J. Phys. Chem. 1986, 90, 6587-6590
6587
Effect of Solvent Structure on Diffusion-Controlled Reactions of Solvated Electron with Solvated Silver Ions in C1-C10 n-Alkanols at 298 K M. S. Tunuli* Chemistry Department, Duquesne University, Pittsburgh, Pennsylvania 15282
and Farhataziz Department of Chemistry, The Texas Woman's University, Denton, Texas 76204 (Received: March 3, 1986; In Final Form: May 21, 1986)
Second-order measured specific rates, k,, for the reaction of solvated electrons, e,, with solvated silver ions, Ag', in C1-C10 n-alkanols at room temperature (-298 K) are reported. These rates vary from 23.4 X lo9 M-' s-] in C1 (methanol) to 0.8 x io9 M-I s - l i n C10 (decanol) and are strongly dependent on the solvent structure reflected in its dielectric constant. The k , values vary approximately as the inverse viscosity, v-', in the diffusion-controlled limit, exactly as predicted by the Debye-Smoluchowski equation. The results (kDsvalues) calculated by assuming a normal anion like behavior for e, and using the Debye-Smoluchowski formalism are (in general) greater than k , values. These differences in the calculated kDs and measured k , are rationalized in terms of an effective distance formalism.
Introduction An electron in its own potential well and surrounded by a layer of configurationally relaxed solvent molecules is known as a solvated electron,' e, (the negative charge on the solvated electron is not shown for the purpose of simplicity). While the reactivity of e, toward neutral scavengers is strongly dependent on the solvent structure (carbon chain lengths for example') the localization energy (reflected in the transition energy corresponding to absorption maximum, E,,,), on the other hand, is almost the same for a large number of normal alcohols.' To understand this sharp contrast in various properties of e, one must look into its structure. A number of related observations offering some insights into the structure of e, are summarized below.' For a large number of n-alkanols ( C l - C l l ) E,,, is located within f 0 . 0 6 eV of 1.87 eV at 303 K. Likewise, the corresponding bandwidth at half-maximum, for all the n-alkanols, are within f0.1 eV of 1.5 eV. Further, no correlation between E,,, values and the long-range interactions determiend either by the static dielectric constant, e,, or the factor ( 1 /e0) - (1 /e,) (where eo is the high-frequency or optical dielectric constant) is found implying that short-range interactions (such as those between the electron and OH dipoles) largely determine the position of E,,, and the bandwidth at half-height. A simple model of e, emerging from the foregoing discussion is sketched in Figure 1 and is composed of two concentric sphere, an inner sphere of radius a and an outer sphere of radius r, = a L, where L is the carbon chain length (the solvent is not rigid and can adapt various configurations as described in the Results and Discussion section). The inner sphere is also termed as the physical zone2 and is further identified as the cavity of e, containing optimally oriented functional groups (OH dipoles). The cavity is known to have a radius a = 1.5 A 3 (a theoretical estimate, for further details see ref 3) that is independent of the alcohol in which it exist^.^ This fact together with the optimal configurations of the functional groups in the cavity leads to optimal interaction of the electron with its surroundings and consequently E,,, is independent of the solvent structure around the cavity. Correspondingly, the carbon chains associated with the OH group constitute the outer sphere or the inactive zoneZof the solvated electron. The insensitivity of E,,, to the structure of the solvent further implies that the carbon chain length has no effect on the electron and O H interactions. However, the inactive zone (the inactivity is with respect to light absorption) is expected to become active with respect to the re-
+
activity of e, with an electron scavenger (a reactant). Further, one expects the material packings (carbon chains) in the outer sphere to offer a considerable hindrance to a reactant advancing toward an electron encapsulated in the cavity. As a consequence, the solvent structure (Le., carbon chain length) would play a vital role in determining the reactivity patterns of e,. In our previous work concerning the diffusion-controlledreaction of e, with neutral species we have clearly established this role of the solvent In this paper we therefore present our results on the reaction of e, with a charged and solvated species, Ag'.
