Magnetic Susceptibilities of Alkali Metal-Ammonia Solutions
2887
Magnetic Similarities and Differences of Some Chemical Models of Alkali Metal-Ammonia Solutions Sldney Golden Chemistry Department, Brandeis University, Waltham, Massachusetts 02 154; Isotope Department, The Weizmann Institute of Science, Rehovot, Israel;'8 and Physical Chemistry Department. The Hebrew University, Jerusalem, lsraep (Received July 23, 1975)
Each of six existing chemical models of alkali metal-ammonia solutions yields the relationship X M X M ~ = P ~(1~- Y)XM + YYM,independent of the model. The molar static magnetic susceptibility, XM, the molar spin susceptibility, X M ~ P ~and ~ , the fraction of unpaired spins, y, are each measurable quantities which depend implicitly upon the temperature and composition of the solutions and are explicitly independent of the models. The XM'Sand YM'Sare characteristic of the models and of the alkali metal M. Existing magnetic susceptibility data, both experimental and theoretical, already give a qualified indication of distinguishability between certain of the models and indicate how a reliable discrimination between them may be effected when data adequate to do so become available.
Introduction The presence of alkali metal anions as essential chemical constituents in alkali metal-ammonia solutions was originally conjectured2a on the basis of theoretical estimates then available for the positive electron affinities of some of the gaseous alkali atoms and the ensuing stabilization that could be expected from the resulting solvation of the anions that they could form. In terms of these constituents, a good quantitative account could then be given of the compositional behavior of a variety of properties of alkali metal-ammonia solution^.^^,^ Soon thereafter, based primarily on correlative spectroscopic evidence, the presence of alkali metal anions in solutions of amines4 and ethers5 could be inferred-and was. Somewhat more direct evidence for the real existence of these anions in appropriate solutions of the alkali metals has come forth in just the past 2 years: (1) analysis of the infrared absorption band exhibited by sodium-ammonia solutions, which band had usually been ascribed entirely to the solvated electron, e-, has revealed the presence of an additional absorbing species (spectrally distinct from the solvated electron) which conforms to the stoichiometry Na-;6 (2) the first pure Na--containing compound (a crystalline salt) has been prepared and identified;7 (3) precise experimental determinations of the electron affinities of several alkali atoms have established the appreciable stability of their anions, M-, in the gas phase;8 (4) theoretical calculations of the electron affinities have been carried out, with results that are in excellent agreement with the measured value^;^ (5) 23NaNMR studies of two nonaqueous solutions of the first prepared sodium anion-containing compound7 have revealed the presence of a new characteristic resonance (distinct from that to be associated with Na+) which exhibits a large diamagnetic chemical shift in accord with the expected diamagnetic susceptibility of Na-.lO The foregoing results would seem sufficient to dispel any doubts as to the real existence of alkali metal anions as constituents of appropriate solutions of the alkali metals. However, because of the considerable attention which *Address correspondence concerning this article to this author at Brandeis University.
ammonia solutions of the alkali metals have received during the more than 100 years they have been known,Il a variety of chemical models has been developed to account for their properties and to correlate them with their presumed compositional behavior. As a consequence, sometimes unusual chemical species have been invoked (depending on the model) which are stoichiometrically equivalent to but differ intrinsically from the alkali metal anions. More importantly, such species are potentially capable of being converted into the anions in pure compounds that may be formed which contain them. Despite the reassuring evidence which has been cited for the real existence of alkali metal anions in appropriate solutions and compounds, therefore, questions regarding the actual nature of the alkali metal-ammonia solutions and the adequacy of the chemical models which have been constructed to account for their properties still merit some attention. It is to the foregoing questions that the present paper is directed. In terms of a fairly general analysis of the magnetic susceptibilities which are to be expected from various chemical models of alkali metal-ammonia solutions, a reasonably reliable discrimination between some of them appears to be possible. Although the magnetic data which are currently available are only adequate to suggest a qualified distinction, it is hoped that the present paper can encourage the future acquisition of such data (both theoretical and experimental) which are adequate to discriminate between the models in unqualified terms.
Chemical Models of Alkali Metal-Ammonia Solutions Table I lists the major chemical species presumed to be formed and subsequently solvated when an alkali metal, M, is dissolved in ammonia, S, a t moderate concentrations, according to six chemical models which have been suggested to describe the compositional behavior of these solutions. The stoichiometric equivalence of the various species in each column of the table is to be noted. Despite any such equivalence, however, the presumed nature of their constitution (reflected in the compositional notation used to describe them) precludes their being regarded as identical. The detailed differences between the various species can be found in the cited references. The Journal of Physical Chemistry, Vol. 79, No. 26, 1975
Sidney Golden
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TABLE I : Major Stoichiometrically Equivalent Species of Various Chemical Models of Alkali Metal-Ammonia Solutions -
.
. _ _
Model I1 111
Paramagnetic species M+.eM + *S-
e-
F F
ee-
IV V
VI
F
M+ M+ M+ M+ M+
Se-
TABLE 11: Basic Chemical Species of Various Chemical Models of Alkali Metal-Ammonia Solutions Model
Paramagnetic species
I
e-
; I
e-
I11
S-
IV V VI
e-
Diamagnetic species
Diamagnetic species
e-, F e-, F
M+,eaM+ M+, M-, S M + , Ml M + , F, M+, F,, F’
The basic chemical species involved in each of the models can be ascertained, by inspection, from Table I and are listed in Table 11; they are all presumed to be solvated. The latter species are capable of reacting and combining with each other to form the remaining species of Table I as well as larger aggregates, e.g. ion-triples, ion-quadruples, etc., through appropriate chemical equilibria postulated by each model. All the models then give a similar (but not identical) account of the compositional behavior of the solutions as the concentration of dissolved alkali metal is varied. Since they are not necessary for our purposes, we omit any description of the pertinent equilibria; they, too, can be found in the cited references. We merely note that all the models are constructed so that only solvated alkali metal cations, M+,and solvated electrons, e-, or solvated anions, S-, prevail as solute species when the alkali metalammonia solutions become increasingly dilute.
