J. Phys. Chem. 1984, 88, 1857-1860 TABLE 11: Second-Order Rate Constants for Ion Association in M-' s-'
ref
anion
16
NO2
cation
solvent
kfa
T, "C
N a+
THI:
1.2 X 10l0
20
K'
HMPA
4.3 X 10'
25
KC
HMPA
4.6
X
IOS
25
Nat
NH,
1.1
X
IO"
-75
K+
Me,SO
slow
25
Na' or K+ HMPA
slow
25
No+ N D - * NO2
1 Oa
-
PhNO,..
l7
11
a0-
the kinetic and thermodynamic data seem to be contradictory, but the apparent contradiction is resolved if the strong interaction between the cation and the lone electron pair on the nitrogen is kept in mind. Some complexes may be formed where the lone pair on the ammonia nitrogen is interacting with the Na' ion and the protons are involved in hydrogen bonding with the anion radical simultaneously. For these complexes the ammonia assists in bringing the ions in close proximity and at the same time provides a mechanism for quick destruction of the ion pair (reaction 4).
Phh02-*
0.
PhNO,-,
However, from Table I1 it is clear that the rate of formation of the ion pair is quite large relative to those of other systems. Thus, the ammonia seems to be assisting the kinetics of ion association while at the same time lowering the equilibrium constant. At first,
-
1857
The rate constant for ion-pair dissociation is kd = k,/K, = 3.6 10l2 s-l. The rate of ion-pair dissociation is so fast that the ion associated complex does not endure for much longer than a few molecular vibrations. X
Registry No. NH,, 7664-41-7; Na, 7440-23-5; PhN02--, 12169-65-2.
High-Temperature Photochemistry. Measurements of the Rate Coefficient for H OH H, from 1160 to 1390 K
+
+ H,O
Sasha Madronich and William Felder* AeroChem Research Laboratories, Inc., Princeton, New Jersey 08540 (Received: July 13, 1983)
+
+
The high-temperature photochemistry (HTP) technique has been used to study the reaction H H 2 0 OH H2 ( k ) in the temperature range 1160-1 390 K. This reaction is a potential interference in all OH kinetic studies above ca. 1000 K when OH is produced by HzO flash photolysis. Values of k were determined at 1158, 1274, and 1387 K from OH resonance fluorescence measurements and were fitted by the simple Arrhenius expression (5.2 f 4.5) X exp[-(11.1 f 1.1) X 1 0 3 / q cm3 molecule-ls-'.
Introduction The flash photolysis/resonance fluorescence (FP/RF) technique has been used in recent years to obtain bimolecular rate coefficients for a large number of hydroxyl radical reactions (see, for example, ref 1 for a review of OH/hydrocarbon reactions). Extension of the temperature range for measurements of such rate coefficients (e.g., ref 1-4) is needed because of their importance in combustion processes. The high-temperature photochemistry (HTP) techn i q ~ eused ~ , ~for the present work extends the temperature range of conventional FP/RF methods to about 1800 K. In most FP/RF studies of O H kinetics, initial concentrations of OH, [OH],, are produced by vacuum ultraviolet photodissociation of water vapor ( 1 ) Atkinson. R.: Darnall. K. R.: Llovd. A. C.: Winer. A. M.: Pitts. J. N . Ad;. Photochem. 1919, 11, 375-488, (2) Zellner, R. J . Phys. Chem. 1979, 83, 18-23. (3) Ravishankara, A. R,; Nicovich, J, M.; Thompson, R, L,;Tully, F, p, J . Phys. Chem. 1981, 85, 2498-503. I
H 2 0 + hv (A 5 185 nm)
-+
-+
OH
+H
(1)
and the relative O H concentration, [OH],, is monitored as a function of time in the presence of a large excess of a second reagent, A. The relaxation of [OH], due to reaction with A is accurately described, in the absence of complicating secondary reactions, by a single exponential decay, and the bimolecular rate coefficient for this reaction is extracted from measurements of decay times at different concentrations of A. In the course of our work on reactions of O H (e.g., with C6H, and with CH,) over the temperature range 300-1800 K in the HTP reactor, we have found that the use of H 2 0 as a photolytic source of OH at temperatures exceeding about 1000 K is complicated by the reaction
H
+ HzO
k -.c
OH
+ H,
(2)
1
(4) Michael, J. V.; Nava, D. F.; Borkowski, R. P.; Payne, W. A,; Stief, L. J. J. Chem. Phys. 1980, 73, 6108-16. (5) Felder, W.; Fontijn, A,; Volltrauer, H. N . ; Voorhees, D. R. Reu. Sci. Instrum. 1980, 51, 195-200. (6) Felder, W.; Fontijn, A. Chem. Phys. Lett. 1979, 67, 53-6.