Experimental Section The n-alkanols used in this work were purified as described p r e v i o ~ s l y .The ~ ~ ~chemicals used in this work were procured from the following sources. Fisher scientific certified ACS: methanol, 1-propanol, 1-butanol; Fluka Puriss: 1-propanol, 1-butanol, 1pentanol (p.a), 1-hexanol, 1-heptanol, 1-octanol, I-decanol; Fluka Purum: 1-nananol; U S . Industrial Chemical Co.: USP absolute ethanol; K and K Chemical: AgC104 anhydrous. Preparation of triply distilled water, cleaning of glass ware, Suprasil irradiation cell (1 cm square tubing) with standard taper joint and stopper, deaeration technique, pulse radiolysis equipment, and data acquisition, analyses, and computation of specific rates by an on-line computer have been described earlier.4,5 Specific rates were measured at the pulse radiolysis facility at the Center for Fast Kinetics Research at the University of Texas at Austin. Solutions were prepared at the Texas Woman's University (Denton, Texas) 1 day before they were taken to Austin. These solutions were prepared by diluting an appropriate volume M solution of AgC10, in a given n-alkanol and 10" of a volumetric flasks were used for this purpose. Five solutions with to 1 varying concentrations of AgC104 (ranging from 1 X X M) in each n-alkanol were used for irradiation at room temperature (-298 K) with 100-ns pulses of -5-MeV electrons from a Van de Graaff. Irradiation conditions were so arranged to ensure that the concentration of e, pertain to its pseudofirst-order decay at 650 nm. The light source (450-W Xenon lamp) used for monitoring the e, was run in the continuous mode only. Every sample was irradiated by five successive electron pulses (10-20-s apart) and the resulting decay curves (at 650 nm) were processed by an averaging program to obtain the pseudo-first-order rate constants, k . The limiting value of k , pertaining to zero (4) Farhataziz; Kalachandra, S.; Tunuli, M . S. J . Phys. Chem. 1984, 88,
(1) Hentz, R. R.; Kenney-Wallace, G. A. J . Phys. Chem. 1974, 78, 514. (2) Kalachandra, S.; Farhataziz, Chem. Phys. Lett. 1980, 73, 465. (3) Schindewolf, U. Angew. Chem., Intern. Ed. Engl. 1978, 17, 887.
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3837. ( 5 ) Kalachandra, S.;Farhataziz; Foyt, D. C. R a d i a f . Phys. Chem. 1983, 21. 509.
0 1986 American Chemical Society
6588 The Journal of Physical Chemistry, Vol. 90, No. 24, 1986 TABLE I: Various Parameters for n-Alkanols at 298 K n-alkanol n.‘ CP €0 0.5445 1.078 1.99 2.64 3.347 4.592 5.68 7.21 9.10 11.0
CI c2 c3 c4
e5
C6 c7 C8 c9 c10
From ref 2 and references therein.
L..b
32.7 24.2 20.5 17.1 13.9 13.3 11.4 10.3 9.1 7.8
Tunuli and Farhataziz
L,.c A
A
5.0 5.7 6.2 6.3 7.0 7.4 7.6 7.9 8.2 8.4
L*.c A 4.7 6.0 7.0 7.7 8.2 8.6 8.9 9.1 9.3 9.4
4.7 6.0 7.3 8.6 9.9 I1 13 14
15 16
From molar volume data (see ref 2).
A
L.w.d
ne
11.5 12.2 13.6 14.2 15.3 16.2 16.8 17.6 18.1 18.0
From ref 2. dCalculated from eq 1 .
1.3265 1.3594 1.3837 1.3993 1.4080 1.4161 1.4242 1.4296 1.4338 1.437 I e
From ref 4 and references
therein. TABLE 11: Measured and Calculated Specific Rates for the Reaction of Solvated Electron with Solvated Silver Ions in Cl-ClO n-Alkanols at 298 K kcaldafor n-alkanol
CI e2 c3 c4 c5 C6 e7 C8 c9 e10
kma
L = L,
L = L,*
L = L,b
L = Le$
Dd
23.4 11.4 7.6 5.6 3.6 2.9 2.7 1.6 1.2 0.8
21.9 12.4 7.2 6.1 5.2 3.8 3.4 2.8 2.4 2.2
22.6 12.1 6.6 5.1 4.2 3.0 2.4 2.0 1.6 1.4
22.6 12.1 6.7 5.4 4.7 3.5 3.1 2.6 2.2 2.1
16.6 9.1 5.0 3.9 3.4 2.5 2.1 1.7
1.23 1.16 0.45 0.27 0.19 0.12 0.08 0.05 0.04 0.03
1,5
I .3
“Units IO9 M-’ s-’ . bCalculated from eq 2, 3, and 4 and L = L, or L = L,. ‘Calculated from eq 2, 3, and 4 and L = L,ff. dFrom eq 4. Units
cm2 SKI.
