J . Phys. Chem. 1987, 91, 1360-1365
1360
aldehydez0(1.471 (10) A). The carbon-carbon bond distances in the phenyl ring have the same value as in other similar molecules. Table I11 compares the molecular structure obtained for benzil in the gas and solid phase. Also included are the results determined for 4,4’-dinitroben~il.’~The agreement between the different investigations is very good. The old X-ray6 and our ED investigation give almost identical results for benzil, and both structure and conformation therefore seem to depend very little on what phase the molecules are in. In the gas phase the molecules are a little closer to the planar anti form, and if any effect was to be (20) Brunvoll, J.; Kolonits, M.; Bohn; R. K.; Hargittai, I. J . Mol. Struct. 1985, 131, 177.
expected, it would be the opposite. But the difference is small. Acknowledgment. We are grateful to cand.rea1. Arne Almenningen and sivhg. Ragnhild Seip for help with the electron diffraction experiment and to Ms. Snefrid Gundersen for technical assistance. Financial support from the Norwegian Marshall Fund and from the Norwegian Research Council for Science and the Humanities is acknowledged. Registry No. Benzil, 134-8 1-6.
Supplementary Material Available: Tables listing correlation matrix for the refined parameters, total scattered intensity, sL‘I,(s), for each plate, and average molecular intensity after background subtraction (6 pages). Ordering information is given on any current masthead page.
Effect of Added Salt on the Optlcal Absorption Spectra of Solvated Electrons in Liquid Ammonia Sidney Golden,+Thomas R. Tuttle, Jr.,* and Salia M. Lwenje Department of Chemistry, Brandeis University, Waltham, Massachusetts 02254 (Received: September 25, 1986)
Optical absorption spectra of solvated electrons in ammonia solutions of sodium iodide at three different temperatures and at three different salt concentrations all exhibited essentially the same identical shape as that observed in pure ammonia. At each salt concentration, the spectra shifted to longer wavelengths as temperature was increased. At each temperature, the spectra shifted to shorter wavelengths as salt concentration was increased. The salt-effected shifts are shown to arise from the interaction of solvated electrons with the added ionic components, principally through ion pairing with sodium cations. Intrinsic shifts of the optical absorption spectra of the pertinent solvated-electronspecies are shown to be related to the changes produced in their standard free energies by the added salt. Theoretical estimates of the intrinsic shifts compare quite well with those obtained from the analysis of the experimental data.
Introduction To date, several publications have dealt with the changes that occur in the optical absorption spectra of solvated electrons in ammonia when salts are added to their solutions. The results published so far, however, do not enable a full assessment to be made of the effects of the added salts. For example, the solvated electron spectra in ammonia have been reported to be blue-shifted slightly when sodium iodide is added to the solutions.l,2 A similar effect has been indicated for dilute alkali metal solutions in amm ~ n i a and ~ - ~in perdeuterioammonia.6 Nevertheless, the optical absorption spectra of the blue solutions which were generated electrolytically in solutions of alkali, alkaline earth, and quaternary ammonium iodides in ammonia have been described as unaffected by changes in the salt concentration.’ In addition, it has been ~ l a i m e dthat ~ , ~a new absorption shoulder at 12 500 cm-I appears in the optical spectra of dilute sodium-ammonia solutions to which sodium iodide has been added. This result has not been confirmed by other^,'-^,^,' however. It is evident that a precise determination of the salt-effected changes which are produced in the optical absorption spectra of solvated electrons in ammonia, as well as their characterization in molecular and structural terms, remains yet to be obtained. This is the motivation for the present investigation. Accordingly, we have determined the optical absorption spectra of increasingly dilute solutions of metallic sodium in liquid ammonia which contained four different fixed concentrations of sodium iodide at three different fixed temperatures. The solvated electron spectra corresponding to each of these fixed conditions were obtained by extrapolating the relevant spectra to infinite Emeritus Professor of Chemistry
dilution in metal. The experimental procedures and results are described briefly in the Experimental Results section. Within experimental precision, the effect of increasing concentrations of sodium iodide is to produce a slight, monotonically increasing blue shift of the solvated-electron spectrum without any significant change in its shape. In the Theoretical Results section, the theory used in analyzing the shift data quantitatively and the results of its application are presented. They lead to the conclusion that the shifts are primarily due to the ion pair of the (solvated) solvent-anion complex8 comprising the solvated electron with the (solvated) sodium cation. A discussion of the results is given in the Discussion section.
