MODELFOR METAL-AMINE SOLUTIONS
135
I
A Model for Metal-Amine Solutions
by James L. Dye and Robert R. Dewald Kedzie Chemical Laboratory, Michigan State University, East Lalzsing, Michigan
(Receive8 August 18,1963)
A general model is proposed to describe the nature of metal-amine solutions. Three types of species are suggested: (1) solvated electrons similar to those in metal-ammonia solutions are responsible for the infrared absorption band and are the main contributors to the conductivity; (2) covalent dimers, similar to those existing in the gas phase for the alkali metals, form in solutions of K, Rb, and Cs and are responsible for the intermediate absorption; (3) combination of a solvated molecde-ion, M2+, with an electron trapped in the field of this ioii gives rise to the absorption a t 650-750 mp commonly found in metalamine solutions. Semiquantitative thermodynamic calculations are presented which lend support to the model proposed and help to explain the diversity of behavior observed for the different alkali metals in a variety of solvents.
Introduction The studies of metal-ethylenediamine solutions reported in the preceding papers1v2prompted us to reexamine the models proposed for metal-amine solutions in general. While no complete theory for these systems has appeared in the literature, some attempts have been made to describe the nature of the various species. In spit,e of the complexity of the spectra, Including the appearance of several bands not found for metal-ammonia solutions, the tendency has been to extend or modify the existing theories OS metal-ammonia solutions. Thus, Blades and Hodgins3 proposed the existence of “amine-type” and “aliphatic-type” traps as well as intermediate types to explain their spectral results in methylamine and ethylamine. The “traps” were assumed to be similar to those of the cavity rnodel in a r n m ~ n i a . ~Symons has suggesteds that the visible absorption (650-750 m p ) is associated with a diamagnetic species5 such as the dimer of the model of Becker, Lindquist, and Alder.6 Cafasso and Sundheim’ present results for solutions of the alkali metals in ethers which seem to fit the general description given by Symons. These authors also stress the importance of a well defined negative cavity for the cations as a prerequisite to solubility. Recently, Windwer and Sundhaims have postulated that the visible (650 mp) absorption is due to a species which shows ne, e.8.r. absorption, and that the in1,ermediate absorptions (808 -980 mp) for K and W b solutions might be associated with a d~ imer.
Dainton, Wiles, and Wrightg have presented strong evidence that the visible absorption peak for potassium in dimethoxyethane and tetrahydrofuran arises from the heterogeneous nature of the “so1ution.” They were able to decrease the absorbance repeatedly by centrifugation of the solution, This suggests that the “solutions” are really colloidal in nature. While this may be the case in these solvents, the reproducibility of our solubility and conductance data for ethylenediamine solutions rules out the colloidal hypothesis for these systems. The results of Dainton, el al., are discussed later in this paper in the light of the present model. Undoubtedly much of the difficulty associa,ted with these systems arises from the conflicting experimental results which have been reported hy different investigators and the lack of reproducibility of results by a (1) R. R. Dewald and J. L. Dye, J . Phys. Chem., 68, 121 (1964). R.R.Dewald a.nd J. L. Dye, ibid., 68, 128 (1964). (3) H. Blades and J. W. Hodgins, Can. J . Chena.. 33, 411 (1955:. (4) R. A. Ogg, Jr., Phvs. Rev.,69, 668 (1946). ( 5 ) M. C. R. Symons, J . Chem. Phys., IS, 99 (1959), Quart. Rm. (London), 30, 1628 (1959). (6) E. Becker, R.€1, Lindguixt, and B. J . Alder, J . Chem. Phys., 25, 971 (1956). (7) F. A. Cafasso and B. R. Sundheim, ibid., 31, 809 (1’959). (8) 8. B. Windwer and B. B. Sundheim, J. Phgs. Chem., 66, 1254 (2)
(1962).
(9)
F. S. Dainton, D. 1\1.Wiles, and A. N . Wright, J . Chepn. SOC., 4283 (1960).
136
JAMES L. DYEAND ROBERT R. DEWALD
given investigator. l,E,lo These disparities probably arise because of slow conversions of one species into another. The model presented here is necessarily complex. Even solutions of metals in ammonia, which show only one absorption peak, are thought to contain a minimum of four important species: (1) the cation of the alkali metal, ( 2 ) the solvated electron or polaron, (3) the ion-pair or monomer, and (4) the ion quadrupole or While we believe these species to be present in amine solvents as well, they cannot account for the visible absorption bands, and we postulate in addition the existence of gas-like covalent dimers and electrons trapped by one-electron bonded M2+ ions. In spite of the complexity of the model, many diverse experimental results can be explained by it, and the species proposed are a t least plausible on thermodynamic grounds.