\ \
\ \
I
I
I I /
1
e,, a, was set equal to 1.5 A,3 and for the radius of the unsolvated silver ion (Le., the crystal radius) we used b = 1.26 A.’ For various assumed configurations of the carbon chain the L values were estimated either from the molar volume data* (for L = L, where s stands for the spherical shape) or from the modelistic considerations2 (for L= Ll and L = L, where the subscripts 1 and c respectively stands for the linear and the coiled configurations). It was further assumed that the maximum linear length of an n-alkanol is Ll and the corresponding minimum length (set equal to L,) pertains to a U-shaped (coiled) configuration of the carbon chain. Values of Ll and L, were then calculated by using CPK atomic model^.^,^ In addition, the effective chain length, Le,, was calculated according to the following formalism: Leff
Figure 1. A simple model of the solvated electron.
concentration of the scavenger, ko, served as the sixth datum point on a plot of k vs. [AgCIO,] according to the well-known equation:
k = ko
+ k,[AgCIO,]
where k,, the measured second-order specific rate, was calculated from the slope of a least-mean-square straight line of such a plot (Le., k vs. [AgCIO,]) for a particular n-alkanol.
Results and Discussion Various molecular (viscosity, 9. and dielectric constant) and structural (length for spherical, L,, linear, L,, coiled, L,, and effective, Le,, configurations of the carbon chain) parameters for C l - C l O n-alkanols are compiled in Table I. The calculated, kakd, and the measured, k,, specific rates for the reaction of e, with Ag+ are given in Table 11. For a given configuration of the carbon chain the values of ri (i = a or b) were calculated from I, = a + L and rb = b + L where the subscripts a and b are used to identify the e, and Ag’, respectively. The distance of closest approach was estimated as ra + rb. Further, the cavity radius of
=
Reff - (a + b )
(1)
2
where, Reff,the effective separation distance at the time of electron transfer from e, to Ag’, was obtained via a formalism proposed by Pilling et aL9 Our results reported in Table I1 can be explained as follows. Utility of Debye-Smoluchowski Formalism. For a diffusion-controlled reaction between charged species it was shown by Debyelothat the Smoluchowskiequation (eq 2 withy= 1 ) modifies to
+
+
kDs = (4~N/1000)(0, Db)(ra rb)f (2) where N is the Avogadro number, D = D, + D, is the mutual diffusion coefficient of the reactants, and
f = (U/kT)[exp(U/kT) -
11-l
(3)
where U = .z,zbeZ/t,Ro,z is the ionic charge, e is the electronic charge, k is the Boltzmann constant, and T i s the absolute tem(6) Baxendale, J. H.; Wardman, P. J . Chem. Soc. Faraday Trans. 1 1973. 69, 584. ( 7 ) Day, M. C., Jr.; Selbin, J. Theoretical Inorganic Chemistry, 2nd ed; Reinhold: New York, 1969. (8) Conner, W. P.; Smyth, C. P. J . Am. Chem. SOC.1963, 65, 382. (9) (a) Pilling, M . J.; Rice, S. A . J . Phys. Chem. 1975, 79, 3 0 3 5 . (b) Pilling, M . J.; Rice, S. A. J . Chem. SOC.,Faraday Trans. 2 1975, 7 1 , 1563. (IO) Debye, P. Trans. Electrochem. SOC.1942. 82, 265.