Experimental Results Essentially the same procedures as those described in earlier investigations carried out in this laboratory1,2~1s’2 were employed (1) Rubinstein, G. Ph.D. Dissertation, Brandeis University, 1973. (2) Rubinstein, G.; Tuttle, T. R., Jr.; Golden, S. J . Phys. Chem. 1973, 77,
282. (3) Gold, M.; Jolly, W. L. Inorg. Chem. 1962, I , 818. (4) Clark, H. C.; Horsfield, A.; Symons, M. C. R. J . Chem. SOC.1959, 2478. (5) Catterall, R.; Symons, M. C. R. J . Chem. SOC.1964, 4342. (6) Burrow, D. F.; Lagowski, J. J. In Soluared Electron, Gould, R. F., Ed.; American Chemical Society: Washington, DC, 1965; Advances in Chemistry Series No. 50, p 125. (7) Quinn, R. K.; Lagowski, J. J. J . Phys. Chem. 1968, 72, 1374. 1969, 73, 2326. (8) Golden, S.; Tuttle, T. R., Jr. J . Chem. Soc., Faraday Trans. 2 1982, 78, 1581. (9) Hurley, I. Ph.D. Dissertation, Brandeis University, 1970.
0 1987 American Chemical Society 0022-3654/87/2091-1360$01.50/0
The Journal of Physical Chemistry, Vol. 91, No. 6, 1987
Solvated Electrons in Liquid Ammonia
1361
TABLE I: Parameters of Solvated Electron Optical Absorption Spectra
T, K 243
[NaI] X M
u,,
cm-'
Y+,
cm-'
u-,
cm-'
A v , , ~cm-' ,
0 4.8 25 48
6366.3 6387.3 6437.1 6475.2
8292.9 8334.9 8389.4 8393.0
4972.2 4999.8 5019.0 5074.2
3321.7 3335.1 3370.4 3318.8
223
0 5.0 26 50
6754.1 6821.2 6846.3 6852.8
8656.1 8720.9 8751.0 8794.3
5383.3 5400.4 5440.6 5511.9
3272.8 3320.5 3310.5 3282.4
203
0 5.2 27 52
7163.3 7207.4 7183.2 7255.9
9031.6 9093.9 9131.8 9175.8
5828.8 5847.9 5893.0 5911.4
3202.8 3246.0 3238.7 3264.3
1.0
.I
vlcm-lxl03l
I
Figure 2. Optical absorption spectra of solvated electrons in liquid ammonia containing 0.005 M NaI at -30 (O),-50 (0), and -70 "C (b). Relative absorbance, F(v),is plotted vs. the frequency of the incident
radiation, Y.
9-
.e .6 PIV)
9
-
.8
5.
6-
d
PIVI
5'
3
4.
.2
.:L 3'
1
0
-
7 .
2
d
6
8
10
I2
ld
I6
IS
20
22
26
0
vlcm-~xlo'l
Figure 1. Optical absorption spectra of solvated electrons in pure liquid ammonia at -30 ( O ) , -50 (0), and -70 OC (D). Relative absorbance, F(v),is plotted vs. the frequency of the incident radiation, u.
