NOTES
4403
amounts of added oxygen in the range of 10-30%. The Si-H to C--H per-bond insertion ratio is 7.2 f 0.1. The results for the trimethylsilane-diaaomethane in the presence of oxygen are photolyses at 4358 given in Table 111. The TEMS/EDMS ratio is constant, 0.79 =!= 0.01, independent of the total pressure and oxygen proportions. The corresponding Si-H to C-H bond insertion ratio is 7.1 f 0.1. Thus, within experimental error, the relative rates of singlet methylene insertion into the Si-H and C-H bonds of dimelhylsilane and trirnethylsilane are the same and independent of wavelength. These values are about 25% lower than that found earlier2 for the SiH/C-H insertion ratio for methylsilane.2 It is possible that this rather small difference is due to systematic errors between the different studies. Comparison of the Si-H to C-H bond insertion ratio for trimethylsilane at 3660 and 4358 A, shows that there is no real. difference in the selectivity of singlet methylene radicals from diazomethane photolyses a t 3660 and 4358 toward the Si-H bond and C-H bonds of trimethylsilaoe. This invariance in selectivity is in agreement with the invariance in selectivity found toward the primary, secondary, and tertiary C-H bonds of the alkanes in this laboratory’ and by Heraog and Carr.6 The higher reactivity of Si-H bonds toward singlet methylene radical insertion relative to C-H bonds is probably due to a combination of effects related to the larger Si-H bond length, opposite polarity of the Si-H bond, and sligh1,ly lower Si-H bond dissociation energy. Recent work on H atom abstraction from silanes by methyl radica1s,16 hot tritium atom reactions with silanes, l7 and electron impact appearance potential measurements on silanes1*indicate that Si-H bond dissociation energies are in general only slightly lower than C-H bond dissociation energies and that these small differences lead to significant reaction kinetic effects. In the alkane systems, C-H bonds to the more highly substituted carbon are slightly more reactive toward singlet methylene insertion, while in the various methyl silane systems the reactivities of the different Si-H bonds are nearly the same, with the Si-H bonds to the least substituted silicon atom appearing to be slightly more reactive. If it is assumed that the preexponential factors for insertion of methylene radicals into the Si-H bonds of methylsilane, dimethylsilane, and trimethylsilane are the same, (which may not be the case), and that activation energy differences are due to bond energy differences, one would conclude that the Si-H bond dissociation energies in dimethylsilane and trimethylsilane are nearly the same, while that in methylsilane is possibly slightly lower. Comparing this possible trend of Si-H bond dissociation energies, primary ,< secondary tertiary, one could speculate that the amount of resonance stabilization of the dimethylsilyl and trimethylsilyl radicals is small compared to the
-
resonance stabilization of the analogous isopropyl and t-butyl radicals. (16) (a) J. A. Kerr, D. H. Slater, and J. C. Young, J . Chem. SOC.A, 134 (1967); (b) T. N. Bell and B. B. Johnson, Aust. J . Chem., 20, 1545 (1967); (c) 0. P. Strausz, E. Jakubowski, H. S. Sandhu, and H. E. Gunning, private communication. (17) F. S. Rowland, A. Hosaka, and T. Tominga, J . Phys. Chem., 73, 465 (1969). (18) (a) S. J. Band, I. M. T. Davidson, and C. A. Lambert, J . Chem. Soc., A, 2068 (1968), and references therein; (b) W. C. Steele, L. D. Nichols, and F. G. A. Stone, J . Amer. Chem. Soc., 84,4441 (1962); (c) G. G. Hess, F. W. Lampe, and L. H. Sommer, ibid., 87, 5327 (1965).
Further Consideration of the Moving Boundary Experiment for the iMeasurement of Transference Numbers
by Richard J. Bearman’ Department of Physical and Inorganic Chemistry, University of New England, Armidale, N.S.W., 2361, and Research School of Physical Sciences, Australian National University, Canberra, A.C.T. Z600,Australia
and L. A. Woolf Research School of Physical Sciences, Australian National University, Canberra, A.C.T. 2600, Austrulia (Received June 9 , 1969)
I n a significant paper, Milios and Newman2 recently reformulated the theory of the moving boundary experiment. For the case where the density below the moving boundary varies linearly with solute concentration, they derived a “volume correction” by using a rigorous form for the regulating function in conjunction with general equations of mass balance. For situations where partial molar volumes are spatially constant everywhere, Bearmana earlier derived the classical Lewis volume correction by observing that an average velocity, the volume velocity, must then also be uniform throughout the system. I n the present note we derive the Nemman-Milios c ~ r r e c t i o nby , ~ applying Bearman’s method to the case where partial molar volumes are necessarily constant only below the moving boundary. We then show that the methods of hlilios and Newman and of Bearman are (1) Correspondence should be addressed to Department of Chemsitry, University of Kansas, Lawrence, Kan. This research was s u p ported in part by a grant from the Office of Saline Water of the U. 9. Department of Interior to the University of Kansas. R. J. B. is also grateful to the ARGC for a travel grant which enabled his commutation between Armidale and Canberra. (2) P. Milios and J. Newman, J . Phys. Chem., 73,298 (1969). (3) R. J. Bearman, J . Chem. Phys., 36,2432 (1962). (4) We interpret the acknowledgment given on p 44 of the reference given in footnote 8 t o mean that the derivation reported in the reference of footnote 2 is due chiefly to Newman. We therefore choose to refer to the volume correction of the latter reference as the “NewmanMilios correction.”
