Reaction Rate Measurements with Cation-Sensitive GIass Electrodes Kinetic Study of the Exchange Reaction between Silver(1)-EDTA and Nickel(l1) G. A. Rechnitz and Zui-feng Linl Department of Chemistry, State Uniuersity of New York, Buffalo, N . Y. 14214 A kinetic study of the exchange reaction Ni(ll)
+ Ag(I)-EDTA
e Ni(ll)-EDTA
+ Ag(I)
was carried out at 25’ C in 0.01M tetraethylammonium borate using cation-sensitive glass electrodes to monitor, selectively, the course of the reaction under varying solution conditions. From the dependences of the reaction rate upon the pH and the concentrations of the various solution species, we propose a four-path mechanism
+
Ni+z AgY-3
+
Ni+2 AgHY-2 Ni+2
2 NiY-2 + Ag+
% NiY-2
+ Ag+ + H +
+ HY-3 5 NiY-2 + H +
Ni+2 + y-4 ? !, NiY-2 for the 9.2 to 10.2 p H region and a two-path mechanism
EXPERIMENTAL
+ AgY-3 % NiY-2 + Ag+ + OHNi+z+ AgY-3 % NiY-2 + Ag+
NiOH+
for the 10.8 to 11.4 pH range, where kit, kI (= kl), k,, k,, and k, were evaluated as 16, lo3.*, l o b . * , 106.0, and 106.8M-l second-’, respectively at 25’ C. A number of equilibrium data for species of silver(1) and nickel(ll), determined directly with the cation-sensitive glass electrodes, are also reported. The usefulness of the ion-selective glass electrodes for the study of fairly rapid, homogeneous solution reactions is demonstrated.
IN VIEW of the rapid response and accurate monitoring capabilities of cation-sensitive glass electrodes for univalent cations (1-5), it should be possible to employ such electrodes for kinetic measurement of selected solution reactions involving suitable cations. Previously (6) we had used cationsensitive glass electrodes in measurements of heterogeneous kinetics; the present work is intended to demonstrate the applicability of these electrodes to the study of homogeneous kinetics. Earlier (7) the pH type glass electrode had been successfully applied to the investigation of some rapid acidbase reactions of bicarbonate ion in a flow system. Other
* On leave from Department of Chemistry, National Taiwan University, Taipei, Taiwan. A. L. Budd, J . Elecrroanal. Chem., 5,35 (1963). G. A. Rechnitz, Record Chem. Progr., 36, 241 (1965). G. A. Rechnitz and G . Kugler, 2.Anal. Chem., 211, 174 (1965). G. A. Rechnitz and G. Kugler. ANAL. CHEM..in Dress. 1967. (5) G . A. Rechnitz and H. F. Hameka, Z. Anal. Chem., 214, 252 (1965). (6) J. E. McClure and G. A. Rechnitz, ANAL. CHEM.,38, 136 (1966). (7) J. A. Sirs, Trans. Faraday SOC.,54,207 (1958).
(1) (2) (3) (4)
1406
.
ANALYTICAL CHEMISTRY
useful fast reaction techniques, including spectrophotometry and voltammetry, have been reviewed elsewhere (8-15). As our test system we chose the electrophilic exchange reaction between Ni(I1) and Ag(1)-EDTA, because of the sensitivity and selectivity ( I , 4, 5) of the cation-sensitive glass electrode for Ag(1) ion. The available data on related systems (IO, 12, 16-19) suggested that the equilibrium and kinetic characteristics of this system might be typical of such exchange reactions as well as of some importance for analytical purposes. Our objective, in demonstrating the utility of cation-sensitive glass electrodes for the study of homogeneous reactions, was to arrive at the fullest possible characterization of the equilibrium and kinetic parameters of the system without resorting to competitive techniques of measurement. For this reason, a rather detailed account of the experimental methods used is included in this paper.
