Viscosity of Mixtures of Hydrogen and Water Vapor at 295°KJ. W. Fox and A. C. H. Smith

Citation: The Journal of Chemical Physics 33, 623 (1960); doi: 10.1063/1.1731214 View online: http://dx.doi.org/10.1063/1.1731214 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/33/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in The viscosity of polymer–surfactant mixtures in water J. Chem. Phys. 100, 5294 (1994); 10.1063/1.467194 Reaction rates of D2+T2 mixtures at 295 K J. Vac. Sci. Technol. A 1, 1441 (1983); 10.1116/1.572037 Studies of hydrogen bonding in the vapor phase by measurement of thermal conductivity and molecularorbital calculations: Methanol–water binary mixtures J. Chem. Phys. 75, 5900 (1981); 10.1063/1.442041 Sound absorption in mixtures of oxygen and water vapor in the temperature range 298–410 K J. Acoust. Soc. Am. 56, 873 (1974); 10.1121/1.1903340 Thermal Diffusion in HydrogenWater Vapor Mixtures J. Chem. Phys. 19, 509 (1951); 10.1063/1.1748267

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LETTERS TO THE EDITOR 623

single nine-line spectrum is obtained as shown in Fig. 1 (a). For this orientation the splitting between lines is minimum (2.9 gauss). Two nine-line spectra are ob­served with the field parallel to the 110 direction [Fig. l(b)]. Also, the spectrum repeats every 90° when the field is rotated around the 001 direction. This signifies that the defect has two nonequivalent sites related by a 90° rotation about the c axis. Since maximum splitting occurs when the field is along the 110 direction, this is the major axis of quantization of this defect. Minimum splitting occurs for directions perpendicular to the 110 defect axis.

One would expect a single nine-line spectrum when the field is along the 100 direction [Fig. 1 (c)], since the two sites would be equivalent for this orientation. Measured line intensities in the basic nine-line pattern actually indicate that the spectra of the nonequivalent sites overlap for this orientation. However, in addition, small lines appear between the lines of the larger pat­tern. The origin of these lines is undetermined. Their intensities, relative to the larger lines, vary by a factor of two for different crystals and different irradiation conditions. Thus, it seems plausible that these lines may be due to a defect similar to the one giving the major spectrum, but with an environment distorted by other types of crystal defects.

The magnitude of the hyperfine splitting in the spectra is consistent with values obtained in other nitrogen bearing compounds. Also, the relative intensi­ties (obtained by integration) in the nine-line pattern shown in Fig. 1 (c) agree nicely with those expected of an unpaired electron interacting with four equivalent nitrogen nuclei. For the orientations shown by Figs. 1 (a) and 1 (b) measured relative intensities in the nine­line patterns deviate somewhat, but not unreasonably, from the expected intensities.

(a)

(b)

(e)

Ho-OOI

FIG. 1. First deriva­tive of ESR spectra for selected orientations of magnetic field II o. (All spectra are not to the same vertical· scale.)

The model proposed to explain the ESR spectra is a linear N4- molecule-ion which lies in the 110 plane. The defect is thought to be located on a line joining two adjacent azide ion vacancies with its molecular axis directed in either the 110 or 110 direction, each site being equally populated. One can conceive of many ways of forming this N4- configuration in KNs, es­pecially when it is being irradiated with ultraviolet light or gamma rays. However, once the existence of this configuration is postulated, the properties and orientation expected for it are in agreement with those observed. Choosing the z axis, or the molecular axis, in the 110 direction, the x axis in the 110 direction, and the y axis in the 001 direction, the measured values of the g tensor are gx = 2.005±0.001, gy = 1.997 ± 0.001, and gz = 2.002±0.001. The hyperfine interaction is found to be A x =A y =2.9±0.2 gauss and A z =9.4± 0.2 gauss.

The assistance of J. E. Mapes in the preparation and orientation of samples is gratefully acknowledged.

* Supported by the U. S. Atomic Energy Commission con­tracts with University of Connecticut and Brookhaven National Laboratory.

I P. W. M. Jacobs and F. C. Tompkins, Proc. Roy. Soc. (Lon­don) A2I5, 254 (1952).

2 F. C. Tompkins and D. A. Young, Proc. Roy. Soc. (London) A236, 10 (1956).

3 J. Cunningham and F. C. Tompkins, Proc. Roy. Soc. (Lon­don) A25I, 27 (1959).

4 J. E. Mapes, R. W. Dreyfus, and P. W. Levy, OMRO Rept. 13A, Watertown Arsenal Conference on Radiation Effects in Materials, October, 1957; Bull. Am. Phys. Soc. 3, 116 (1958).

• R. W. G. Wyckoff, Crystal Structures (Intersience Publishers, Inc., New York, 1957).

Viscosity of Mixtures of Hydrogen and Water Vapor at 295°K

J. W. Fox AND A. C. H. SMITH*

Department of Physics, University College, London, England

(Received April 12, 1960)

I N the course of an investigation1 of the viscosity of partially dissociated moist hydrogen by measuring

the rate of damping of the oscillations of a small pen­dulum at pressures where the mean free path islnot negligible compared with the diameter of the bob, we had to measure the viscosity of molecular hydrogen containing about 2!% of water vapor at about 20°e. The water vapor was added in order to obtain adequate concentrations of atomic hydrogen. Our results showed that the viscosity of the moist hydrogen was about 7% greater than that of the dry gas. Since we could find no experimental or computed values for comparison, we computed the first approximation to the viscosity of the mixture at 295°K over the complete range of water vapor content.

