INDUSTRIAL AND ENGINEERING CHEMISTRY
1648
3. A gas mixture has the composition tabulated below. Calculate the viscosity of this mixture a t 293” K. Pure Component Viscosity (7), Poise
Vol. %
Component
Equation 14 may be regarded as a summation of partial viscosities of each component. Thus,
Each component is called the i t h component in turn and its partial viscosity calculated by the relation
P ( 2 ) = function of
kT
- from
Vol. 43, No. 7
Hirschfelder et al.
X = mole fraction
molecules and the molecules in the configuration for which they have the maximum energy of attraction, ergs e l k = an effectiveotemperature (see Table I and Equations 5 a n d 6 ) , K. 4 = function of molecular weights and viscosities of the components of a mixture, defined by Equations 12, 13, and 15 I.C = viscosity p* = viscosity a t 1 atmosphere e
= energy difference between the separated
Subscripts 1, 2 = components 1 and 2 of a mixture c = a critical property-Le., temperature, preseure, or volume cp. = viscosity in centipoise8 i , j = components i and j of a mixture rn = entire mixture r = reduced property LITERATURE C I T E D
(1) Bromley. I,. A.. Cniv. Calif. Radiation Lab., Declassified Atomic Energy Commission R e p t . 525 (November 1949).
Details of the calculation are presented in tabular form as follows : i
j
ci
&.
Mj
3and4)
Xi
x i
Xi4ij
cot
Ot CO H2 CHI Nz C2Hs
0.731 0.884 1.682 1.368 0.828 1 620
1.375 1.571 21.83 2.744 1.571 1 404
0.72 0.73 0.18 0.67 0.72 1.03
0.048 0.048 0.048 0.048 0.048 n 048
0.003 0.264 0.172 0.026 0.482 0 005
0,0022 0.1930 0.0310 0.0174 0.3470 0 0032 0.6958 0.6235 0.8963 1.6099 0.8954 0.4188 0.6379
Component
Pi
+ii (Figs.
LXi4Zl
( b y similar procedure) ibv similar orocedure) ..imiiar ‘procedure! by similar procedure) .by similar procedure) :by similar proccdure)
ZXl@%l
1 1 . 0 0 x 10-6 0.65 52.00 8.45 3.06 95.30 0.71 171.1 X = viscosity of mixture
(2) Buddenberg, J. W., and Wilke, C . R., IND.EKG. CHEM.,41, 1345 (1949). (3) Chapman, S., and Cowling, T. G., “Mathematical Theory of Nonuniform Gases.” Cambridge, University Press, 1939. (4) Comings, E. IT., and Egly, R. S.,IND.ENG.CHEM.,32, 714- ! 8 (1940). (5) Grunberg, L., and Nissan, 9.H., Ibid., 42, 885 (1950). (6) Herning, F., and Zipperer, L., Gas-u. Wasserfach, 79, 45-54. 69-73 (1936). (7) Hirschfelder, J. O., Bird, R. B., and Spotz, E. L., Chem. Revs., 44, 205-31 (1949). (8) Hirschfelder, J. O., Bird, R. B., and Spotz, E. L.. J . Chcm. Phva., 16, 968-81 (1948). (9) Hubbard, R. M..and Brown, G. G., ISD.ENG.CHEM.,35, 1276 (1943). (10) Kennard, E. H., “Kinetic Theory of Gases,” p. 154, New York. McGraw-Hill Book Co., Inc., 1938. (11) Lange, N. A., “Handbook of Chemistry,” Sandusky, Ohio, Handhook Publishers, Inc., 1949. (12) Licht, W., and Stcchert, D. G., J . Phys. Chem., 48, 23-47 (1944). (13) Meissner, H. P.. Chem. h’ng. Progress, 45, 149 (1949). (14) Perry, J. H., “Chemical Engineers’ Handbook,” New York, McGraw-Hill Book Co., Inc., 1950. (15) Uyehara, 0. A , , and Watson, K. PI.,A‘utl. PefroZeum News, 36, R764 (1944). (16) Wilke, C. R., J . Chem. Phys., 18, 517 (1950). RECEIVED November 7. 1950.
The experimental viscosity of this mixture was 171.4 X poise (6) which compares favorably with the value 171.2 X calculated above. Use of exactly calculated -&$ values by Equation 15 leads t o a calculated viscosity of 171.4 X 10yR (16). Such close agreement between calculation and experiment is fortuitous. NOMENCLATURE
A. = Angstrom units E ( r ) = potential energy between molecules as a function of separation r (see Equation 1) f = temperature function of viscosity (see Equation 5 ) ,
(y)
Table I1 k = Boltzmann constant, ergs/” K. M = molecular wei h t of gas m = mass of an indfividual molecule
r = separation between molecules r. = collision diameter for low velocity head-on collisions, A. T = absolute temperature, ’ K. Tb = normal boiling point, K. T , = critical temperature, O K. kT V = function of - from Hirschfelder el al. e V , = critical volume, cc. P, = critical pressure, atmospheres
Addendum In an article entitled, “Vapor-Liquid Equilibrium Data for Commercially Important Systems of Organic Solvents,” by A. S. Brunjes and C. C. Furnas [IND. ENG.CHEY.,27,396-400 (1935)], which gave the data for the system n-butanol-n-butyl acrtate and n-butanol acetate, the following temperature data were omitted from Tables V and VI: Run No. 1
2 3 4 5 6
ii
8 9
10
T h e Lummus Co. New York. N. Y.
Temp.,
C.
116.9 109.8 96.3 83.3 75.5 68.5 65.2 63.0 61.0 60.0
A.
S.BRUNJES
