COMMUNICATIONS TO THE EDITOR
2808
The Volume Change on Neutralization of
A Suggested Mechanism for the
Strong Acids and Bases
Hydrogen-Fluorine Reaction. 11. The Oxygen-Inhibited Reaction
Sir: We recently reported' a limiting apparent molal volume of -5.25 ml. mole-' for aqueous sodium hydroxide at 25". From this value and those for hydrochloric acid and sodium chloride given by Harned and Owen2we obtained a volume change a t zero ionic concentration of 21.86 (sign error in ref. 1) ml. mole-' for the reaction H+(aq)
+ OH-(aq)
=
HzO
Dr. Redlich has kindly pointed out3that the limiting value for the apparent molar volume for hydrochloric acid listed in ref. 2 is based on an incorrect extrapolation to zero concentration. Accordingly, we have redetermined apparent molal volumes of hydrochloric acid a t five concentrations from 0.002 to 0.024 M by the dilatometric method.' The results confirm the theoretical limiting slope4 and extrapolate to +v" (HC1) = 17.82 0.02 ml. mole-'. Our results are in excellent agreement with the earlier work of Redlich and Bigele i ~ e n but , ~ are not in agreement with the results of Geffcken and Wirth or the +v0 values (18.20 and 18.07) quoted by Harned and Owen2 that are based on extrapolations with limiting slopes considerably smaller than the theoretical slope. Combination of +v0 (HCI) = 17.82 ml. mole-', +v" (NaOH) = -5.25 ml. mole-' from our previous work,l +v0 (NaC1) = 16.61 ml. mole-' from the work of KrUis6 (obtained by extrapolation based on the correct limiting slope), and the molar volume of water leads to AVO = 22.11 ml. mole-' for the neutralization reaction represented above. The change from our previous value arises entirely from the revision in dv0 (HCI) from the values reported by Harned and Owen.2
*
(1) L. G. Hepler, J. M. Stokes, and R. H. Stokes, Trans. Faraday SOC.,61,20 (1965).
(2) H. S. Harned and B. B. Owen. "The Phvsical Chemistrv of Eiectrolytic Solutions, 3rd Ed., Reinhold Pudlishing Corp., New York, N. Y.,1958,p. 361. (3) 0. Redlich, personal communication to L. G. H., 1965. (4) 0.Redlich and D. M. Meyer, Chem. Rev., 64, 221 (1964). (5) 0.Redlich and J. Bigeleisen, J . Am. C h m . SOC.,64, 758 (1942). (6) A. Kruis, 2. physik. Chem., 34B, 1 (1936).
PHYSICAL CHEMISTRYDEPARTMENT UNIVERSITIOF NEW ENGLAND ARMIDALE, N.S.W., AUSTRALIA DEPARTMENT OF CHEMISTRY CARNEGIE INSTITUTE OF TECHNOLOGY
PITTSBURGH, PENNSYLVANIA RECEIVEDJUNE 14, 1965
The Journal of Physieal Chemistry
L. A. DUNN R. H. STOKES L. G. HEPLER
Sir: Recently, Levy and Copeland have studied the rate of reaction between hydrogen and fluorine, first in a flow system diluted with nitrogen' and secondly in a static system, in the presence of oxygen2in the temperature range 122-162". A previous communicationa suggested a mechanism for reaction in the absence of oxygen; the present communication indicates how that mechanism can be expanded to describe the oxygen-inhibited reaction. Levy and Copeland2 found that small amounts of oxygen greatly decrease the reaction rate but that soon the rate reaches a limiting value and is unaffected by further oxygen addition. The limiting rate was found to be approximately proportional to the fluorine concentration and the square root of the hydrogen concentration. This result can be explained by the reactions
(F- 2HF + (wall?)
'/2
0 2
The numbering of the last three reactions, indicated by primes, conforms to the numbering frequently used for these hydrogen-oxygen chain reaction steps. When small amounts of oxygen are added to hydrogen-fluorine mixtures, reaction 6 competes with the step
H
+
ks F2
+HF
+F
(2)
At large oxygen concentrations reaction 2 is over(1) J. B. Levy and B. K. W. Copeland, J . Phys. C h a . , 67, 2156 (1963). (2) J. B. Levy and B. K. W. Copeland, ibid., 69,408 (1965). (3) R.9. Brokaw, %%id., 69,2488 (1965). (4) B.Lewis and G. Von Elbe, "Combustion, Flames, and Explosions of Gases,'' Academic Press Inc., New York, N. Y.,1951.