containing Rb+, the peak a t 890 mp, characteristic of R b solutions, is obtained. As discussed in the preceding papers,',2 the results obtained by other investigators in a number of solvents can be correlated with our results in ethylenediamine if one bears in mind the slow conversions which are possible among the various species and the possibility that B catalyzed decomposition of one species can occur without immediate disappearance of the others. We first consider the three types of species separately, discussing the structural features and properties of each one and the experimental evidence for its existence. Then we consider the nature of the conversion reactions and factors which influence the reaction rates. Next, thermodynamic arguments are invoked to explain the diversity of the results observed with different metals and solvents, and, finally, the model is used to explain some experimental observations of other investigators!,
Experimental Basis for the Model
Assignment of Absorptions Infrared Absorption and the Solvated Electron. We postulate that the infrared absorption (1280 mp in ethylenediamine) is due to the solvated electron, existing alone and in ion-pairs, triple-ions, and quadrupoles similar to the principal species in dilute metalammonia solutions. The alkali metals and alkaline earth metals in liquid ammonia show only a single absorption (unless a large excess of a common ion is added13) in the infrared. This broad absorption band, tailing well into the visible, is attributed to an electron in a cavity surrounded by polarized solvent molecule^.^^ The infrared absorption in amines is also very broad and extends into the visible. A solution of sodium in either methylamine or ethylamine shows only the visible peak, but upon addition of ammonia an infrared absorption maximum appears and the visible absorption decrease^,^'^^ with the infrared peak becoming more pronounced a t higher ammonia concentrations. At about 50% ammonia, no visible peak remains. The addition of diethyl ether or tetrahydrofuran to solutions of sodium in ammonia causes a decrease in intensity of the infrared absorption and the appearance of a visible absorption maximum.16 These results fit in most naturally with the assignment
The spectra of metal-amine solutions clearly require a minimum of three types of absorbing species. For example, potassium and rubidium show three absorption regions having different relative intensities under different conditions. The rate a t which the absorbance decays during decomposition varies from one peak to another and from one sample to another so that the spectra cannot arise from fewer than three absorbing species. The shape and position of the absorption peak a t 660 mp are both independent of the metal, but the intensity of this peak relative to the infrared absorption depends strongly upon the metal, and the peak does not appear at all for solutions of cesium in ethylenediamine. Similarly, the shape and position of the infrared absorption appear to be practically the same for all metals, but sodium shows very little infrared absorption. The position of the intermediate absorption band observed for potassium, rubidium, and cesium solutions depends upon the metal. The various species are only slowly interconverted. This is most striking in the case of lithium in which the half-time for the conversion is a t least several minutes. Other investigators have also commented upon the different decay rates for different spectral bands.Erlo Experiments in which a solution containing one of the alkali metals is mixed with a salt solution of another alkali metal show that the various species are interconvertible and that the 660 mp and intermediate species a t least depend upon the metal. For example, when a solution of R b in ethylenediamine (which shows only a shoulder at 660 mp) is added to a solution containing Na+ (but not Ka), an intense peak appears at 660 mp. Conversely, when a solution of Li is added to a solution The Journal of Physical Chemietry
(10) H. J. Eding, Ph.D. Thesis, Stanford University, 1962. (11) E. C. Evers, J . Chem. Educ., 38, 590 (1961). (12) M. Gold, W. L. Jolly, and K. S. Pitzer, J . Am. Chem. Soc., 84, 2264 (1962). (13) H. C. Clark, A. Horsfield, and M. C. R. Symons, J. Chein. Soc., 2478 (1959). (14) J. Jortner, J . Chem. Phys., 30, 839 (1959). (15) G. Hohlstein and I;. Wannagat. 2. anorg. allgem. Chem., 288, 193 (1957).
