surprising because, generally, data measured by dynamic methods are higher than those determined by static methods. The values for the heat of adsorption and the entropy of lithium chloride salt for the transition from anhydrous to monohydrate were calculated as detailed by Thakker et al. (1967, 1968). The heat of adsorption of LiCl-HzO given by Slonim and Huttig as 1465 B.t.u. per pound of water agreed with our calculated value of 1490. The calculated entropy change was 6.361 B.t.u. per pound of water per degree Rankine. The calculated free energy change was 1924 B.t.u. per pound of water.
Acknowledgment
The assistance and suggestions given by R. E. Peck are gratefully acknowledged. The authors also thank D. V. Punwani for help with this manuscript. literature Cited
Chi, C. W., Ph.D. thesis, Illinois Institute of Technology, 1968. Foote, H. W., Foote Mineral Co., Exton, Pa., unpublished data, 19B.i.
nois Institute of Technc Conclusions
Ti;l&r,
M. T., Chi, C. W., Peck, R. E., Wasan, D. T., J . Chem. Eng. Data 13, 553 (1968).
The vapor pressures of several hygroscopic salts were measured using the method described. An experimental method for the determination of the transition point for the hydrates has also been established. These and other details are given b y Thakker et al. (1968) and Chi (1968).
RECEIVED for review April 26, 1968 ACCEPTEDApril 21, 1969 Work supported in part by the American Gas Association, and by the basic research funds of the Institute of Gas Technology, where the study was carried out.
DETERMINATION OF THE MICROSCOPIC SURFACE AREA OF POLYETHYLENE F I L M RUTH SELA, CHIYA EDEN, AND HANS FEILCHENFELD Department of Physical Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel An apparatus for measuring the surface area of plastic film by the krypton adsorption method has been developed. The surface area of a polyethylene film was measured and its roughness factor shown to be about unity.
N COSK'ECTIOS with the reactions on the surface of polymeric material, we were interested to know the microscopic surface area of a polyethylene film. It is known that the microscopic surface area of solids may be considerably larger than that calculated from their macroscopic dimensions; the iatio of the microscopic to the macroscopic surface is termed the roughness factor. Since polyethylene can be looked upon as a very viscous liquid, the roughness factor was expected to be not much greater than unity. The problem was therefore to determine the microscopic surface area of a substance with a very low specific surface area. For this purpose Beebe, Beckwith, and Honig have suggested (1945) determining the B E T adsorption isotherms with krypton a t 78" K. (boiling point of nitrogen). I n the usual experimental arrangement the adsorption vessel is connected through a capillary tube with the pressure gage at room temperature. The vessel is immersed up to a mark on the capillary tube in boiling nitrogen. I n that case the volumes a t 78" K. and room temperature are sufficiently well defined. Such an arrangement is suitable for powders which can be introduced through the capillary tube. As polyethylene film could not be introduced in such a way, it was necessary to use a relatively wide tube to connect the cold and warm sections; this had the further advantage of avoiding pressure drops due to thermal transpiration (Knudsen effect). On the other hand, a special method had to be developed t o reduce the uncertainty in defining the cold and warm zones. 818
l&EC
FUNDAMENTALS
Procedure
The adsorption vessel used (Figure 1) was about 10 mm. in diameter and 150 mm. long; at its upper end i t was connected through a conical ground joint to a storage vessel, a vacuum line, and a Pirani vacuum gage. A measured amount of polyethylene film was crumpled and introduced into the lower portion, A , of the adsorption vessel. Adhesion to the wall was avoided by a small number of protrusions. Two thermocouples, B and C, were glued with epoxy resin to the outer wall above the lower portion of the adsorption vessel, a t a vertical distance of 4 mm. from each other. Over the upper thermocouple, C, a heating wire was mound and connected to a variable power source, D. ,4 vacuum flask with liquid nitrogen was jacked up until the surface of the boiling nitrogen reached the upper thermocouple and the current through the heating wire was adjusted until the upper thermocouple showed room temperature. The nitrogen level was kept such that the lower thermocouple indicated the boiling point of nitrogen. The surface, E, bisecting the distance between the two thermocouples was taken as the dividing line between the volume at 78' and 300' K. (thermostated room temperature). The volumes were determined in the usual way by weighing with water. Results
Before determining the surface area of polyethylene film, the apparatus was tried out on y-alumina powder. The sur-
I
0
I
I
1
0.05 0.10
I.
I
0.20 0.25
035 P/
p,
I
0.30
1
Figure 2. BET adsorption isotherm of krypton at 78" K. on polyethylene film Figure 1. Apparatus
face areas of two samples of the same powder were determined by the new method and with nitrogen in a conventional apparatus. The. results agreed with each other. A high pressure polyethylene film, 160 X 205 mm., which weighed about 0.5 gram, was used. I n Figure 2 the adsorption isotherm a t 78" K. is shown in the form of a B E T plot. The slope and intercept as determined by least squares were 4.20 and 0.64 (mm. Hg)-', respectively. The area a krypton molecule occupied was taken to be 0.195 sq. mm. Hence the true surface area was calculated to be 67,100 sq. mm., compared to a geometrical surface area of 65,600 sq. mm. It follows that the polyethylene film had a roughness factor of
1.02-i.e., the macroscopic and microscopic surface areas were practically identical. Nomenclature
P Po
= = = AP =
equilibrium adsorption pressure of krypton a t 78' K. vapor pressure of krypton a t 78' K. 2.8 mm. of Hg pressure decrease due to adsorption
literature Cited
Beebe, R. A., Beckwith, J. B., Honig, J. RI., J. A m Chem. SOC. 67. 1554 (1945).
RECEIVED for review November 11, 1968 ACCEPTEDJ u n e 10, 1969
DETERMI NATION OF CHEMICAL POTENTIAL COMPOSITION DERIVATIVES B Y EQUILIBRIUM SEDIMENTATION H A R R Y T. C U L L I N A N , J R . ,
AND JOHN
P. L E N C Z Y K
Department of Chemical Engineering, State University of New York at Buflalo, Buflalo, N . Y . 14214 An experimental technique for the direct determination of chemical potential composition derivatives in liquid systems is described. The results of equilibrium sedimentation experiments conducted on a Beckman Model L ultracentrifuge are reported. The analysis of the data obtained for a typical system with known solution thermodynamics indicates that such a technique is feasible for the measurement of these thermodynamic derivatives in multicomponent liquid systems.
IT HAS been suggested (Cullinan, 1968) that equilibrium sedimentation experiments be used for the direct determination of chemical potential composition derivatives of liquid systems. The equilibrium concentration distribution in a centrifugal field is directly related to the net sedimenting force through these thermodynamic derivatives. These quantities are of great importance in relating practical diffusion coefficients based on concentration driving forces to fundamental diffusion coefficients based on chemical potential driving forces. The possibility of direct determination as opposed to differentiation of experimental activity data has led to the present investigation.
The ultimate aim of this work is the direct evaluation of the matrix of chemical potential composition derivatives in multicomponent liquid systems by equilibrium sedimentation. Activity data for systems for which diffusion coefficients have been determined (Cullinan and Toor, 1965; Schuck and Toor, 1963) are generally lacking. At best only data on binary pairs are available. To calculate fundamental diffusion coefficients for these systems semiempirical expressions have been used to extend the binary activity data to the concentrated multicomponent region. Subsequent differentiation yields estimates of the quantities needed (Cullinan and Cusick, 1967), but, in view of the accuracy of binary data and VOL.
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