NOTES
1819
describe how, with the aid of recently published graphs,2 Levich’s technique can be extended to obtain estimates for the cases where the static meniscus away from the wall may be curved, such as in a vessel of small radius or in a reduced gravitational field. The analysis presented for the flat plate film behavior on p 678, 679, and the top half of p 680 of ref 1 carries over unchanged for our problem. (The assumption that the film thickness be small compared with the radius of the vessel is, of course, needed.) The resulting expression for the constant asymptotic film thickness, ho, for a withdrawal velocity that is not too large can be written as ho = 1.34(po/g)”/”/~
=
1
(Bfw
+
lw
(1)
where p is the liquid viscosity, vo is the bulk velocity of the fluid, r is the surface tension, and K is the curvature at the wall of a meridian of the static meniscus. (The coefficient 1.34 in eq 1was calculated using a computed value of 0.643 for 01, the asymptotic dimensionless film curvature, rather than the less accurate value of 0.63 given in eq 133.24 of ref 1.) The appropriate value of K to insert into eq 1 for any cylinder radius and gravitational field can be found from ref 2. From eq 1 of ref 2 one obtains that for a perfectly wetting liquid (0’ contact angle) K
f
- 1)
where a is the radius of the vessel and B = pga2/u is the bond number (a dimensionless parameter) where p is the liquid density and g is the gravitational acceleration; the values of f W , the dimensionless meniscus height at thewall (r = 1) and A, twice the dimensionless mean curvature a t the meniscus center ( r = 0), can be read directly as a function of B from the graphs for zero contact angle in Figures 2 and 5 of ref 2, (see Figure 1). Limiting values for K and ho for very large B (essentially horizontal meniscus away from the wall) and very small B (essentially hemispherical meniscus) can be obtained using the asymptotic expressions for fn. and X given in ref 2 . For very large B, eq E a , 18, and 23 of ref 2 yield K = (l/a) 42, so that
r =I Figure 1. Static meniscus meridian. The variables r and f, which are the ones used in ref 2 , are dimensionless. The radius of the cylinder is a. The quantity K denotes the meridian’s curvature at T = 1, and X/2a its curvature at r = 0.
tional to the vessel radius and depends more strongly on the surface tension.
Acknowledgment. This note is an outgrowth of a discussion with G. D. Bizzell, G. E. Crane, and H. :\I. Satterlee in which the author mas made aware of the problem and the pertinent contents of ref 1. The work mas performed in part under Contract KAS 311526 of Lockheed Research Laboratory with NASALewis Research Center and in part under the auspices of the U. S. Atomic Energy Commission. (2) P. Concus, J . Fluid Mech., 34, 481 (1968).
The Absolute Reactivity of the Oxide Radical Ion with Methanol and Ethanol in Water1 by R. Wander, Bonnie L. Gall, and Leon M. Dorfman Department of Chemistry, T h e Ohio State University, Columbus, Ohio 4 8 H O (Received Sovember 349 1969)
which is the same as the expression given by eq 133.26 of ref 1 (after the value of a is corrected). For very small B, eq 9 of ref 2 yields K = l/a, so that ho = 1.34~(p~o/a) ‘Ia
for this case. Note that for large B the film thickness is independent of the vessel radius and, as noted on p 681 of ref 1, is only weakly dependent on the surface tension. For small B , on the other hand, ho is propor-
The reactivity of the basic form of the hydroxyl radical, o-, formed in the radiolysis of water by the ionic dissociation283 of OH
OH
0-
+ €I+
(1)
(1) This work was supported by the U. S. Atomic Energy Commission. (2) J. Rabani and M . S. Matheson, J . P h y s . Chem., 70, 761 (1966). (3) J . L. Weeks and J. Rabani, ibid., 70, 2100 (1966).
