(6)T. Biegler, D. A. J. Rand, and R. Woods, J. Electroanal. Chem., 29, 269 (1971). (7)W. Visscher and M. Blijlevens, J. Electfmnal. Chem., 19, 387 (1974). (8)D. A. J. Rand and R. Woods, J. Electroanal. Chem., 44, 83 (1973). (9)D. A. J. Rand and R. Woods, J. Nectroanal. Chem., 36,57(1972). (IO) D. J. G. lves and G. J. Janz, "Reference Electrodes", Academic Press, New York, 1961,p 112. (11) V. A. Gromyko, Elektrokhim., 7, 885 (1971).
David A. J. Rand Ronald Woods CSIRO Division of Mineral Chemistry P.O. Box 124, Port Melbourne Victoria 3207, Australia RECEIVEDfor review January 13, 1975. Accepted March 7, 1975.
Prediction of Partition Coefficients in Liquid-Liquid Systems Sir: The recent paper by Menheere, Devillez, Eon, and Guiochon ( 1 )in this journal is rather important as it is one of the first steps to interpret liquid-liquid equilibria as used in chromatography in terms of physical parameters of the liquid system used. This is of great importance in a time when choosing phase systems is still mostly done by trial and error procedures with support of some semi-empirical rules. I t seems, however, that for this type of correlation with parameters of the liquid phases, the interfacial tension is a rather arbitrary choice. Of course, factors determining interfacial tension may be for a great deal the same as those determining partitioning of solutes, but the same probably will hold for such things as the dielectric constant or the activity of the solvent components. When comparing Figure 4 from the author's paper with Figure 2 of the publication in which the K values were presented (2), one is struck by the similarity of both graphs, both showing a family of curves without intersections. Both graphs differ only in the nature of the abscissa. The regularity observed by the authors, i.e., the fact that the tangents to the curves for all solutes at a certain phase composition intersect a t one point, a t first sight can be suspected to be also present in Figure 2 of Reference (2). Now it can be shown mathematically that this regularity is independent of the nature of the abscissa; if it is present in a plot of In Kj vs. interfacial tension, it will be present in plots vs. other parameters which determine the phase composition unambiguously. T o prove this we start with Equation l of the authors d In K ,
___~ -
-
do
In K j - B(o,) go - A(Q,)
( x - x,)
x = A'(x,) =
d In K j
da
do
b,)Z (UJ (3)
If we now substitute Equation 1 of the authors, we get:
X,
-
do ( 0 0 ) dx
as substitution of these coordinates in Equation 5 yields an identity independent of Kj. The fact that the correlation found by the authors is not unique for interfacial tension does not eliminate its significance, however. The correlation which holds with a reasonable precision, as shown in their paper, is mathematically equivalent with
In K j , z = ajaz
+
b,
(7)
where a; is a parameter of the solutes j , and a, and b, are parameters of the phase systems z. The method of principal components ( 3 )used before (2) on this data set yielded a correlation with two factors In K j , z = a j a z
+
bjb,
( 8)
with 9.5% mean squared error, but this correlation obviously does need more parameters. As a simpler model yields about the same precision the eigenvectors la,J and lb;l found by factor analysis cannot be independent. Indeed, Table VI of Reference (2) shows that there is a strong correlation between the first two factors ( r = 0.941 between columns denoted ail and ai2). Therefore, with little loss of precision we can use
bj = s
+
maj
(9)
for prediction of the second factor element of a steroid from the first element. Substitution of this in the correlation for Kj yields In K,, = u p ,
which we can express also as
+
All tangents for different j intersect a t the point
(1)
in which we added index j to K, as it is valid within the attained precision for all solutes, and added an index o to u in order to distinguish it from the moving coordinate u. In this equation A(o,,) and B(g,) are the coordinates of the intersection point of all tangents drawn a t a value uo. Now choose any other coordinate system x , In K wherein the vertical direction again In Kj is plotted and the x coordinate is some parameter of the phase system like water content or dielectric constant. Clear& x will be a function of u and vice versa. In this new plot, we draw tangents to the curves. A tangent to the curve for solute j drawn at a value of x of xo has the equation
In K = In Kj(a,)
(4) or
f
(s
+
ma,)&, = aj(ae
+ mb,) +
Sb,
(10)
which has exactly the same structure as correlation 7 (two parameters for the phase system, one for the solute) and ANALYTICALCHEMISTRY, VOL. 47, NO. 8, JULY 1975
1483
which also predicts intersection of all tangents in a graph as discussed in one point. This correlation would predict the In Kj values with a mean squared error of 0.0089, which corresponds to a standard deviation of 10%in K. The possibility of using a unit vector for the solutes (1or a constant for all solutes, as occurs in the second term of Equations'7 and 10) or of using some measurable parameter can be very elegantly tested by the procedures discussed by Weiner et al. ( 4 - 6 ) . I t seems, however, that for meaningful investigations on this point, more extensive data sets, having both a larger range in character of phase systems and of solutes, should be used. Therefore a discussion on rotation of vectors to measurable parameters, or to unit vector (which, as is pointed out in Reference ( l ) , might be identified with the molar volumes) was not carried out in the paper in which the steroid partition coefficients were presented.
