301 1
Reactions of Beams of LiCl and LiBr with KCI Surfaces
2, respectively, While the lines in the log 4 us. log [(V Vo)/ Vo] plot are virtually parallel in the "high" temperature region, the lines in the diffusivity plot appear to converge. In spite of the different molecular shapes, the diffusion coefficients of the halogenated benzenes and normal paraffins are within a narrow band a t the boiling points. No trend of D for the halogenated benzenes a t fixed volume expansion is observable. The same is true with respect to the volume expansion a t the freezing point. On the other hand, the volume expansion a t the boiling points has about the same value for molecules of similar shape. Conclusions We can summarize the foregoing by the following points. (1)Equation 2 is not universally applicable for liquids. (2) Equation 2 is restricted to temperatures corresponding to Tr greater than about 0.46 at which unhindered molecular rotation is possible. (3) Equation 3, suggested by Hildebrand for self-diffusion, does not conform to experimental results. (4) The modified form of eq 3 (eq 4) represents the diffusivity well.
(8) L. D.Eicher and B. J. Zwoienski, Science, 177,369 (1972). (9) J. H. Hildebrand and R . H. Larnoreaux, J. Phys. Chem., 77, 1471 (1 973). (IO) A. R. Ubbelohde, "Melting and Crystal Structure," in "Phase T;ansi-
tions," Solvay Institute, 14th Chemistry Conference, Interscience, London, 1971. (11) H. Ertl and F. A. L. Dullien, A.l.Ch.E. J., in press. (12) H. Ertl, and F. A. L. Dullien, Proc. Roy. SOC.,Ser. A, in press. (13) D. B. Davies and A. J. Matheson, Trans. Faraday SOC., 63, 596
(1967). (14) H. H. Landolt and R. Bornstein, "Zahlenwerte und Funktionen," 6th ed, Vol. I I, Part 5a, Sprlnger-Verlag, Berlin, 1969. (15) L. D. Eicher and 8.J. Zwolenski. J. Phys. Chem., 76,3295 (1972).
Appendix. Nomenclature
B B' C D m n u
V Vo
T
= constant, mol-I cm sec
= constant, cm2 sec-l = constant, cm2 sec-I = self-diffusion coefficient, cm2 sec-l = exponent (eq 4) = number of data points = specific volume, cm3 mol-I = molar volume, cm3 mol-1 = constant (eq 2 , 3 , and 4), cm3 mol-I = temperature
Greek Letters References a n d Notes J. H. Hildebrand, Science, 174,490(1971). A. J. Batschinski, 2. Phys. Chem., 84,643 (1913). A. A. K. AI-Mahdi and A. R. Ubbelohde, Trans. Faraday SOC., 51,
361 (1955). J. H. Hildebrand and R . H. Larnoreaux, Proc. Nat. Acad. Sci. U.
I$
= absolute viscosity, mol cm-I sec-l = mean standard error = fluidity (=1/7),mo1-I cm sec
w
= constant (eq I), cm3 mol-l
7 e
S.,
69,3428(1972). E. A. Moelwyn-Hughes, "Physical Chemistry," Pergarnon Press, New York, N, Y . , 1961,pp 717-719. A. A. Miller, Macromolecules, 4,757 (1971). A. A. Miller, J. Phys. Chem., 67,2809 (1963).
Subscripts c r
= critical
= reduced
Reactions of Beams of Lithium Chloride and Lithium Bromide with Potassium Chloride Surfaces Robert 8. Bjorklund and Joseph E. Lester*' Department of Chemistry and Materials Research Center, Northwesfern University. Evanston, lllinois 60201 (Received July 5, 1973) Publication costs assmted by the Materials Research Center, Northwestern University
As a test of an equilibrium treatment of gas-solid reactions, we have used a mass spectrometer to measure the reaction products of LiCl and LiBr molecular beams with KCl single crystals as a function of beam flux and crystal temperature. The data exhibit an increase in the dimerization of beam molecules and certain reaction products with decreasing crystal surface temperature. Using the calculated equilibrium partial pressures of the reaction products, one can correctly predict the trends of the experimental data with varying crystal temperature and beam flux, but not the relative measured concentrations of products. The agreement is better at higher temperatures.
Introduction Interpretation of the evaporation rates of the products of the vaporization of solids and of the products of gassolid reactions by the use of equilibrium thermodynamic properties was first attempted by Langmuir. His analysis
of vaporization rates using the kinetic theory of gases was quite successful in correlating the vaporization rates of several metals with their equilibrium thermodynamic properties. Recently, Batty and Stickney have applied a quasiequilibrium approach to analyze the data from the The Journal of Physical Chemistry, Vol. 77, No. 25, 1973
Robert B. Bjorklund and Joseph E. Lester
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reaction of gaseous 0 2 and solid tungsten and molybdenum at high temperature (>1200"K) and low pressure.2a They introduced an experimentally determined equilibration parameter for the impinging 0 2 , and were able to improve the agreement between the measured evaporation rates of the volatile products and the calculated equilibrium partial pressures. Since more accurate thermodynamic data are available for the alkali halides. a similar comparison for the reaction of one alkali halide beam with another alkali halide crystal a t a lower temperature (