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624 LETTERS TO THE EDITOR

"'0 H

" co ., '0 e"I'O

~

0'9

o ()os to

FIG. 1. Viscosity '1mi. of mixtures of hydrogen and water vapor at/:295°K plotted against molar fraction x. of water vapor; upper curve from diffusion data, lower from combining laws.

The method of computation and the notation are given by Hirschfelder, Curtiss, and Bird.z As accurate measurements have been made of the viscosities of the pure components, only the two quantities 'l/IZ and A12* are required, both of which depend upon the interaction of hydrogen (suffix 1) and water vapor (suffix 2) molecules. Two methods were applied for determining '1/12, one involving empirical combining laws relating the force constants describing the molecular interac­tions and the other a value of the coefficient of diffu­sion D12 obtained from experimental data.

The constants used in the computation were as follows, viscosities being expressed in poises:

T=295°K '1/1 =0.8858X 10-4 calculated from the empirical formula

given by Woolley, Scott, and Brickwedde3

'l/z = 0.9440X 10-4 calculated from the measurements of Braune and Linke4

'l/12=0.9855X 10-4 calculated by applying combining laws5

AI2*=1.094 from Table J-N2 DI2 =0.980 cmz secl at T=295°K, p=1 atm, extrap­

olated from the measurements of Schwertz and Brow6

'1/12= 1.118X 10-4 calculated from D12.7

The viscosity of the mixture is given by 'l/mix = (1 + Z) / (X + Y), where the first value of '1/12 gives

X = 1.1289x12+ 1. 7889xIX2+ 1.0593x22; Y =0.6564(0. 12633x12+ 7.3859xIX2+9.4666xl) ; Z = 0.6564 (0.11190x!2+ 11.515xIXZ+8. 9365xl) ,

and the second value changes the coefficients of XIXZ to 2.0294, 6.5106 and 9.9130 in X, Y, and Z, respec­tively. Xl and Xz are molar fractions of hydrogen and water vapor respectively.

Values of 'l/mix computed from these expressions are plotted in Fig. 1, the upper curve ('1/12 derived from diffusion data) being ·preferred. The rapid initial in­crease of viscosity with increasing water vapour content

is seen to be due to the occurrence of a maximum of 'l/mix about 35% greater than '1/1 at a value of Xz of about 0.3 (upper curve). The main reason for this maximum is the similarity of the viscosities, combined with the large difference between the molecular weights of the pure gases. The fact that '1/12 is greater than either '1/1 or'l/z is also a contributing factor. The maximum occurs nearer to xz=O than to Xz= 1 because M2 is much greater than MI.The computed values of 1/mix for a molar fraction of water vapour of 0.025 are 0.9541 X 10-4

and 0.9404X 10-4 poise, respectively. These represent increases of 7.7% and 6.2% respectively over the viscosity of pure hydrogen and agree reasonably well with our experimental results.

* Now at Convair, A Division of General Dynamics Corpora­tion, San Diego, California.

1 J. W. Fox and A. C. H. Smith (to be published). 2 J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, M olecuJar

Theory of Gases and Liquids (John Wiley & Sons, Inc., New York,1954).

3 H. W. Woolley, R. B. Scott, and F. G. Brickwedde, J. Re­search Nat!. Bur. Standards 41,379 (1948).

4 H. Braune and R. Linke, Z. Phys. Chern. A148, 195 (1930). 5 The Lennard-Jones potential is used for the interaction be­

tween the hydrogen and water vapor molecules. The combining laws are given' on p. 600 and the values of the constants used in applying them are also given on p. 214 and p. 947 of this book, except the force constants referring to the interaction of the hydrogen molecules. Here new values were calculated based on measurements3 covering a temperature range centered about 295°Kj these values were uI=2.914 A and .J/k=41.7°K. The force constants calculated for the unlike molecules were U12= 2.747 A and <t./k= 147.1 OK.

6 F. A. Schwertz and J. E. Brow, J. Chern. Phys. 19, 640 (1951). 7 In this derivation AI2* was taken as 1.094. Since AI2* is a

slowly varying function of T* this should produce no significant error.

HI_P31 Spin Coupling in Phosphate Esters

GERALD O. DUDEK

M allinckrodt Laboratory, Department of Chemistry, Harvard University, Cambridge 38, Massachusetts

(Received March 14, 1960)

RECENTLY Axtmann, Shuler, and Eberlyl dis­cussed the influence of alkyl substitution on the

HI-P3! spin-spin coupling constant in trialkyl phos­phates of the type (R-CHzOhP=O. It was noted by these authors that "the addition of more electron­releasing substituents, i.e., more methyl groups, not only decreases the coupling but does so markedly."

Their interesting findings included, however, only compounds which are electron-releasing with reference to trimethyl phosphate; the foregoing generalization was further tested by measuring the coupling constants in phosphate esters with strongly electron-withdrawing substituents attached to the methylene group. As a measure of the relative electronic or inductive powers of these compounds, the Taft 0"* function2 is convenient and has found previous application in NMR studies involving the fluorine chemical shift.3 In the first part

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