Reaction of ea;
+ H30+
931 (PCM75-08691). (2) To whom requests for reprints should be addressed. (3) F. A. Momany, R. F. McGuire, A. W. Burgess, and H. A. Scheraga, J . Phys. Chem., 79, 2361 (1975). (4) These computer programs and their description, and all associated geometric and energy parameters, are available on magnetlc tape from the Quantum Chemistry Program Exchange. Write to Quantum Chemistry Program Exchange, Chemistry Department, Room 204, Indiana University, Bloomington, Ind. 47401 for standard program request sheets, and then order No. QCPE 286. (5) F. A. Momany, L. M. Carruthers, R. F. McGuire, and H. A. Scheraga, J. Phys. Chem., 78, 1595 (1974). (6) R. F. McGuire, F. A. Momany, and H. A. Scheraga, J. Phys. Chem., 76, 375 (1972). (7) J. F. Yan, F. A. Momany, R. Hoffmann, and H. A. Scheraga, J. Phys. Chem., 74, 420 (1970). (8) A. Shimada, Bull. Chem. SOC. Jpn., 32, 325 (1959). (9) T. R. R. McDonaldand C. A. Beevers, Acta Crystallogr., 5,654 (1962). (10) G. M. Brown and H. A. Levy, Science, 147, 1038 (1965). (11) R. Shiono, D. W. J. Cruickshank, and E. G. Cox, Acta Crystallogr., 11, 389 (1958). (12) H. van Koningveld, R e d . Trav. Chim. Pays-Bas, 87, 243 (1968). (13) I. Nitta, S. Seki, M. Mamotani, K. Suzuki, and S. Nakagawa, Proc. Jpn. Acad. Scl., 26, 11 (1950). (14) R. S. Bradley and S. Cotson, J. Chem. Soc., 1684 (1953).
inflexible molecules may prevent optimal hydrogen bonding approaches of H4and OI8. The hydrogen bond is nearly linear, with the 0-H-0 angle above 162' for all bonds, and above 170° in most cases. The calculated lattice energies and experimental sublimation energies agree fairly well. The calculated energies are smaller in magnitude than the observed values. However, the latter may contain contributions from sources which are not taken into account in these computations, such as vibrational terms. Acknowledgment. We thank Drs. L. G. Dunfield and F. A. Momany for helpful discussions and Marcia Pottle for aid with the computer programs. References and Notes (1) This work was supported by grants from the National Instituteof Aging and from the National Institute of General Medical Sciences, of the National Institutes of Health, US. Public Health Service (AGO0322 and GM-14312), and from the National Science Foundation
The Reaction of ea; 4- H30f. Concentration Effects of Acid or Salts C. D. Jonah, J. R. Miller, and Max 8. Matheson" Chemlstry Division, Argonne Natlonal Laboratory, Argonne, Illinois 60439 (Received January 17, 1977) Publication costs assisted by Argonne National Laboratory
The rate constant, k(e,; + H30+),has been measured in dilute HC104,alone and with LiC104added up to 2.5 M, and in concentrated HC104,alone and with LiC104or NaC104added up to 2.5 M. The rate constant has the same dependence upon total concentration either for HC104alone or for HC104+ LiC104. The results show that changes in k(e,; + H30*) are determined by changes in the diffusion-controlledencounter rate and by changes in the 'activities of e,, and H30+. Any time-dependent effect in the rate constant is not more than 10% for hydrated electrons with lifetimes longer than 30 ps.