0022-3654/84/2088-1857$01.50/0
Reaction 2 is also important in combustion systems. The reverse reaction is a step in H2/02 flame chemistry and has been the subject of many studies (ref 3 and 7 and references therein), but no direct experimental data are currently available on reaction (7) Dixon-Lewis, G.; Williams, D. J. Compr. Chem. Kinet. 1977, 17,
1-248.
0 1984 American Chemical Society
Madronich and Felder
1858 The Journal of Physical Chemistry, Vol. 88, No. 9, 1984
MULTICHANNEL SCALER
COLLIMATOR HEAT SHIELD
IIIIII
n
PHCITOLYSI
Ill//
d ur HEATING WIRE
Y
LIGHT TRAP
Figure 1. Optical plane of HTP reactor.
2. Flame kinetic measurements provide the only information thus far reported.*sg In this paper we first describe qualitatively the effects of reaction 2 on O H temporal profiles above 1000 K and then report values of k(7') deduced at temperatures at 1158, 1274, and 1387 K from resonance fluorescence measurements of the temporal behavior of [OH],. The effects of reaction 2 must be considered in the interpretation of all high-temperature studies of O H kinetics in which H 2 0 is the photolytic precursor. The k( 7') measurements reported here are the first to be obtained outside a flame environment. Experimental Section The high-temperature photochemistry (HTP) apparatus used in this work is described in detail el~ewhere.~ Briefly, it consists of an alumina reaction tube, suitably heated and insulated, in which reaction zone gas temperatures as high as 1800 K can be achieved., Reaction zone temperature, pressure, and concentrations of reagents can be varied independently. The values of k(7') reported below were obtained in three experiments at 1158, 1274, and 1387 K. Argon diluent was used at total pressures near 200 torr and flow velocities from 23 to 37 cm s-l. Additional semiquantitative observations of the [OH], profiles were made at 1158 K and 100-torr (Ar) total pressure (flow velocity 60 cm s-l) to confirm the predicted (see below) effect of changes in flow and diffusion losses on the measured [OH], profiles. The intersection volume of four coplanar optical ports, shown in Figure 1, defines the reaction zone. The H 2 0 vapor is photolyzed by using a flash lamp (1 atm of Ar, 20-70 J/pulse). O H resonance radiation for monitoring [OH], is provided by a microwave-excited diagnostic flow lamp (3% H 2 0 in He, l-torr total pressure). The OH resonance fluorescence is viewed at right angles to the flow lamp through a collimator and an interference filter (310 nm, 20% peak transmission, 10-nm bandwidth) by a photomultiplier tube operated in the photon-counting mode. The time-dependent fluorescence intensity, which is directly proportional to the O H concentration, is measured by accumulating the signal over 2000 flashes with a multichannel scaler (100 p / channel); the accumulated signal is then transferred to a microcomputer for analysis. Results A typical fluorescence intensity (E [OH]) profile, obtained from H 2 0 photolysis at 1274 K, is shown in Figure 2. The decay is due to the removal of OH from the observation zone by diffusion (8) Fenimore, C. P.; Jones, G.W. J . Phys. Chem. 1958, 62, 693-7. ( 9 ) Dixon-Lewis, G.; Sutton, M. M.; Williams, A. Trans. Furaday SOC. 1965,61, 255-62.
0 ' 0
5
10
15
20
25
t, ms
Figure 2. Typical OH fluorescence intensity profile.