in preparing needed samples and in adjusting and controlling temperatures. Each sample was prepared, using high-vacuum techniques, in apparatus constructed entirely of quartz except for a Pyrex access valve (Fisher-Porter 795- 120-0004) and the graded seal used to attach it to the body of the apparatus. Absorbance measurements were made with a Cary 14R spectrophotometer operating in its infrared mode. Full details of the experimental procedures used can be found in ref 13. The optical absorption spectra of dilute solutions (- 1 X to 5 X lo4 M) of sodium in ammonia were determined in the wavelength range 425-21 50 nm. The solutions were at each of the temperatures 203,223, or 243 K; they contained added sodium iodide at each of the concentrations (measured at 223 K): none, 0.005, 0.026, or 0.05 M. Each spectrum consisted of a single, broad, featureless, asymmetric band with a long high-frequency tail, in accordance with the results of earlier observation^.'-^^^^^^"* Tabulated absorbances A ( v ) for the solutions are given in ref 13. The behavior discernable for v, the frequency of maximum absorbance, and A v l j z , the half-height absorbance width, is in agreement with that reported previously.'q2 The solvated-electron spectra were obtained by determining the spectra corresponding to the solutions which were infinitely dilute in metallic sodium. In order to deal with the spectral influence of the solvated sodium anionic species, especially at the lowest temperatures, use was made of the redox model of metalammonia solution^.'^ With the assumption that the frequency-integrated absorption was proportional to the number of electrons responsible (10) Stupak, C. Ph.D. Dissertation, Brandeis University, 1984. (11) Hurley, I.; Tuttle, T. R., Jr.; Golden, S . In Metal-Ammonia Solurions, Lagowski, J. J., Sienko, M. J., Eds.; Butterworths: London, 1970; p
503. (12) Stupak, C. M.; Tuttle, T. R., Jr.; Golden, S . J . Phys. Chem. 1984, 88, 3804. ( 1 3) Lwenje, S . Ph.D. Dissertation, Brandeis University, 1985. (14) Golden, S.; Guttman, C.; Tuttle, T. R., Jr. J . Chem. Phys. 1966, 44, 3791.
2 vlca-lx103 1
Figure 3. Optical absorption spectra of solvated electrons in liquid ammonia c6ntaining 0.026 M NaI at -30 (0),-50 (0), and -70 OC (b). Relative absorbance, F ( v ) , is plotted vs. the frequency of the incident
radiation, Y.
1
Figure 4. Optical absorption spectra of solvated electrons in liquid ammonia containing 0.05 M NaI at -30 (O), -50 ( 0 ) , and -70 O C (b). Relative absorbance, F ( u ) , is plotted vs. the frequency of the incident
radiation, Y. for the absorption (Thomas-Reiche-Kuhn sum rule), the extrapolation involved plotting area-normalized spectra vs. the degree of spin pairing of the solvated electrons determined from the redox model. Parameters for the extrapolated bands are given in Table I. (Y+ refers to the higher frequency at half the maximum absorption, v- to the lower frequency at half the maximum absorption, and A v l l z to their difference.) The effect on the extrapolated spectra of just increasing the temperature is shown in Figures 1-4. They indicate a spectral shift to longer wavelengths with no essential change of shape. The latter feature was established quantitatively, as follows. Each infinitely dilute spectrum at a given salt concentration was
1362 The Journal of Physical Chemistry, Vol. 91, No. 6, 1987 TABLE 11: Temperature-Induced Spectral Shiftso [NaIIb X T, K IO-', M Av, cm-I rmsd 243 0 -805 0.0094 223 0 -420 0.0061 243 223
5.0 5.0
Golden et al. ID.
9-
f
E.
0.990 0.990
-816 -415
0.0101 0.0069
0.987 0.993
-798 -406
0.0199 0.0140
0.988 0.999
7
QlVl
654.
243 223
26 26
3.
2i
243 223
50 50
-814 -41 1
0.0133 0.0104
1.006 0.999
I.
04
6
5
4
"Reference spectrum at 203 K. bSalt concentration nominal. See Table 111.
8
7
v
(
~
-I
~
~
1
9
~
o
10
~
Figure 6. Optical absorption spectra of solvated electrons at -50 O C in liquid ammonia containing NaI: 0 (0),0.0050 (a), 0.026 (D), and 0.050 M (0). Relative absorbance, F(u), is plotted vs. the frequency of the incident radiation, U.
4
5
6
7
8
3.
Y ( 0m-1x1~3 I
2-
Figure 5. Optical absorption spectra of solvated electrons at -30 OC in liquid ammonia containing NaI: 0 ( O ) , 0.0048 (a), 0.025 (D), and 0.048 M ( 0 ) . Relative absorbance, F(v),is plotted vs. the frequency of the incident radiation, u.
normalized to unit height at its maximum, yielding the normalized spectrum The normalized spectrum at the lowest temperature, 203 K, was chosen as a reference spectrum, P ( v ) . Another of the spectra, F(u),was expressed in terms of the reference frequencies as F(vi - Av), where Av is a constant frequency shift of the spectrum. This shift was determined by minimizing the quantity
I.