Introduction The rate constant for the reaction ea&
+ H,O+-+H t H,O
(1)
has been measured in dilute solution by a number of workers,' with a preferred value for kl of 2.3 X 10" M-l s-'. Although, this is a rapid reaction it is still only about one fifth the diffusion-controlled encounter rate: the latter being very high owing to the high diffusion constants of eaq-and, especially, H30+. In the presence of added salts up to ionic strength about 0.05, kl for dilute acid obeys the Bronsted-Bjerrum equation
as shown by Czapski and S~hwarz.~ k I ois the value at ionic strength, p, equal zero and the 2 s are the units of electronic charge on e a i (-1) and on H30+ (+I). In concentrated solutions of HC1 or HC104 Hunt and his colleagues4used his stroboscopic pulse radiolysis technique to determine kl and found k1 varied from 1.0 to 1.4 X 1O1O between 0.3 and 5.0 M acid with a shallow minimum at about 1 M. Schwarz5 interpreted these results in terms of ionic strength effects (activity coefficients) plus time
dependent effects at the highest concentrations (shortest times). We have remeasured kl in both dilute and concentrated perchloric acid, with and without added salt. In this paper we present these results and from them deduce that activities and encounter rates control reaction 1 and that there are no important time-dependent effects at times greater than 30 ps. Experimental Section Apparatus. For experiments with dilute acid the Argonne ARC0 electron linac was used with standard pulse radiolysis techniques involving photomultiplier detection! Electron pulse length was set at 4 ns. A pulsed xenon lamp was used as the analyzing light for measurement of e, - at 600 nm. Cell length was 5 cm with one light pass. bell filling techniques have been previously r e p ~ r t e d . ~ Rate constant measurements at high acid concentrations were made with the Argonne stroboscopic pulse radiolysis apparatus,8 which has a time resolution of about 40 ps. The microwave linac is pulsed 60 times per second, each pulse consisting of a main pulse containing more than 90% of the charge and with a width (fwhm) of 30 ps. The beam is spread horizontally, and about 30% in the center is intercepted by a Cerenkov generator (contains 1atm of xenon), while the rest of the beam is passed around a 270° The Journal of Physical Chemistry, Vo/.81, No. 9 , 1977
C. D. Jonah, J. R. Miller, and M. S. Matheson
932
Hunt averaged Our data
0L
0.0I
I
I
I
I
1
I
1
0.I
M
1
1 1.0
I
I 10.0
HC104
+
Figure 1. The rate constant, Me,( H,O+), as a function of HCIOl concentration: 0 ,values from Bronskill, Wolff, and Hunt (ref 4). Where more than one measurement was reported for a given concentration in ref 4, the values for that concentration have been averaged. 0, our results for two separate experiments.
e,
magnet to delay it by a fixed time and then focussed in the reaction cell. The focussed single pulse deposited 1.5 krads eV/g) in the irradiated volume. The light generated in the xenon gas is delayed a variable amount by mirrors moving at a constant speed, so as to change the light path length at a constant rate. The moving mirrors cause the Cerenkov light pulse to scan the cell absorption from a time 500 ps before the corresponding electron pulse enters the cell to 3500 ps after. This relatively wide time range enabled measurements of kl over a wider concentration range than is possible when measurements are restricted to the time between fine structure p u l ~ e s .The ~ electron and light pulses pass collinearly through the 2-cm long cell. The hydrated electron absorption was measured at 600 nm. Since solutions are repetitively pulse irradiated, a flow system was used to minimize product build up. A non-linear least-squares fitting of the experimental data was used to evaluate k l . Corrections were made for the small decay of the hydrated electron in the spurs.g In pure water this decay was measured as 17% from 0.1 to 3.0 ns, which is smaller than earlier theoretical predictions. Further, we found the decay essentially the same in pure water and 3.0 M LiC104, indicating spur reactions are largely unaffected by such a salt concentration. Materials. For dilute acids triply distilled water was used to make solutions, while water purified by deionization and filtration using Continental Water Co. equipment was used for concentrated acid solutions. Perchloric acid Reagent Grade double vacuum distilled (G. Frederick Smith Chemical Co.) was diluted appropriately to prepare solutions. In some experiments with dilute acid the concentrations were checked by titration with standard base. Lithium perchlorate anhydrous Reagent, sodium perchlorate hydrated Reagent (NaC104-H20),and calcium perchlorate hydrated Reagent (Ca(C1O4)y6Hz0)from G. Frederick Smith were used as received. Results and Discussion We have remeasured kl in pure concentrated solutions of perchloric acid and our results are compared with those of Bronskill et al.4 in Figure 1. The agreement is good in the region of overlapping concentrations. Owing to the higher frequency of his linac Hunt has a time resolution about a factor of 2 better than ours. On the other hand, our single more intense fine structure pulse enables us to measure rate constants at longer times (lower concentrations). Note that the minimum for kl is at 1 M perchloric acid (Figure l),while the minimum for the mean activity coefficient,y, of HC10;’ is at lower concentrations, 0.3-0.4 M. Further, as pointed out by S c h w a r ~if, ~one The Joirrnd of Physical Chemistry, Voi. 81, No. 9. 1977