137
MODELFOR METAL-AMINE SoLuwoNs
of the infrared absorption to thc “ammonia-like” solvated clcctron. The conductances of potassium, rubidium, and cesium in ethylenediamine also support the assignment of the infrared absorbing species to the solvated electron. Dilute cesium solutions show only the infrared absorption. The conductance can be described by the Shedlovsky function including ion association. The value of the limiting equivalent conductance gives nearly the same Walden product as the alkali metals in ammonia. I’otassium and rubidium, which show both visible and infrared absorption peaks in dilute solutions, behave in a similar fashion to cesium but with significantly lower values of conductance. Sodium solutions, which show no significant infrared absorption, have a much lower conductance and exhibit a concentration depcndence of the equivalent conductance different from the other metals. Since the dielectric constant of ethylenediamine is significantly lower than that of ammonia, one would expect a greater fraction of the electrons to be present as ion-pairs, triple-ions, and quadrupoles. We would, therefore, expect a lower magnetic susceptibility for the infrared species in ethylenediamine than in ammonia. To summarize, we attribute the infrared absorption In amine systems to the solvated electron in the species: (e-), (M+.e-), (e-.M +.e-), ($1 +.e-.M +), and (M+.e-)z. These species will be collectively referred to as “solvated electrons.” T h e Intermediate A bsorptions.-The absorption maxima a t 840, 890, and 1030 mp for potassium, rubidium, and cesium, respectively, are attributed to covalent dimers similar to those found in alkali metal vapors. The peak positions for potassium and cesium correlate well with the intense transitions ‘ 2 , + ‘Z, for the gaseous dimers. The centers of these transitions in the gas phase lie a t 860 and 940 mp, respectively.16 No data for this transition for the Rbz system are given by Hcrzberg. The absorbance of the dimer is more important relative to the infrared absorbance a t high concentrations, consistent with its assignment to a dimeric species. Int’eraction of the dimer with the solvent would be essentially through van der Waals forces so that the wave length of the dimer absorption would not be expected to undergo a large shift from the gas phase value. Thermodynamic arguments presented later show that the dimer is reasonable for potassium, rubidium, and cesium, but t.hat it,s concentration, cven in saturated lithium arid sodium solutions, should be very small, in agreement with the absence of absorption attributable to the dimer for these metals.
:.
T h e Species Absorbing at 650-750 mp. The most novel and puzzling feature of metal-amine solutions is the absorption peak shown by solutions of lithium, sodium, and potassium at 660 mp in the ethylenediamine system. This peak appears only when lithium, sodium, or potassium ions are present, although the nature of t,he absorption is independent of the metal. The studies of spectra show that this species can be converted only slowly into the others, requiring several minutes in the case of lithium solutions. This observation would seem to require the presence of one or more covalent bonds which are broken in the conversion. If the 660-mp absorption were due to a “monomer” unit of the Becker- Lindquist-Alder type,6 with an electron in an expanded orbital about the solvated ion, the exchange of the electron, according to MJM+tewould be expected to be rapid.” Indeed, we would expect even the exchange of solvent molecules in the primary solvation layer to be very fast. Thcse observations force us to conclude that a t least two alkali metal ions arc covalently bonded to one another by a t least one electron. This cannot be the normal covalent dimer since the peak position is independent of metal in contrast to the intermediate peaks which we have attributed to the normal dimer. We conclude, therefore, that the one-electron bonded molecule-ion, &I2+, is associated with the 660-mp species. This conclusion is further strengthened by the fact that for lithium and sodium, a t least, the bond strengths of the molecule-ions, Liz+, Na2+, and Kz+ in the gas phase are apparently greater than those of the by about 35%. Qualimolecules, Liz, Na2, and Kz18,19, tatively then, it is logical that the ion M2+ forms in solution since the bond strength is larger than for Mz, and the resulting ion and electron can gain solvation energy sufficient to overcome the ionization energy. I t is necessary to describe next the nature of the absorption associated with the molecule-ion. While t,he Mz+ “core” is required to explain the slow conversion ~~
(IS) G. Heraberg. “Spectra of Diatomic ~Wolecules,”D. Van S o s trand Co., Inc., X r w York, N. Y.,1950. (17) Prof. J. Jortner, of the Hebrew University, Jerusalem, Israel, indicated in a rwent personal cornrnunic:ation that this electron transfer could inderd be slow because of the requirements of the Pranck-Condon principle. In order for the electron to transfer to a cavity in the solvent, the transition ststc would have to be made nearly symmetrical by tht:rmal motion and this could be a slow process. (18) R. F. Barrow, N. Travis, and C . V. Wright. N d u r e . 187, 141 (1960); E. W. Robertson and It. F. Barrow. Pror. Chem. Soc., 329 (1961). (19) J. James, J . Chem. Phys., 3, I, (1935); J. Faulkncr, ibid., 27, 369 (1957).