Magnetic Susceptibilities of the Models That the major chemical species invoked by each model are expressible as composites of the basic chemical species they also invoke is evident from Tables I and 11. A similar composite nature is to be expected for larger aggregates that may be formed. As a result, suitable additive and constitutive properties, as regards the basic chemical constituents of the alkali metal-ammonia solutions, can serve to discriminate between some (or all) of the models. In particular, the magnetic susceptibility which is to be ascribed to the dissolved alkqli metal, a property which has played a crucial role in our developing understanding of these systems,15J9~20 will be dealt with here for that purpose. To be explicit, we assume: (1) the molar magnetic susceptibility, Xk, of the kth basic chemical species (Table 11) is the algebraic sum21 of a diamagnetic part, x k d , and a paramagnetic part, Xkp; (2) the value of Xkp is entirely due to a common value of the spin paramagnetic susceptibility of that xosPin; (3) the molar diamagnetic susceptibility of any composite chemical species is the sum of the corresponding quantities of its constituent basic chemical speciesz3;(4)the molar paramagnetic susceptibility of any composite chemical species arising in models I, 111-VI is the sum of the corresponding quantities of its constituent basic chemical species, while for those arising in model I1 it is just that of the unpaired paramagnetic constituent that it contain^.'^ The Journal of Physical Chemistry, Vol. 79, No. 26, 1975
Ref 13
14 15
16 17,18
F
With these assumptions, it follows that the molar static magnetic ~ u s c e p t i b i l i t y , l ~XM, J ~ ~attributable ~~ to the dissolved alkali metal, is expressible as
where fk is the ratio of the total amount of the kth basic chemical constituent (combined or not) to the total amount of dissolved alkali metal and fk’ is a similar ratio modified in accord with assumption 4. Furthermore, the molar spin s u ~ c e p t i b i l i t y , ~X~ ,M~ ~~, attributable ~~~ ~ ~ , to the dissolved alkali metal is expressible as
By merely invoking electrical neutrality of the solutions and material balance among the metal-containing species, we are able to obtain from eq 1 and 2 that XM
- X M w n = (1- Y)XM+ YYM ‘
(3)
= XMwin/XOwin
(4)
where is the fraction of unpaired spins per mole of dissolved alkali metal. The essential invariance of the form of eq 3 to the actual model used to obtain it is noteworthy. The expressions for X M and Y Mfor the various models are given in Table 111. Because of the presence of two basic paramagnetic species in models V and VI, viz., e- and F, and three basic metal-containing diamagnetic species in model VI, viz., M+, F2, and F’, we have int‘roduced
- (Xed + XM A X F ~= XF? - (XFP + X M + ~ ) AXF = XFd
a = ([e-]
- [Fl)/([e-l + [FI)
0 = ([F’] - [Fz])/([F’] + [Fz])
(5)
(6)
(7) (8)
the bracketted quantities being the total concentrations of the indicated species (in combination or not). Apart from the X M of model VI and the YM’S of models V and VI, the remaining entries are presumably independent of the detailed compositions that the models ascribe to the solutions and of their temperatures. Such dependence is implicit in the XM and x$Pin of eq 3, as is y , which are measured quantities that are independent of the specific model considered. To the extent that the constituent species of an alkali metal-.-ammoniasolution are justifiably composites of the basic chemical species pertinent to a given model, the addition of chemically inert solutes, e%., unreactive salts having the same metal cation, to the solution will not alter the form of eq 3. Except for model VI, the X M ’ Swill be identical with those already given; except for models V and VI, so will the YM’s.However, even the exceptions can be expected not to change appreciably in value from that obtained in
Magnetic Susceptibilities of Alkali Metal-Ammonia Solutions
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TABLE 111: Coefficients of Eq 3 for Various Chemical Models of Alkali Metal-Ammonia Solutions Model
XM
YM
I I1 I11 IV
X M +d
1
V
.
+
Xe- d
x M + d + Xe-d
+
‘
I
C-ra>
~~~d
VI
TABLE IV. Some Independently Estimated Values of XM
Li 106xe-d - 0.7 -2 9 -16; -17 -3 7 -67; -40 Na 106xe-d - 4 -5 8 -87 K 106xe-d - 1 5 -68 -140 Rb 106xe-d - 22 cs 106xe-d - 35 -8 8 -220 Reference 28. b Reference 29. C Reference 30-32.
(9)
but it is evident that the theoretical information needed to verify this relationship still needs to be obtained.
Potential Distinguishability between the Chemical Models As stated at the outset, there appears to be no adequate experimental data currently available to exploit the analysis of the preceding section for obtaining an unqualified discrimination between the various models which have been considered. In fact, many of the measured values of XM and X M ~ reported P ~ ~ by different investigators frequently turn out to be incompatible with a basic requirement of eq 3, viz.
-
Metal, M
XM,loe6 cm3/mol
[MI, M
T,K
Ref
Na
