where
and
Further, M i are the molecular weights and T is the temperature. T h e expression for a j j is obtained from that of aj, by interchanging the subscripts. Q!2,2)* and T* are reduced collision integral and temperature, respectively. u is the collision diameter and 6 is a potential parameter (Monchick and Mason, 1961). We consider the experimental data on 11 binary systems: Trautz and Heberling (1931) on NH3-H2, NH3-N2, and “30 2 ; Jung and Schmick (1930) o n ”3-air, NH3-CH4, HC1air, S O Z - C O ~and , H2S-air; Trautz and Narath (1926) on HCl-H2; and Trautz and Weizel (1925) on s02-H~. The viscosity data used for polar and nonpolar pure gases are the same as referred to by Mathur and Saxena (1965). The potential parameters required for the calculation of 7 , and q i j are taken from Hirschfelcler et a / . (1964), Mason and Monchick (1962), and Monchick and Mason (1961). The mixture viscosities \rere calculated from Equations 1 and 2 for all the systems and a t those tempstratures and compositions for which the direct experimental values are available. I t was found that Brokaw’s method invariably underestimates the viscosity values, so that the experimental values are greater than the calculated values. For all the 224 calculations made, including pure and binary mixtures, the average absolute deviation is 3.0% and remains the s,ame even for 174 mixtures. T h e rigorous theory of Mason and Monchick (1962) on the other
hand reproduces the data within an average absolute deviation of 1.0%. I n the calculation by Brokaw’s method (1965) the amount of information needed is the same as in t h e rigorous theory method. Further, as Brokaw’s method is inferior t o the rigorous theory method in predicting viscosity values, a simpler and more accurate method would be useful. We outline such a procedure below. We prefer t h e use of experimental viscosity values for the pure components instead of theoretical values. Further, for each system we compute Q I 3 a t the lowest temperature and use the same values even a t the higher temperatures. This modified Brokaw’s method reproduces the experimental data on 174 mixtures within an average absolute deviation of 1.8%. If only those mixtures are considered where the calculations are made using determined a t a lower temperature, we get for 95 such mixtures the average absolute deviation of 1.2%. These results favorably compare with other similar methods used very often for estimation of viscosity of mixtures. Acknowledgment
We are grateful to the Ministry of Defence, New Delhi, for supporting this work and for the award of a research fellowship to P. K. Tondon. literature Cited
Brokaw, R. S., J . Chem. Phys. 42,1140 (1965). Hirschfelder. J . 0..Curtiss. C. F.. Bird. R. B.. “Molecular Theorv of Gases and Liquids,” Fkley, h e w York, 1964. Jung, G., Schmick, H., 2. Phys. Chem. B7,130 (1930). Mason, E. A , , Monchick, L., J . Chem. Phys. 36,2746 (1962). Mathur, S., Saxena, S. C., Brit. J . Appl.Phys. 16,389 (1965) Monchick, L., Mason, E. A., J . Chem. Phys. 35, 1676 (19611. Trautz. M.. Heberlinn. R.. Ann. Phvsik 10. 155 (1931). Trautz; M.; Narath, Ann. PhysA 79, 657 (1926). ’ Trautz, M., \Veizel, W., Ann. Physik 78, 305 (1925).
x.,
P. K. T O N D O N Department of Physics Cniversity of Rajasthun Jaipur, Rajusthan, India
S. C. SAXENA Thermophysical Properties Research Centet Purdue University Lafayett?, Ind.
RELATION B E T W E E N BOILING P O I N T CHANGE AND VIBRATIONAL FREQUENCY S H I F T I N M E T H Y L AND ETHYL, HALIDES Relation exists between the logarithm of the temperature difference, log lAT1, formed between the normal boiling point values of methane and its homologs, CH3X (X = F, CI, Br, I), and ethane and its homologs, C2H5X, vs. the corresponding vibrational frequencies: ~3 and Y6 for methyl halides, and the C-X bond stretching and C-C-X bond bending frequencies in the ethyl halide series.