I
Chemicals. Most chemicals, either of analyzed or certified grade, were used without further purification. AgN03 and NiSO, stock solutions were prepared by dissolving samples of these salts in deionized water. The concentrations of the stock solutions were checked by means of potentiometric titration for Ag+ with C1- or EDTA using a cation-sensitive glass electrode as the indicator electrode, and, for Ni(II), with Ca+* in presence of trace amounts of Ag’ and excess EDTA using Ag metal as the indicator electrode (20), respectively. In the latter titration, the glass electrode was not suitable as an indicator electrode because of the extremely low concentrations of Ag+ involved. Eastman-Kodak 10 aqueous tetraethylammonium hydroxide (TEA) was used to prepare TEA-borate and TEA-acetate buffers and TEAEDTA stock solutions. Weighed amounts of boric acid or EDTA (H4Y) were suspended in water and a calculated (8) E. F. Caldin, “Fast Reactions in Solution,” Wiley, New York, 1964. (9) P. Delahay, “New Instrumental Methods in Electrochemistry,” Interscience, New York, 1954. (10) M. Eigen and R . G. Wilkins, Adcan. Clrem. Ser., 49,55 (1965). (11) M. Eigen, Pure and Applied Chem., 6, 99 (1963). (12) R. H. Holyer, C. D. Hubbard, S. F. A. Kettle, and R. G. Wilkins, Inorg. Chem., 4, 929 (1965). (13) D. W. Margerum, Record Chem. Progr., 24, 237 (1963). (14) F. J. W. Roughton, “Technique of Organic Chemistry,” Vol. 8, S. L. Fries & A. Weissberger, Eds., Interscience, New York, 1963, p. 699. (15) N. Tanaka, “Polarography, No. 3, Kagaku no Ryoiki, No. 69,” Nankaido, Tokyo, 1965, p. 1. (16) M. Eigen,Z. Elektrochem., 64, 115 (1960). (17) D . W. Margerum and B. A. Zabin, J . Phys. Cliem., 66, 2214 (1962). (18) L. G. Sillen and A. E. Martell, “Stability Constants of MetalIon Complexes,” Special Publication No. 17, The Chemical Society, London, 1964. (19) N. Tanaka and Y . Sakuma, Bull. Chem. SOC.Japan, 32, 578 (1959). (20) J. S. Fritz and B. B. Garralda, ANAL.CHEM.,36,737 (1963).
amount of TEA was added to bring the solution to a final p H of approximately 11. In the case of TEA-acetate, equivalent amounts of TEA and acetic acid were mixed together. These solutions were stocked in polyethylene reagent bottles to avoid contamination. In spite of the fairly high stability of Ag(1)-EDTA (18), reduction of Ag+ by EDTA (21) was observed even in pure Ag(1)-EDTA solutions. A 2 X 10-3M Ag(1)-EDTA solution could stand for 72 hours without visible coloration if kept in the dark and a t temperatures below 30" C. Laboratory illumination caused yellow coloration in several hours, and direct sunlight much more rapidly. After long standing, black Ag powder was obtained in each case. Various color changes were observed during standing, apparently due to change of particle size of Ag. To avoid error from reduction of Ag+ by EDTA species, both Ag(1)-EDTA and test solutions were freshly prepared before kinetic runs each day. The possible effects of the formation of Ag,H2Y and Ag,Y (22-24) and of precipitation of Ag,O and Ni(OH)2 were pretested in detail and taken into consideration in the preparation of solutions and in the selection of reaction conditions. To 50 ml of 0.02M borate buffer, a desired amount of Ag(1)-EDTA was added; after the solution was made up to slightly less than 100 ml, the pH was preadjusted with 0.2M HCIO, to avoid precipitation of Ag,O during the next addition of AgN03. The desired amount of Ag+ was then added dropwise with vigorous stirring and the final volume was made up to 100 ml. This procedure is essential if completely homogeneous solutions of high pH are to be prepared. Apparatus. A Beckman research model pH meter was used as a potentiometer and preamplifier in connection with a Photovolt Model 43 recorder to obtain potential-time curves. A Beckman Zeromatic p H meter was employed to measure the p H of the test solutions. p H measurements were made before and after each run with accuracy of 1 0 . 