e, in CI-C10 n-Alkanols
The Journal of Physical Chemistry, Vol. 90, N o . 24, I986 6589
perature. Other quantities appearing in the above equations have been defined earlier in this paper. Values of the diffusion coefficients were calcuated from Stokes-Einstein equation:
D = kTRo/6nqrarb
(4)
A comparison of kDs (Le., kald for L = L,) and k, values in Table I1 reveals that the theory/experiment agreement is quite reasonable. However, a more careful analysis of these data indicates that kDs > k, and this is particularly well pronounced for higher (C4-C10) n-alkanols. This discrepancy between theory and experiment is attributable to the followings. First, the L, values estimated from the molar volume data do not adequately represent the actual chain lengths and that the assumption of spherical shape of n-alkanols is not valid. Second, the separation distance at the moment of electron transfer is greater than Ro estimated under the assumption that L = L,. These possibilities are further elabora ted. Application of CPK Radii. Here we explore the possibility that L # L, and instead we use L = Ll and L = L, obtained via CPK atomic m ~ d e l s . The ~ . ~ specific rates calculated from these L values, kcalcd,are constrasted against k, in Table 11. Clearly, the agreement between k, and kcalcd for L = LI is excellent. From this we conclude that the Debye-Smoluchowski equation, eq 2, satisfactorily reproduces our k, data providing that L = L , is granted. However, such a calculation of kDs requires that e, must diffuse as a normal anion. Further, it must be pointed out that the measured mobilities of e, in a number of n-alkanols cannot be explained on the basis of the assumption that e, behaves as a normal anion.I4J5 In view of the foregoing discussion we conclude that the agreement between theory and experiment obtained under the assumption of L = LI is simply fortuitous. In addition, setting L = L, implies that the solvent molecules are rigid (which is not reasonable). Role of Effective Radii. The first report concerning kDs> k, came from Hart and Anbar" who attributed this to Reff> Ro and pointed out the possibility of a tunneling path in the reaction mechanism. Later on similar data were reported by MillerI2 and by Kroh and S t r a d ~ w s k i . ' ~To explain these data Pilling and Rice9 proposed the use of an exponential sink term in the Smoluchowski formalism and showed that the effective radii, ReRrthus obtained were in fact greater than Ro. In keeping with the literature we therefore wish to seek a similar interpretation for ourdata. Thus, we suggest that the encounter distances, Ro, between the actual reactants of radii ra and rb be replaced by an effective distance, Reff,between two fictitious reactants of radii, ra,effand rb,eff Further, we require that Reff> Ro which is a necessary condition for obtaining a better agreement between kDs and k, (see eq 2 and 3). Consequently, we can replace eq 2 and 3 by the following:
where Ueff= zazbe2/csReff and R e , = ra,eff + rb,eff.Furthermore, ra,eff= a + Leffand rb,eff= b + Le, and Leffis given by eq 1. Next, we consider the following mechanism of electron transfer from e, to Ag+. These reactants approach each other via a process of mutual diffusion and at a separation distance Reff> Ro the electron tunnels to Ag+.
e,
R.fi - - - +
Ag+
kt
Ag
(1 1) Hart, E. J.; Anbar, M. The Hydrated Electron; Wiley-Interscience: New York, 1970; pp 187-188. (12) Miller, J. R. Chem. Phys. Lett. 1973, 22, 180. (13) Kroh, J.; Stradowski, Cz.Int. J . Radiat. Phys. Chem. 1973, 5 , 243. (14) Allen, A. 0. Natl. Stand. Ref. Data Ser., Natl. Bur. Stand. 1976, No. 58. ( 1 5 ) Farhataziz; Kalachandra, S. Radiat. EJJ Lett. Sect. 1983, 68, 139. (16) Miller, J. R.; Willard, J. E. J . Phys. Chem. 1972, 76, 2641.
1 1.2
Figure 2. Plots of log k , vs. log q for the reaction of solvated electron with solvated silver ions in C1-CIO n-alkanols (circles). Crosses are the corresponding plot for the reaction of solvated electron with phenanthrene.
