H+] 2 + ks[NdY][H+]3 where kl, k2, lq and ks are 0.35M -1 min -1, 3-4 × 105M-2 min 1, 1.1 × 10SM 2 min-~ and 1.4 × 1013M-:~ rain-1 at 25°C in 0-01M ammonium acetate buffer solution. A monoprotonation process cannot be observed. In acid solution the exchange reaction proceeds by a protonation and bimolecular collision processes. In neutral solution the bimolecular collision process is predominant. Although dependence of the rate on the hydrogen ion concentration is also observed in neutral solution, it is not attributed to the protonation process but to the bimolecular collision process in which hydrogen ions participate. INTRODUCTION
WE HAVEbeen studying theft-decay effects of the chelate compound 149NdDTPA in aqueous solution paying attention to the bond rupture of the complex[l]. The decay effects were found to be closely related to an isotopic exchange reaction. For better understanding of the fl-decay effects, therefore, knowledge of the isotopic exchange reaction is essential. Although isotopic exchange reactions of metal polyaminocarboxylate chelate compounds have been studied by many workers[2-9], systematic studies over a wide pH range have scarcely been reported. Rate equations in which the hydrogen ion concentration appears are only a first step because: (1) it cannot be determined whether protonation of the complex or dissociation of the protonated complex determines the rate, and (2) measurements of the acid formation constant of the protonated chelate (MHnY) are generally incomplete. 1. 2. 3. 4. 5. 6. 7. 8. 9.
Unpublished work. S. S. Jones and F. A. Long, J. phys. Chem. 56, 25 (1952). C. M. Cook, Jr. and F. A. Long, J. Am. chem. Soc. 80, 33 (1958). R.H. Betts, O. F. Dahlinger and D. M. Munro, Radioisotopes in Scientific Research, Proc. Intern. Conf., Paris, 1957. Vol. 2, p. 326. Pergamon Press, New York (1958). M. Tsuchimoto, Bull. chem. Soc.Japan 38,478 (1965). M. Tsuchimoto and K. Saito, J. inorg, nucL Chem. 27,849 (1965). S.S. Krishnan and R. E. Jervis, J. inorg, nucl. Chem. 29, 87 (1967). R. E. Jervis and S. S. Krishnan, J. inorg, nucl. Chem. 29, 97 (1967). P. Glentworth, B. Wiseall, C. L. Wright and A. J. Mahmood, J. inorg, nucl. Chem. 30, 967 (1968). 1287
1288
T. ASANO, S. O K A D A and S. T A N I G U C H I
In the present paper, we attempt to obtain further information about the isotopic exchange reaction of the neodymium D T P A chelate compound over a wide pH region, although a complete elucidation of our empirical rate equation has not yet been attained. EXPERIMENTAL Materials. Radioactive 147Nd (Tit2 = 11.1 d) was produced by pile neutron irradiation of commercail neodymium oxide and was used as tracer. Neodymium D T P A complex solution was prepared by adding an equivalent amount of neodymium nitrate solution to Na2DTPA stock solution. The latter solution was prepared by dissolving one equivalent of D T P A (Diethylenetriaminepentaacetic acid) in two equivalent of sodium hydroxide solution and standardized by titration against standard copper ion solution by using PAN (1-(2pyridylazo)-2 naphthol) indicator. Procedure. A solution of neodymium nitrate labeled with 147Nd was mixed with the neodymium D T P A complex solution. Each solution was made up in 0.01M ammonium acetate buffer solution. The pH of the solution was adjusted by addition of either ammonium hydroxide or acetic acid to an accuracy of---0.05. The reaction mixture was thermostated to the 25---0. I°C. At appropriate time an aliquot was passed through a Dowex 50 X-8 cation exchange column. The radioactivity of the eluate was measured by a scintillation counter with a well-type NaI(TI) crystal. RESULTS
The exchange reaction between neodymium ion and its D T P A complex was studied over a concentration range of 1 × 10-4M-1 × 10-3M of each reactant and a pH range of 5-5-7.0. The results were plotted using Mackay's formula[10],
In(l--F)=
Rt(a+b) ab
where F is fractional exchange obtained at time t, and a and b represent the molar concentration of neodymium ion and its D T P A complex, respectively. Representative results at four pH values are shown in Fig. 1. An apparent zero time exchange of about 10 per cent was observed. Therefore, the fractional exchange was corrected by the method of Prestwood and Wahl[11]. The rate was calculated from the half time of the exchange. The exchange reaction was found to be first order with respect to the neodymium D T P A complex concentration over the whole range of pH studied. Dependence of the rate on the neodymium ion concentration is shown in Fig. 2. Even at pH 5.5 some dependence on the neodymium ion concentration is observed. The order with respect to the neodymium ion concentration changes from one at pH 7.0 to 6.5, to 0.6 at pH 6.0 and 0.3 at pH 5.5, respectively. The order also increases slowly with increasing neodymium ion concentration. The dependence of the rate on the hydrogen ion concentration is shown in Fig. 3. The order with respect to the hydrogen ion concentration increases with decreasing pH value. In the same pH range the order with respect to the hydrogen ion concentration also increases with decreasing neodymium ion concentration. For the curve D the 10. O. E. Myers and R. J. Prestwood, Radioactivity Applied to Chemistry (Edited by A. C. Wahl and N. A. Bonner), 2nd Edn., p. 7. Wiley, New York (1958). 11. R.J. Prestwood and A. C. Wahl, J. Am. chem. Soc. 71, 7177 (1949).
