4142
rates and between corresponding iodides and tetraphenylborates indicate a maximum uncertainty in the A0 values of 0.20 unit or about 0.5%. Thus, the apparent level of accuracy and the general consistency of the over-all results are relatively good for this exploratory conductance study. Single-ion limiting equivalent conductances were obtained by the method of Coplan and FUOSS,~ which is based upon the assumption that the limiting conductances of the triisoamylbutylammonium and the tetraphenylbora1,e ions are equal in any solvent. Limiting ionic equivalent conductances (ohm-' em2 equiv-') in NM2PY are as follows: Ka+, 14.7; K f , 14.7; I-, 26.9; c104--, 27.2; (i-Am)3BuN+, 12.0; BPh4-, 12.0. Within experimental error, the potassium and sodium ions are iso-conducting in SM2PY. Comparing the behavior of these ions in noncyclic amides, it is interesting to note that the potassium ion is very slightly more conducting than the sodium ion in N,K-dimethylf ~ r r n a m i d e whereas ,~ their roles are reversed in S , N dimethylacetamide.'O It is concluded from the above results that NM2PY is an excellent dissociating solvent since all of the salts are completely dissociated within the experimental concentration range. It is also worthwhile to point out that XJ12PY, adiponitrile, and methanol have almost identical values for dielectric constants (32.0, 32.45, and 32.62, respectively) ; the dissociating powers of MN2PY and adiponitrile5 toward electrolytes are comparable to, and possibly greater than, that of methanol." (9) D. P. Ameli and P. G. Sears, J. Phys. Chem., 59, 16 (1955). (IO) G. R . Lester, T. A. Gover, and P. G. Sears, ibid., 60, 1076 (1956). (11) R. L. Kay, C. Zawoyski, and D. F. Evans, ibid., 69, 4209 (1965).
A Pressure-Jump Study of the Kinetics of
Uranyl 10111 Hydrolysis and Dimerization' by P. A. Hurwitz Department of Chemistry, Universitg of Massachusetts, Boston, Massachusetts
and G. Atkirison Department of Chemistry, University of Maryland, College Park, Micryland (Received June 6 , 1.967)
During the past few years, there have been several studies of the kinetic and equilibrium reactions of The Journal of Physical Chemistry
NOTES
uranyl ion in acidic, aqueous solutions. Baes and Meyer2 studied the hydrolysis mechanism and equilibrium constants of uranyl ion in acidic, aqueous nitrate media. From the Baes and illeyer study, we have been able to evaluate rate constants for the various equilibria using the pressure-jump method while Eyring and co-workers3 have evaluated the same system using the temperature-jump method.
Experimental Section For our experiments, analytical reagent grade uranyl nitrate hexahydrate was purchased from Fisher Scientific Co. As a precaution the reagent was dried over concentrated sulfuric acid. Before using, the purity of the material was qualitatively examined by comparing experimental and literature absorption coefficients. We found that the material was uranyl nitrate hexahydrate within a few per cent of our determination. Each soIution was prepared by weighing out appropriate amounts of uranyl nitrate and then diluting to a known volume with distilled, demineralized water. An inert electrolyte such as potassium nitrate was not required to adjust the ionic strength, since the sensitivity of the method would have been seriously reduced by traces of nonreacting ions. For various initial concentrations of uranyl nitrate the ionic strength was not uniform. The effect of this inconsistency on the final conclusions did not appear to be significant. Each solution was brought to the desired pH by dropwise addition of dilute NaOH and/or dilute "03. The pressure-jump apparatus was constructed from a diagram given by Yeager4 and co-workers. The solution cell was constructed from Lucite with the added advantage that the platinum electrodes were threaded to the Lucite. Such a means of attachment allowed for possible electrode adjustment. The cell was connected in turn to a Wheatstone bridge. Since we are only interested in measuring relative changes of the cell resistance, our bridge requirements are different from the usual conductance bridges. The bridge was constructed from available commercial components and mounted in an aluminum chassis. Special precautions were taken to insulate the components, and coaxial connections were made wherever feasible. Both the input and output connections to the bridge were isolated from the oscillator and detector, respectively, (1) The experimental work reported here was done at the University of Maryland under Grant 14-01-001-405 from the Office of Saline Water of the U. 5. Department of the Interior. (2) C . F. Baes, Jr., and N. J. Meyer, Inorg. Chem., 1, 780 (1962). (3) M.P. Whittaker, E. M.Eyring, and E. Dibble, J. Phys. Chem., 69, 2319 (1965).
