F. BAUMG~RTNER AND L. FINSTERWALDER
108
On the Transfer Mechanism of Uranium(V1) and Plutonium(1V) Nitrate in the System Nitric Acid-Water/Tributylphosphate-Dodecane by F. Baumgktner and L. Finsterwalderl University of Heidelberg, Heidelberg, Germany (ReceivedOctober 93,1969)
Using the single-drop method as experimental technique, the initial transfer rates of uranium(1V) and plutonium(1V) have been determined between aqueous nitrate or nitric acid and TBP dissolved in dodecane. The r e sults of kinetic measurements have been interpreted in terms of chemical interface reactions. As soon as the metal enters the interface either in ionic or neutral form it is an interfacial complex which adds TBP molecules by degrees from the organic phase as well as nitrate anions from the aqueous phase. No evidence exists of a distinct sequence in the addition of the ligands; that means that the TBP reacts not only with the neutral metal compound but also with the ionic species. The interfacial complexes cannot be distinguished according to the phase they came from. Equilibrium is obtained by a dual transformation of the interfacial complexes either to the organic or to the aqueous phase and not by two reactions running independently in opposite directions.
Experimental Section
Introduction
The solutions of TBP and dodecane were prepared by weighing distilled TBP and dodecane. The solutions were treated several times with a solution of 10% sodium carbonate and washed with distilled water. Metallic plutonium was dissolved in HC1 and precipitated using HZO2. The precipitate was washed with 1 N HN03 and 2 N H202until the washings proved to be free of chloride ions. Then the precipitate was dissolved in concentrated HNOa at 80-90". Aqueous and organic solutions were prepared from the aqueous stock solution by dilution and extraction. Other chemicals used were all analytical grade. HN03 and uranium in concentrations exceeding 10 pmol/ml were titrated potentiometrically by a method described by Motojima and I z a ~ a ,Uranium ~ concentrations below 10 gmol/ml were determined by R photometric procedurelo with dibenzoylmethane. PlutoUOz(NOa)z*TBPz U0t2+ 2NOa STBP nium was determined by a-counting in nitric acid P u ( N O ~ ) ~ * T B P ~ solutions by a method given by Bhhr and Thiele." Pu4+ 4NOaSTBP Figure 1 shows the basic features of the experimental chemical process because the rate of mass transfer was still dependent on the stirring speed. Kinetic predictions can be examined more easily by using the initial (1) Part of a thesis submitted by L. Finsterwalder to the Technical University of Munich in partial fulfillment of the requirements for the reaction rates. This still applies to the extraction prodegree Ph.D. cess where the state of equilibrium is caused by a super(2) H. T. Hahn, US-Report HW-32626 (1954) ; J . Amer. Chem. SOC., position of the forward extraction and the reverse strip 79,4625 (1957). (3) (a) J. B. Lewis, AERE CE/3-1366 (1956), Nature, 178, 274 reaction. (1956) ; (b) L. L. Burger, HW-62 087 (1959). A method particularly suited for the determination (4) W. Nitsch, Dechema Monograph., 5 5 , 1965. of the initial rates is the single-drop method in a tech(5) W. Nitsch, 2.EZektrochem., 69,884 (1965). nique described by N i t ~ c h . ~ -The ~ drop method has (6) W. Nitsch, Chem. Ing. Tech., 38, 525 (1966). Nitsch investigated the extraction of carbonic acids in the system CCL-HeO. He been applied already in recent years to the extraction found the rate of transfer to the drops was controlled solely by SI chemof uranium(V1) with TBP.'** I n these cases, however, ical reaction at the interface. the results were interpreted with hydrodynamical mod(7) H. A. C. McKay and D. Rees, AERE-CIR-1199 (1953). els and not according to chemical reaction. Further(8) W. Knoch, and R. Lindner, Z . Elelctrochem., 64, 1020 (1960). more, these experiments were not detailed enough with (9) K. Motojima and K. Izawa, Anal. Chem., 36,733 (1964). respect to concentration dependences for conclusions to (10) C. A. Francois, ibid., 30,60 (1958). (11) W. BBhr and D. Thiele, KFK-499, KFK-503 (1966). be made about chemical kinetics. The first studies of mass transfer in the system uranium(VI)-HN03/TBP (tributylphosphate) diluted in hydrocarbons have been carried out by Hahna2 He followed the nonsteady-state system coming to equilibrium and found agreement with pure diffusion processes. Lewisa" and then Burgerabused the stirred-cell method to elucidate the transfer effects a t the interface. Both authors found a steady decrease of the transfer coefficient during the approach to equilibrium. From this Burger proposed a steady change of mechanism during the process of extraction. Our work b a s undertaken to examine further the influence of a chemical reaction at the interface on the speed of mass transfer. The idea of a chemical resistance can be shown to be likely by setting up the chemical equation for the extraction process. Burger could not assign the resistance to a,
+
+
+ +
The Journal of Physical Chemistry
TRANSFER MECHANISM OF URANIUM (VI) AND PLUTONIUM (IV) NITRATE
I
109
l0gTlU
10-6
10
-.
