Aq
+ U p - Cpq G constant
(16)
so that in the abscrice of a numerically large spectral variation of u (maxima and minima being then essentially absent), a relatively large number of p and q cornbinations may satisfy the same spectrum. This problem is, clearly, not limited to the use of eq. 1 nor to the use of the experimental criterion used here (uspectra). It is bound to be encountered also 011 basing the analysis on other types of distribution or on using as experimental criteria turbidity spectra or the variation of scattering with the angle of obscrvatiom68 This lack of single-valuedness of results to be expcctcd in very I~ctcrodisperscsystems can be relieved, however, by using, in addition to u-spectra, the two esscntislly ecluivalcnt criteria just named. X subsequent paper in tliis series will be concerned with this possibility. VIII. The Effect of Dispersion The theoretical u-spectra given in this paper were derived for ?n = 1.20. This relative refractive index applies, in the case of polystyrene, to the middle of the visible spectrum. The experimental spectra, on the other hand, are affected by the dispersion of m. As pointed out in the preceding paper,a the dispersion of polystyrene is sufliciently small in thc visible so
as not to introduce a significant change in particle size determined in the visible in monodisperse systems a t various wave lengths. The same applies to the theoretical spectra, used for the determination of size distributions. This point was checked in detail for H.D.1. On taking the variation of m with X into account, the a-values varied by -3.5, 0, and +2.3y0a t 6O00, 5461, and 46513 A.,respectively, relative to the u-values calculated for a constant 712 of 1.20. This shift is so small compared to the height of ttic rectangles in Fig. 1 that % qn values would be pointless. a correction of ~ 1 and Since v i for polystrene in water varies by 1.2y0over the portion of the visible spcctrum uscd in Fig. 1, one can statc th:tt a check of the dispersion effect is indicated and to be advised only in systems where Ant is larger than 0.0 1. Acknowledgment.--Thc authors are indot)ted t o Prof. Arthur F. Stevenson of the Physics Departniciit, Wayne ,State University, for numerous valuable discussions and w r y helpful suggestions. They also are very appreciative of the most, effective aid given hy Dr. J. H.I,. Watson, Director of thc Physics Department, Edsel B. Ford Institute for 3LIedical Research, by providing us with extensive electron-microscopi(: material for size distribution analysis.
THE EXTRACTION OF ACIDS BY BASIC ORGANIC SOLVENTS. 11. TRIBUTYL PHOSPI-IATE-HYDItORRORSIC ACID’ BY D. C. WHITSEY~ AND R AI, DIAMOSI) I‘nwrence Radiation Laboratmu, UniLwsily of California, Berkeley, Calijornin IZeceiued .]fay 16, 1063 An investig:ttion h,w been ni:& of the cxtrwtion of hydrobromic arid from aqueous solutions into dilute solutions of tributyl phosphttte (’I’HP) in CCl,. T h e prinripctl speoies ivhirh was found to extract over the range 1-10(;< ‘I’BP iind 3-8 JT aqueous IlUr concentration was IIaO+.3TBI’.~H10 ...Br-, with 0.2 5 I/ 5 1.0; that is, only the trisolvated hydronium cstion and bromide anion were observed. This result is interpreted in t e r m of a proposed general model for such strong acid-basic solvent extraction systems.
Introduction Tlic system IIBr-1320-tributyl phosphate has rcceived but scant attention in the literature. Baldwin, et CZZ.,~ and Tuck and Diamond4extracted HSr into pure tributyl phosphate (TBI’) as part of their studies on acid extraction, and both gmups found that the organic phase increased its water content by three molecules for each acid molecule extracted. If a one to one acidTBI’ complex is assumed, this indicates four water molecules per acid molecule in the extracted complex. I 7 X 10' ohm) and were stored in sealed amber-glass bottles to prevent decomposition. Procedure.-The methods used in the equilibrations, water and acid analysis, and infrared analysis of the acid-TBP solutions have been described.* Owing to the unstable nature of concentrated HBr solutions, the two phases were shaken together for only 15-30 min. Equilibrium was assumed to have been achieved by analogy with the HClO, extractions, which have been shown to require less than 15 min. to reach an equilibrium distribution? lmmediately after shaking, the phases were centrifuged and separated. All determinations on the organic phase were completed within 6 hr. after separation; no appreciable decomposition or discoloration of the phase was apparent during this time. All experimental work was done a t room tempeiature, 23 i: 2O.
Id'
2 x IC2
M
5x16'
TBP(tota1)
Fig. 2.--T'ariation of acid content of organic phase with total TBP concentration for initial aqueous HBr concentrations of (from bottom to top) 3.21, 4.28, 5.17, 5.57, 6.07, 6.48, 7.12, 7.50, 8.08, and 8.53 AI.
organic phase activity coefficients are going to be neglected. Furthermore, if the experimental conditions are chosen so that only a small fraction of the TBP molecules are involved in the extracted acid complex, the organic phase essentially retains the properties of the inert diluent. Changing the concentration of the TBP or of the acid will then have only a slight effect on the activity coefficients of these species in the organic phase, but the resulting variation in the extraction will yield
Results Data were obtained on the acid and water content of the organic phase for T B P solutions of 10, 5 , 2.5, and 1o-/cby volume TBP in CC1, (corresponding to 0.366, 0.183, 0.0915, and 0.0366 M TBP) which were equilibrated with acid solutions ranging from 3 to 8 M in HBr. Insufficient extraction below 3 M HBr fixed the lower limit, and decomposition of the HBr above 8 114 set the upper limit. The results of the acid determinations are shown in Fig. 1, where the organic phase acid is plotted vs. the aqueous HBr concentration, [H+Icoi, activity on a log-log scale. Since little activity COefficient data are available for HBr concentrations above 4 m, it was assumed that yHBr yHC104 for the region between 4 and 12 me9 I n order to observe the dependence of the extracted species on TBP, the amount of acid extracted as a function of the TBP concentration was determined for several aqueous acid concentrations. The results are shown in Fig. 2 as log-log plots of the organic phase HBr concentration us. the total TBP concentration. In Fig. 3 is shown a plot of organic phase mater COcentration us. the organic phase acid concentration. The mater content is corrected for the water not associated with the acid-complexed TBP, that is, for the water dissolved in the CC1, and for that bound as TBP.H,O. The former quantity is taken as the product of the solubility of mater in CC1, times the water activity times the volume-fraction of CCl, in the organic phase. The latter quantity, usually the larger one, is determined either by infrared analysis or from the relationship [TBP.HzO] = 0.15 [TBP]. Both of these methods have been described in the previous paper,' and both give the same results. (9) R. H. Stokes and R. A. Roblnson, "Electrolyte Solutions," 2nd Ed , Butterworth and Co., Ltd., London, 1959, p. 491.
Dec., 1963
EXTRACTIOK OF ACIDSBY BASIC ORGAXICSOLVENTS
lo-‘ I-
I
I
2585 I
I
0.16
0.12
H+(organic) Fig. 3.--Variation o f water content in the organic phase with organic phase acid concentration, for total TBP concentrations of 0 , 0.0915; m, 0.183; and A, 0.366 LYI. The water content does not include the water dissolved by CCl4 or complexed as TBP . HzO.
Discussion The equation for the extraction of HBr by dilute solutions of TBP can be written as nTBP(,)
+ H + + Br- + xHzO = o.