Co MMUN~CATIONSTO THE EDITOR
2809
whelmed. Reaction 6 is well known from studies of the hydrogen-oxygen reaction; it inhibits so that hydrogen and oxygen will not combine at atmospheric pressure and temperatures much below 500°, except in the presence of a suitable catalyst. Although the H02 radical is sufficiently stable that it inhibits hydrogen-oxygen below -500°, at higher temperatures chains may be continued through the slow reaction EO2
+ H2
-
H2Oz
+H
Since the hydrogen-fluorine reaction continues, albeit at a reduced rate, it seems reasonable that HO2 must react with fluorine, as in reaction 7. Reaction 8 is a reasonable bimolecular chain-termination step, while reactions 2’, 3’, and 1’ are familiar links from the hydrogen-oxygen branched chain. (Reactions 1’, 2’, and 3’ must be included to account for the fact that in the presence of a large amount of oxygen the reaction rate is independent of oxygen concentration.) Water is not detected as a reaction product since it further reacts to yield H F and ~ x y g e n . ~ By applying the steady-state approximation to the concentrations of hydrogen, fluorine, and oxygen atoms and also the OH and H 0 2 radicals and remembering that k6[M@)]>> k2’, the following rate expression is obtained
Actually the various third-body efficiencies in reaction 6 should be considered
+
h [ M @ ) ]= k6,~,([H2] 0.43[N21
+ 0.35[02] f fFz[F2l
+ fHF[HFI)
Here fF, and fHF are the third-body efficiencies of F2 and H F relative to hydrogen (the efficienciesfor nitrogen and oxygen are from Lewis and Von Elbe4). We might guess that fF* 0.3 (by analogy with nitrogen and oxygen) ; based on this assumption an analysis of the data of Levy and Copeland’s2 Figure 3 indicates that fHF 1. Thus, the mechanism predicts a rate proportional to about the first power of the fluorine concentration and a somewhat lower order with respect to hydrogen. An over-all rate constant can be obtained by equating the theoretical rate expression with the empirical formula of Levy and Copeland
-
-
kover-all =
klk2‘k, [&I -- kV% ksks
+ 0.43[N21 + 0.35[02] [Hzll”
Values so calculated are shown in Table I. The overall rate constants show slightly less variation, percentagewise, than the empirical 1.5-order rate constants.
Table I: Rate Constants for the Hydrogen-Fluorine Reaction at 132”O -Rate -Initial
Fa
0.032 0.066 0.129 0.066 0.132 0.066 0.066 0.066
mole fraotions-
HZ 0.032 0.066 0.129 0.132 0.066 0.264 0.396 0.527
Oz 0.794 0.659 0.659 0.659 0.659 0.659 0.527 0.396
constants-
ka/,, a.u.-’/Z
Nz 0.142 0.209 0.084 0.143 0.143 0.011 0.011 0.011
Av.
m h - 1
(ref. 2)
0.14 0.14 0.14 0.16 0.15 0.18 0.20 0.26 0.17 i= 0.03
kover-all,m h - 1
0.38 0.28 0.22 0.25 0.29 0.23 0.24 0.31 0.27 & 0.04
Total pressure 695 torr; from Table I11 of ref. 2.
In summary, the mechanism proposed here seems to provide an adequate description of the oxygen-inhibited reaction between hydrogen and fluorine. The experimental data for smaller oxygen additions can perhaps help to elucidate further the combination of the mechanisms set forth here and in the preceding communication. (5) V. A. Slabey and E. A. Fletcher, N.A.C.A. Technical Note 4374, Sept. 1958.
LEWISRESEARCH CENTER AND SPACE NATIONAL AERONAUTICS ADMINISTRATION OHIO 44135 CLEVELAND,
RICHARD S. BROKAW
RECEIVED JUNE22, 1965
Parachor and Surface Tension of Amorphous Polymers Sir: Knowledge of the surface tension of polymers is of interest, on the one hand, as a means of elucidating the nature of the bulk and surface structure of polymeric liquids‘ and, on the other hand, because of its controlling influence on such practical applications of polymers as spinning, adhesion, and stability of dispersions. The critical surface tension yc of wetting of solid polymers, obtainable from contact angle data by a procedure proposed by Zisman12has often been employed as an estimate of the surface free energy of polymers, but there always remained the question of the precise relation between yc and the true surface free energy. For this reason, there has recently been a growing interest (1) H.W. Starkweather, Jr., SPE Trans.,5 , 5 (1965). (2) W. A. Zisman, “Advances in Chemistry Series,” No. 43, American Chemical Society, Washington, D. C., 1964, p. 1.
Volume 69,Number 8 August 1966
