1506
J . Phys. Chem. 1988, 92, 1506-1510
reaction with the notable exception of the CI reactions. The C1 reactions at 298 K do not fit the pattern established by the O(3P), H, and OH reactions. The temperature dependence of the C1+ C2H2reaction is also quite different in that the rate constant decreases with an increase in temperaturek2whereas for the O(3P): H,4and OHz2reactions with C2H2the rate constant increases with (22) Michael, J. V.; Nava, D. F.; Borkowski, R. P.; Payne, W. A,; Stief, L. J. J . Chem. Phys. 1980, 73,6108. See also: Perry, R. A.; Atkinson, R.; Pitts, Jr., J. N. J. Chem. Phys. 1977, 67, 5577. Perry, R. A.; Williamson, D. Chem. Phys. Lett. 1982, 93, 337. Atkinson, R.; Aschmann, S. M. Int. J . Chem. Kinet. 1984, 16, 259.
an increase in temperature.
Acknowledgment. This work was supported by the NASA Planetary Atmospheres Program. We thank H. Okabe for providing the sample of diacetylene and F. Nesbitt for performing the modeling calculations. Registry No. 0, 17778-80-2; C1, 22537-15-1; C,H2, 460-12-8. (23) Perry, R. A. Combust. Flame 1984,58,221. See also: Atkinson, R.; Aschmann, S M. Combust. Flame 1984, 58, 217.
Effects of Melectrtc Permmivlty and Vlscosity on Dlffusion-Controlled e,- 4- S Reactions in Alcohol/Water Mixed Solvents Yadollah Maham and Gordon R. Freeman* Department of Chemistry, University of Alberta, Edmonton, Canada T6G 2G2 (Received: May 19, 1987; In Final Form: September 9, 1987)
The rate constants k2 of nearly diffusion controlled reactions of solvated electrons with solute are related to the electrohydrodynamic properties of the solvent: the viscosity q and dielectric permittivity E of the bulk solvent. Data for reactions with neutral (polar and nonpolar) and charged solutes in methanol/water and ethanol/water mixed solvents are analyzed to display the effects of q and E. The data support earlier reports that the diffusion coefficients D(e;) c D(R0-) in alcohols and water, but why this is so remains a question
Introduction
During the study of solvent effects on solvated electron reaction rates with neutral solutes'-9 there has been a persistent lack of agreement with Stokes-Smoluchowski behavior? An attempt was made to introduce the static dielectric permittivity as another correlation parameter,'^^ because charge-dipole and charge-induced-dipole interactions between the electron and the reactant molecule would be screened by polarization of the medium. Although the idea was reasonable, the magnitude of the effect was too great to be explained in a simple manner.3 Reactions with charged scavengers appeared to agree satisfactorily with Bronsted-Debye behavior.' The present work examines previously reported results in a consistent manner, with a view to finding the source of the apparent effect of the static permittivity upon electron reaction rates. Rate constants with neutral and charged scavengers are compared with the limiting ionic conductance of K'RO- in alcohol/water mixed solvent^,^.^^*" where RO- is an alkoxide or hydroxide ion. The mobility of e; in hydroxy solvent^'^-^^ and mixed hydroxy solvents3 appears to be similar to that of the RO- ions, but there is a persistent suspicion that the reported values of mobilities of (1) Barat, F.;Gilles, L.; Hickel, B.; Lesigne, B. J . Phys. Chem. 1973, 77, 1711. (2) Bolton, G. L.; Freeman, G. R. J . Am. Chem. SOC.1976, 98, 6825. (3) Micic, 0. I.; CerEek, B. J . Phys. Chem. 1977, 81, 833; in Table I the first set of data is for ethanol solutions and the second set for methanol solutions. (4) Milosavljevic, B. H.; Micic, 0. I. J . Phys. Chem. 1978, 82, 1359. (5) Afanassiev, A. M.; Okasaki, K.; Freeman, G. R. J. Phys. Chem. 1979, 83, 1244. (6) Idriss-ali, K. M.; Freeman, G. R. Can. J . Chem. 1984, 62, 2217. (7) Maham, Y.; Freeman, G. R. J . Phys. Chem. 1985,89, 4347. (8) Maham, Y.; Freeman, G. R. J . Phys. Chem. 1987, 91, 1561. (9) Senanayake, P. C.; Freeman, G. R. J . Phys. Chem. 1987, 91, 2123. (IO) Tissier, M.; Douheret, G. J . Solution Chem. 1978, 7, 87. ( 1 1) (a) Kay, R. L.; Broadwater, T. L. J . Solution Chem. 1976,5, 57. (b) Spivey, H. 0.;Shedlovsky, T. J . Phys. Chem. 1967, 71, 2165. (12) Schmidt, K. H. Int. J . Radiat. Phys. Chem. 1972, 4 , 439. (13) Fowles, P. Trans. Faraday SOC.1971, 67, 428. (14) Freeman, G. R. In Kinetics of Nonhomogeneous Processes; Freeman, G. R., Ed.; Wiley: New York, 1987; Chapter 2 and references therein.