and flow, while the shape at early times is largely attributed to reaction 2, which produces OH radicals on a time scale comparable to that of flow and diffusive losses. The form of this early time structure could be altered by varying the [H20]; at fixed temperature and total pressure, it showed several distinct modes of behavior. For example, at 1274 K and 200 torr, the following apply: (i) For [H,O] 5 1014molecules ~ m - decay ~ , profiles were simple exponentials, due to the slow rate of reaction 2, but the O H fluorescence intensity was very weak due to the small value of [OHIO. (ii) For 1014 < [H20] < 1015 molecules ~ m - production ~, of O H by reaction 2 resulted in [OH], profiles flattened at early times. (iii) for 10l5 < [H20] < 5 X lOI5 molecules ~ m - maxima ~, in the [OH], profiles were seen, with the time to the maxima increasing with increasing [H20], but never exceeding about 4 ms. (iv) For 5 X l O I 5 < [H20] < 10l6molecules ~ m - maxima ~, were again observed, but the time to the maxima decreased with increasing [H20]. (v) For [ H 2 0 ] > 10l6molecules ~ m - no ~ ,maximum could be observed, because reaction 2 went to completion on a time scale shorter than could be resolved by our apparatus. At these large [H20], the decays appeared to be simple exponentials, but the fluorescence signal intensity was found to decrease with increasing [H20],presumably due to rapid quenching of the OH fluorescence by the H 2 0 . In a few experiments performed at lower total pressure (100 torr), the range of water concentrations over which maxima could be observed was much narrower. In other experiments, the flash lamp energy was reduced by a factor of 4. Although the overall signal was reduced by about a factor of 4, the shape of the decay profiles was unchanged. All of these observations are quantitatively consistent with the kinetic scheme, presented below, based on the effects of reaction 2. Equal concentration of the radicals O H and H are formed instantaneously (on the time scale of the present measurements) by photodissociation of H20. We estimate, on the basis of vacuum UV flash lamp actinometry, that less than 5 X low4of the H 2 0 is dissociated. Thus, at the highest value of [H20], 10l6molecules ~ m - discussed ~, here, the [OH], is less than 5 X 10I2 molecules ~ m - ~Radical-radical . reactions (e.g., OH + O H 0 + H 2 0 ) are therefore unlikely to be important. Complications due to the reverse reaction
-
OH
+ H2
k'
H
+ H20
(2')
can also be excluded because of the low fractional photodissociation of H20. That these possibly complicating reactions have negligible importance here is further supported by the lack of an observable flash lamp energy effect (over the range of flash lamp energies used) on the shape of the [OH], profiles.
The Journal of Physical Chemistry, Vol. 88, No. 9, 1984 1859
High-Temperature Photochemistry TABLE I: Rate Coefficient Determinations f o r H + H,O -+OH + H,
I ~
H+H20-OH+H2
1200 r
P,
cm inolecules
T, K
torr
s-’
cm-3
1158 1274 1387
210 200 190
23 26 37
1.0-18.0 0.8-10.8 1.0-9.7
k, ~ r n - ~
-I
residual,b
molecule-’ s-’
u)
S-
800
I
a
(3.7 2 0.8) X (8.7 2 1 . 2 ) X ( 1 . 8 2 0.4j x
10-13
From slope of a , vs. [ H , O ] plots; precision is 20. vs. [H,O] plots; precision is 2u.
65 77 2s
t t
h
52 55 14
400
From
n -
intercept of a ,
Following their production, H and O H radicals are removed from the reaction zone by flow and diffusion. Concurrently, reaction 2 removes H atoms and produces O H radicals. To a first approximation, removal of O H and H by flow and diffusion can be modeled by first-order rate coefficients p 1 and p2, respectively (this approximation will be relaxed somewhat below; cf. eq B). The rate equation for [OH] can then be integrated analytically to give the predicted variation of the O H fluorescence intensity,
2
0
4
6
8
1
0
1
2
[H20], 1015 cmT3
Figure 3. Pseudo-first-orderrate coefficients u2 (0)and a, (A); cf. eq B. The slope of the u2 vs. [H20] plot is k.
Z(t):
I ( [ ) = I(0) exP[-Pit](l + (1 - exP[-(%
+ a3)tl)az/(az + a3)1
10-l~ r
(A)
I c
where
-i3 I
a2
= k[H,O]
-
E 5
= P2 - Pi The parameters Z(O), p l , a2, and a3 which appear in eq A can, in principle, be determined by fitting this equation to the observed O H decay profiles (such as Figure 2 ) with a four-parameter nonlinear least-squares method. However, the slow convergence and false minima associated with such a methodi0 make it desirable to reduce the number of fitting parameters. This reduction was accomplished by ratioing time-dependent O H fluorescence intensity curves for different values of [H,O] at constant total gas density and temperature, yielding the fitting function a3
m
Y
10-l~
C
where
r = [HzOI’/[HzOl
ai = I(O)[%
razI/(I’(o)[a3 + a211
and a2 and a3 are defined as in eq A. Equation B also reduces errors due to the first-order approximation for flow and diffusion removal rates. This approximation can lead to serious errors if more than one decay rate is to be extracted from the OH temporal profiles. Data analysis with eq B was implemented by using the gradient-expansion least-squares algorithm given by Bevington.’ Data points were weighted by the square of the reciprocal of their uncertainties, which were estimated by propagating the counting uncertainties (square root of the number of counts) through eq B according to the prescriptions given by Cvetanovic et a1.I2 The fitting procedure yielded reduced x2 values of 1.0 f 0.2, indicating the appropriateness of the functional form of eq B to represent the data. The k( r ) values obtained by this procedure and the experimental conditions under which they were obtained are summarized in Table I. Figure 3 shows the values of a2 and a3 obtained at 1274 K as functions of [H20]; qualitatively similar data were obtained at 1158 and 1387 K, over H 2 0 concentrations ranging from 1 X lOI5 to 1.8 X 10l6molecules cm-I. Values of a2 are seen (10) Carrington, T. In?. J. Chem. Kinet. 1982, Z4,517-34. ( 1 1 ) Bevington, P. R. “Data Reduction and Error Analysis for the Physical Sciences”; McGraw-Hill: New York, 1969. (12) Cvetanovic, R. J.; Singleton, D. L.; Paraskevopoulos, G. J . Phys. Chem. 1979,83, 50-60.