Volume 68, Number 1 January, 1964
138
JAMES L. DYEAND ROBERT R. DEWALD
__I
of the peak to the infrared absorption, the shape and position of the 660-mp peak are both independent of the metal. This leads us to propose that the absorbing electron is trapped by the solvated M2+ion in perhaps the same way as the electron is presumed to be trapped in a monomer unit of the Becker-Lindquist-Alder theory. Since the resultant electron density would be largely outside of the primary solvation layer, the nature of the cation in M2+would have little effect upon the electronic energy levels. The transition occurs a t 660 mp, while the corresponding transition for the solvated electron occurs a t 1280 mp. Therefore, the depth of the potential well for the electron about the cation is probably considerably greater than for the solvated electron. One must explain then why the electrostatic potential around a simple solvated cation does not trap an electron to yield an absorption peak in the visible region. Certainly, if Mz+ can trap an electron with about 21 kcal. of extra stabilization energy, we would expect the simple ion M + to be able to do so as well. A plausible explanation for this difference in behavior of Mz+ and M + may be found by considering the secondary solvation energy. An electron in an orbital about the solvated ion would screen the positive charge: so that, niuch of the secondary solvation energy of the ion would be lost. For the simple alkali ions in ammonia, this secondary solvation energy varies from 40.0 to 31.5 kcal. mole-’ for Li+ and Cs+, respectively.20 Unless the excess electronic energy for the electron trapped by the ion is of this magnitude, the “monomer” would not be expected to form. An estimate of the secondary solvation energy of the alkali metal ions and molecule-ions may be made using the Born equation as was done by Coulter for metal-ammonia solutions.20 The solvated ions are not spherically symmetric, but measurements on models yield an average van der Waals radius of about 1.8 8. for ethylenediamine, which gives secondary solvation energies varying from 29 kcal. mole-’ for Cs+ to 36 kcal. mole-’ for Li+. Similar measurements on a, model of Lit+, using an internuclear distance of 2.9 yield a secondary solvation energy of about 27 kcal. mole-’. We are unable to calculate the increase in binding energy of the electron in going from the solvated state to the positive ion ‘6trap,”b ~ the t separations of the ground and excited states for the two species differ by about 21 kcal. mole-I. Thus, it seems possible that the electron could be trapped by the large M2+ ion but not by bt simple M+ ion because of the lower secondary solvation energy of the former. The bonding electron in the molecule-ion an “trapped” electron wouId be expected to result in a triplet ground state. However, the ‘visible absorption
in amines has been attributed to a diamagnetic species5 based upon the absence of an e.s.r. signal for systems which have only the visible peak. Thus, Fowles, McGregor, and Syrnonsz1 reported that sodium in ethylenediamine shows no e.s.r. absorption, Windwer and Sundheims report that it gives a “detectable” signal of 0.75-gauss line width. Recently, V O S , using ~~ a Varian spectrometer with 100-kc. modulation, observed a relatively strong signal from sodium in ethylenediamine. Estimates of the number of free spins by comparison with DPPH indicated that virtually all of the electrons could have been contributing to the signal. It should be realized, however, that estimating the absolute number of free spins is difficult and can easily be in error by a t least an order of magnitude. It is, therefore, not possible to state unequivocally a t this time whether the 660-mp species is paramagnetic or diamagnetic. Quantitative susceptibility studies are urgently needed to answer this question. In summary, we propose that the species absorbing a t 660 mp consists of a solvated molecule-ion, Mz+, which has trapped an electron outside of its primary solvation sheath. We propose to represent this species by Mz+.e- and to call it the “ionic-covalent dimer.”
Equilibria and Conversion Rates The ionic-covalent dimer is probably in rapid equilibrium with the molecule-ion and the solvated electron according Lo fast
M2+.e- J_ M2+
+ e-
(1)
This equilibrium is presumed to lie far to the left. The molecule-ion can also undergo the slow cmversion slow
Ma+
2M+
+ e-
(2)
If the decomposition reaction involves mainly the Bolvated electron and the solvent according to e-
+ SH +S- + 0.5&
(3)
in which SK represents the solvent, then reaction 3 could proceed rapidly enough to reduce the electron concentration to such a low value that on y the 660-rnjl absorption would be appreciable. Reaction 2 could be slow enough to prevent the rapid disappearance of the 660-mp absorption. If this is the case, then the discrepancies among the spectral results of different investigators can be accounted for. L. V . Coulter, J. Phue. Chem., 57, 553 (1953). (21) G. 15’. A. Fowles, W. R. MeGregor, and M C. R. &mons, J. Chcm ~ O O C .3399 , (1957). (22) I(. D. VOS,Ph.D. Thesis, Michigan State University, 1962. (20)
MODELFOR A
M
~SOLUTIONS ~ ~
~
A