Volume 73, Number 12 December 1969
4404 quite equivalent when applied to the systems considered in their respective papers.
The Regulating Function From eq M2, 1.13, M5, and M9,‘” 1lilios and Newman derive the general form5bfor the regulating function (eq R‘I17). Since their starting equations are equivalent t o eq B 2 . 4 ~and B2.6 (including the ensuing discussions), and B3.4, the theory of Bearman leads rigorously to the identical result. The discrepany between eq M17 and Bearman’s equation for the regulating function, eq B5.3, is only superficial and disappears when it is noted that Bearman should have cancelled bo/fi0’, the ratio of partial molar volumes of solvent above and below the boundary, which was unity, according to his assumption of constancy of partial molar volumes. Evidently, the path of derivation followed by Milios and Kewman is superior because it shows clearly that the regulating function is valid whether or not the partial molar volumes are constant.
Sufficient Conditions for the Lewis and Newman-Milios Corrections Bearman obtained the Lewis correction for the solvent velocity by assuming constancy of partial molar volumes to extend from the bottom electrode through the moving boundary. I n the next paragraph, we show that the Bearman method leads to the Newman-Milios correction, eq 3128, under the weaker assumption that the partial molar volumes are spatially constant below the moving boundary. For simplicity, the derivations of Milios and Newman and of Bearman each proceeded through consideration of specific systems, which, unfortunately, were different. However, when due allowance is made for the differences, eq M28 follows from eq B5.1 and the general form of the regulating function ( N . B . a = l/ijo’by eq 5 and 6 below). Since we have shown the method of derivation of the regulating function in the preceding section, all we have left to show is that eq B5.1 remains valid under the weaker assumption. But that is simple, for eq B5.l follows from eq B4.1 through B 4.6 applied beneath the boundary, and these are valid in the present context: equations B4.1-B4.5 are thermodynamic and hydrodynamic identities, and eq B4.6 holds below the boundary because the partial molar volumes are assumed to be constant beneath it. I n other words, the condition of constancy of volume velocity below the boundary leads t o the Newmani‘lilios correction whereas the condition of constancy of volume velocity throughout the system leads to the Lewis correction. The second condition is a special case of the first, so we deduce that: the Kewman-Ililios correction reduces to the Lewis correction when the volume velocity is everywhere constant.6 The Journal of Physical Chemistry
NOTES
Equivalence of the Approaches of Milios and Newman and of Bearman The methods of both Nilios and Newman and of Bearman lead to the Newman-Milios correction. Bearman makes the assumption that the partial molar volumes of both solvent and solute are spatially constant below the moving boundary, while Milios and Yewman make the thermodynamic assumption that below the boundary = a beg (1) where cg is the concentration of solvent, CB is the concentration of electrolyte, and a and b are constants. One may well ask why the two different assumptions lead to the same result. The answer is that they are equivalent. Milios and Newman nearly state this (ref 2, p 302) when they point out that our eq 1 (their eq 23) implies that the partial molar volume of solvent is constant below the boundary. However, they do not state that the partial molar volume of solute must then also be constant. Moreover, they especially stress the usefulness of eq l, which obscures its limitations to all but the most perceptive readers. Therefore, we now prove very explicitly that the only class of salt solutions satisfying both assumptions are those with thermodynamically constant partial molar volumes. Into eq 1 we substitute the relations eo = x ~ / ( x ~ ~ ~ Z B ~ ~ Band ) cB = ZB/(Q,~, 4 X B ~ B ) , where x’s are mole fractions and 8 s are partial molar volumes, and obtain
+
+
+
+
XO = U ( X ~ S ~ XBSB) bXB (2) Twice differentiating eq 2 with respect to XB = 1 - zo leads, a t constant temperature and pressure, with the aid of the thermodynamic identity7
dSB XBB
=
- x 0-
dS, dx B
(3)
to
(4) For the simultaneous validity of eq 3 and 4 we must have &B _ _ - dao_ =o (5) dxg bXB Hence f i and ~ go are thermodynamic constants. ( 5 ) (a) We prefix equations from the paper of Milios and Newman with an “M” and equations from the paper of Bearman with a “B;” (b) advocated earlier by L. J. M. Smits and E. M. Duyvis, J. Phys. Chem., 70, 2747 (1966), and ibid., 71, 1168 (1967), and, still earlier, by G. S. Hartley, Trans. Faraday Soc., 30,648 (1934). (6). An alternative sufficient condition for the Lewis correction to be valid is for the partial molar volumes below the boundary to be constant, and, simultaneously, i o = Go’, without the partial molar volumes being constant through the boundary. Hence, despite the implication of Bearman to the contrary, the constancy of partial molar volumes through the boundary is not a necessary condition for the validity of the Lewis correction. (7) For example, derivable from R. J. Bearman and B. Chu, “Problems in Chemical Thermodynamics,” Addison-Wesley Publishing Co., Reading, Mass., 1967, p 109, eq 4.29.