04
i= 1
8
J
10
9
TABLE III: Salt-Induced Spectral Shifts" [NaI] X lo-', M 4.8 25 48
Au, cm-' 26 66 110
rmsd 0.0037 0.0071 0.0029
0.994 0.990 1.003
223
5.0 26 50
46 76 122
0.0038 0.0065 0.0054
1.000 1.000 0.999
203
5.2 27 52
31 67 113
0.0085 0.0121 0.0080
0.996 0.989 0.989
T,K
(2)
where N is the number of spectral points used to match the two spectra. Values of N ranged between about 45 and 70. Here, f is an adjustable factor which relaxes the rigid requirement that the maximum normalized absorbance of the shifted spectrum be unity, and thereby frees points in the neighborhood of the maximum absorbance to participate properly in the least-squares fitting process. From Table 11, we note thatfis extremely close to unity in all cases and rmsd is at most 2.0%, and usually far less, confirming the existence of a temperature-independent spectral shape for each salt solution. The effect on the extrapolated spectra of just increasing the concentration of added sodium iodide is shown in Figures 5-7. They indicate that small shifts of the spectra to shorter wavelengths occur with no essential change in shape. The foregoing procedure was also used to establish the quantitative salt independence of the extrapolated spectra at each temperature. With the salt-free spectrum at each temperature as the reference, the results of Table 111 were obtained. Again we note that f is extremely close to unity in all cases and that rmsd is at most 1.2%, and usually far less, confirming that the shifts occur with essentially no change in spectral shape. Because the salt-induced spectral shifts were not large in relation to the judged a priori uncertainty of 1 1 0 cm-I, various determinations of these shifts were made using different portions of
7
Figure 7. Optical absorption spectra of solvated electrons at -70 OC in liquid ammonia containing NaI: 0 ( O ) , 0.0052 (4), 0.027 (D), and 0.052 M ( 0 ) . Relative absorbance, F(u), is plotted vs. the frequency of the incident radiation, u. The deviant points near 5000 cm-l are probably unreliable on account of solvent absorption in that region.
243
- Av))*]'/~
6
V I c1-1x1~3
N
rmsd = [ ( I / N ) k : ( F o ( v i-)F ( v i
5
" Reference
f
system salt-free.
TABLE I V Variously Determined Salt-Induced Spectral Shifts [NaI] X T,K M Au," cm-' Au,b cm-' A U ,cm-' ~ A u , cm-I ~ 243 4.8 26 42 28 46 25 66 97 47 101 48 110 100 102 103 223
5.0 26 50
46 76 122
65 95 138
17 57 129
47 85 125
203
5.2 27 52
31 67 113
62 100 143
19 64 83
31 83 104
"From Table 111. *From u+ of Table I. 'From dFrom restricted spectral range fit. See text.
u-
of Table I.
The Journal of Physical Chemistry, Vol. 91, No. 6,1987 1363
Solvated Electrons in Liquid Ammonia
TABLE V. Bjerrum Ion-Pair Equilibrium Properties
T,K
--
Keb X 10-3, M 3.76 3.76 3.76
0.7106 0.4852 0.4002
0.448 0.326 0.293
Y+2
100
243
80
223
5.0 26 50
4.15 4.15 4.15
0.7196 0.4956 0.4091
0.449 0.327 0.293
203
5.2 27 52
4.54 4.54 4.54
0.7270 0.5044 0.4166
0.451 0.328 0.293
I
-5
[NaB]' X 10-3, M 4.8 25 48
60
4
40
"Concentration equal to that of NaI in solution. bAn interionic size parameter of 5.5 8, was used. 20
0.02 0.03 0.04 0.05 Ma11 Figure 8. Shifts in wave numbers of solvated electron optical absorption -70 "C. bands vs. molar salt concentrations: ( 0 )-30, (+) -50, and (0) The solid line was obtained by using eq 14 at -50 " C to determine shifts. 0
0.01
r
the spectrum. Several of these, summarized in Table IV, reflect the range of possible variability of the shift values. We judge the most reliable values to be those in the final column; they were determined from the best fit of the extrapolated spectra in the range of 0.4-0.6 relative absorbance, where the uncertainties in shift determination are apt to be the smallest. These shifts are plotted against the salt concentration of their solutions in Figure 8.
