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INDUSTRIAL AND ENGINEERING CHEMISTRY ACKNOWLEDGMENT
Acknowledgment is due t o R. Kjellgren for valuable assistance given in the various phases of this study. LITERATURE CITED
(1) Assoo. Official Agr. Chem., Official and Tentative Methods of Analysis, 5th ed., 1940. (2) Bernoulli, A . L., Schenk, M., and Hagenbuch, W., Helo. Chim. Acta, 13, 534 (1930). (3) Cramer, F. B., and Purves, C. B., J . Am. Chem. Soc., 61, 3458 (4)
(5) (6)
(7) (8) (9) (10) (11) (12)
(1939). Dolmetsch, H., Franz, E., and Correns, E., J . makromol. Chem. [37], 1, 180 (1944). Ekenstam, A. af, Ber., 69, 549, 553 (1936). Ekenstam, A. ai, “Uber Cellulose-Losungen in Mineralssiuren,” Lund, Sweden,Blom, 1936. Ibid., p. 58. Gardner, T. S., and Purves, C. B., J . Am. Chem. Soc., 64, 1539 (1942). ENG.CHEM.,ANAL.ED., Genung, L. B., and Mallatt, R. C., IND. 13, 369 (1941). Hess, K., and Ljubitsch, N., Ber., 61, 1460 (1928). Heuser, E., “Chemistry of Cellulose,” p. 226, New Yolk, John Wiley & Sons, 1944. Ibid., p, 589.
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(13) Heuser, E., and Chamberlin. G. X.. J . Am. Chem. Soc., 68, 79 (1946). (14) Heuser, E., and Green, J. W., IND. ENG.CHEM.,33,868 (1941). (15) Hofmann, E., German Patent 227,198 (1909). (16) Kammerer, H., and Carius, L., Ann., 131, 159 (1864). (17) Lipmann, F., and Tuttle, L. C., J . Biol. Chem., 153, 571 (1944). (18) Lynen, F., Ber., 73, 367 (1940). (19) Malm, C. J., and Clarke, H. T., J . Am. Chem. Soc., 51, 274 (1929). (20) Marschall, A., Kunstseide u. ZeZZwoZle, 24, 462 (1942). (21) Miles, G. W., and British Celanese, Ltd., British Patent 263,810 (1926); U. S. Patent 1,787,542 (1926). and Dreyfus, C., U. S. Patent 1,742,611 (1926). (22) Miles, G. W., (23) Schulz, G. V., and LGhmann, H. J., J . pralct. Chem., 157, 238 (1941). (24) Stanim, A. J., and Cohen, 1%‘. E., J . Phys. Chem., 42, 921 (1938). (25) Staudinger, H., and Reinecke, F., Ann., 535,47 (1938). RECEIVEDSeptember 9, 1946. Presented before the Division of Cellulose Chemistry at the 110th Meeting of the AYERICAW CHEMICALSOCIETY, Chicago, 111. T h e greater portion of the work reported here was sponsored as a n Institute Project b y the U. S. Army Quartermaster Corps., Q M C Contract No. W44-109qm-907,a n d was carried out i n cooperation with Ralph C. H. Siu, director of biological laboratories, Philadelphia Quartermaster Depot. Permission t o publish this work was obtained from t h e Commanding General.
Adsorption Isotherms for Binary Gas Mixtures D. B. BROUGHTON, Massachusetts Institute of Technology, Cambridge, Mass. From the second law of thermodynamics, a relation has been derived that must exist between the isothermal adsorption equilibria for single components and for their binary mixtures a t constant total pressure. This relation is useful in checking the consistency of such data. The usual equations, derived from an extension of the Lang-
muir theory to binary adsorption, are not consistent with this relation, except in special cases. Two sets of literature data have been compared with the derived relation, and show a semiquantitative agreement, although the data are not sufficiently complete for adequate evaluation of their consistency.
c
3. Pump B off the surface reversibly, until the surface ie again bare.
ONSIDERABLE interest exists in the application of selective adsorption t o the separation of mixtures not readily amenable to the more common techniques of distillation or extraction. To determine the applicability of this method to a given system, equilibrium data are required. In obtaining such data for binary systems, uncertainty may arise as to whether true equilibrium was reached experimentally, as the rate of displacement of one adsorbed material by another may be slow. Consequently, it is desirable to have a method of analyzing such data to determine whether true equilibrium values have been obtained. h relation which permits such a test of the data can be deiived from the second lan- of thermodynamics. Visualize a chamber, filled with adsorbent, with two inlet lines. Each inlet line is fitted Kith a semipermeable membrane; one line is permeable t o gas A and the other to gas B. Gases A and B are available a t pressure P , and can be fed through reversible isothermal expansion engines to the respective inlet lines. Carry out the following processes reversibly and isothermally:
1. Starting with adsorbate-free surface, admit A by expanding from P t o pa (in equilibrium with the adsorbent holding nA moles). Continue until the pressure on the chamber reaches P and the surface holds n; moles of A. 2. Displace A with B, by admitting B through the engine and membrane a t its equilibrium pressure. Simultaneously, draw off A and recompress to P , so as to maintain the total pressure in the chamber a t P. Continue until A has been displaced entirely and B is present on the surface in the quantity n: moles at pressure
P.
The work done by the system in each step is given by the expressions :
The net work performed by the system in this cycle must be zero. Equating the sum of the work terms to zero and simplifying,
INDUSTRIAL AND ENGINEERING CHEMISTRY
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aPAn:,
100
(5)
= I f a
80 60
The terms a and n i can be considered as empirical constants. The Langmuir theory of adsorption has been extended by Markham and Benton ( 3 ) to binary mixtures of gases, which, singly, follow the Langmuir isotherm. The equations developed give the equilibrium for binary mixtures in terms of the constants of Equation 5 for each of the two pure components:
40
20
d 10 8 6
(7)
4
It can be shown t h a t Equations 6 and 7 are consistent with the second-law requirements only for the special case where n; = n; or for the trivial case‘ where there is no mutual disIt is, of course, possible for placement-that is, apa and bpB
