Communications to the Editor TABLE I: no.
1 2 3 4 5 6 7 8 9 10 11 12
The Journal
of Physical Chemistry, Vol. 82, No. 25, 1978 2753
Surface Tension and fa Values of Several Liquids at 25 “C
H bonding groupa
liquid 1-Hexane Cyclohexane Chloroform Carbon disulfide Methyl iodide 1,4-Dioxane Ethyl acetate Acetone Acetic acid 1-Propyl alcohol Ethylene glycol Water
P P P P M M M
M S S S S
eq l b
expt
Y - T(dr/ dT) expt, dyn cm-’
18.2 22.8 26.1‘ 26.4 24.5 32.4 24.2 20.5 19.3c 18.5 28.4 6.7
17.gd 24.4e 26.6e 31. 6e 29.4d 32.8d 23.0d 22.3d 27. 3e 22.6d 48.0f 71.8d
48.6 60.2 66.0 77.2 45.9 42.0 58.8 59.0 56.0 45.0 26.8 47.4
7,
dyn cm-’
geometric model 4.810
4 . 0 0 ~ ~ 3 . 8 1 ~ ~ 3.22a
13.0 12.0 12.0 11.8 12.3 11.0 12.3 12.7 9.8 9.6 7.5 8.0
10.9 10.0 10.0 9.8 10.2 9.1 10.2 10.6 8.2 8.0 6.2 6.7
10.3 9.5 9.5 9.3 9.8 8.7 9.7 10.1 7.9 7.6 5.9 6.3
8.6 8.0 8.0 7.9 8.3 7.5 8.2 8.5 6.6 6.4 5.0 5.4
From ref 3 and 4. From ref 5 and 6. From ref 2: P, poorly; M, moderately; S, strongly hydrogen bonded liquid. A. Weissberger, Ed., “Techniques of Chemistry”, Vol. 11. “Organic Solvents”, 3rd ed., Wiley-Interscience, New York, 1970. e Landolt-Bornstein, “Eigenschaften der Materie in ihren Aggregatzustanden”, 3. Teil, Springer-Verlag, Berlin, 1956. R. W. Gallant, Hydrocarbon Process, 46, 183 (1967). a
an internal surface. He further applies the lattice modell to the same nonpolar liquids and finds a reasonable agreement with both models. His calculations too are all based on well-known thermodynamic relations, in which only macroscopic parameters of the liquid are used. In the present communication, the following extensions of the above theories are discussed: (1)I have applied the Rosseinsky’s relations, and his procedure as well, to geometric forms other than the sphere solely, using formally a tetrahedron, a cube, and an octahedron in the continuum model, with an internal surface. Also the hypotheses concerning the changes of volume and of surface area of the cavity of a single liquid molecule were analogous with those in ref 7 . (2) I have applied these procedures further to hydrogen bonded fluids. The dimensionless quantity cr of Rosseinsky7 equals at 25 “C approximately 1 - (298/y)(dy/dT) and it is hence calculable from the experimental values of y and T(dy/ dT). Performing thus for the geometric bodies mentioned above the calculations made for the sphere of radius a ( a means now the length of the side of the body), we obtain for the geometric factor f the following data:9 for a tetrahedron 4.81, for a cube 4.00, for an octahedron 3.81, and for a sphere 3.22. Numerical values of the product fa calculated from y(T) and f for some selected liquids are compared with the lattice value 8l in Table I. It follows from the table that the models is for the nonpolar liquids 1-4 a much better approximation than the other geometries. The same is true for such nonpolar liquids as methylene chloride, 1-pentane, 1-octane, and toluene, as expected. Rather surprising, on the other hand, is the behavior of liquids 5-8 and of ethyl ether,I because they belong to the class of moderately hydrogen bonded fluids.2 In addition, at least in some of them (acetone, methyl iodide), polar interactions play a more significant role, owing to their relatively high dipole moments. Nevertheless, the models for these liquids is a better approximation than the other investigated geometric forme. This conclusion is not valid, of course, for the strongly associated liquids 9-12 in Table I, for other carboxylic acids, and for monohydric, as well as polyhydric alcohols. We can conclude that the simple models of fluids mentioned above are a good approximation not only for nonpolar liquids, but also for at least some moderately hydrogen bonded ones. If a sphere in continuum is a better approximation than the other geometries, then formula (1) also holds for the liquid. Neither of the theories is directly applicable to strongly associated fluids however. These 0022-3654/78/2082-2753$01 .OO/O
problems will be further explored in the future.
