KENNETH A. ALLES AYD IT7.J. MCDOWELL
1138
The expression for the uiijmolecular first-order rate constant is then given by m
- P,
k = b:ll n=n*
(16)
where kz = as for all n, and the X1)s are computed for the various values of n as indicated above. Equation 16 was then evaluated by machine computation, and plots of log (k,/lc,) vs. log (koM/k,) were made. ( k , = iimlc; Ido = lim /~/~11.)Equation iM-
m
-11-0
15 implies that 12, calculated by this theory is equal to k , calculated by Kassel theory for a model having the same values of s, v, hv’/kT and v.*; the two theories also lead to the same value of Ita. The salient features of the results are illustrated in Fig. 1 through 4. A comparison of Fig. 1 and 2 shows that iiicreasilzg the number of degrees of freedom decreases the discrepancy between the Kassel theory curves and those obtained by our theory. Coniparison of Fig. 2, 3, and 4, in which v / a , the ratio of the cheniical sink rate factor to the parameter governing intramolecular energy transfer, takes on the values 10, 50, and 100, respectively, indicates that decreasing the cxffi(ieiicy of intramolecular energy transfer causes a
Vol. 67
very marked broadening of the transition region between the low and high pressure h i t s . 6vib ii? all cases is equal to kv‘/li. As we had predicted earlier,6 the weak intramolecular energy transfer theory always leads to curves having a broader transition region between the low and high pressure limits. Variation of &,b end n* produced relatively niinor effects; increasing n” tends to make curves calculated by the two theories more similar. Machine calculations on the vibration of highly 4c 9-11 indicate that energetic triatomic energy “scrambling” among the normal modes is extremely rapid; this casts doubt on the utility of the model discussed here. We mould like to mention a suggestion made by Prof. Slater that the effects of anharmonicities may be substantially less extreme in more complex niolecules; this possibility makes the model discussed here somewhat more reasonable. Konetheless, as pointed out by one of our referees, the effects of anharinonicity mill certainly be large juqt prior to the molecde’s decomposition, no matter how large the molecule may be; the effects of anharn3onicities in such highly distorted molecules may 11-ellbe quite important. TI7e are currentlv working on machine calculations to investigate Slater’s rather reasonable conjecture. Acknowledgment.-We are indebted to Prof. Frank Buff and Dr. Everett Thiele for helpful discussions.
THE THORIUM SULFATE CQlIPLEXES FROM DI-n-DECYLL4311SE SULFATE EXTRACTION EQCILIBRIA BY KENNETH A. X L L E NAND ~ W.J. MCDOTVELL Oak Ridge Xational Laboratory, Oak Ridge, Tennessee3 Received December 14, 1969
A general method is described for obtaining aqueous complex formation constants from solvent extraction equilibria, The method involves experimentally controlled constancy of the chemical potentials in the aqueous phase, constant composition of the equilibrium organic phase being used a3 the criterion. A single-parameter Debye-Huckel equation with an arbitrarily fixed distance term is used as an analvtic model for the ionic interactions of the aqueous species. At constant sulfuric acid activity, constant extra-tant concentration, and constant organic thorium molarity the distribution of thorium between di-n-decvlamine sulfate in benzene and aqueous phases of varying sulfate ion concentrations is shown to lead to the fo!lming values of the hithertounreported formation constants of the thorium tri- and tetra-sulfate complexes, at zero ionic strength, K23 = [Th(S04)a-31 = 5.7 f: 1.2 and KS4= [Th(S04)4-41 = 0.009 f:0.003. [Th(SOa)r-‘I [SO*-* I [Th(SOa)zl[SO,-’]
Introduction Formation constants and energy data for the aqueous mono- and disulfate complexes of thorium have been r e p ~ r t e d . ~A search of the literature has been unsuccessful in finding any published reference to species containing more than two sulfates per thorium. The existence of such negatively charged species has been inferred by Kraus and Nelson4 from the negative slopes of plots of thorium distribution ratios bet-cveen an anion-exchange resin and aqueous phases of varyinp sulfate ion concentration. Corresponding solvent extraction data, taken under experiniental conditions ensuring constant composition of the organic phases, became available in the di-n-decylamine sulfate ex(1) Deceased. (2) operated for the U.S.A.E.C. by Union Carbide Nuclear Company. (3) (a) E. L. Zebroski, 1% UT.Alter, and F. K. Heumann, J . A m . Chem. Sac., 7 8 , 5646 (1951): (b) A. J. Zielen, %bad.,81,5022 (1939). (4) K. A. Kraus and F. Kelson, ORNL, private communloation, 1959.