Volume r4>Number 8
April 1 6 , 1970
NOTES
1820 has been determined recently on a relative basis4 for the reactions with methanol and ethanol
+ CH30H = *CH20H + OH0- + CzHsOH .CzHdOH + OH0-
=
(2) (3)
This has been done by competition kinetics using as reference reaction
0-
+
0 2
=
03-
(4)
and observing 0 3 - a t 430 nm, the maximum6-8 of the uv absorption band, in the absence and presence of the alcohol. The values4 reported, kz = 5.2 X lo8 Ill-l sec-' and k3 = 8.4 X lo8 M-' sec-' at 25" are thus related to the rate c ~ n s t a n t ~ = , ~2.5 X lo9M-l sec-l, and were obtained from a complex function of kl,k2, or k3, ~ O H + C H , O H or ~ O H + C ~ H ~ OKOH H, and K , (the dissociation constants for the hydroxyl radical and for water), the alcohol concentration, and the oxygen concentration. It would be desirable to determine kz and k3, as well as the analogous reactions of OH, absolutely by direct observation in pulse radiolysis, of the formation curves (in reactions 2 and 3) of the alcohol radicals which absorblo in the far-uv. However, the absorption of CzH40H is very weak, the extinction coefficientlOrll being about 250 M - l cm-' a t 290 nm, and the absorption overlapping that of the OH radical12 in this region, so that this experiment, for the reactivity of OH, is very difficult. However, at sufficiently high pH, lc, and k3 may be determined directly since the alcohol radicals undergo ari ionic d i s s ~ c i a t i o n ' ~ , ~ ~
-
+ H+ . CzH40- + H +
(5) . CzHdOH (6) to form anion radicals for which the molar extinction coefficients a t 290 nm are slightly less than lo3 M - I cm-l, the pK's being, respectively, 10.7 and 11.6. We report here the direct determination of absolute values for kz and k3by this method. *
CHzOH
eaq-
CHZO-
Experimental Section The detailed pulse-radiolysis technique used in this laboratory, with a Varian V-7715A electron linear accelerator as pulse source, has been described.8 Electrons of 3.5 to 4.0-RIeV energy with a pulse duration of 50 to 400 nsec and a pulse current of 300 to 325 mA were used. The dose per pulse a t maximum current with a 0.1-psec pulse was approximately 6 X 10l6 eV/g. The formation of the radical anion was observed spectrophotometrically a t 360 nm using an RCA 1P28 photomultiplier. Quartz reaction cells8 mere used with the analyzing light making a double pass through 20 mm of cell width. The absorption was measured through a 1.5-mm exit slit of the monochromator with a B & L No. 33-86-07 grating, so that the band pass of the analyzing light was 11.0 nm. The Journal of Physical Chemistry
Triply distilled water was used in the preparation of all solutions. Concentrated sodium hydroxide, 19.4 M , was prepared from Baker Analyzed Reagent. Sodium carbonate is insoluble in this solution and can be filtered out. The reaction of 0- with carbonate ion is, in any case, not of serious concern since the rate constant is reported3 to be less than lo7 L4!I-1 sec-l. The solution was diluted to the desired pH which was determined by titrating with a standardized acid to a phenolphthalein end point. All runs were done at pH >13.3 so that the concentration of OH formed would be negligible compared with 0-, the pK2r3being 11.9. 1Uethanol was Baker Analyzed Reagent which was refluxed with added sulfuric acid and 2,4-dinitrophenyl hydrazine and distilled. U. S. I. Chemical Co. ethanol was used without further purification. The alcoholic solutions for individual runs were prepared with the use of a bulb technique as described,16 which permitted the concentration of reactant to be varied in a sealed cell system while maintaining the same initial starting solution. This procedure was advantageous as it maintained a constant natural decay of 0-, which varies slightly from one solution to another, over each concentration series. As many as five concentrations of alcohol could be handled in the same cell. Ilfethano1 was varied over the concentration range from 0.45 X to 4.5 X M , and ethanol from 0.22 X 10-3 to 2.2 x 10-3 M . All solutions were saturated with KZOat slightly less than 1 atm (which gives approximately 2 X At) to convert the hydrated electron to 0 -
+ NzO = Nz + 0-
(7)
The N 2 0 was USP anhydrous, with an assay of 98.5%, and was used without further purification.
Results and Discussion Because of the occurrence of reaction 7, the system (4) B. L. Gall and L. M. Dorfman, J . Amer. Chem. SOC.,91, 2199 (1969). (5) G. Czapski and L.
M .Dorfman, J . Phys. Chem., 68, 1169 (1964). (6) J. W. Boag and G. E. Adams, 18th Annual Symposium on Cellular Radiation Biology, Houston, Texas, published by Williams and Wilkins Co., Baltimore, Md., 1965. (7) G. E. Adams, J. W. Boag, and B. D. Michaels, Proc. Roy. SOC., A289, 321 (1966). (8) W. D. Felix, B. L. Gall, and L. 11.Dorfman, J . Phys. Chem., 71, 384 (1967). (9) G. E. adams, J. W.Boag, and B. D. Michaels, Xature, 205, 898 (1965). (10) I. A. Taub and L. AI. Dorfman, J . Amer. Chem. SOC.,84, 4053 (1962). (11) L. M. Dorfman and I. A. Taub, ibid.,85, 2370 (1963). (12) J. K. Thomas, J. Rabani, M.S. Matheson, E. J. Hart, and S. Gordon, J . Phys. Chem., 70, 2409 (1966). (13) K . D. Asmus, A. Henglein, A. Wigger, and G . Beck, BeT. Bunsenges. Physik. Chem., 70, 756 (1966). (14) 121. Simic, P. Keta, and E. Hagon, J . Phys. Chem. 73, 3794 (1969). (15) J. L. Dye, M. DeBacker, and L. M. Dorfman, J . Chem. Phys.
in press.