0022-3654/88/2092-1506$01.50/0
electrons in alcohols and water actually correspond to those of RO-. Diffusion and Conductance The molar conductance A, of ions i is related to their mobility 1.11
A, = z , ~ P ,
(1)
where z, is the number of elementary charges on ion i, 3 = NAE is the Faraday, and NA is Avogadro's constant. The diffusion coefficient D, is related to the mobility and therefore to the molar conductance Dl
= A,k!3T/(ztNAE2)
(2)
where kB is Boltzmann's constant and T i s the temperature. The rate constant k2 of a diffusion-controlled reaction between species i and j is
k2 = 4i?N,(Dl
+ D,)(R, + R,)
(3)
+
where (R, R,) is the reaction radius of the pair. Values of the diffusion coefficients vary with the solvent. For alcohol/water mixed solvents it is assumed that the relative variation of the diffusion coefficients of the solvated electron3 and scavenger are roughly similar to that of the molar conductance of potassium alkoxide/hydroxide at infinite dilution, Ao. Coulombic Interaction between e; and Solute
The Coulombic interaction between the solvated electron and the scavenger molecule affects the value of the rate constant k215
k2 = ~ * N A ( D+ , Dj)(Ri + R,lf where
~
( 15) Debye, P. Trans. Electrochem. SOC.1942,82, 265.
0 1988 American Chemical Society
(4)
e,-
+ S Reactions in Alcohol/Water Mixed Solvents
The Journal of Physical Chemistry, Vol. 92, No. 6, 1988 1507
?E
1
\
\
&
?
2
~
~
,
OO
1
1
1
1
60
40
20
1
,
100
80
mol % H20
+
+
Figure 2. Ratio k2(e; S)/Xo(K+ e;) in methanol/water mixed solvents. Values of k2 at 292 K from ref 4, except CCI, at 294 K from ref 3. X,from Figure 1. 0 , nitrobenzene, A,oxygen; 0,p-benzoquinone; V,hydrogen peroxide; carbon tetrachloride; A,ratio X 0.75 (see text).