References and Notes (1) (2) (3) (4)
H. T. Davis and L. E. Scriven, J . fhys. Chem., 80, 2805 (1976). A. F. M. Barton, Chem. Rev., 75, 731 (1975). G Allen, G. Gee, and G. J. Wilson, Polymer, 1 (4), 456 (1960). E. B. Bagley, T. P. Nelson, and J. M. Scigliano, J . Paint Techno/.,
43, 35 (1971). (5) Landolt-Bornstein,“Technik”,4. Teil, Bandteil a, Springer-Verlag, Heidelberg, 1967, p 835. (6) R. C. Weast, Ed., “Handbook of Chemistry and Physics”, 57th ed., Chemical Rubber Company Press, Cleveland, Ohio, 1976/1977, F 16-20. (7) D. R. Rosseinsky, J . fhys. Chem., 81, 1578 (1977). (8) L. Onsager, J . Am. Chem. SOC.,58, 1486 (1936). (9) P. Becher, J. Colloid Interface Sci., 38, 291 (1972). Route du Centre 6 CH- 1723 Marly, Switzerland
Ivan Vavruch
Received October 27, 1977; Revised Manuscript Received June 26, 1978
Upper Limits to the Gas Phase Reaction Rates of HONO with NH, and O(,P) Atoms Publication costs assisted by the Ford Motor Company
Sir: The acid-base reaction between gaseous HNO, and NH3 has been observed to occur rapidly,l and nitrous acid (HONO) might also be expected to be very reactive toward NH,. Conversely, O(,P) atoms react very slowly with HNO, ( h 5 3 X cm3/molecule s).’ No measurement of the reaction rate of O(,P) with HONO has been reported although Hampson and Garvin3 suggest that the rate is probably faster than that of O(3P) with “OB. In this communication, we report upper limits to the reaction rate constants for O(,P) and NH3 with HONO which demonstrate that neither of these reactions is rapid. All measurements were carried out in a discharge-flow reactor equipped with a temperature controlling jacket and a movable injector tube. The linear flow velocity was 260 cm/s, and the maximum linear flow distance was 80 cm. The concentrations of the reactants at the end of the flow tube were measured by expanding the gases through a nozzle-sampling orifice into a quadrupole mass spectrometer equipped with an electron impact ion source. The apparatus and the experimental technique have been described in detaiL4 The HONO concentration was monitored at its parent mass (47 amu) in all experiment^.^ Two methods were used to generate HONO in the reactor at concentrations of 2-10 X lo1, molecules/cm3. In the 1978 American Chemical Society
2754
The Journal of Physical Chemistry, Vol. 82, No. 25, 1978
first method, a solution of dilute (0.01 N)aqueous NaNOZ was mixed with dilute (5wt%) aqueous H2S04as described by COX.^ The gaseous products of this reaction were allowed to flow directly into the movable reactor inlet tube using water as the carrier gas. In the second method, an equilibrium mixture of NO, NOz, H20, and HONO was prepared and was injected into the reactor inlet tube through a calibrated flow meter. The water concentrations in the reactor were calculated to be 1.6 X 10l6and 5 X 1014 molecules/cm3 for the first and second methods, respectively. Results were identical using either generation method. For the measurements on reaction 1, O(,P) atoms were O(3P)+ HONO = products (1) generated by titration of N(4S)atoms with NO(UHP). The O(3P) concentration (5-10 X 1014atoms/cm3) was measured at several positions along the length of the reactor by NOz titration and at the end of the reactor by the calibrated mass spectrometer. In measuring the rate of reaction 1,it is important to assess any interference from the recombination process, OH + NO + M = HONO M ( h = 1.5 X cm3/molecule s)., We can estimate an upper limit to a steady state OH concentration by measuring the decay of O(3P)atoms in our reactor, which would be enhanced by the fast reaction, OH 0 = O2 + H (h = 4.2 X 10-I' cm3/molecule s ) . ~ The decrease in O(3P) concentration of less than 50% along the length of the reactor tube indicates that the OH concentration is less than 5 X 1O1O molecules/cm3. Combining this OH concentration with the measured NO concentration in the reactor (NO = 1 X 1013molecules/cm3), we estimate that the rate of formation of HONO by the three-body recombination would be less than 1% of the observed consumption rate of HONO and, therefore, is negligible. The decay in the HONO ion signal in the presence of excess O(,P) is linear with inlet probe position, and a total decrease of approximately 25% is observed at the maximum reaction distance of 80 cm at room temperature. The bimolecular rate constant, hl, obtained by assuming that the observed HONO decay resulted totally from reaction 1was reproducible to &35% at room temperature with an cm3/ average value for six runs of hl3O0 = 1 x 10-l~ molecule s. However, the rate constants measured at 355 K varied from 1to 5 X cm3/molecule