LITERATURE CITED (1) P. Menheere, C. Devillez. C. Eon, and G. Guiochon. Anal. Chem., 46, 1375 (1974). (2) J. F. K. Huber, E. T. Alderlieste, H. Harren, and H. Poppe. Anal. Chem., 45, 1337 (1973). (3) P. Whittle, Skand. Aktwrietidskrift, 35, 223 (1952). (4) P. H. Weiner. E. R. Malinowsky, and A. R. Levinstone, J. phys. Chem., 74, 4537 (1970). (5) P. H. Weiner and D. G. Howery, Can. J. Cbem., 50, 448 (1972). (6) P. H. Weiner and D. G. Howery, Anal. Cbem., 44, 1189 (1972).
H.Poppe Laboratory for Analytical Chemistry University of Amsterdam Nieuwe Achtergracht 166 Amsterdam, The Netherlands
RECEIVEDfor review February 3, 1975. Accepted February 21, 1975.
Loss of Osmium during Fusion of Geological Materials Sir: The recent paper by Nadkarni and Morrison ( I ) describes a procedure by which the noble metals can be determined in geological materials. In this method, thermal-neutron activation is used to produce the radioactive isotopes of interest. Following irradiation, the geological matrix is destroyed by fusion with Na202 and NaOH. The noble metals ,are separated from the gross radioactivity by adsorption on an ion-exchange resin (2) selective for the noble metal ds electronic configuration. The resin is then analyzed by gamma-ray spectrometric techniques to determine the amounts of noble metals present. In the course of examining this procedure, we have found that osmium is not quantitatively determined as had been implied by the authors (1).In fact, about half of the osmium in the sample can be routinely lost, and no acknowledgment of this fact has been incorporated into the procedure. We have used the radioactive tracer 15.3-d lglOs and appropriate Ge(Li) gamma-ray spectrometric equipment to study the radiochemical procedure outlined by the authors (1). Osmium losses were determined by comparing tracer fusion samples with appropriate unfused tracer standards. Mechanical losses were monitored with nonvolatilizing noble metal radioactive tracers. Osmium tracer, and presumably osmium standard, tend to oxidize to the volatile and poisonous tetroxide Os04 during the fusionldissolution step. During the fusion alone, approximately 5% of the osmium was routinely volatilized. Fusion temperature and duration appear to be important factors here. Upon dissolution of the melt with HzO and dilute HC1, the amount of osmium volatilized ranged from about 5% to as much as ~ 3 0 % The . most serious losses, however, were encountered when the dissolved melt was boiled with addition of "03 to destroy the peroxide. From ~ 3 0 % to as much as =95% of the remaining osmium was volatilized at this point. The losses are related to the duration of boiling and appear to be independent of the addition of HN03. By standardizing the fusion/dissolution step, we have observed total osmium volatilization losses around 60% with a relative standard deviation of no better than ~ 0 . 1 These . losses are compatible with chemical yield data observed for similar fusion techniques ( 3 , 4 ) . It is not known whether during fusion the percent losses of radioactive tracer osmium (and standard osmium) are different from percent losses of geologically bound osmium. This is obviously a subject of needed study. Notwithstand1484
ANALYTICAL CHEMISTRY, VOL. 47. NO. 8, JULY 1975
ing, our data indicate that tracer volatilization losses during fusion per se are