0 2 pH units; no significant change of p H was observed during the exchange reaction. The electrochemical cell consisted of a Beckman 39278 cation-sensitive glass electrode and a Beckman 39170 reference electrode. The indicator electrode was preconditioned in, and allowed to come to thermal equilibrium with, the test solution before each run. Measurements were carried out in a thermostated cell a t 25 =t 0.02" C unless otherwise specified. Procedure. The exchange reaction was initiated by injecting an aliquot of Ni(1I) solution (pH -6) into the Ag(1)EDTA test solution after attainment of thermal equilibrium. A glass tube about 3 mm in diameter, which had been coated inside with Beckman Desicot, replaced the conventional metal syringe tip. After Ni(I1) solution was taken into the syringe, the piston was drawn up so as to leave a small air space a t the tip; the tip was then inserted into the test solution and the recorder system was actuated. When a steady initial cell emf had been attained (usually after a few seconds), the Ni(I1) solution was injected quickly against the vigorously moving stirrer. In this manner, efficient mixing was apparently obtained in less than 1 second and smooth potential cs. time curves could be recorded. A typical potential-time trace is given in Figure 1. Potentials before and after the 'reaction were accurately ( 1 0 . 2 mV) measured with the potentiometer and used in the evaluation of the actual concentration of Ag+, the completeness of the reaction, and the (21) A. Fabrikanos, S. Athanassion, and K. H. Leiser, 2. Narur,forsch., 18b, 612 (1963). (22) L.. E. Brydia, Univ. Microfilm (Ann Arbor, Mich.), Order No. 64-11. 433, 1964, p. 138. (23) M. Cotrait and J. Joussot-Dubin, Bull. SOC.Clzim. France, 114 (1966); C.A., 64,153517 (1966). (24) F. Strafelda and J. Bauer, Cull. Czech. Chem. Commun., 29, 3160 (1964).
T
I mv
1
I
kI0 s e c . 1
Figure 1. Potential-time reaction
trace during exchange
[AgYlo = 1.8 X 10+M, [.4g], = 9.9 x lO-jM, [Xi], 1.g5 X 1W6M, pH = 9.80, p = 0.01M,temp = 25" C
=
conditional stability constant of Ag(1)-EDTA. The reproducibility of the kinetic data was =tlOzif the stirring rate was properly selected. The technique described is capable of following the reaction rate provided the rate of potential change does not exceed 2 mV/second corresponding to a rate of Ag+ concentration change of 7 X 10-6A4,kecond a t the 10-4M concentration level. This limitation was found experimentally and may have arisen from the sluggish response of the recorder system to the quickly changing signal from the electrodes or from difficulties in the evaluation of the initial rate from the emf cs. time plots. In earlier flow system experiments we have found the response time of the glass electrode itself to be less than 0.5 seconds (6). In the present study, the initial reaction rate, co, was of primary interest and conditions could be selected to circumvent any difficulties arising from the response time of the recording system. Calibration curves of emf cs. pAg, used in the conversion of AEIAt to ACjAt, were obtained every day before or after the kinetic runs; uH+was converted to CIIAaccording to Kielland (25). PRELIMINARY EXAMINATION
OF THE GLASS ELECTRODE RESPONSE