+,
- 0
0
50
100
mol O/O H 2 0
Figure 1. Limiting conductance X,of ions in mixed solvents: A, meth, 0, A, e; = anol/water; B, ethanol/water. 0 , K+;'o." 0, C1-*lo.li * , eI-. l2-I4 T = 298 K, except 294 K for RO-. 9
and U(R) is the potential energy between the reactants at distance R = R,+ RY The factor f affects the probability of the reactants attaining the distance R at which reaction occurs. The potential energy between e; and a solute with permanent dipole moment M isI6
where tois the permittivity of vacuum and t is the relative permittivity of the solvent. For a nonpolar solute with polarizability (Y the Coulombic interaction energy isI6 U(R) = - ( ~ [ ~ / ( 2 ( 4 . ~ t o ) ~ e ~ R ~ )
(7)
Equations 4-7 display dependences of k2 on t for reactions of e,- with neutral scavengers. Alcohol/Water Mixed Solvents Alcohol/water mixed solvents have wide ranges of viscosity" and static permittivityls and have special structures on the alcohol-rich and water-rich sides.I9 They are therefore excellent systems for the study of solvent effects on reaction rates. The molar conductances of ions decrease relatively rapidly upon the addition of small amounts of methanol or ethanol to water (Figure 1). The conductances in water are not related to the crystalline ionic radii,20because smaller ions are more strongly solvated and have a greater tendency to drag solvent molecules with them as they migrate. The hydroxide ion has a relatively high mobility because it migrates by protons hopping in the opposite direction.21 In alcohols, however, alkoxide ions have mobilities similar to those of other ions (Figure 1). The minimum in alkoxide mobility at 10 mol % water implies that alkoxide ions can participate in the enhanced hydrogen-bonded solvent structure (16) Entelis, S. G.; Tiger, R. P. Reaction Kinetics in the Liquid Phase; Wiley: New York, 1976; Chapters 1, 2. ( 1 7). Timmermans, J. Physio-Chemical Constants of Binary Mixtures; Interscience: New York, 1960; Vol. 4. (1 8) Adhadov, Y . Y. Dielectric Properties of Binary Solutions; Pergamon: Oxford, 1981. (19) (a) Hydrogen Bonded Soluent Systems; Covington, A. K., Jones, P., Eds.; Taylor and Francis: London, 1968. (b) Franks, F.; Ives, D. J. G. Q. Rev., Chem. Soc. 1966, 20, 1. (20) Alfenaar, M.; De Ligny, C. L. R e d . Trau. Chim. Pays-Bas 1961, 86, 929. (21) Erdey-Gruz, T. Transport Phenomena in Aqueous Solutions; Wiley: New York, 1974; Chapter 4.
00
20
40
60
80
100
mol O/O H20 Figure 3. As Figure 2, for ethanol/water. 0 , nitrobenzene; A, oxygen; 0, iodine; V, hydrogen peroxide; carbon tetrachloride. The nitrobenzene rate constants are 298 K from ref 1; other data from references in Figure 2. 0 , A, +, ratio X 0.65 (see text).
+,
that occurs at this alcohol/water composition.22 k,(e; + S)/X,(K+ + e;) Reported values of diffusion coefficients of e; are similar to those of RO- in hydroxy solvent^.^^'*^^^ As a zeroth-order approximation we take the diffusion coefficient of the scavenger molecule S to be equal to that of a potassium ion. Equation 3 then rearranges to
The left side of eq 8 is plotted against solvent composition for several scavengers in methanol/water (Figure 2) and ethanol/ water (Figure 3). The ratio for hydrogen peroxide is nearly independent of composition in both solvent systems, whereas the ratio for the other scavengers is higher in pure alcohol than in pure water. Hydrogen peroxide is strongly hydrogen bonded in both alcohols and water, and its diffusion coefficient is apparently similar to that of the potassium ion. Diffusion coefficients of most of these scavengers have not been reported in the three solvents, but that of carbon tetrachloride at 298 K is m2/s) 1.5 in water, 2.2 in methanol, and 1.5 in ethanol.23 The ratio D(K+)/D(CCl,) is therefore 1.3 in water, 0.63 in methanol, and 0.40 in ethanol. Carbon tetrachloride is not hydrogen bonded, and its diffusion coefficient in the alcohols is much larger than that of an ion. (22) Leu, A. D.; Jha, K. N.; Freeman, G. R. Can. J . Chem. 1982,60,2342. (23) Hammond, B. R.; Stokes, R. H. Trans. Faraday Soc. 1955,51, 1641.