Kinetic studies on isotopic exchange
1289
1.0 '9
'7
I
pH = 7 . 0
H = ...='5 h •3
2
4
pH = 6 . 0 6
8
,
10
,
12
14
16
Time,hr
Fig. I. Semi-logarithmic plot of ( 1 - F) against time at various pHs: [NdDTPA] = 2× 10-3M; [Nd 34] = 5 × 10-4M.
pH = 5"5
D ~ o/
p.=
6
o
..J I
.'.2
4:0
3:8
~6
~'4
3:2
~0
-- Log [Nd3*3
Fig. 2. Dependence of rate on neodymium ion concentration: [NdDTPA] = 2× 10-3M. (Plots represent experimental results and lines represent results calculated using the rate equation).
k i n e t i c order i n c r e a s e s f r o m 0.3th to s e c o n d with d e c r e a s i n g p H v a l u e from 7.0 to 5.5. DISCUSSION T h e rate e q u a t i o n d e r i v e d f r o m the e x p e r i m e n t a l results is R M m i n -1 = k l [ N d Y ] [ N d 3+] + k 2 [ N d Y ] [ H + ] [ N d 3+] + k 3 [ N d Y ] [ H +] + I q [ N d Y ] [ H + ] 2 + k s [ N d Y ] [ H + ] 3.
1290
T. ASANO, S. O K A D A and S. T A N I G U C H I
/
I
7
/
~
Z
/
7
'
Slope=2
S pe 03
7:0
'
gs
'
--
Log I'H+]
go
5:5
Fig. 3. Dependence of rate on hydrogen ion concentration: [NdDTPA] = 2 × 10-ZM; I-1, [Nd 3+] = 1 x 10-3M; ©, [Nd a+] = 5 × 10-4M; A, [Nd a+] = 2 × 10-4M; O, [Nda+l --1 × 10-4M. (Plots represent experimental results and lines represent results calculated using the rate equation).
The D T P A ligand is abbreviated as Y hereafter. A plot of R/[NdY] vs. [Nd a+] should be linear at the constant pH value. This linear relation is shown in Fig. 4, where the intercept of curve D is nearly zero. The slopes of the lines in Fig. 4 which correspond to kl + ks[H+], are plotted against the hydrogen ion concentration and shown in Fig. 5. From the slope of the line in Fig. 5, rate constant kl and k2 were determined to be 0.35M -1 min -1 and 3.4 × 105M-2 min -1, respectively. From the values of the intercepts in Fig. 4, rate constant lq and k5 were calculated to be 1.1 x 10aM -2 min -1 and 1-4 x 101ZM-z rain -1, respectively. The contribution of the diprotonation process to the exchange reaction is so great that the ka value, the rate constant of monoprotonation process, could not be determined. A B,C,D
n
25""10
A
=23. 8 ~.211- 61
~19" 4
c
X
17-2 i
15 " 0(
2
i
i
4
I
I
6
I
I
8
I
I
I0
rNdS+]X104 M Fig. 4. R/[NdDTPA] vs. [Nd 3+] at various pHs: [NdDT PA] = 2× 10-3M; I-q, pH = 5-5; O, pH = 6.0; A, pH = 6.5; O, pH = 7.0.
Kinetic studies on isotopic exchange
1291
15 13
E11 0 X
~9 + 7 5
3
o:s
i:0
1:5
2-'o
2:5
3:o
[H+3XIO ~ M
Fig. 5. kl + I%[H+] vs. [H ÷] for the results obtained in Fig. 4.
