LASERPHOTOLYSIS OF ALKALIMETAL-AMINE SOLUTIONS I n water, the concentration dependence of r zis of prime importance and the vacancy volume is of lesser importance. Two reasons for this appear to be operative : (1) there apparently is greater dielectric shielding of a first coordination shell solvent molecule in water, i.e., the quantitya1 01 = pEl,,/kT is smaller so that first coordination shell vacancy considerations are less important, and (2) ammonia behaves more like a simple fcc quasilattice liquid than does water. One manifestation of this latter effect is the multiplicity of the phases of ice that occur at relatively low pressuresl2 with the result that a simple quasilattice model does not apply to water. A somewhat surprising effect is contained in the decrease of AER and ASR for deuterons in CsI and MgCIZ solutions (Table 111). A kind of compensation e$ect is present; asAER decreases TASR decreases almost proportionately. However, (d In Tl/dM)o is negative for MgClt solutions and positive for CsI solutions. Both salts appear to disrupt strongly the hydrogen bonding in water a8 evidenced by the decrease in both AER and ASR. Similar ideas to explain the negative hydration effect of ions like Cs+ and I- have been put forth by
3285
Samoilov,zzbut he considers only a variation in AE and not A S which also appears to occur. Salts which give rise to negative B coefficients in water are generally referred to as “structure breakers” and the positive B coefficient salts as “structure By reference to Table IV it may be seen that the B coefficient generally has the opposite sign to Vf, the ionic free volume. In the Davis and L i t o v i t ~ ~ ~ two-state model for water, the ice structure has p v = 0.20 and the close-packed structure has p , = 0.083. Thus salts with positive B coefficients favor the closepacked structure (Vf < 0) and salts with negative B coefficients favor the ice structure (Vf > 0). Hence from this point of view the terminology referred to above should be modified. I n both cases the salts greatly disrupt the hydrogen bond structure of the solvent water as pointed out previously by Frank and Evansz3and others. (21) D.E. O’Reilly, J. Phgs. Chem., 74, 3277 (1970). (22) 0.Ya. Samoilov, “Structure of Aqueous Electrolyte Solutions and the Hydration of Ions,” translated by D. G. Ives, Consultants Bureau Enterprises, Inc., New York, N.Y.,1965. (23) H.S. Frank and M. W. Evans, J. Chem. Phys., 13, 507 (1945).
Laser Photolysis of Alkali Metal-Amine Solutions by D.Huppert and K. H. Bar-Eli Department of Chemistry, TeGAviv University, Tel-Auiu, Ierael
(Received March 6,1870)
Solutions of sodium in propylenediamine (PDA) and ethylenediamine (EDA) were photolyzed by a giant pulse ruby laser. It was found that (a) the 670-mp species (V species) is 70% bleached immediately after the pulse (time resolution 70. The temperature dependence of the recovery kinetics is shown in Figure 8. Plots of log k / 6 us. 1 / T are shown both for the recovery of the V 670-rn~species and the decay of the ir 1000-mp species. The energies of activation obtained are 5.5 and 7.0 kcal/mol, respectively. The EDA data were taken over a smaller temperature range because of the higher melting point of EDA and the slopes are therefore less accurate. l/200
1
eo0
I
I
700
Amp
I BM)
i I
mo
Figure 7. Plot of the reciprocal of measured kinetic constant us. wavelength, in PDA: 0 , points below the isosbestic point; A, points above the isosbestic point; solid curve, original absorption curve normalized to the highest experimental point.
least 70% of the original V species has disappeared. If we assume that there is a one to one ratio between the formed ir species and the bleached V species, as indeed is suggested by the second-order kinetics, we obtain ~ ~ ~ 0 ~ / e 6= 7 0 1/3. Knowing the ratio ODlooo/OD~7~ < The Journal of Physical Chemistry, Vol. '74, No. 17, 19'70
Discussion Of all the species which are considered t o exist in it is obvious solutions of alkali metals in amines,2,a*g~10 that the metal cation (in our case Na+) is not involved in the photolysis, mainly because it is not expected to absorb at all in the visible region. The solvated electron, even if it absorbs in this region, like the solvated (8) S. Nehari and K. H. Bar-Eli, to be published. (9) E. Becker, R. A. Lindquist, B. J. Alder, J. Chem. Phys., 2 5 , 971 (1956). (10) M . Gold, W. L. Jolly, K. S. Piteer, J. Amer. Chem. Soe., 84, 2264 (1962).
LASERPHOTOLYSIS
OF
3289
ALKALIJJETAL-AMINE SOLUTIONS
the values of the second-order rate constants with different amounts of NaI are given, together with the calculated rates. These latter values are calculated on the assumption of a primary salt effect log k
=
log ko
+~QZAZB~G
where
2 60
=
T/?