1
1
1508 The Journal of Physical Chemistry, Vol. 92, No. 6,1988
The scavengera O2and 1, are also not hydrogen bonded. The D ( K + ) / D ( S )ratios for these scavengers can be approximately normalized to the values in water by using the CCl, data in the preceding paragraph, multiplying the values in pure alcohol by 0.63/1.3 = 0.5 in methanol and 0.40/1.3 = 0.3 in ethanol. Since &,(K+) i= &(e;) in the pure alcohols, the ratio kz(e; S)/Xo(e; K+) was adjusted for the larger D ( S ) of the non-hydrogen0.5)/2 = 0.75 in bonded scavengers by multiplying by (1 methanol and (1 0.3)/2 = 0.65 in ethanol (filled points in Figures 2 and 3). The adjusted curves are similar to those for nitrobenzene and benzoquinone. The latter compounds have polar groups that would be solvated in a manner intermediate between the hydrogen-bonded hydrogen peroxide and the nonpolar carbon tetrachloride, oxygen, and iodine. The high values of kz/Xo for nonpolar scavengers in the alcohol-rich solvents (Figures 2 and 3) reflect the much smaller diffusion coefficients of ions than of nonpolar solutes in these solvents. This composition region corresponds to zones a and b of the four composition zones detected for k2 with solvent viscosity q.7-9 The Walden product of qXo for solvated electrons is apparently much smaller in the alcohol-rich than in the water-rich solvents, as observed for normal ions."
Maham and Freeman
+
+
+
+
Static Permittivity eS
log qk, for electron capture by biphenyl in otherwise pure alcohol solvents increases approximately linearly with Although the graph in ref 24 displays log qp against c;l, the qp values are actually qkz(e; C12Hlo)multiplied by a constant. The product qk, suggests a Stokes correlation between the diffusion coefficients in the pure alcohol solvents and the inverse of the viscosities. This allows eq 4 to be transformed to9
+
i 0
1
2
3
I
4
I
5
1
6
I
7
8
9
1OO/€,
+
Figure 4. Product of the liquid viscosity 7 and k2(e; nitrobenzene) as a function of ';6 in pure alcohol solvents at 298 K. Values of k2 and 7 are from the references indicated: methanol and e t h a n ~ l , ~ I-propanol ~~' and 2-propan01,~~*~' 2-methyl-1-propanol and 2 - b u t a n 0 1 , and ~~~~~ 2-methyl-2-propan01.~~~~ Values of cs from ref 29. Full line calculated from eq 9-1 1; see text.
is greater, so the probability is smaller in primary and secondary alcohols than in tertiary alcohol^.^-^^^^ For this reason the values of qk, in the primary alcohols fall below the calculated curve that passes through the 2-methyl-2-propanol point (Figure 4). The value of qk, in water is about fourfold larger than one would expect from the alcohol curve (Figure 4). This is attributed to the larger diffusion coefficient of e; in water than in methanol and e t h a n ~ l . ' ~ - ' ~ The slope of the In qp against 'e; curve in ref 24 actually biphenyl) plot against corresponds to the slope of a In qk,(e; es-I. The slope is 6 times greater than can be explained with eq 5, 7, and 9, using the mean polarizability of biphenyl ( a = 2.29 X C.m2/V, or i?/4aeo = 20.6 X m3)31and a relatively m. The disagreement would be greater small value of R, 2 X if a larger value of R were used. The reaction of e; with biphenyP2 in methanol is 18-fold farther from the diffusion-controlled limit than is the reaction with nitrobenzene in that solvent,, so the plot in Figure 1 of ref 24 is much more affected by electron trap depth than is that in the present Figure 4. The value of p(e;) in methanol suggested in ref 24 is at least an order of magnitude too small. The variation of qk, with 'e; in methanol/water (Figure 5) and ethanol/water (Figure 6) mixed solvents is different from that in a sequence of pure alcohols (Figure 4). This is necessarily true, because the point for