Theoretical Results Except for the salt-free ammonia solutions, the extrapolated spectra which have been obtained cannot be due only to uncombined solvated e l e c t r o n ~ . ' * ~Depending ,'~ upon the sodium iodide concentration, ion pairs of this species with sodium cations also must be present. To verify this, we will suppose that our solutions are infinitely dilute in metal and sufficiently dilute in salt so that only ions and ion pairs are present as solutes. We then need deal only with the equilibrium Na+.A-
+ Na+ + A-
Values of KB, aB,and y*, determined from Bjerrum's theory,Is are shown in Table V. [We note here that a triple-ion content of less than 5% is e~timated'~,''for the most concentrated salt solution used here.] The K Dat 243 K compares favorably with a reported value for Ks at 240 K obtained from electrical conductivity measurements on sodium-ammonia solutions.I8 [Smaller values measured at lower temperatures possibly resulted because other reactions of the solvated electrons than ion-pairing were not taken into account.] The extrapolated spectra of the salt solutions evidently must be superpositions of those due to S-and Na+.S-. P r e v i ~ u s l y , ' ~ ~ ~ ' ~ the spectra from these two species were assumed to be indistinguishable. However, later workI0,l2has shown that small relative displacements of two absorption bands have a negligible effect on the resultant band shape. Hence, we can suppose that the individual normalized band shapes, which we designate as F,(v) and Fip(v),respectively, are, at most, slightly displaced versions of the same band shape. N o direct resolution of the composite spectrum to establish this seems likely, however. In the foregoing terms, together with Beer's law, a typical normalized extrapolated spectrum must be expressible as
From this, the corresponding mean frequency of absorption is
(3)
where all species are ammoniated and A- stands for the solvent-anion complex,* s-,corresponding to the solvated electron or a hypothetical "Bjerrum anion", B-, that enables eq 3 to be accurately described by Bjerrum's ion-association theory.15 From eq 3, we have
(4) where -y* is the mean activity coefficient for the ionic species. The mole fraction of uncombined anions A- is aA
[A-I [Na+.A-] [A-]
+
-
KA/-Y*2 [Na']
+ KA/y+2
(5)
(KS/KB)
(1
-a
~ ) / +a K~s / K B
which we write as AV = asAvo
With some slight loss of generality, we next assume that y+ is the same for S- and B-. Then, we can obtain
as =
where, because of spectral shape stability, Jomdv Fk(v)is an invariant independent of k. Upon subtracting (v)", the mean absorption frequency of the solvated electron in the pertinent salt-free solution, we get
(6)
For finite (Ks/KB), as will equal unity if and only if aBis unity; this will be the case only when the solutions are infinitely dilute in all ionic constituents. (15) See, for example, Robinson, R. A,; Stokes, R. H . Electrolyte Solutions; Butterworths: London, 1959; p 392.
+ (1 - CXS)AV~,
(10)
This expression relates the observed shifts to intrinsic shifts of the uncombined solvated electron and its ion pair, and their relative amounts. A testing of eq 10 is hampered by two main limitations: (1) we do not know the value of the intrinsic shifts Avo and Aqp and how they are affected by changing salt concentrations; (2) we (16) Fuoss, R. M.; Kraus, C. A. J. Am. Chem. SOC. 1933, 55, 2385. (1 7) Fuoss, R. M.; Accascina, F. Electrolytic Conduction; Interscience: New York, 1959; p 249. (18) Dewald, R. R.; Roberts, J. M. J . Phys. Chem. 1968, 72, 4224.
1364 The Journal of Physical Chemistry, Vol. 91, No. 6,1987
Golden et al.
Yo
120 1.313
(K, /KB)
100
-
Avo. -12.78 cm-'
Yo,
Avl,= 222.67~1~1-I
00
*l/2
= 7.86 cm-'
/
J
s
4 40
20
0
0.1
0.2
0.3
0.4
0.5
0.6
Figure 9. Best least-squares fit to eq 14. Salt-induced shifts, Au, are plotted vs. [ l + (KB/Ks)(ae/(l - aB))]-'. The solid line is the best fit: ( 0 )-30, (+) -50, and (0)-70 O C .
really do not know as and how it depends on salt concentration, although we presumably do know aBand its dependence on salt concentration. To make such a test, therefore, we introduce three simp!ifying assumptions: ( 1 ) because of a relatively strong local interaction presumed to exist between a solvated electron and a sodium cation in an ion pair, we will suppose that IAvol