The reactions proposed also indicate that a “buffereffect” should operate when a solution contains solvated electrons and ionic-covalent dimers. As long as an appreciable concentration of solvated electrons exists in the solution, reaction 1 would be suppressed and the 660-mp absorption should not change much. When the concentration of e- drops to a low value, the 660mp absorption is no longer “buffered” and can decrease morc rapidly. Such an effect could be responsible for the decay rates observed with a solution of lithium in etlhylenediamine, as shown in Fig. 1. After correcting
‘2500
650A A
TOTAL ABSORBANCE
650 inp ABSORBANCE (corrected 1
1 .o
‘G
d
x
j $ 0.1
-
t,
----
‘+\ ‘i,b
w
I
1
I
I
~
~
~
139
~
Thermodynamic Considerations Because of the magnitude of solvation energy effects, it is impossible to make calculations of the concentrations of the various species based upon the properties of the alkali metals alone. I t can be demonstrated, however, that the species proposed are plausible on thermodynamic grounds. In addition, calculations can be made which give the trends to be expected as one moves from one metal to another. The general procedure is to assume the presence of the type of species being considered and to estimate its concentration in the saturated solution of one of the alkali metals from experimental data (spectra, solubilities, and conductances). The concentration of the same type of species is then calculated for all of the other alkali metals and compared with experiment. Solvated Electron Concentration. While the species absorbing a t 660 mp presumably contributes to the conductivity, as evidenced by the conductance of sodium solutions, its contribution is much lower than that due to solvated electrons. Therefore, in calculating the concentration of solvated electrons, the contribution of the 660-mp species to conductance was ignored. Cesium shows only the 1280-mp absorption in dilute solutions, and the equivalent conductance obeys the Shedlovsky equation. The value of the limiting Walden product, Am, obtained by extrapolation, agrees reasonably well with that for metal-ammonia solutions. For these reasons, we used cesium as a “standard” in calculating the conductance and total solvated electron concentration in the saturated solutions of the other metals. A saturated solution of Cs in ethylenediamine a t 25’ (C = 0.0543 M ) has an equivalent conductance of 26.2 kohlrausch units. Using D = 12.9, T~ = 0.0154 poise, A. = 204, and d = 6.0 A., we obtain the equations 204
A, = - . _ _ 1 3.874E
+
for the “tail” of the infrared absorption, it can be seen that the 660-mp absorbance did not change significantly with time until the solvated electron concentration dropped to a low value. It is also presumed that the conversion of the covalent dimers in potassium, rubidium, and cesium solutions to the other species is slow as indicated by the decay of the spectra. Of course, the conversions observed were probably heterogeneous in nature so that the true conversion rate is slower than that observed. In addition, the conversions should be more rapid for the heavier alkali metals.
Ci
=
(4)
A
c,
Ai
K
=
(Cif,)z
(7)
for the equilibrium Cs(s)
Cs+(en)
+ e-(en)
For the saturated solution of Cs, this gives: Ci A G O = +6.9 kcal. mole-’. 0.0096 M , K = 9 X
=
Volume 68, Number 1 January, 1964
140
Jams L. DYEA N D ROBERT R. DEWALD
To calculate the concentration of solvated electrons in the saturated solutions of the other alkali metals, the difference between the standard free energies of formation of the particular alkali metal ion and cesium ion in liquid ammonia, obtained from Jolly's tabulation,2awas assumed to be the same in ethylenediamine. Jolly gives A G O values of -54, -43.6, -47.0, -47.5, and -48 kcal. mole-I for Li+, Na+, K+, Rb+, and Cs+, respectively. Using A G O = +6.9 kual. mole-' for the standard free energy of formation of Csf and e- in ethylenediamine gives values of +0.9, +11.3, +7.9, and +7.4 for the standard free energies of formation of Li+, Na+, K+, and Rb+, plus the solvated electron, respectively. From these values and eq. 4, 5, and 7, the specific conductances of the saturated solutions can be calculated and compared with experiment. The apparent dissociation constants of the ion-pairs in K, Rb, and Cs solutions are nearly the same (-1.5 X according to the Shedlovsky treatment of conductance data.2 We can write, therefore, that
in which C' is the total concentration of solvated electrons and Ci is the concentration of dissociated electrons. This equation may be solved for C' using eq. 5 and 7 and the standard free energies given above and compared with the total electron concentration estimated from spectra and solubilities. The results of these calculations are given in Table I. In view of
Table I : Calculated and Observed Specific Conductances a n d Electron Concentrations in Saturated Solutions of the Alkali Metals i n Ethylenediamine
Metal
Li Na
K Rb CS
--Specific Calcd.
conductance-Obsd.
Very highb 1.7 X 4 . 5 x 10-4 7 . 8 x 10-4 Standard
1 . 5 X 10-2 6 X lo-' 3 . 0 x 10-4 3 . 2 x 10-4 1 . 4 X 10-3
Total solvated electron r-----molarity---Calcd. Estimateda
>Ib l X lou4 1 x 10-2 3 x 10-2 7 X 10-2
0.1