water in Figure 4 is much above the alcohol curve. The negative slopes in Figures 5 and 6 are caused by the decrease of p(e;) upon addition of alcohol to water. The initial positive slope at the water end of most of the curves might reflect change of either p(e;) or f. Plots of qX, against e;l for a number of ions in ethanol/water display a positive slope at the water end (Figure 7), so we attribute most of the positive slope in Figures 5 and 6 to change of electron mobility. Electron diffusion coefficients in these solvents do indeed appear to be similar to those of RO- ions,3 although we cannot suggest why that should be so in the alcohol/water mixtures. The equilibrium OH- + ROH ~t H,O + RO(12)
+
where ri and r, are the effective radii of species i and j for diffusion. nitrobenzene) in a number of alcohol solvents log qk2(e; plotted against e;l is also approximately linear (dashed line in Figure 4, data from ref 5 , 7, 9, and 25-29). Equations 5 , 6, and 9 provide the full curve in Figure 4. Using the dipole moment C-m, equivalent to the non-SI of nitrobenzene (A4= 1.41 X 4.22 X lo-'* e s ~ c m )a, relatively ~~ small value of R, 2 X m, and a value of qk, at f = 1 chosen to put the curve through the 2-methyl-2-propanol point, we obtain
+
log qk, (Pa.m3/mol) = 3.66
+ logf
(10)
where
f = x ( e . - 1)-1
(5')
x = -123/~,
(11)
and at 298 K
The term 3.66 in eq 10 could correspond to effective radii for m for nitrobenzene and 1 X 10-Io m diffusion of about 3 X for e;. The reaction of e; with nitrobenzene in alcohols is not quite diffusion controlled?*26 The probability of reaction per encounter is somewhat smaller in solvents where the electron solvation energy (24) Ponomarev, A. V.; Makarov, I. E.; Pikaev, A. K. High Energy Chem. 1985, 19, 150. ( 2 5 ) Cygler, J.; Freeman, G. R. Can. J. Chem. 1984, 62, 1265. (26) Senanayake, P. C.; Freeman, G. R. J . Chem. Phys., in press. (27) Gallant, R. W. Physical Properties of Hydrocarbons; Gulf Publishing: Houston, TX,1968; Vol. 1, 2. (28) Senanayake, P. C.; Gee, N.; Freeman, G. R. Can. J . Chem., in press. (29) Maryott, A. A.; Smith, E. R. 'Table of Dielectric Constants of Pure Liquids". Natl. Bur. Stand. (US.)Circ. 1951, No. 514. (30) Nelson, R.D.; Lide, D. R.; Maryott, A. A. Selected Values of Electric Dipole Moments for Molecules in the Gas Phase; NSRDS-NBS 1 0 US. Government Printing Office: Washington, DC, 1967.
at 293 K has an equilibrium constant equal to 2.1 for methanol and 0.8 for ethan01.l~ These values are not far from unity and are apparently similar to those of the solvation equilibria of electrons in the mixed solvents. Is e; actually ROH; in hydroxy
solvent^?^^*^^ (31) Landolt-Bornstein, Zahlenwerte und Funktionen, 6 auflage; Springer-Verlag: Berlin, 1951; 1 Band, 3 Teil, pp 509-515. (32) Pikaev, A. K.; Sibirskaya, G. K.; Kabakchi, S. A. Dokl. Phys. Chem. (Engl. Transl.) 1971, 198, 554. (33) Tuttle, T. R.; Golden, S.;Lwenje, S.;Stupak, C. M . J . Phys. Chem. 1984, 88, 3811; erratum 1985, 89, 2436.
e,-
+ S Reactions in Alcohol/ Water Mixed Solvents
mol % H20
H20 mol O h 100 80 60
40
20
0
~
1 7 60,
,20
4r
0
4-
=
,
The Journal of Physical Chemistry, Vol. 92, No. 6,1988 1509
3
i?
4$
E h
n
m'
4
a 2
&
"I
Y 7
cu
Y
c 2
-
c 1
I
Oi
O
1
3
1
loo/€, F i e 7. t)h,as functions of for ions in ethanol/water mixed solvents at 298 K. Values of A+ from ref 3 and 11, t) from ref 17, and t, from ref 18. A, e; RO-(294 K); 0, C1-; v, Na+.
3
2
I 4
I
1
2
1oo/c,
is;
Figure 5. t)k,(e; + S) at 292 K as functions of 'e; at 294 K in methanol/water mixed solvents. S: 0 , nitrobenzene; +, CC1,; 0,p-benzoquinone; A,0,; V, H202. Data for k2 from ref 3 and 4; data for q and e, from ref 17.
mol OO/ H20
H20 mol
Y
P
m'
z
E
0
:
2
1
.:i
1
0
3
2
1
4
1OO/€,
Figure 8. k2(e; + NO3-) and &(e; + NO