/
’//
0.1-
+== Figure 1. Experimental setup.
setup similar to that of NitschS4 The primarily unloaded drops pass up or down through the loaded continuous phase, Overall mass transfer is determined by chemical analysis of a 5-cc drop sample. Transfer area is calculated assuming drops as perfect spheres. Unwanted mass transfer during formation and breakup of drops is eliminated by runs with different throughputs. The overall mass transfer per unit area is plotted vs. the reciprocal throughput and extrapolated to infinite throughput. At infinite throughput, formation time of drops is zero and, therefore, side effects are eliminated. This procedure was repeated with four different contact paths to produce a time-mass transfer plot. The initial slope of the curve represents the initial reaction rate which is entered into the double logarithmic graph.
Figure 2. Initial transfer rates of U(V1) from an aqueous phase of 3 N nitric acid into 20, 10, and 5% TBP.
-
cakwlated vu!ues
o o o
experhmtu! values
P
A
+I
V
Results and Discussion The experimental results of the forward and reverse extraction are shown in Figures 2-5. . The forward reaction of uranium (aqueous to organic), Figure 2, does not exhibit a first-order reaction with respect to the metal concentration according to the nominal eq 1
+ nX + 2TBP --+ MX, TBP:, MX, TBPz Masn++ nX- + 2TBP Masn*
----t
(1) (2)
I n addition, the diverging lines show an influence of the TBP concentration on the reaction order of the metal. The initial rates of the back extraction which is a dissociation described by eq 2 depend on the free TBP and nitrate concentration. The rates tend to a, maximum transfer rate when either the free TBP or the nitrate concentration goes to zero. Experiments with and
t
Figure 3. Calculated and experimental transfer rates of U(V1) from an organic phase of 20, 10, and 5% TBP into an aqueous solution of 0.1, 1.5, and 3 N nitrate. Volume 74, N u m b 1 January 8, 1070
F.B A U M Q ~ R T N E RAND L. FINSTERWALDER
110
l.0
i 1.0
0.1
TBp
-
calculated values o o o experhenhl vabes
0.0; 0.b2
Figure 5. Calculated and experimental transfer rates of PuIV in 3 N nitric acid into 20, 10,and 5% TBP.
0
am ,
0.1
i
004
002
0.008 001
006
0.1 forward
Figure 4. Calculated and experimental transfer rates of Pu(1V) from an organic phase of 20, 10, and 5% T B P into an aqueous solution of 3 N nitric acid.
&
_I opposing
without HNOs in the organic phase showed no sign& cant differences because the transfer speed of HNOa is about one order of magnitude higher than that of the U and Pu. Thus, the HNOa complexed TBP in the organic phase was considered to be effectively free TBP. Plutonium extraction experiments have been conducted at acid concentrations ranging from 0.8 to 3 N HNOa. However, strip experiments were limited to an aqueous solution of 3 N "08 in order to avoid hydrolysis and polymerization of plutonium(1V). Furthermore, experiments with an organic phase concentration exceeding approximately 0.1 M plutonium are hampered by formation of a third phase. (The similarities between the plutonium and uranium plots perhaps indicate a similar course even beyond the measurable range.) A key to the understanding of the transfer mechanism is offered by the organic to aqueous transfer reaction which we will call the reverse reaction. According to the nominal eq 2 the initial rates should only depend on the metal concentration in the organic phase +
v = ka(MX, TBPz)
(3)
Experiments show, however, that the rate is decreased by the presence of nitrate or nitric acid in the aqueous phase and by unbound TBP in the organic phase
G
=
ka(MX, TBPz)F-'(NOs-, TBP)
The Journal of Physical Chemistry
4
forword
(4)
lnitial transfer rete
T e r s e and opposing to forward
f
forward
and opposing to reverse
State of equilibrium
Figure 6.