Because only a limited amount of information ( I , 4, 6) concerning the response of cation-sensitive glass electrodes to Agi is available, it seemed desirable to examine the response of the glass electrode to Ag+ in various aqueous media. In pure water, the plot of E ES. pAg was essentially Nernstian; the slope was exactly - 59 mV per decade of [Ag+] in the pAg range of 2.7 to 5.5. In 0.1M tvis(hydroxymethy1)-aminomethane (THAM) of p H 4.0 to 6.1, the plot was linear with a slope of 56 mV in the pAg range of 1 to 5 at 26.8" C. A Beckman microflow cell was used, according to the procedure of McClure and Rechnitz (6), in order to avoid contamination of the AgC solution by leakage from the reference electrode junction. In solutions of THAM of higher pH, even at the 0.01M concentration level, the E-pAg was notably curved, probably owing to complex formation between THAM and A&+. (25) J. Kielland, J . Am. Clzem. SOC.,59, 1675 (1937). VOL. 39, NO. 12, OCTOBER 1967
1407
Table I. Stability Constants of Ag(1)-EDTA and EDTA I* = 0.01 temp, "C -log Ki log KH log K3 log Kd 15 7.37 3.46 6.28 10.39 25 7.28 10.25 3.36 6.17 10.11 3.29 6.06 35 7.15
This was confirmed by measuring the potentials of Ag(1)THAM systems at various pH's. With solutions, both 5 X lO-3M in THAM, 1.25 X 10-3M and 1.25 X lO-4M in Ag(I), respectively, the potentials were practically constant at 3.5 5 pH 6.0, but decreased rapidly when the pH was increased. A mean value of 106.79was obtained for the overall formation constant of Ag(I)-(THAM)z, by using our experimental value of 8.0 for the pK) of THAM for this medium instead of the literature value of 8.07 obtained in 0.1M K N 0 3 (18). This value agrees well with Kemula's value (26) of 106.70, obtained using the pH glass electrode, and 106.'8, obtained with the Ag metal electrode, both at 20" C and in 1.OM KNOB. In view of the small response of the Beckman 39137 glass electrode to alkyl-substituted ammonium ions (3, 4), an even smaller,response of the Beckman 39278 glass electrode to tetraalkylammonium ions would be expected (1, 4). The fact that tetramethylammonium ion does not form complexes with EDTA (11) further increases the suitability of TEA ion as the buffer counter ion. In 0.01M TEA-borate buffer of pH 7.6 to 10.2, the slopes of E-pAg were almost constant at 62 to 63 mV per decade with a slight increase as the pH increased, With increasing concentration of the buffer, however, the slope increased almost linearly from 59 mV (pure HzO) to 118 mV (0.1M buffer) in the p H and pAg regions of 8 to 9 and 3.7 to 4.7, respectively. We attribute this observed effect to the formation of a weak (unknown) silver(1) complex; in order to avoid this complication, we chose the 0.01M TEA-borate buffer as our reaction medium. TEA-phosphate buffers were not suitable because the solubility of Ag(1)-phosphates is too low. TEA-phenolate was too unstable to be used; rapid coloration of this buffer solution was observed in the presence of AgN03. TEA-acetate was suitable in the pH range of 4-6. EQUILIBRIUAl AND ANALYTICAL MEASUREMENTS In order to evaluate the formation constants of Ag(1)EDTA, the Ag concentration of solutions containing constant analytical concentrations of metal and ligand was measured as a function of pH. Below pH 5.5, the potential was constant, indicating negligible complex formation between Ag+ and EDTA species; gradual lowering of the potential was observed with increasing pH. Using 0.01M TEA-borate and 0.01MTEA-acetate as the buffer systems and a total concentration of 2-5 X 10-4M Ag(1) and EDTA at various pH's, the formation constants of Ag(1)-EDTA wcre obtained (Table I). The ionization constants of EDTA were evaluated from knowledge of AH'S (27) and further corrected for ionic strength according to the Debye-Hiickel (26) W. Kemula, W. Brachazek, and A. Hulaniki, Theory Struc. Complex Compds., Paper Symp., Wroclaw, Poland, 1962, p. 605fpublished, 1964). ( 2 7 ) H.J. L. Tillotson and L. A. K. Stavely, J. Chem. SOC., 3613 (1958). 1408
ANALYTICAL CHEMISTRY
theory. In the evaluation of the formation constant of AgHY-2, KH, Equation 1 was used, where K3 = [HzY-*]/[H+][HY-'], K4 = [HY-3]/[H+][Y-4], Kt = [Ag+][Y-']/[AgY-3], and [Ag+], and [Ag+], are the total and equilibrium concentrations of Ag+,