NOTES The thermodynamic constancy of the partial molar volumes below the boundary implies their spatial constancy, so that the Bearman method yields the Newman-fi!Iilios correction. At first sight it is conceivable that there may be spatial uniformity even though eq 1is not obeyed. I n that case, it would seem that the method of Bearman gives the Newman-Milios correction whereas the method of h4ilios and Newman is not applicable. However, as Milios pointed out in his thesis,8 there inevitably will be concentration gradients in the neighborhood of the electrode; and these are sufficient to also destroy the applicability of the Bearman theory unless the partial molar volumes are constant wherever there are concentration gradients below the moving boundary. Thus far, we have shown that equivalent assumptions are used in the approaches of Milios and Newman and of Bearman in deriving the Newman-Milios correction. To complete the demonstration of the equivalence of the two theoretical methods, we note that they both lead to the regulating functiong’ and, when the partial molar volumes are constant through the liquid junction, also to the Lewis c o r r e ~ t i o n . ~ ~
4405 Electron Paramagnetic Resonance of Nitrosodisulfonate Ion with Oxygen-17 and Sulfur-33 in Natural Abundance
by J. B. Howell and Douglas C. McCain Department of Chemistry, University of California, Santa Barbara, California 98106 (Received June 11, 1969)
The epr spectrum of the nitrosodisulfonate ion
(SO~)ZYO-~, has been frequently studied, and except for the sulfur-bonded l7O(S-l70), coupling constants have been reported for all atoms in the ion. Recently the nitrogen-bonded 170(N--170)was seen after chemical preparation with labeled oxygena2 Line width variations allowed the relative signs of the nitrogen and N-liO coupling constants to be determined.
Conclusions We have shown that the approach of Bearman, like that of Milios and Newman, leads to the general form of the regulating function and to the Lewis and Newmanhlilios corrections. Because the assumption of constancy of partial molar volumes below the moving boundary is well concealed in the method of Milios and Newman and because they do not show the constancy of volume velocity, which links the theory of the moving boundary to the theory of mutual diffusion,”” we tend to prefer the Bearman approach.lob We are less confident than Milios and Newman that forcing experimental thermodynamic data for co to assume the form of eq 1 “does not greatly limit the usefulness of the transference number equation.” I n essence, such a force-fit replaces the assumption that partial molar volumes are constant through the boundary by the assumption that they are constant below the boundary. The new assumption undoubtedly represents an improvement since it concerns a binary, rather than a ternary, solution, but a quantitative estimate of the extent of improvement has not yet been obtained.
(8) P. Milios, “A Theoretical Analysis of the Moving Boundary Measurement of Transference Numbers,” Masters Thesis, University of California, Berkeley, Sept 1967 (UCRL-17807), p 21. (9) (a) Demonstrated in the fourth paragraph of this note; (b) Demonstrated in the preceding section for the case of Bearman and in the reference of footnote 2 for the case of Milios and Newman. (10) (a) C f . J. G. Kirkwood, R. L. Baldwin, P. J. Dunlop, L. J. Gosting, and G. Kegeles, J . Chem. Phys., 33, 1506 (1960), especially section 111; (b) It is entirely possible, however, that for the case of vertical electrodes, briefly mentioned by Milios and Newman, the mass balance technique may prove to be more useful.
Figure 1. A p a r t of the spectrum of (SO&N02- showing the central 14N line (VLN = 0) off scale, two 5 8 5 lines ( m ,=~ .i.S/*) and two ‘’0 lines (mo = .i.6/%) marked by arrows. Magnetic field increases to the left. The horizontal line represents 1 G.
We have obtained the spectrum of a very dilute solution of purified K2(SO&NO dissolved in deoxygenated dimethyl sulfoxide (DMSO). The weak lines in Figure 1 are assigned to the outermost, m = f 5 / 2 , of the six lines derived from interaction with the l7O nuclear spin in an ion with one 14N. Assignment of these lines to any other set in the li0 multiplet would predict lines displaced farther out from the center of the multiplet in positions where no lines are observed. Statistically, these li0 lines should be about one-tenth the intensity of 33Slines, and very nearly this ratio is (1) J. J. Windle and A. K. Wiersema, J . Chem. Phys., 39, 1139 (1963). (2) Z. Luz, B. L. Silver, and C. Eden, ibid., 44,4421 (1966).
Voltime 73, Number 1$l December 1969