1821
NOTES
tions, and with different pH and different pulse length in some cases. Five such sets were done for methanol and six for ethanol. There is no significant depletion of the alcohol with succeeding pulses a t the low pulse intensity used. The values for Icz and k3 may be obtained from the slopes of the straight lines in Figure 2 . The individual sets show no increase in the rate constant with decreasing pH, indicating that OH (which reacts more rapidly than 0- with the alcohols16)plays no significant role. The values obtained are IC2 = (5.8 i 0.8) X 108 and IC3 = (11.3 rt 1.7) X lo* M-' sec-' a t 25", both slightly higher than the values from competition kinetic^,^ but within agreement according t o the indicated experimental uncertainty. It is clear from the data that reactions 2 and 3, rather than 5 and 6, are rate determining. From the data, considering the highest ethanol concentration used, we may conclude that the rate constant for reaction 6, which should be written in the form
k-4
TI ME
1p e c
Figure 1. Rate curve for the formation of .CzH40- observed a t 360 nm following a 300-nsec electron pulse in a n aqueous M ethanol. solution a t p H 13.92 containing 4.3 x I
Y
OF-
+
Y)
/t
I
0V
I
mA
z IO' I
g A
I 1.0
I 2.0
I
3.0 I
m
"
1 4.0 IV*
,
lo
.z
5.0
Figure 2. Plot of the observed first-order rate constant from formation curves (as in Figure 1) vs. alcohol concentration. T h e individual points represent the following experimental conditions. Ethanol: A, p H 13.80; 0, p H 13.78; A, p H 13.92; 0, p H 13.90 with 50-nsec pulse, 0, p H 13.89 with 50-nsec pulse (the pulse width for all other conditions ranged from 200 to 400 nsec). Methanol: A, p H 13.63; 0 , p H 13.76; 0, p H 13.83; W, p H 13.33; A, p H 13.46. T h e data for each set have been normalized to zero intercept.
consists exclusively of 0- as the reactive species, with the slight exception of H-atom, formed t o the extent of 10%. At the high p H used, however, this is converted rapidly t o ea,-H
+ OH-
= eaq-
+ H20
(8)
and hence also to 0-. A typical rate curve for the formation of 'CzH40is shown in Figure 1. It is clear that, at the low pulse intensities used, a well-defined plateau is formed, the rate of the radical anion association reaction being sufficiently slow. These formation rate curves were found to fit closely to a first-order rate law. The observed first-order rate constants, obtained from the slope of such linear first order plots, show a linear dependence upon alcohol concentration with a positive intercept which varies slightly from one solution to another. All the data for both methanol and ethanol are presented in Figure 2 which shows a plot of the observed rate constant, normalized t o zero intercept, against alcohol concentration. Each set of points represents a single solution with three to five different alcohol concentra-
SC2HIOH
+ OH-
= *CzH40-
+ HzO
(9)
is k6 > 3 X lo7 M-' sec-l, but may of course be much higher. Acknowledgment. We are indebted to Mr. John Richter for his invaluable help in maintaining and improving the electronic detection system and for operating the linac. It is a pleasure to acknowledge helpful discussions with Mr. Norman Shank and Professor J. L. Dye. (16) P. Neta and L. M. Dorfman, "Radiation Chemistry I," Advances in Chemistry Series, No. 81, American Chemical Society, Washington, D. C., 1968, p 222.
Conductance of Dilute Aqueous Solutions of Hexafluorophosphoric Acid at 25' by E. Baumgartner,l Margarita Busch, and R. FernAndez-Prinil Cdtedra de Fisicoquimica, Ftd. Quimica g Farmacia, Universidad de Chile, Santiago, Chile (Received December 1 , 1969)
I n the course of research on the behavior in dipolar aprotic solvents of simple inorganic acids which are strong in aqueous solutions, we became interested in studying hexafluorophosphoric acid. The reasons for this were that (a) PF6- is a very symmetric ion having a rather large crystallographic radius (2.95 A) ;2 (b) the scanty references to HPF6in literature3indicate that it is a strong monobasic acid in aqueous solutions; (c) (1) Department of Chemistry, University of Maryland, College Park, Md. 20740, where correspondence should be addressed. (2) H. Bode and G. Teufer, Acta Crgst., 8, 611 (1955); H. Bode and H. Clausen, 2. Anorg. Chem., 265, 229 (1951). Volume 74, Number 8
April 16, 1970