Direct potentiometric titrations of Ag+ with EDTA, using the glass electrode as indicator electrode, were feasible provided that the concentration of Ag(1)-EDTA was higher than 2 X 10-4M at the end point and the pH was kept above 9. Titrations using the Ag metal indicator electrode were also successful and yielded titration curves similar to those of Strafelda (28). These titration methods were successfully employed in the simultaneous determination of the AgN03 and EDTA concentrations in the solutions, Two salts, reportedly with the formulas, AgzHzYand Ag4Y, have been found (22-24). Upon addition of a solution of AgN03 to a solution of Na2HzYunder vigorous stirring, a heavy white precipitate appeared immediately; the precipitate appears rod-shaped under the microscope (x200). The precipitate was dried over calcium chloride. Oven drying was not necessary and actually avoided because drying at 100" C changed the color of the precipitate from pure white to deep gray, although the precipitate has been reported as thermally stable up to 140" C (24). The solubility of the salt is pH-dependent, as would be expected from the weakly acidic character of EDTA. In pure water, the pH after saturation with the salt was 4.0 to 4.3; even in 0.01M borate buffer, the change of pH from the initial pH of buffer was remarkable (9.8 to 8.7, for example). The equilibrium concentration of Ag+ in HzO was 2.8-2.9 X 10-3M; assuming complete dissociation of the salt at such a low pH AgzH2Y
2 Ag+
+ HY-2
(2)
the solubility could be calculated to be 1.4-1.5 X lO-3M, which can be compared with 1.05 X lO-3M in HzO (24) and 2 X 10-3M in 0.1M K N 0 3 at pH 4.3 to 4.4 (22). Potentiometric titration of Ag+ with C1- after dissolving the salt in 3M HClO, gave a slightly higher silver content; accordingly the salt was assumed to be slightly contaminated with Ag,Y. Infrared observation (23) supports this assumption. The present potentiometric method is thought to be superior to the earlier titration method because it is nondestructive and, furthermore, avoids the painstaking filtration step. The Ag4Y salt was obtained by adding AgN03 to AgY-3, or to EDTA, keeping the pH of the solution above 8. The precipitate is silk-white and appears as fine needles under the microscope (x200). The solubility in 0.01M borate buffer of pH 8.9 was evaluated from the equilibrium concentration of Ag+ measured with the glass electrode. Because in basic solution and in the presence of a large excess of Ag+, AgZYw2 (29) might be formed as well as AgY-3, the relevant equilibria are Ag,(AgY) Agz(Ag,Y)
2 Ag+
F?
3 Ag+
+ (AgzY)-'
+ (AgY)-3
(3)
F? 3 Ag+
(4)
+ (AgY)-'
Therefore, the molar solubility of the Ag4Y salt will be between 0.50 and 0.33, the molar concentration of Ag+ in equilib(28) F. Strafelda, Coll. Czech. Chem. Commun., 27,343 (1962). (29) J. Joussot-Dubin and M. Cotrait, J. Chim. Phys., 61, 1211 (1964).
TIME (sec.)
Figure 2. [AAg] us. time plots in exchange reaction at high pH ( p = O.OlM, temp = 25" C ) [AgYIo = 4.93 X lO-4M (1) [Agl, = 0 (no excess), [Nilo = 3.92 = 10-6M pH = 11.42 (2) [Aglo = 4.95 X 10-BM,[Nil,, = 2.63 X 10-JM pH = 11.03
Figure 3. Dependence of cO/[NiIoon [AgYIo
rium with the precipitste. The [Ag+] at equilibrium was 5.70 x 10-4M; hence the solubility would be between 1.92 X 10-4Mand 2.S8 X 10-4M. Brydia (22) reported the solubility of Ag4Y, via EDTA titration, as 2.8 X 10-4M in 0.1MKN03 at pH 6.7 to 6.8. The rate of precipitation of Ag4Ywas confirmed to be much slower than the rate of the exchange reaction between Ag(1)EDTA and Ni(I1). Furthermore, formation of the precipitate occurred after an induction period ranging from approximately 48 to 500 seconds (apparently pH independent) for our range of solution conditions. Thus, the formation of the Ag4Ysalt does not interfere with the study of the homogeneous exchange reaction under the conditions used.