assumes r(H+)-y(e,,3 = r(HVy(C10,) then the observed reduction of kl in concentrated solutions is much greater than can be accounted for by activity factors alone. Schwarz, proposed that “a reaction between charged species, even when not diffusion limited, will exhibit a time-dependent rate constant”. The charged reactants eventually establish concentration gradients around each other, owing to attractive or repulsive potentials. In the present case ea< and H30f will attract each other, and “if the reactants are distributed uniformly initially, the rate constant will increase with time”,5 that is kl will be depressed at higher concentrations. To relate our experiments to Schwarz’s theory we need to estimate the ages of ea[ in our solutions. In earlier work on time- or concentration-dependent rate constants,” we noted that the effective time after eaq-formation in our experiments that corresponds to a given solute concentration should be taken as the half-life calculated from the experimental rate constant observed for that particular concentration plus 25 ps. The 25 ps was added as an estimated correction for the finite widths of electron and light pulses. For e,; in 1M HC104we estimate on this basis that the average age of the hydrated electrons during the kl determination is 88 ps. According to Figure 1in Schwarz’s paper one should expect a reduction of 30% in kl from the time-dependent effect alone. Since Hunt’s experiments were carried out similarly to ours, at 2.5 and 5.0 M acid the average e,; ages would be about 30 and 20 ps, respectively, and the corresponding time-dependent reductions in kl about 45 and 50%. We shquld emphasize at this point that this Coulombic field-induced,time-dependent effect discussed by Schwarz is not the same as the ionic strength effect proposed by Coyle, Dainton, and Logan.12 They noted that if ;e! is suddenly produced in a high concentration of reactive ionic solute, eaq-may react with the solute before acquiring an ionic atmosphere. For such a case the coefficient in eq 2 would be reduced from 1.02 to 0.51 at short times. The effect proposed by Coyle et al. requires that the reaction be diffusion controlled or very nearly so, whereas the type of reaction examined by Schwarz must be fast but definitely slower than diffusion controlled. Further, for ea; + H30+the Coyle et al. effect would predict a higher rate constant at shorter times owing to greater Coulombic attraction before ea; acquires its ionic atmosphere, whereas the time dependence of the Schwarz type predicts a lower k at shorter times before the equilibrium concentration of H30+is built up around ea;. To measure the importance of the ionic strength in reducing kl,we measured this rate constant in dilute (3 x and M) and concentrated HC104 with added LiC104. We chose LiC104 because its mean activity coefficient is rather close (slightly higher) to that of HC10;’ even up into molar concentrations. These results are shown in Figure 2. Our average for kl in pure dilute HC104 extrapolated to zero ionic strength using eq 2 was (2.3 f 0.2) X lo1’ M-’ s-l in agreement with the value taken from the literature.’ The line in Figures 1 and 2 begins at 1.90 x lo1’ at 0.01 M concentration, this value being calculated with eq 2 and :k = 2.3 X lo1’. In Figure 2 kl for dilute acid plus LiC104 is in good experimental agreement with the line for k l in pure HC104 out to 2.5 M. The results with concentrated acid also show the rate constant is similarly affected by added LiC104or HC104, that is, the observable effect within experimental error depends entirely on total ionic strength. The points for concentrated acid in Figure 2 do lie an average of about 7 % above the line for pure HC104from Figure 1 but this
+ H30+
Reaction of ea;
933
-
i 0 0
A
0 0.0I
0.01 M Ht 0 . 0 5 M HS 0 . 5 M HS
1 1
0.I
I
/
1.0
10.0
H C 1 0 4 -t L I C 1 0 4
+
Figure 2. The rate constant, yea; H30f), as a function of total HC104 LiC104concentration: -, the line for pure HC104 copied from Figure 1; 0,dilute H,O+; 0, 0.01 M HC104; 0,0.05 M HC104; A, 0.5 M HC104. The points for dilute HC104are actually plotted against total ionic strength oPsolutions prepared by diluting a parent sorution, 3.7 M LiC104 0.1 M Ca(C104)2,of p = 4.0. The LiC104, when used in high concentrations, appeared to have an impurity (assumed to be carbonate) that neutralized a fraction of the dilute HCIO.,. Before use the 3.7 M LiC104 0.1 M Ca(CIO& was allowed to stand several days protected from the atmosphere. A trace of fine precipitate settled out, and the supernatant liquid was carefully decanted.