I
lbgd t g / p o l r t
(1000my
- owvt
ZA and ZB are the charges of the reacting ions and p is the ionic strength; k and ICo are the rate constants in the presence and absence of salt, respectively. A value of M was taken for the dissociation constant of NaI in PDA (a value similar to 7.3 X 10-6 M for the dissociation constant of potassium amide in amrnonial3 was arbitrarily taken) and a value of 12.5 was taken for the dielectric constant of FDA in order to calculate the Debye-Huckel activities. Addition of XaI caused slight enhancement of the rates, although the calculated rates go in the other direction and to a much greater extent. We conclude, therefore, that no primary salt effect is operative, and no reaction between ions occurs. The only species which conforms with these results is the metallic anion, and the reaction scheme is therefore
I
A plot of measured k / e vs. X / q in PDA: 0 , 1000 mp; A, 670 mp.
Figure 9.
electron in mTater,11,12 is not expected to return to its ground state a t such a slow second-order rate. One would expect the relaxation to the ground state to be a fast (>lo9 sec-') first-order mechanism. The other species, ie., the monomer, the metal anion, and the dimer designated as 31, M', and AIz by Arnold and Pattersona or XI+- .S-,&I:-, and AI+. -&I:- by Tuttle2, et al., may all undergo photodecomposition, and relax a t a second-order rate. In order to test which of these possibilities is more plausible, we added large amounts of sodium iodide before the flash. All the kinetics with added sodium iodide were second order. This, therefore, excludes species of the type RI: (or M + . .S-), ie., the monomer or of the type ATz (or M + . .?\!t-),i e . , dimer, from being involved in 'the photolysis, because one would expect a pseudo-firstorder relaxation with excess sodium ions. I n Table I a
Table I k/r,
Exptl, Calcd, Exptl, Calcd,
670 mp 670 r n M 1000 my 1000 my
cm/sec,
k/e, cm/sec,
with no NaI
10-9 I V KaI
0.4
x
lo6
, . .
1.9 X ...
lo5
0.65 0.124 1.7 0.573
X lo6 X IOJ
X lo6 X lo6
N2e3(2). 'Iz 2.3(DRT)1~2(1000)'~z
N-,-L- 11 + e-
(1)
RI + e- -+ AI-
(2)
(second-order rate). I n this scheme, a primary salt effect is not expected, and the enhancement in rate is probably due to secondary effects. This result agrees very well with the work of Matalon, Golden, and Ottolenghi, l 4who attributed the visible band in solution of alkali metals in elhglamine to a negative ion. The ir band, similar to the ir band in ammonia, is attributed to the solvated electron. The difference in activation energies in the visible and ir regions is probably caused by a blue shift of the ir band on cooling, and this increases the extinction coefficient which causes an apparent decrease in the measured rate. (A blue shift on cooling is also observed for the visible band; however, since we measure near the maximum, its effect on the rate mill be much smaller.) We may also treat the results as if they were diffusion controlled, according to an equation first developed by Srnoluchowski.
h/€> om/sec, 10-1 M
NaI
1.O 0.05 2.42 0.233
(11) E. J. Hart and J. W. Boag, J . Amer. Chem. Soc., 84, 4090 (1962).
X 106 X 106
(12) E. J. Hart and J. W. Boag, Nature, 197, 45 (1963). (13) W. R. Halves, J . Amer. Chem. Soc., 55, 4422 (1933).
X lo6 X lo5
(14) S.Matalon, S. Golden, and M. Ottolenghi, J . Phys., Chem. 7 3 , 3098 (1969). (15) M. V. Smoluchowski, Z . Phys. Chem., 92, 129 (1917).
The Journal of Physical Chemistrv, Vol. 7 4 , S o . 17, 2970
NOTES
3290 The final result obtained after introducing the Einstein-Stokes relation between diffusion and viscosity is
+
2RT (RA RB)' 300017 RARB
#I$=-
in l./mol sec, where RA and RB are the radii of the reacting species. A plot of the measured rate us. T/q should give a straight line, and this is indeed the case, as is shown in Figure 9. From the ratio of the slopes of the V and ir bands, one ~ derived ~ ~ above. Also obtains E ~ ~ ~ ~1/3 / as E was from the results a t 1000 mp, one gets EIOOO
=
4.1
x
103(n
+
where n is the ratio RA/RB. A value of n = 1 gives el000 = 1.6 X lo4 l./mol cm in fair agreement with the value obtained for other cases of solvated electrons.16 Since the lines obtained in Figure 9 are fairly straight and their slopes give reasonable values for the extinction coefficients, we may consider it as an argument in favor of a diffusion-controlled mechanism.
When the reacting species are ions, one should multiply the right-hand side of the above equation by the factor" 6 e' - 1 where ZAZBe2 6 = D ~ T ( R A RB)
+
ZA, Zg are the charges of the reacting ions, RA,Ru are their radii, and D is the dielectric constant. Taking D = 12.5 and reasonable assumptions for the radii, the value for the correction term will be just. -6, ie., e2/D(RA R B ) ~ ( ~ / ifT we ) assume the reaction to be eX a + + Xa. This would result in a straight-line plot of k / e us. 1/17. Since our measurements were done over a narrow range of temperature (200-300"1