A characteristic feature of tunnel electron transfer is the logarithmic (nonexponential) dependence of the reagent (e.g., e, in the present case) concentration on time. Our data for the reaction of e, with Ag+ in all the n-alkanols show that the absorption of e, decays exponentially with time indicating that the diffusion controls its reactivity. It must be pointed out that the absence of nonexponential decay should not be taken to imply that the tunneling path is not involved in the reaction mechanism. The absence of logarithmic decay of the e, absorption can be attributed to the following. For the mechanism shown in eq 7 and 8 the k, is given by km = k t k ~ ~ / ( k+t ~ D S )
(9)
now, if the rate is controlled by diffusion then k, = kDs and consequently the kinetic characteristics of the tunneling path (eq 10) would not show up. A number of other reasons which lead to the masking of the tunneling characteristics are discussed in detail in ref 17. We now turn our attention to the calculation of Reffusing the formalism proposed by Pilling and Rice,9 i.e.
R e f f= Ro[l + (1.15
+ In ( A / a D ) / a R O ) ]
-
(10)
where the frequency factor A k T / h (h is the Planck constant) and the parameter a is known to have values between 0.5 and 0.8 A-1.9 The kcalcdobtained from eq 5, 6, and 7 and L = Leffare compared against k, in Table 11. The agreement between these specific rates in C5-C10 n-alkanols is excellent. Further, this agreement is better than the corresponding agreement found for L = L, and by using Debye-Smoluchowski eq 2 (compare column 4 and 6 in Table 11). For solvents in which D > 4 X cm2 SKIeq 10 does not apply because it was originally deduced under cm2 s - I . ~ This explains why the assumption that D < 4 X kald for L = Leffand k, values in Cl-C4 n-alkanols do not agree (see column 7 in Table 11). Previously, we have shown that for a reaction between e, and a neutral scavanger such as phenanthrene, ph (in n-alkanols), the latter must pierce through the inactive zone of the former (see Figure 1) in order to seek the electron residing in the c a ~ i t y . ~ . ~ In view of the varied properties of the inactive zone (as compared to the bulk) one does not expect the specific rates of such a reaction to obey the Smoluchowski equation. A characteristic feature of the reactions obeying Smoluchowski equation is that their specific rates are reproduced by an empirical equation of the type:4,'8 k, = Av-' (1 1) where A is a constant for a given reaction. In sharp contrast to this, a plot of k, for the reaction of ph with e, in CI-CIO n-al(17) Zamaraev, K. I.; Khairutdinov, R. F. Chem. Phys. 1974, 4 , 181. (18) Farhataziz; Tunuli, M. S. Proc. Int. Cong. Radiat. Res., 7th 1983, A1-3.
J . Phys. Chem. 1986, 90, 6590-6594
6590
as compared to the interpenetration distance. In conclusion, we have demonstrated that the reactivity of e, with Ag' is governed by the long-range interactions. Further, when the radius of e, is estimated from L = L,, and the DebyeSmoluchowski estimation of the specific rate is made, the agreement of k , with kald is remarkable. A further improvement in this agreement results when one assumes that L = Leffand the Leffis given by a tunneling formalism. In addition, the distances at the moment of electron transfer are larger than the corresponding contact distances and unlike neutral scavengers no interpenetration of Ag' into the outer sphere of e, is required. Registry No. Ag, 7440-22-4; methanol, 67-56-1; ethanol, 64-17-5; propanol, 71-23-8; butanol, 71-36-3; pentanol, 71-41-0; hexanol, 11127-3; heptanol, 1 1 1-70-6;octanol, 11 1-87-5; nonanol, 143-08-8;decanol.
kanols revealed that (see Figure 2).
k, = where A = 4.6 X lo9 and x = 0.45.2 This departure of x from unity has previously been attributed to the interpenetration of the reaction partnew2 On the contrary, the mechanism in eq 7 and 8 precludes the interpenetration of the reaction partners and hence indicates the inapplicability of eq 12 to the reaction of e, and a charged species such as Ag'. For such a mechanism one expects an empirical equation of the type given by eq 13 to hold. Inspection of Figure 2 reveals that
k , = 1.4 X lolog-'
'
(13)
which, in our view, confirm the possibility that the reaction between e, and Ag' takes place while the reactants are far apart
I 12-30-1.