traction system5 The present paper describes a general method, incorporating Debye-Huckel activity corrections, for obtaining complex formation constants from such data. The method is used in the computation of constants for the formation of the thorium triand tetrasulfate complexes. Experimental The materials and procedure used in making the thorium distribution measurements have been described previously.6 Solutions (Sa2SOI-H2S04) of varying sulfate ion concentration and constant sulfuric acid activity (6.4 x 10-5 31) were prepared according t o data compiled by B a e ~ . While ~ these tests extended t o higher ionic strengths than were covered in Baes’ treatment, titration of the equilibrated organic phases for total acid confirmed the constancy of aqueous sulfuric acid activity to within the precision of the titration, f:O.5%. Other parameters were held as constant as practicable: total amine molarity 0.1 f:0.0005, temperature (5) W. J. XlcDowell and K. A. Allen, J . P l y s . Chem., 66, 1358 (1961). (6) C. F. Baes, J r . , J . A m . Chem. Sac., 79,5611 (1957).
May, 1963
THO~ZIUM SULFATE COUPLEXES FROM DI-~-DECYLAMINE SL-LFATE EXTRACTION
25 f 0.05" and total thorium molarity 0.005 f 0.000005. Constant total thorium concentration was used to establish constant organic thorium levels since extraction coefficients were high and nearly all the thorium was extracted.7 All the sulfate variation data were obtained from equilibrations done by the quiescent interface technique,8 s o that the data are illternally consistent in this regard. Method.-In interpreting experimental information reflecting the activity behavior of aqueous species from observation of their equilibrium distribution to an organic phese, it is necessary to have some knowledge of the chemical potentials in the organir phase. Since activity data in organic phases are almost entirely lacking, the remaining alternative is to keep the composition of the organic phase constant in regsrd to all distributing species. Under these conditions one may be sure t h a t the equilibrium aqueous species activities are also constant, since their chemical potentials are the same as in the organic phase, if all solutions are homogeneous and organic phase concentrations are held well below their individual solubility limit^.^ Thus, the essential part of the method used here is that the organic extractant phases were kept a t essentially identical composition throughout the entire series of experiments, during which the aqueous sulfate ion concentration varied. The aqueous-insoluble organic extractants are ideal for this arrangement since they allow an organic phase of known and reproducible composition which is easily analyzed for the distributing ions of interest. In addition to the conditions described above it is also necessary to have an evalaation of the relative activity coefficients of the aqueous ionic species. For this purpose a Debye-Huckel expression was used, of the form
I n the calculations involving this equation the value of p wa: set a t 2 . This corresponds to a mean interionic distance of -6 A . , a reasonable value not far from that chosen by others in similar systems Thus, using an aqueoun phase W, distribution experiments are run in such a way that a metal ion of charge i, M + I , varies in concentration while an anion of charge j , A - I , also changes concentration, the two changes compensating each other so as to maintain constancy of the activity of the species RIAi,,, as shown by its constant concentration in the organic phase and therefore constant chemical poten1,ial in both phases. One further convenient experimentalconditionis that [&I+'] ertedb
I = 2
I = O
IC1 = 159 Qol = 1 9 X lo1 Ti01 = 1 9 X 108 K L = 2850 QOZ = 4 0 X 105 K o =~ 1 3 X IOL0 &12 = 2 1 X 102 KIZ = 6 8 x I O 3
p1 = 166 Q~~ = 2 o x 103 K~~ = 2 o x 1 0 6 pZ = 3610 QOZ = 5 1 X lo5 I C 0 2 = 1 6 X 1O1O Q1z = 2 6 X 102 Ki2 = 8 2 X lo3
[ThSOa+2][H+]/[T~+4][HS04-]; Kz =
=
[Th(SOd)z][H+]/[Th+4][HS04-]. 4 = [ThSOd +21/[Th [S04-‘] = Ki/K(~soa); &oz = [Th(SOa)I/[Th+41[SOc~212 = K z / K z C ~ s o a log , ; KO* = log Qol - 0.509(- 16)Ii/2/(1 21’12); log Koz = log Qo2 - 0.5091 -24)Zi/2/(1 f 211/z); Kiz =
+
Koz/Ko1. TABLE111
1.2
0.3
VOl. 67
COMPARI~ON : FoRMATIoN O F DINEGQTIVE SULFQTE C O M P L E X
LL a
FROM x E U T R 4 L SPECIES
0.8
0.2
Reaction
ro2soa+ soa-? F? U02(S04).-2
0.4
0.1
0 0
02
0.6
0.4
s[o-:
0.8
1,
i.0
0 1.2-
M.