[Aglo = 9.9 X lo-", pH = 10.20, [Nilo = 1.06 x 10M-5(0) 6.6 X 10-6M(A),3.98 X 10--6M(O),p = O.OlM, temp = 25" C
2.5
1
2.0 I .5
1.0
0.5
RESULTS AND DISCUSSION
0.0
If the exchange reaction Ni(I1)
+ Ag(1)-EDTA
+ Ni(I1)-EDTA
+ Ag(1)
[Nil
(5)
is allowed to take place in the presence of a large excess of Ag(1)-EDTA, the reaction will obey first-order kinetics and, because the backward reaction can be neglected, Equation 6 will be applicable, where [Nil,, and [Nil0 are concentrations of Ni+2at t = t, t = 0 and charge is omitted for simplicity. log[NiI,
=
log[Ni10 - kt/2.303
(6)
We can obtain the expression
AC/t
=
ko[AgYlo[Nil
for the early stages of the reaction, indicating that the secondorder rate constant of an irreversible exchange reaction can be evaluated from the initial rate, (AC/t)o, of the pseudo zeroorder reaction. Figure 2 illustrates the evaluation of several runs with kinetic data obtained at extremely high pH and low [Aglo. The initial rate approximation holds accurately for at least the first 10% of the reaction course; ko is pH dependent. Because AC = C t - CO= CO(e2.303AE/0.059 - l), and if AE is small, we obtain Equation 8 from 7 AEjt
=
0.059 ko[AgY]0[Ni]0/2.303CO
Figure 4. Dependence of co(mV/second) on [Nilo O.OlM, temp = 25' C [AgYIo = 1.18 X 10-4M, (1) [A& = 6.0 X lO+M, pH (2) [AgJo 9.9 X lO-jM, pH
p =
(8)
Thus, ko can be evaluated from the initial rate of potential change. By combining Equations 7 and 8, it is easy to derive
=
9.92 10.20
Equation 9, which permits interconversion of the initial rate from potential to concentration units. ACjt
(7)
x IO'(M1
=
0.039 CoAElt
(9)
The constant of 0.039 is obtained by correcting the theoretical Nernstian slope with the actual value, 62 mV/decade, with E in mV. From the dependence of co on [Nil0 and [AgYIo in the pH range of 9.2 to 10.2, the initial rate was found to obey the rate equation uo = -(d[Ni]/dt)o = (d[Ag]/dt)O= ko[AgYlo[NiIo
(10)
in which ko is dependent on both [HI and [Agl~. In Figure 3 the dependence of fi0/[NilOon [AgYIo with constant [HI and [Agio is illustrated. Because the linearity of uo/[Ni]o - [AgYIo is independent of [Nile, Equation 5 must also be the firstorder with respect to [Nil@. This is confirmed by Figure 4 in which uo in mV/second rather than Mlsecond is plotted against [Nil@at constant [AgYIo, [HI, and [Aglo. The excelVOL. 39, NO. 12, OCTOBER 1967
* 1409
5
0
Figure 5. Plots of k, P = 0.01M, temp = 25"
15
10
C
(1 +)I:[
-
20
25
us. 1/[Agl0 0
[AgYlo = 1.195 X 10-4M, [Nil0 = 3.98 X lO-BM, (1) pH = 9.98 (2) pH = 10.20
=
kr
+ k1r[H1 + kr~r[H]/[Ag]of k~v/[Aglo
(11)
and kI, kII, kIII, and krv can be evaluated separately from Figure 5 and from Figure 6. Only the effect of [HI on ko will be significant in the very high pH range. The detailed effect of [Ap], on ko could not be studied in the region of pH 10.8 to 11.7 because of Ag,O precipitation; however, this effect is believed to be negligible. At constant [AgYIo of 5 x M, and with or without the addition of excess Ag+ (in the former case, [Agio = 5 X lo-", ko was linearly dependent on [HI, as shown in Figure 7. It is important to note here that [Nilo was kept in the range of 1.32 to 3.92 X lO-SM, more than twice the concentration usually used for studies in the