Vapor-Phase Composition above the Cd1,-NaI
and the Th1,-NaI Systems
Timothy D. Russell General Electric Company, Lighting Research Laboratory, Nela Park, Cleoeland, Ohio 441 I 2 (Received: May 9, 1986)
The activities of Cd12 in NaI and of ThI, in NaI have been determined by using vapor-phase UV absorption spectroscopy. The activity coefficient, y, for the Cd1,-NaI system was found to be constant below 0.05 mole fraction of CdI, and equal to 0.23. For the Th1,-NaI system, y was found to be constant below 0.06 mole fraction of ThII and equal to 0.02. No vapor-phase hetero complexes of CdI, or ThI, with NaI were observed. The effects of vapor-phase dimerization of NaI on its absorption spectrum are discussed and temperature-dependent spectra are presented.
Introduction Thorium and cadmium are important metallic additives which affect the color temperature and the life of metal halide ( M H ) discharge lamps containing N a I and ScI,.'s2 The cadmium is added as a Hg-Cd alloy while the thorium is added as ThI,. Cadmium acts as a getter by reducing the partial pressure of iodine during lamp operation and thereby promoting the deposition of thorium onto the tip of the electrode where it functions as an activator by lowering the work function of the tungsten surface. The operation of the thorium-tungsten electrode in metal halide arc tubes has been previously described by W a y m ~ u t h . , , ~Basically, the thorium concentration at the electrode tip is governed by the equilibrium expressions for the dissociation of thorium iodide and the vaporization of condensed thorium: ThI,(g) = T U ) + xUg)
(1)
Th(g) = Th(c)
(2)
If the partial pressure of Th(g) due to the dissociation of thorium iodide exceeds the equilibrium vapor pressure of Th(c) at the electrode tip temperature (-2500 K), then thorium deposits onto the electrode tip. The Th(g) pressure can be seen to be dependent on both the thorium iodide partial pressure, which is determined by the activity of ThI, in the molten iodide dose, and the iodine partial pressure. The iodine partial pressure itself is dependent upon the partial pressures and the intrinsic dissociation constants of the metal iodides that are present in the arc tube. (1) Spencer, J. E.; Bhattacharya, A. K.
US.Patent N o . 4360756, 1982. (2) Khoury, F.; Waymouth, J. F. U.S. Patent N o . 3313974, 1967. (3) Waymouth, J. F. Electric Discharge Lamps: M.I.T. Press: Cambridge, MA, 1978. (4) Gilliard, R. P.; Russell, T. D. Presented at the 37th Annual Gaseous Electronics Conference, October 1984; paper HB-2.
0022-3654/86/2090-6590$01.50/0
During manufacturing, arc tubes are dosed with Hg, NaI, Sci,, and ThI, plus various impurities such as 0, and H 2 0 which are inadvertently introduced. Once the lamp is operated, the ScI, reacts with 0, and H 2 0 producing HgI, according to the following overall reactions: 2ScI,
+ 3H20 + 2Si0, + 3Hg = Sc,Si207 + 3Hg1, + 3H2 (3)
4Sc13
+ 3 0 , + 4SiO2 + 6Hg = 2Sc2Si207+ 6Hg12
(4)
(The individual steps of the above reactions may involve the formation of Sc,O, and ScOI.) Analogous reactions between ThI, and 0, and H,O producing HgI, are also believed to occur. The Hgl, that is present decomposes in the high-temperature arc of an operating lamp into H g and I atoms. According to eq 1 and 2 above, if the iodine pressure due to the dissociation of HgI, is sufficiently high, thorium is prevented from depositing on the electrode, which results in a high work function electrode and poor lumen maintenan~e.'-~ The addition of cadmium to the arc tube results in the following overall reactions: Cd + HgI, = CdI, + Hg (5) 6Cd
+
+ 7Si0,
= 6Cd1,
+ 2Sc,Si207 + 3Si
(6)
In reaction 5, cadmium getters the iodine from Hg12 and forms CdI, which dissolves in the molten iodide dose. In reaction 6. cadmium reacts with ScI, and the silica wall of the arc tube again producing CdI,. Within a short time (minutes), all of the cadmium added to the arc tube reacts to form CdI,.' By reacting with HgI,, which would vaporize and subsequently dissociate during lamp operation, and forming CdI,, which dissolves in the molten dose, cadmium effectively lowers the partial pressure of iodine in the arc. The extent to which the pressure of iodine is lowered is dependent upon the activity of CdIz in the
0 1986 American Chemical Society