+
+
+
L :2.0
L
" I
1
1
"I
coefficients) affect klequally within the experimental error of 10%. Since the addition of LiC104cannot induce time dependence of the kind discussed by Schwarz, we conclude that up to 2.5 M HC104any time-dependent effect must affect k(e,( + H30+)by less than 10%. Probably the use of a potential for ionic attraction that is applicable to dilute solutions5 overestimates the time dependence to be expected in the solutions used in our experiments. Thus, with respect to local excess concentrations induced by ionic attraction, Olivares and McQuarrie14have calculated the radial distribution function for the hard sphere model of a 1-1 electrolyte. Using a contact radius of 4.25 A, they found that for a 0.009 11 M solution the concentration of oppositely charged ions about a given ion at the contact radius is about 4.4 times the bulk concentration, while for a 1.0 M solution this ratio is only about 2. The lower this ratio becomes in concentrated solutions, the lower will be the magnitude of the expected time dependence. Activity and Diffusion Coefficient Effects on kl. Having concluded that there is no appreciable time-dependent effect in our results, we can make estimates of the other factors reducing kl in concentrated solutions. However, with our present knowledge, these estimates, while informative, are only approximate. We separate the observed rate constant k&d into the diffusion-controlled encounter rate constant, kd, and the specific reaction rate constant, k,.15 We assume that
1
-
kobsd
H C I O 4 +LiCIO,=I.OM
4
1 kd
+ -1 k,
k,O is the specific rate constant at p = 0, and k, = k7:y(H+)y(e,;) = k;y*(H.e) where y(H.e) is the mean activity coefficient of the acid H30+.-ew-in the given solution. For pure water, where y(H.e) = 1 we can calculate k d = 10.6 X 10" M-'s-l using the Debye equation16
M HC104
+
Figure 3. The rate constant, k(e,; H30+), as a function of HC104 concentration measured in solutions where [HCIO4] \LiC104] = 1.0 M: 0, experimental measurements; -, 2.3 X 10'oy (HC104).
+
is a systematic deviation for all measurements in this experiment including, as can be seen, those for pure HC104 (0.01,0.05,and 0.5 M). Further evidence that LiC104and HC104have nearly identical effects on kl is seen in Figure 3. From 0.01 M HC104+ 0.99 M LiC104to 1.0 M HC104 the experimental results are closely constant. Following Schwarz we assumed y(H+)y(e,J = y(H+)y(ClOJ = y2(HC104).To estimate y2(HClO4)in LiC104we proceeded as f01lows.l~We assumed "the logarithm of the activity coefficient of either component in a mixture maintained at constant molality is therefore a linear function of the composition". Further, since LiC104 and HC104 have a common ion, we assumed the log y(HCIO,), for infinitely dilute HC104in 1 M LiC104is equal to log y(LiC104), for infinitely dilute LiC104 in 1 M HC104, and that log y(HCIOQ)o= 1/2[10gy(for pure 1 M HC104)+ log y(for pure 1 M LiC104)]. Since the activity coefficients for LiC104 and HC104do not differ greatly, the errors introduced by this interpolation process should be small. The activity coefficient, y(HClO,), estimated in the various solutions was squared and multiplied by klo = 2.3 X 10" M-l s-l, Figure 3. We see that the activity coefficient is nearly constant, and that y2 so estimated fails to account for almost half the reduction in kl. Conclusion of Time Dependence. The results summarized in Figures 1-3 show that the addition of either HC104 or LiC104 (electrolytes with nearly equal activity