(4) H . Hoffman, J. Stuehr, and E. Yeager, ONR, Contract Nonr 1439(04), Project N R 384-305, Technical Report 27, 1964, p 12.
NOTES
4143
Table I :" Relaxation Spectrum of Uranyl Dimerization a t 25'
k-1, M - 1 see-1
70bd,
[UOzr +lo
[lJOZ'+]
IUOzOH +I
0.0208
0.0201
3 . 4 x 10-6
0.0304 0.0208
0.0280 0.0207
5 . 7 X 10-6 1 . 0 x 10-6
PIb 3 . 5 x 10-7 9 . 8 X lo-* 3.2 x
IT IC
2.2
x
10-7
1.4 X 5.2
x
PH
maec
2.93
0.25 5.0 0.25 4.7 0.25
3.01 10-lo
2.40
e
All concentrations in moles per liter.
*D
3
M-1 aec-1
M
>3.3 X lo6 ... >3.9 X lo6
...
...
50
x ...
>1.0
... Av
kz,
Approximate ionic strength
0.06
76
...
0.09
..
. ...
los
>2.7 X IOb
0.06
63
(U02)1(0H)22+. T E (UOZ),(OH),+.
by General Radio shielded transformers, Model 578-C. With a 50-kc signal, good results were obtained using a General Radio tuned amplifier and null detector, Type 1232-A. The signal was rectified using a very simple diode detector circuit. This rectified signal was fed directly into a Tektronix Model 502 oscilloscope fitted with a Polaroid camera attachment. The oscilloscope was triggered internally. Several experiments were carried out where the oscilloscope was triggered externally using a piezoelectric crystal with a charge amplifier. Similar results were obtained for both triggering modes. The rate constants were given for a temperature of 2". Each relaxation time represents an average 25 of a t least three photographic determinations. The individual oscillograms could be evaluated to yield relaxation times with a relative error of *20%. The pressure above the reaction and comparison solutions was released spontaneously. For 0.0075 in. thick Mylar disks, the change in pressure was generally 30 atm. The rupture time for these disks was on the order of 250 bsec. In order to determine the rupture time, more commonly referred to as the apparatus response time, we employed a solution of 0.1 M MgS04. The relaxation time for the reaction Mg2+ S042N1gS04 is less than 1 ~ s e c . The ~ unassociated electrolyte barium benzenedisulfonate was used as the comparison with the h/lgS04experiment. For the uranyl experiments the nonreacting solution was ikIgSO4 having a concentration such that both cells would have very nearly the same resistance. In this manner, we could then sort out the disturbing effects of the change of resistance due to physical effects from those due to the chemical relaxations. Unlike Eyring3 and co-workers, our experiments indicated that there were two relaxation effects occurring. We observed a fairly rapid relaxation time that coin-
*
+
cided with our instrument rise time and a slower one having a value of about 5 msec. Although we are dealing with a coupled system, the relaxation times were separable and we could therefore evaluate the rate constants associated with two of the three equilibria involved in this study.
Results and Treatment of Data The separate relaxation times were evaluated from a plot of the logarithm of the signal amplitude os. time; the straight line obtained indicated a single relaxation process is being observed for that particular time range. The values of the relaxation times, the concentrations of the various uranyl ion species, and the rate constants are summarized in Table I. The derivation of the relaxation times in terms of rate constants and equilibrium concentrations which follows is based on the equilibrium constants proposed by Baes and Meyer.2 Accordingly, the uranyl equilibria with their corresponding equilibrium constants a t 25" are U02'+
+ H2O
ki
UO2OH+ k-
+ H+
1
K1 2UOz2+
+ 2Hz0
kz k- a
(UOz)z(OH)2'+
= 2 X
(1)
+ 2H+
K2 = 1.2 X lo-'
+
kr
3u0z2+ 5Ha0 k-
(U02)3(0H)s+ a
(2)
+ 5H+
K B= 6 X
lo-''
(3)
(5) M. Eigen, G. Kurtze, and K. Tamm, Z . Elektrochem., 57, 103 (1953); M. Eigen, 2.Physik. Chem. (Frankfurt), 1, 134 (1954).