In order to make the rate equation fit the experimental data, one has to assume an additional reaction opposing the reverse reaction. This opposing reaction is controlled by components of both phases, so we may conclude that this opposing reaction takes place at the interface. Let us call the chemical species which is located at the interface an interfacial complex (IFC). Of course the I F C means, probably, several complexes with different numbers of nitrato and TBP ligands attached to the metal ion. It is possible to withdraw the IFC in two directions from the interface: one way causes transfer to the organic phase and the other to the aqueous phase.12 It can be assumed that the IFC is the same, independent of the phase from which it has come to the interface. The opposing step starts already at the very beginning of the extraction process when still no solute is transferred to the other phase but only the interface is loaded. The reverse extraction, however, increases (12) A. A. North and R. A. Wells, BuU. Inst. Mining Met., 702.484 (1966).
TRANSFER MECHANISM OF URANIUM(VI) AND PLUTONIUM(IV) NITRATE with buildup of solute in the initially unloaded phase, Thus the opposing step can be compared to the desorption step in a cycle of absorption and desorption a t the interface. As a result, the kinetic equation of one direction must include terms describing the kinetics of the opposite direction (Figure 6). The concentration of the IFC, an essential part of the rate equation according to this model, can be derived using a modified Langmuir's adsorption isotherm. I n our case we have to take into account that the withdrawal of the IFC from the interface takes place with different probabilities f a and f o into the aqueous and organic phase. The interface concentration NIFCof the initial transfer rate considered here is obtained from the balance between entry into the interface kc(1 - N I F C )from one direction and the withdrawal from the interface into both phases (fa 4-fo)NIFC kC
NIFC= f a
+ + ack
(5)
fo
where the units are f, (l/sec); u, effective cross-section (cmz/mol) for entry from the aqueous or organic phase; k , probability of entrance from the aqueous or organic phase into the interface (cm/sec) ; and c, metal concentration in the aqueous or organic phase [mmol/cma]. The step from the interface into the aqueous phase has to be a dissociation and the step into the organic phase an associat'ion. The probability of dissociation fa can be regarded to be independent of TBP and nitrate concentration. Experimental results show that the probability of association, fo, is dependent on the square of the TBP concentration
111 const ---(TBP)2(NOa-)Zk
f*
=
1
a ~ a
' + k-caa a a
const + ---(TBP)2(NO~-) fa
f a
(7) Correspondingly, the initial equation of the reverse reaction is 4-
V
(t
=
1 dm 0) = - - = fa(N1Fc) = A dt koco
1
+ const -(TBP)2(N03-)2 fa
koa, + --eo
(8)
f a
From the experimental results of the plutonium back extraction into 3 N "03 (Figure 4) the following values for eq 8 can be derived by trial and error technique v(t = 0) =
8.0 x 10-3(pu)o
c
1
(mmol/cm2
+ 35. OTBP2 + 7 . ~ ( P U ) ~
The agreement of this empirical equation with the experimental data of plutonium is shown in Figure 4. The experimental data for uranium back extraction from the organic phase into a solution of 3 N and 1.5 N NaN03 (Figure 3 ) can be represented also in a satisfying way by eq 8 with the constants 5.86 X 10-a(U) 3 N NaN03: 6(t = 0) = 1 190(TBP)2 10.6(U)
+
1 . 5 N NaN03: 6(t = 0) =
1
+
+
5.86 x 10-3~ 24(TBP)2 10.6(U)
+
I n the case of negligible TBP or NO3- concentration, eq 8 reduces to According to experimental results, the nitrate participates in uranium and plutonium extraction with differ.. ent reaction orders x. For the uranium extraction we found a mean reaction order x = 1.75 and about x = 2.5 for plutonium. This was the result of additional transfer measurements from 0.82 N and 1.5 N HN03 beside the 3 N " 0 3 experiments. This difference to the nominal values of 2 and 4, respectively, seems to arise from the different dissociation states of the ionic species. The disagreement with recently published exact second-order dependence of nitrate in uranium extraction may be caused by the low nitrate concentration used by those authors.13 Utilizing the experimental result ( 6 ) in connection with ( 5 ) yields the kinetic equation for the initial forward reaction rate: ( A = area of interface)
c
v(t =
0)
=
koco Koa0
(9)
l+,.co
Ja
This maximum transfer rate has also been plotted in Figure 3 (0.01 N NO3-). I n the case of plutonium, this maximum rate cannot be checked experimentally because of hydrolysis. As mentioned above, a calculation of the reaction rate of the forward extraction from data gained from the reverse extraction should be possible with eq 7 and would be a confirmation for the model used here. For this calculation additional knowledge of the diffusion probabilities of entrance k and of the cross section u is necessary. As a first approximation we put uaq = gorg and k,, = leorg. There are reasons to do so; to become an IFC, the organic complex necessarily has to enter the interface with its hydrophilic end. Fur(13) A. I. Yurtov and A. V. Nikolaev, Russ. J. Phys. Chem., 41,705 (1967).