where N is Avogadro's number, D is the sum of the diffusion coefficients (DH+ = 9.3 X and De- = 4.96 X cm2s-'), r is the reaction radius (5.5 X cm), and ro is the Debye length (7.1 X lo-' cm in pure water at 25 "C). With kOM = 2.3 X lolo and kd = 10.6 X lo1', eq 3 gives k? = 2.94 X lolo M-l s-' at zero ionic strength. In HC104+ LiC104 = 1 M we estimate kd, DH+ = 6.0 X cm2s-l in 1 M NaC1.I7 (We were unable to find data on DH+ for HC104,LiC104,or NaC10, solutions.) De- was cm2 s-l, assuming that k(ea; estimated as 4.2 X CH,N02) for 0.05 M CH3N02is reduced from 3.5 X 10" in the absence of LiC104 to 2.95 X 10" M-' s-l in the presence of 1.0 M LiC104solely by the change in De-. (A rather similar dependence on concentration was found for k(ea,- CH3N02)in Ca(C104)2solutions.) The diffusion constant for nitromethane in pure water is only about 30% of De- in pure water. The total diffusion constant in 1 M LiC104then is 0.715 that in pure water, and 10.6 X 10" is reduced to 7.6 X lo1' M-' s-' by this factor alone. This is an upper limit since the Coulombic attraction of ea; and H30+will be reduced in a 1M HC104or LiC104 solution. A lower limit for k d in such solutions is 4.2 X 10" M-ls-l, which is the diffusion-controlled encounter rate in the absence of any Coulombic attraction. We choose kd = 6.0 X 10'O M-' s-l, noting that a 10% error in this value will yield a lesser error in the activity coefficients to be estimated, because l / k d is smaller than l/k,. With kobsd = 1.2 X 10" and kd = 6.0 X lolo M-' S-l for 1 M HC104 we calculate k, = 1.5 X lolo M-l s-l from eq
+
+
The Journal of Physical Chemistry, Vol. 8 1 , No. 9 , 1979
Communications to the Editor
934
0 O.OItjH‘
4 are significant, because the experimental deviations within an experiment were less than the deviations between experiments. We restate our earlier conclusion that up to 2.5 M HC104 any time-dependent effect must affect k(e, - H30+)by less than lo%, and add that up to 2.5 M (Helo, + LiC104 or NaC104)changes in this rate constant are determined by changes in the diffusion-controlled encounter rate and by changes in activity coefficients. Acknowledgment. We wish to thank Barbara B. Saunders and William A. Mulac for the measurements of klin dilute HC104solutions and we thank Don Ficht and Lee Rawson for consistent excellent operation of the Electron Linac. We are also grateful for Robert M. Clarke’s invaluable assistance.
+
it
1 0
0.01
I .o
0.I
10
MHCI04 t NaClO,
Flgure 4. The rate constant, (e/a; 4- H30+), as a fun& of total HCD4 4- NaCIO, concentration: -, the line from Figure 1 for pure HC104; 0, 0.01 M HC104; 0 , 0.05 M HCi04; 0 , 0.5 M HC104.