Fig. 2.-Fractions of total thorium existing as the various sulM fate complexes, at constant sulfuric acid activity of 6.4 X and varying ionic strength as shown.
THORIUM EXTRQCTIOSS AT COKSTAKT AQVEOUSSULFCRIC ACIDACTIVITY aH2soa= 6.4 x 10-5 M (Organic phase constant a t 0.1 M amine, 0.07 A I H2904, -0.005 M Th) &AQUEOUSPHASE COMPOSITIONS FOR
[HZSO~I~~Q, :if
0.094 ,097 ,100 ,105 ,105 ,110 ,115 ,130 ,136 ,142 ,149 ,160 ,166 ,172 ,180 ,185
. 190
0.006 ,018 .040 ,088 .095 ,130 ,185 ,360 ,464 ,558 ,653 ,840 ,934 1.028 1.12 1.21 1.30
0.033 ,037 ,053 ,085 ,093 .I20 ,165 ,317 ,414 ,505 ,597 .77 .86 .94 1.03 1.12 1.20
[Thlaq,” PJf
I M,
6 00 6 33 7 35 8 75 9 46 10 5 12 0 18 1 21 3 25 7 28 7 36 8 41 9 46 5 52 6 58 2 64 8
0.166 ,189 ,246 ,360 ,386 ,480 ,630 1.124 1.43 1.71 2.00 2.54 2.82 3.08 3.36 3.63 3.89
Simultaneous least squares analysis (by computer) with the distribution data in Table I gave K Z = 6 and Ksa = 0.009 (specifically, [Th(SO&] = 5.78 = t ~ 0.76 p M , K Z 3= 5.7 f. 1.2, K24= 0.054 =k 0.009, and K34 =
AhD
Th(R0a)i
Source
7 8 80
ilhrland, 1961 (potentiometric) Ahrland, 1951 (spectrophotometric) Kraus and Xelson, 1957 (anion exchange) (ref. 4) Allen, 1958 (TO$ extraction) Present paper
6 Th(S04)2 S 0 a - 2 6 F? Th(SOn)3P VOTE: Neither of these reactions is subject t o Debye-Htickel ionic interaction corrections, since A(Z,z) = 0.
-+
0.0095 f 0.0028, a t 95% confidence limit of error), evaluated at zero ionic strength. It is interesting to note that the constants for the formation of the dinegative species UOz(S0,)z-2 and Th(SO&-2 appear to be the same (Table 111). These constants were used together with those from the literature (Table Ii) to evaluate the fractional distribution of the thorium among its aqueous species as a function of sulfate ion concentration at constant sulfuric acid activity, Fig. 2. Note that this is not the ‘%otal” analytical sulfate, but the actual as shown in Table I. The fractional distributions were further used with the leasf squares evaluation of [Th(S0&1 = 5.78 dl6 to synthesize thorium concentration curves for comparison with the experimental points (Fig. 1). The agreement above [SOq-2] = 0.1 is good. The experimental points shorr slightly more curvature than does the calculated curve. This could be taken as suggesting perceptible contribution from a still higher sulfate complex, but the difference is not sufficient t o warrant testing such a possibility with these data. Acknowledgment.-It is a pleasure to give due credit to G. N. Case for technical assistance in the experimental work, to the ORNL Analytical Di.i-ision for aqueous thorium determinations, to the ORNL Mathematics Panel for advice and computer service, and to C. F. Coleman for in\-alunhle aid in editing the manuscript. K2JK.23 =
TABLE I
UOzSo,
K