Glentworth et al. also reported that the monoprotonation process could not be observed in the C e D T P A system[9]. The values of these rate constants are plausible in comparison with the corresponding ones obtained in other systems [9, 12]. Consequently, the following rate equation describes the results: R M rain -1 = 0.35[NdY][Nd 3+] + 3.4 × 10~[NdY][H+][Nd 3+] + 1.1 × 108[NdY][H+]2 + 1.4 × 1013[NdY][H+] 3. Comparison of the calculated values with the experimental values are shown in Figs. 2 and 3, where the lines represent the results calculated using the rate equation. The calculated values are in satisfactory agreement with the experimental values. A probable substitution process to interpret the first and second terms of the rate equation may be a simple bimolecular collision process (simultaneous rupture mechanism). Such a substitution process can also be explained by the step-wise dissociation mechanism which was considered preferable to the simultaneous rupture mechanism[13]. For the third and fourth terms, two reaction mechanisms can be considered: those are (1) unimolecular decomposition of the protonated complex (SE1)[3, 7, 8] and (2) acid-induced dissociation of complex (SE2)[2, 9]. If we can evaluate each value of the acid formation constants, some speculation about the protonation processes, SE 1 and SE2, will be possible. However, such a speculation is impossible, because the acid formation constants of multiprotonated complexes which behave as strong acids cannot be determined [14]. Krishnan and Jervis[7, 8] tried to explain the protonation process by using 12. T. Asano, S. Okada, K. Sakamoto, S. Taniguchi and Y. Kobayashi, J. inorg, nucl. Chem. 31, 2127 (1969). 13. F. Basolo and R. G. Pearson, Mechanisms of Inorganic Reactions, p. 200. Wiley, London ( 1958). 14. T. Moeller and L. C. Thompson, J. inorg, nucl. Chem. 24,499 (1962).
1292
T. ASANO, S. O K A D A and S. T A N I G U C H I
Crystal Field Theory. This fails in the case of the rare earth complexes because o f insufficient information about crystal field effects of the 4 f e l e c t r o n orbitals. Consequently, the probable reaction processes are summarized as follows: 1. Bimolecular collision process N d Y 2 - + ,Nd~+ __, N d Y , N d + -..., Nd3++ , N d Y 2 NdHY-+
* N d 3+ ---) N d H Y * N d ~+ ~ Nd3++ * N d H Y - .
(1) (2)
2. Protonation process N d H Y - + H + "--* NdH~Y ~ Nd3++ H2Y 3-
(3)
N d H 2 Y + H + '-* N d H 3 Y + ~ Nd3++ H3Y 2-
(4)
H , Y ~5-"~- + *Nd 3+ - ~
* N d H n Y ~2-~-
(n = 2 or 3).
(5)
In these processes, one cannot determine whether the first or second step is ratedetermining. In ammonium acetate solution, the rare earth metal ions form acetate complex ions of the type M(Ac), t3-"~+ where n = 0,1,2, 3 or 4 [ 15, 16]. Glentworth e t al.[9] reported that reaction terms, dependent on hydrogen ion and metal ion concentrations in C e D T P A system, were affected remarkably by the change of an acetate ion concentration. T h e y suggested that the effects of the acetate ion concentration were due to the formation of the acetate complex ions. T h e s e effects in the present system would be great because of weak ionic strength such as c a . 0.01. Therefore, in view of the acetate ion effects the rate equation and reaction schemes described above should be overall ones under the conditions so far studied.
56
6-0
6~
~0
5.5
pH
6-5
60
~0
pH
Fig. 6. Contribution of elementary reaction rate terms with pHs for [Nd a+] = 1 x 10-4M (I) and 1 × 10-3M (II): Curve A, kl[NdY][Nda+]; Curve B, Iq[NdY][H+][Nda+]; Curve C, Iq[NdY][H+]~; Curve D, Iq[NdY][H+] a. 15. A. Sonesson, Acta chem. scand. 12, 165 (1958). 16. R. S. Kolat and J. E. Powell, lnorg. Chem. 1, 293 (1962).
Kinetic studies on isotopic exchange
1293
It becomes clear that the four elementary reaction processes (1), (2), (3) and (4) compete with each other in the exchange reaction. Evidently from the rate equation, the contribution of each elementary reaction to the overall reaction is affected by the concentration of neodymium ion and pH, but not by the concentration of complex ion. The percentage contributions of each elementary reaction at different pH values are shown in Fig. 6. Figures 6(I) and (II) show the distribution at constant neodymium ion concentrations of 1 x 10-4M and 1 × 10-:~M, respectively. In the pH range of 5.5-6.0, the protonation process is predominant at low concentration of neodymium ion, and the contribution of the bimolecular collision process becomes greater with increasing neodymium ion concentration. In the pH range of 6.5-7.0, the bimolecular collision process is predominant. The dependence of the rate on the hydrogen ion concentration observed at pH 7.0-6.5 (see Fig. 3) is not to be attributed to a protonation process but to a bimolecular collision process in which hydrogen ions participate. Acknowledgement-The authors wish to express their gratitude to Dr. J. Tsurugi (Chairman of Department of Chemistry of this Institute) for his continuing guidance and encouragement.