Volume 74, Number 1 January 8 , 1970
112
R. P. RASTOGI AND B. P. MISRA
thermore, the cross section of the IFC will be determined more or less by the area occupied by the butyl ligands. Finally, the effective molecular weight of the ionic complex with its coordinated water should be similar to the molecular weight of the organic complex. With these assumptions, the initial rates for the forward reaction of plutonium from 3 N HNOa can be calculated by using (7). The constants are const
-k,(N03-)Z =
but our simple adsorption-desorption model yields only a first-order reaction of the metal. This deviation suggests additional to the nitrate or TBP reaction the possibility of exchange reactions between the association from the bulk phases with single IFCs such as UOzN03TBP +
+ UOzN03TBPz+
--j
UOz(N03)2TBP2 UOz(NOa)2TBP
280 X lov3 (cm7/mmo12sec)
+ U02N03TBPz+
--j
Uoz(r\T03)2
f a
const
- (NOa-)’ =
fa
35.0 (cm6/mmo12)
+ UOZTBP++
+ UOZN03TBP+
This additional mechanism of organic complex formation might present an explanation of the enhanced transfer velocities of uranium compared to those of plutonium. Generally speaking, exchange reactions at the interface might also be the cause for some synergisms unexplained up to now.
The agreement with experimental data is surprisingly good as is shown in Figure 5. The extraction experiments of uranium with TBP show a reaction order for uranium exceeding 1 in the linear range (Figure 2),
Acknowledgments. We are indebted to Mr. G. Hoffle and T. Fritsch for experimental assistance.
Cross=PhenomenologicalCoefficient. XII. Kinetic Theory of Nonlinear Transport Processes in Nonuniform Gases
by R. P. Rastogi and B. P. Misra Department of Chemistry, University of Goralchwr, Gorakhpur, India (Received May 6 , 1989)
The theory of Chapman and Cowling for nonuniform gases involving third approximation to the distribution function has been examined to understand the departures from linear phenomenological equations. It is found that terms containing products of gradients and higher order space derivatives of barycentric velocity appear in transport equations but higher powers of a single force do not occur. The second-order terms are negligible in the transport equation for mass flux as well as energy flux. Tensorial character of nonlinear transport equations obtained by Taylor-type expansion has also been examined.
Introduction The state of a gas is characterized by the distribution function f which depends on the peculiar velocity, the radius vector, and the time t. The kinetic processes can be understood provided the time dependence of f can be explicitly characterized.’ For a stationary gas the distribution function is Maxwellian and is denoted by f 0 , I n a nonstationary situation the distribution function can be written as2 f
+ 4(1) +
= f”(1
TI;* Journal of Physical Chemistry
#JZ)
+ . . .)
(1)
where for#&’) and fOt#P) are, respectively, the second and third approximation to the distribution function. I n the first approximation, f = f”. Kinetic derivation of transport equations is not possible using the first (1) I. Prigogine, “Nonequilibrium Statistical Mechanics,” Interscience, New York, N. Y., 1962. (2) (a) S. Chapman and T. G. Cowling, “The Mathematical Theory of Nonuniform Gases,” Cambridge University Press, Cambridge, 1960. Unless stated otherwise, all notations in this paper conform to this reference. (b) S. Chapman and T. G. Cowling, Proc. Roy. Soc., A179, 159 (1941).