Relationships can be found by plotting the logarithm of the temperature difference, log IATi, formed between the normal boiling point values of methane and its homologs, CH3X (X = F,Cl,Br,I) and ethane and its homologs, C*HsX, against the corresponding vibrational frequencies v 3 and in the case of methyl halides, and the C-X bond stretching and C-C-X bond bending frequencies in the ethyl halide series
(Figure 1). T h e results are given in Table I. Despite the possible uncertainties in the chosen boiling point values (Table I), it seems reasonable t o observe (Figure 1) that the frequency shifts in methyl halides correlate with the respective calculated log A T ’ values yielding smooth curves. T h e ethyl halide correlations, however, appear to be nearly linear. I t would, therefore, seem plausible to believe that this VOL. 7
NO. 2
M A Y 1968
315
Table 1.
Normal Boiling Point, T,, C. -161.37a
Compound Methane, CH4
Methyl fluoride, CH3F
-78.414
Methyl chloride, CH&l
- 24.09
Methyl bromide, CH3Br
3.457
Methyl iodide, C H d
42.50
Summary of Data
Reference Timmermans, 1950 Timmermans, 1950 Timmermans, 1950
] A T [ , C. 0
137.280
732
Timmermans, 1950 Timmermans, 1950
164.827
61 1
203.870
533
82.956
Vibrational Frequency, Cm. Reference Ye
v3
...
...
...
1048
Bennett and Myer,
1196
Bennett and Myer, 1928 .. Joint Army, Navy, Air Force (JANAF), 1963 Bennett and Mver. 1928 Bennett and Myer, 1950
1928 __--
~~
Joint Army, Navy, Air Force (JANAF), 1963 Bennett and Mver. 1928 Bennett and Myer, 1950 ,
Ethyl fluoride, CZHSF Ethyl chloride, C&&l
-32.0 12.28
Ethyl bromide, C2H6Br
38.4
Ethyl iodide, CzHsI
72.42
880
I
.
Bend
...
...
...
...
56.62 100.90
810 658
Nielsen et al., 1954 Daasch et al., 1954
415 336
Nielsen et al., 1954 McDevitt, 1961
127.02
560
McDevitt, 1961
292
161.04
497
McDevitt, 1961
262
Green and Holden, 1962 Pai, 1932
0
Timmermans, 1950 Swarts, 1924 Timmermans, 1950 Timmermans, 1950 Timmermans, 1950
952
c-c-x
Stretch
-88.62
1020
I
c-x Ethane, CzHe
Reference
...
Value taken from saturated vapor pressure data (C. J. Timmermans. 1950) at 760 mm. of Hg.
T h e correlation presented (Figure 1) confirms the already indicated relations (Kashaev, 1966) for homologous n-paraffin, n-alcohol, and cycloparaffin compound classes. Literature Cited Legend: -
0 A
2ot IO
O
v3 Frequency] Melhyl Holldes
v6 Frequency C-X Strelch
Ethyl Holides
0 C-C-X Bend 4
I
I
I
I
1
I
I
correlation implies that the given frequencies not only d o not appreciably interact with other characteristic modes of the excited molecule, but are themselves determined by the nature of the given substituent atom C-X and C-C-X bonding type and the relative steric and electrostatic effects connected with these substituted halogens. This also confirms the views expressed in a n earlier study (Lielmezs, 1966).
316
I&EC FUNDAMENTALS
Bennett, W. H., Meyer, C. F., Phys. Rev. 32, 888 (1928). Daasch, L. N., Liang, C. Y., Nielsen, J. R., J . Chem. Phys. 22, 1923 (1954). Green, J. H. S., Holden, D. J., J . Chem. SOC. 1962, p. 1794. Joint Army, Navy, Air Force (JANAF), U. S. Air Force Contract No. AF 04 (611) 7554 ( l ) , 1963. Kashaev, S. K. G., Opt. i Spektroskopiya 21, 308 (1966). Lielmezs, J., Nature 211, 742 (1966). McDevitt, N. T., U.S. Dept. Comm., A.S.D. Tech. Rept. 61-202 (1961). Nielsen, J. R., Smith, D. C., Ferguson, E. E., Sounders, R. A , , J. Chem. Phvs. 22, 1923 (1954). an J . Phys. 7, 522 (1932).
jANIS LIELMEZS Department of Chemical Engineering T h e University of British Columbia Vancouver 8, Canada
RECEIVED for review May 29, 1967 ACCEPTED December 18, 1967