lower pH range. Under such pH conditions there is no doubt that Ni(I1) would be precipitated as Ni(OH), if Ni+z alone were allowed to attain equilibrium (18). Fortunately, the reaction of N P 2with OHor H 2 0 to form NiOH+ and Ni(OH)2 is a stepwise process (30, 31), and the formation of NiOH+ will be fast with OHand fairly sluggish with H 2 0 ( I ] ) , while the formation of Ni(OH)2 is likely to be sluggish with both OH- and HzO, because the nucleation and growth of precipitates is usually slow (32). Nephelometrically, we confirmed that the pre(30) F. Achenza, Ann. Chim. (Rome), 49, 628, 848 (1959); C.A., 54, 55b (1960). (31) S. W. Benson, "The Foundations of Chemical Kinetics," McGraw-Hill, New York, 1960, p. 305. (32) A. E. Nielsen, "Kinetics of Precipitation," Pergamon, London, 1964, p. 104. 1410
ANALYTICAL CHEMISTRY
15
10
25
20
30
35
x to" (51
c,
lent linearity of this plot shows that Equation 9 is correct. is a linear function of At constant pH, ko, or uo/[AgY~o[Ni~o, the reciprocal of [A&. Linear dependence of ko on [HI at constant [A& was also observed. In Figures 5 and 6, these two plots are given with correction for ko because of Ni+2 hydrolysis (see below). Because of the low stability of AgY+, changes in pH will shift the equilibria between AgY-3, Ag+, Y-4, and other solution species; therefore, the values of [Ag] vary slightly in spite of the presence of excess Ag+. The effect of [Agio on ko is less marked at high pH than at low pH (Figure 6). From the data of Figures 5 and 6, ko can be expressed as ko
5
Figure 6. Effect of CE+on k,
at various Ag+ con-
centralions a = 0.01M, temp = 25' C
[AgYI, = 1.195 X 10b4M,[Nil0 = 3.98 X IO-BM, [A& = (1) 1.0 = 10-4M (2) 1.9 x 1 0 - 4 ~
cipitation of Ni(0H)z does not take place in three minutes when [Nil0 is 10-4M and the pH is 10.3, in the absence of AgY-3. It will be reasonable now to assume that upon addition of Ni(I1) to the test solution, even though the pH is extremely high, Ni(OH)2 would not be formed because Ni(I1) will be instantly consumed in the exchange reaction in the presence of a large excess of AgY-3; the results of Figure 7 support this assumption. In the pH range of 10.8 to 11.4, the exchange reaction is likely to proceed via the paths NP2
+ OH-
Kh/Kw
NiOH+
+ AgY-3 NiY-2 + Ag* + OHLI NifZ + AgY-3 NiY-2 + Ag+ ku
NiOH+
-
Thus the initial rate can be expressed by uo = kI'[AgYl~[NiOHl~ f kdAgY10tNil0
(12)
where [NiOHIo is the actual initial concentration of NiOH+, and [Nilo is the initial concentration of Ni+2. The observed rate constant, ko, can be expressed as ko (1
+ [HI/&)
= kr'
+ kdHI/&
(13)
and if l>>[H]/Kn, Equation 13 will become ko = kr'
+ kr[H]/Kh
(14)
Clearly, Figure 7 gives only an approximate description of the dependence of ko on [HI. Many authors (18, 33) have studied the hydrolysis of Ni+2 and the solubility of Ni(OH)2. Their data vary widely, (33) D. D. Perrin, J. Chem. Soc., 3644 (1964).
Table 11. Summary of Rate Constants for Exchange Reactions Paths (All at p = 0.01 and 25' C) Data from Figure 5 Figure 6 Figure 7 Mean
X
k I = kl, M-l 2.6 x 1.0 x 0.9 x 1.5 x
I
second-'
kII, M-2 second-' 1 . 7 X 10'2 1 . 2 x 10'3
103 103 103 103
kIII, M-l second-'
krv, second-'
x x
109 109
0.2 0.4
...
x
109
0.3
16 16
1.0 1.1
...