s under identical experimental conditions. This suggests that either surface catalysis or reaction of HONO with low concentrations of unidentified radical species more reactive than O(3P)could be affecting the reaction. Because of the possibility of unknown interfering reactions, the current data are sufficient only for obtaining an upper limit to the homogeneous-bimolecular rate constant of reaction 1, k1300 I 1 X cm3/molecule s. The lowest values of k l measured at elevated temperatures indicate that this upper limit remains unchanged in the temperature range 300-355 K. The reaction of NH, with HNOBhas been observed to be very rapid.l We have attempted to better quantify this rate as a standard for evaluation of the reaction of HONO with NH3. During the H N 0 3 experiments, the NH3 concentration in the flow reactor was maintained at approximately 3 X 1014 molecules/cm3, and the H N 0 3 was injected through the movable inlet at concentrations of 3-10 X l O I 3 molecules/cm3. The linear flow velocity was 260 cm/s, and the total pressure was 4.5 torr (NJ.Under these conditions, more than 90% of the HNO, (monitored a t either 63 or 46 amu) was consumed in 0.048 s. White deposits were observed on the flow tube at times between 0 and 0.015 s after mixing. Since we cannot determine from these data whether the reaction occurs primarily in
+
+
0022-3654/78/2082-2754$0 1.OO/O
Communications to the Editor
the gas phase, on NH4N03aerosol particle^,^ or on the reactor surface, the data cannot be used to derive definitive information about the gas phase reaction. However, the overall reaction is very fast, and we estimate that in our reactor the concentration product [NH,] ["OB] is greater than the value (5.8 X loz7 moleculez/cm6) needed for particle nucleation as estimated by Heicklen and Luriaa7 Similar experiments were carried out mixing HONO (2-10 X 1013molecules/cm3) with a high concentration of NH3 (2.5 X 1OI6 molecules/cm3). The flow velocity was 260 cm/s and the mixture contained 4.5 torr of N2. The 47 amu peak decreased by only 10% after a reaction time of 0.27 s at these concentrations. Approximately one half of this decrease results from the effect on the nozzle sampling system of the rise in pressure in the reactor from 4.5 to 5.25 torr when the pure NH3 is added. Assuming that the 10% decrease in the 47 amu ion signal at room temperature could totally be attributed to reaction 2, we HONO NH, = products (2)
+
calculate an upper limit to the bimolecular rate constant, k2 I 1.5 X cm3/molecule s. Thus, the gas phase reaction between HONO and NH3 is at least four orders of magnitude slower than the rate of reaction between HNO, and NH3 in our reactor. Furthermore, there is no evidence of particle nucleation at water concentrations from 5 X 1014to 1.6 X molecules/cm3. References and Notes (1) E. D. Morris, Jr., and H. Niki, J . Phys. Chem., 75, 3193 (1971). (2) C . J. Chapman and R. P. Wayne, Int. J. Chem. Kinet., 6, 617 (1974). (3) R. F. Hampson, Jr., and D.Garvin, Nail. Bur. Stand. (U.S.), Spec. Pub;., No. 513 (1978). (4) E. W. Kaiser and S.M. Japar, Chem. Phys. Lett., 54, 265 (1978). (5) E. W. Kaiser and C. H. Wu, J . Phys. Chem., 81, 187 (1977). (6) R. A. Cox, J. Photochem. 3, 175 (1974). (7) J. Heicklen and M. Luria, Int. J . Chem. Kinet., Symp. No. 1 , 567 (1975). Chemistry Department Engineering and Research Staff Ford Motor Company Dearborn, Michigan 48 12 1
E. W. Kalser" S. M. Japar
Received December 27, 1977; Revised Manuscript Received September 11, 1978
Rate Constants for Self- and Cross-Termination of Transient Radicals by Modulation Electron Spin Resonance Spectroscopy Publication costs assisted by the Department of Energy
Sir: Apart from a large number of rate constants for bimolecular self-reaction of transient radicals in solution only few data are known on the cross reactions of unlike ~pecies.~-j For several years time-resolved spectroscopic techniques have been the main source of information on the kinetics of short-lived radicals in solution, and the lack of data about cross reactions reflects the difficulties in analyzing the decay curves for systems containing two (or more) kinds of radicals which terminate with comparable rates in different self- and cross reactions. This communication describes a spectroscopic technique which allows an analysis of the kinetics of systems with two kinds of species present. Instead of using time-resolved decay curves lifetimes of transients may be equally well determined from the response of transient concentrations to harmonically modulated i n i t i a t i ~ n . ~ If - ~two kinds of 0 1978 American Chemical Society