0.7
0.8 0.Q 1031K ~ ~- ~
1.o
Figure 4. Arrhenius plot for k ( 0 : (0)this work. Flame data: (A) ref 8; (V) ref 9. From reverse reaction: (-) shock tube data, ref 15, as revised in ref 7; (---) fit to FP/RF data, ref 3 and 16. (-) Fit to combined data of this work and from reverse reaction data of ref 3 and
16.
to increase with increasing [H20],as expected from the definition of a2 in eq B. Extrapolation of the a? data to zero [HzO] yielded small but nonzero residual intercepts with large relative uncertainties (see Table I). The origin of these residuals is not clear, but it is most likely a result of the incomplete cancellation of transport losses in eq B. The observation of a smaller residual at higher flow velocity (see Table I) appears to support this interpretation. Thus, k was obtained from linear weighted least-squares slopes of the az vs. [H,O] plots. The slopes of a3 vs. [HzO] plots were not statistically different from zero, in accord with the definition of a3.
Discussion In Figure 4, k values measured in this work are compared with previous measurements in flames and with values calculated from data on the reverse reaction (reaction 2’) and the equilibrium ~onstant.’~ The present measurements alone are fitted by the simple Arrhenius expression k = (5.2 f 4.5) X exp[-(ll.l f 1.1) x l O 3 / U cm3 molecule-’ s-] (1 3) “JANAF Thermochemical Tables”; Dow Chemical Co.: Midland, MI, continuously updated.
J. Phys. Chem. 1984, 88, 1860-1864
1860
between 1158 and 1387 K. This fit lies more than a factor of 2 higher than the predictions of Johnston-Parr calculation^,^^ which give k(7‘) = (4.3 x exp(-9410/7‘) cm3 molecule-’ SKI. A similar discrepancy is noted between our measurements and the 1285 K value for k extracted from flame measurements by Fenimore and Jones.* The flame measurement by Dixon-Lewis et al.9 falls about 30% below the extrapolation of our k data to their measurement temperature, 1070 K. Somewhat more consistent agreement is found with values calculated from k’(7‘) and the equilibrium constant. At high temperature, we use the 1200-1800 K shock tube measurements of Gardiner et a1.lS(as modified by Dixon-Lewis and Williams7 in view of more recent data for the H O2 reaction). Other high-temperature data on k’are reviewed in ref 7. Our data are seen to be larger than the values derived from the shock tube k’ values by about 50%. To compare the present data with direct k’measurements at lower temperatures, we have taken the FP/RF data of Tully and Ravishankara16 and of Ravishankara et aL3which, together, span the temperature range 250-1050 K. Their individual k’data points were converted to values of k and were best fitted by nonlinear least squares to the expression k ( T ) = (2.2 X 10-20)T3.04-
+
(14) Mayer, S.W.; Schieler, L.; Johnston, H. S.Symp. (Int.) Combust., [Proc.] 1967, 11, 837-44. (15) Gardiner, W. C., Jr.; Mallard, W. G.; McFarland, M.; Morinaga, K.; Owen, J. H.; Rawlins, W. T.; Takeyama, T.; Walker, B. F. Symp. (Int.) Combust., [Proc] 1973, 14, 61-75. (16) Tully, F. P.; Ravishankara, A. R. J. Phys. Chem. 1980,84, 3126-30.