Volulne 71. Number 1.2 November 1967
NOTES
4144
The observed relaxation times r can be expressed as a function of the desired rate constants and known equilibrium concentrations by simple analysis of eq 1 and 2, respectively. This treatment is possible because two separable relaxation times are observed. To obtain the particular relaxation expressions, it is only necessary to linearize in the usual manner the rate law expressions for eq 1 and 2.'j For the system described by eq 1, the reciprocal of the relaxation time is given by 1 -
=
k-l(U020H
7
+ E) + kl
(4)
where k-1 and kl are the bimolecular and unimolecular rate constants having the units of M-l sec-l and sec-', respectively. The bars above the species signify equilibrium concentrations, but the charges of the ions have been neglected here in order to simplify the notation. For the system described by eq 2, in which the dimer species results, the reciprocal of the relaxation time is given by
where kz is the bimolecular rate constant for the dimerization. The factor CY, in this case, accounts for the rapid equilibrium step occurring in eq 1. This factor is explicitly
CY =
6[dimer] - kl - UOzOH H 6[UOZ]
(6)
I n the absence of appreciable monomer (UO20H), a should be zero. Examination of eq 6 shows that 6ldimerl
-
relaxation process may have been negligible for our conditions.
Discussion The lower limit for kdl of -3 X lo6 M-l sec-l is consistent with the value of 1.5 X 1O'O M-' sec-' directly determined by the dispersion of the dissociation field effect.' Alternately, an a priori calculation of kW1can be made using the Smoluchowski-Debye-Eigen theory of diff usion-controlled reactions which agrees with the directly determined value.* As Eyring3indicated, the possibility of uranyl nitrate complexation kinetics should be considered. Therefore, another experiment involving the same initial concentration of UOzZ+was carried out a t a pH of 2.4. At this pH the concentration of dimer is reduced. We no longer observed the slower relaxational process. The more rapid relaxation was still present and attributable to reaction 1. This experiment does not conclusively prove the observation. However, the temperature-jump work3 included a series of similar experiments in which the NO3- concentration was varied. For these latter experiments, the relaxation time was observed to remain essentially constant. The independence of the relaxation time on NO3- precludes the occurrence of any uranyl nitrate complexation. In our case when the pH was lowered the slower process disappeared; this result can be most easily reconciled with dimerization as opposed to complexation. The value determined for kz is 63 sec-' a t 25" a t an ionic strength of 0.06 M . The value determined by Eyring and co-workers3 is 116 M-' sec-I at 25" at an ionic strength of 0.5 M . Since reactions between species of the same charge are observed to increase in rate with increasing ionic strength, the rate constants determined in this work agree very well with that of Eyring. There remains then the question of other possible uranylhydroxy species. There is a t least another mechanism3 for reaction 2, specifically the consideration of
+
2UOZ2+ H 2 0 A third relaxation time was not actually resolved a t higher pH or higher concentrations of uranyl nitrate. It was only possible to determine the rate constant for the monomer-dimer equilibrium and to establish a lower limit for the protolytic reaction (k-1) of eq 1. It might indeed be possible to observe the trimer formation even though the concentration of trimer is sometimes as low as lo-' M for the present experimental conditions. Alternately, the magnitude of the trimer The Journal of Physical Chemistry
kz
+
(UOz)2(OH)3+ H +
Inclusion of this latter possibility, however, does not alter the interpretation presented here. (6) AT. EiPen and L. DeMaever in "Techniaues of Orzanic Chemist&," Vo1.-VIII, A. Weissbe;ger, Ed., John- Wiley a l d Sons, Inc., New York, N. Y., 1963, Part 2. (7) D. L. Cole, E. M. Eyring, D. T. Rampton, A. Silsars, and R. P. Jensen, 153rd National Meeting of the American Chemical Society, Miami, Fla., April 9-14, 1967. ( 8 ) Cf.ref 6, p 1032.