1 . 5 X 10l2
1.1
...
kI', M-l second-'
...
The values of kI, kI1, kIII, and krv evaluated separately from the data of Figures 5 and 6 as well as those for kr' and kI evaluated from Figure 7 are summarized in Table 11. The values of kz, k3, and k4 can now be evaluated by introducing K4, K H ,and K i into kII, kIII, and kIv. Taking K4 = 1010.3, KH = 103.4, and Kf = 10-7.3, k2,k3, and k4were thus calculated to be lo5.*,106.0,and 106.8M-l second-', respectively. Our data show the reactivity of Ag(1)Y to be very high, similar to that found in the previously studied (12) Ag(1)-1,lo-phenanthroline system. It is then of interest to compare the rate constants for the general paths
/
and 5
0
10
15
c,
x IO'f
20
25
(E)
Figure 7. Dependence of ko on CH+ at high pH and with various [Nil0 O.OlM, temp = 25' C [AgYIo = 4.93 X lO-'M, NIOM [Agl~(excesslM 3.92 x 10-6 2.63 x 10-6 4.95 x 10-6 1.32 = 10-6 4.95 x 10-6 p =
(0) (0) (A)
however, and are not fully convincing. By following Achenza's technique (30), we reevaluated Kh as 10-lO.OM at 0.01M ionic strength. Using Kh = 10-lO.o, the values of [H]/Kh were calculated to be 0.04 to 0.17 at pH's of 10.8 to 11.4, and, after correction for [H]/Kh, kI' and kr were evaluated as 16 and 898M-l second-', respectively. Because the reactivity of NiOH+ is much lower than that of Ni+2 and because the relative concentration of NiOH+ will be much decreased in the lower pH region, the contribution of paths involving NiOH+ to the overall reaction rate will become negligible below pH 10.2. In the region of pH 9.2 to 10.2, the following four reaction paths contribute predominantly to the overall reaction.
+ Ag+ N P 2 + AgHY-2 2 NiY-2 + Ag+ + H+ Nif2
+ AgY-3
Ni+2 + HY-3
NiY-2
5 NiY-2 + H+
Ni+2 + y-4
,?!
=
kzKHK4Kt,kIII
RECEIVED for Review October 24, 1966. Accepted July 20, 1967. Work supported under NIH Grant GM-14544 and NSF Grant GP-6485.
NiY-2
These paths agree with the rate expression given in Equation 11, with kr = kl, kII
In general, k2 is greater than k (34) and the ratio kz/kl varies from -10 to -1000 according to the nature of M(l)and M(z,, the ionic strength, and the temperature (34-36). Therefore, in view of the high reactivity of AgY-3, an even higher reactivity for AgHY-* would be expected; our value of 105.8 for k2, which is comparable to that for kn, is not surprising. The fact that our value of k3 is higher than the literature value of 10j.3(16,17,19), arises from differences in the ionic strength of the respective reaction media; if the Debye-Hiickel theory is applicable here, a value as high as would be expected (our value is 106.0), Elsewhere (36), a value of 106,2 for kl has been reported for an ionic strength of 0.5M. The value of k4is much lower than expected. Some contribution from a path involving direct reaction between AgHY-2, HY-3, Y-4, and Ni(I1) to the overall reaction in the higher pH range (10.8-11.4) is possible. If we consider the situation in pure AgY solutions, the equilibrium concentration of Y-4 (free EDTA) and HY-3 can be calculated as being approximately lO-3% of the AgY concentration; if we use the present rate constants for these reactions the total contribution would be approximately 10%; therefore, our evaluation of kl' and kl while neglecting these paths will be reasonable.
=
k3K4Ki,and krv = k4kz
(34) N. Tanaka and M. Kamada, Bull. Chem. SOC.Japan, 35, 1596 (1962). (35) N. Tanaka, H. Osawa, and M. Kamada, Zbid.,36,67 (1963). (36) T. R. Bhat, D. Raahamma, and J. Shankar, Znorg. Chem., 5 , 1132 (1966).
VOL. 39, NO. 12, OCTOBER 1967
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