exp(-8620/ T ) cm3 molecule-’ s-I. This expression, extrapolated through -1550 K, is shown in Figure 4; it lies some l(t30% below our measurements. Finally, when the present data are combined with those of ref 3 and 16, the fit k ( T ) = (1.09 X 10-20)T3I s exp(-8570/T) cm3 molecule-’ s-’ is obtained for the temperature range 250-1400 K. The present measurements of k ( T ) are unique in that no knowledge is required of other rate constants (as in shock tube and flame studies), molecular parameters (as in Johnston-Parr calculations), or equilibrium data (as in FP/RF and shock tube studies) to calculate k from k’. Nevertheless, the general agreement between k( 7‘) values obtained by these different techniques is fairly good, especially with respect to the temperature dependence over the temperature range of the present measurements. Thus, if a local activation energy is defined over 1160-1390 K, the values 20.4 (Johnston-Parr), 25.8 (shock tube, from k’), and 25.0 (FP/RF, from k’) kcal/mol fall within 15% of our determination, 22.1 k 2.2 kcal/mol.
Acknowledgment. This work was supported by the Department of Energy, Chicago Operations Office, under Contract No. DEAC02-77ER04169. We thank Drs. R. B. Klemm and J. J. Michael of Brookhaven National Laboratory for helpful discussions of this work. We express special appreciation for the advice and support of this work by the late Dr. 0. W. A d a m of the Department of Energy. Registry No. Water, 7732-18-5; hydroxyl, 3352-57-6; atomic hydrogen, 12385-13-6.
Influence of Specific Reactant-Solvent Interactions on Intrinsic Activation Entropies for Outer-Sphere Electron-Transfer Reactions Joseph T. Hupp and Michael J. Weaver* Department of Chemistry, Purdue University, West Lafayette, Indiana 47907 (Received: July 25, 1983)
The physical basis of the solvent contribution to the intrinsic activation entropy, AS*int, for outer-sphere electron-transfer reactions in homogeneous solution is examined in terms of the entropic parameters for the constituent electrochemical half-reactions. A relationship for calculating AS*intis derived which takes into account specific reactant-solvent interactions for the isolated redox centers by employing electrochemical reaction entropy data. This relation yields rather larger and more structure-sensitivevalues of than those deduced on the basis of the usual dielectric continuum treatment. These considerations indicate that the more negative values of AS*i, typically extracted from experimental kinetic data arise largely from the modification to the specific reactant-solvent interactions within the precursor complex caused by the proximity of the other redox center.
Introduction In recent years increasingly detailed and sophisticated theories of outer-sphere electron-transfer kinetics have been formulated.’ These enable rates and activation parameters to be calculated from reaction thermodynamics together with reactant and solvent structural information. Although treatments of inner-shell (intramolecular reactant) reorganization have reached a high degree of sophistication,2 the important contribution to the free energy barrier arising from outer-shell (noncoordinated solvent) reorganization is usually treated in terms of the classical dielectric (1) For recent review, see: (a) Schmidt, P. P. in “Electrochemistry-A Specialist Periodical Report”; Chemical Society: London, 1975; Vol. 5, Chapter 2. (b) Ulstrup, J. “Charge Transfer Processes in Condensed Media”; Springer-Verlag: West Berlin, 1979. (c) Cannon, R. D. “Electron Transfer Reactions”; Butterworths: London, 1980. (d) Dogonadze, R. R.; Kuznetsov, A. M.; Mariagishvili, T. A. Electrochim. Acra 1980, 25, I. (2) Brunschwig, B. S.; Logan, J.; Newton, M. D.; Sutin, N. J . Am. Chem. SOC.1980, 102, 5798.
0022-3654/84/2088-1860$01.50/0
continuum model as originally formulated by M a r ~ u s . While ~ comparisons between theory and experiment for bimolecular outer-sphere processes show reasonable agreement in a number of cases, significant and often large discrepancies still remain.4~~ Among other things, such discrepancies call into question the quantitative validity of the dielectric continuum model, especially in view of the well-known failure of similar treatments to describe the thermodynamics of ion solvation. In principle, a useful way of monitoring the influence of outer-shell solvation upon electron-transfer energetics is to evaluate entropic parameters since these are expected to arise chiefly from the changes in the degree of solvent polarization associated with electron transfer. The activation entropy, AS*, as for other reorganization parameters, can usefully be divided into “intrinsic” (3) Marcus, R. A. J . Chem. Phys. 1965, 43, 619. (4)Brunschwig, B. S.; Creutz, C.; McCartney, D. H.; Sham, T.-K.; Sutin, N. Discuss. Faraday SOC.1982, 74, 113. (5) Hupp, J. T.; Weaver, M. J., submitted for publication.
0 1984 American Chemical Society