3. The ratio of this to 2.94 X 1O1OM-l s-l, k, in pure water, gives y2(H.e)o= 0.51 or y(H-e)o= 0.714 for infinitely dilute H30+-.e,p- in 1M HC104. From Robinson and Stokes as discussed above, this activity coefficient is the geometric mean of the activity coefficients for 1M HC104 = (0.826) and for 1 M H30+-.eaq-. This gives us y(H.e) = (0.714)’/0.826= 0.62 in 1 M H30+-.ea;. We now apply these approximations to klmeasured in HC104 NaC104 solutions. The activity coefficient for 1 M NaClO is 0 63 very close to our estimate for y(H.e) in 1 M H30’.-eai-, so we might expect y(H.e) to be about 0.62 for reaction of ea; with dilute acid in 1 M NaC104. From Figure 4 kobsd for 0.01 M HC104in 1.0 M NaC104is 0.98 X lolo and with kd = 6.0X lo”, k, = 1.17 X lolo M-’ s-l yielding y(H.e) = 0.63 for dilute H30+-ea; in 1 M NaC104. In view of the uncertainties in k d plus experimental error the agreement should not be overemphasized. Note also in Figure 4 that increasing HC104 for a given total concentration of HC104 NaC104raises kobd, which is in accord with the fact that activity coefficient vs. concentration curve for HC104is substantially higher than for NaC104. The small and consistent differences in Figure
+
+
References and Notes (1) (a) M. Anbar, M. Bambenek, and A. B. Ross, Natl. Stand. Ref. Dafa Ser., Nafl. Bur. Stand., No. 43 (1973); (b) A. B. Ross, bid., No. 43, Supplement (1975). (2) (a) H. A. Schwarz, Radiat. Res., Supplement 4, 89 (1964); (b) M. S. Matheson, Adv. Chem. Ser., No. 50, 45 (1965). (3) G. Crapskl and H. A. Schwarz, J. Phys. Chem., 66, 471 (1962). (4) M. J. Bronskill, R. K. Wolff, and J. W. Hunt, J. Chem. Phys., 53, 4201 (1970). (5) H. A. Schwarr, J. Chem. Phys., 55, 3647 (1971). (6) M. S. Matheson and L. M. Dorfman, “Pulse Radiolysis”, M.I.T. Press, Cambridge, Mass., 1969, Chapter 3. (7) E. J. Hart and M. Anbar, “The Hydrated Electron”, Wiley-Interscience, New York, N.Y., 1970, Chapter IX. (8) C. D. Jonah, Rev. Sci. Instrum., 46, 62 (1975). (9) C. D. Jonah, M. S. Matheson, J. R. Miller, and E. J. Hart, J. Phys. Chem., 80, 1267 (1976). (10) W. J. Hamer and Y.-C. Wu, J. Phys. Chem. Ref. Data, 1, 1047 (1972). (11) C. D. Jonah, J. R. Mlller, E. J. Hart, and M. S. Matheson, J . Phys. Chem., 79, 2705 (1975). (12) P. J. Coyle, F. S. Dainton, and S. R. Logan, Proc. Chem. Soc., 219 (1964). (13) R. A. Robinson and R. H. Stokes, “Electrolyte Solutlons”, 2nd ed, Academic Press, New York, N.Y., 1959, pp 432-437. (14) W. Olivares and D. A. McQuarrie, J. Chem. Phys., 65, 3604 (1976). (15) R. M. Noyes, Prog. React. Kinet., 1, 137 (1961). (16) P. Debye, Trans. Electrochem. SOC.,82, 265 (1942). (17) N. K. Roberts and H. L. Northey, J. Chem. Soc., Faraday Trans. 7, 70, 253 (1974). (18) K. H. Schmidt, Inf. J. Radiat. Phys. Chem., 4, 439 (1972).
COMMUNICATIONS TO THE EDITOR Comment on “Interaction of Sodium Dodecyl Sulfate with the Hydrophoblc Fluorescent Probe, 2-p-Toluidlnylnaphthalene-6-sulfonate” Publication costs assisted by the Technical University of Denmark
Sir: In a recent study by Chiang and Lukton’ the variation of the critical micelle concentration (cmc) of sodium dodecyl sulfate (SDS) in various NaCl concentrations was reported by the increasing fluorescent intensity measurements of 2-p-toluidinylnaphthalene-6-sulfonate (TNS). These authors also compared the variation of cmc with the molarity of added salt as measured by other methods in The Journal of Physical Chemistry, Vpl. 81, No. 9, 1977
their Table I. In their Figure 2, Chiang and Lukton gave a plot of log (cmc(M))vs. log (cmc(M) + molarity of added salt) at 25 OC, as measured by the fluorescent intensity method only. Their analysis of this data is the subject of this comment. In Figure 1we give all the data: i.e., both from literature and fluorescent intensity measurements, as given in Table I by Chiang and Lukton. It is clear that the literature data agree with the well-established linear relation between log (cmc(M))and log (cmc(M) + molarity of added salt)? The fluorescent data, on the other hand, does not show any simple linear relationship, as argued by Chiang and LuMon from a plot in their Figure 2. Further, they also show in
