GAS MIXTURES ON SOLID ADSORBENTS by Charles E. Speer B. S., University of Texas 1949 6ubmitted in Partial Fulfillment of the Requirements for the Degree of Master of Science from Massachusetts Institute of Technology 1949 Signature redacted Signature redacted Super v or 7 -~ Head ot Department WY zKi4 asx*T loTh l$aqevITU ~. eitt rzo'1 alne.xIiOi p*I eziJ lo Ineim~fV1Ju Ialtsoz nl belclmjU4 *oneloa lo qe$88m lo 69,130( i~oloririoeT lo eiwttztaaI alessvuoasM 'A..AA.ASR.g Las -io vxoqjia ;fn9mlrxsq9(l 'J'o bBOH 00, APR rl qC) Dept. of Chemical Engineering Mass. Institute of Technology Cambridge 39, Mass. September 1, 1949 Professor Joseph S. Newell Secretary of the Faculty M.I.T. Cambridge 39, Mass. Dear Sir: The thesis entitled, "Correlation of Data for Ad- sorption of Binary Gas Mixtures on Solid Adsorbents," is hereby submitted in partial fulfillment of the re- quirements for the degree of Master of Science in Chemical Engineering. Respectfully submitted, Signature redacted Charles E. Sped iii TABLE OF CONTENTS Page I. Tables - - - - - -- - -------------- II. Figures - - - - - - - vi III. Summary - - - - - - - - - - - - - - - - - - - viii IV. Introduction - - - - - - - - - - - - - - - - - 1 V. Literature Survey - - - - - - - - - 3 VI. Thermodynamic Test of Data - - - - - - - - - - 5 VII. Solid Fugacity Functions - - - - - - - - - - - 25 VIII. Precision - - - - - - - - - - - - - - - - - 53 IX. Results - - - - - - - - - - - - - - - - - - - 54 X. Appendix - - - - - - - - - - - - - - - - - - - 55 A. Original Data - - - - - - - - - - - - - - 56 B. ?Functions - - - - - - - - - - - - - 66 C. solid Fugkcity Functions - - - - - --- - - 71 D. Sample Calculations -- - - - - - - --- 76 E. Nomenclature - - - - - - - - - - - - --- 77 F. Literature Citations - - - - - - - - - - - 78 iv TABLES Page I. Hydrocarbon Systems Analyzed - - - - - - - 4 II. Broughton's Test of Data - - - - - - - - - 23 Original Data Ethylene-Propane-PCC - Ethane-Propane-PCC - - Isobutane-Butene-l - - Acetylene-Ethylene-PCC Ethylene-Propane-PCC Methane-Ethylene-CG - - Ethylene-Ethane-CG - - Ethylene-Propylene-CG - Ethylene-Propane-CG - - Propane-Propylene-CG - Propane-Propylene-GLC - Methane-Ethylene-SG - - Ethane-Ethylene-SG- - - Ethane-Propane-SG - - Isobutane-Butene-l - - Acetylene-Ethylene-SG - Propane-Ethylene-SG - - Ethylene-Propylene-SG - Propane-Propylene-SG - EthyleneoEthane-SG - - 56 56 57 57 58 58 59 59 60 60 61 61 62 62 63 63 64 64 6b 65 (Functions AXXI. AXXII. AXXIII. AXXIV. AXXV. AXXVI. AXXVII. AXXVIII. AXXIX. AXXX. AXXXI. AXXXII. AXXXIII. AXXXIV. AXXXV. AXXXVI. AXXXVII. AXXXVIII. AXXXIX. Ethylene-Propane-POC - Ethane-Propane-PCC - - Isobutane-Butene-l-PCC Acetylene-Ethylene-PCC Ethylene-Propane-PCC - Methane-Ethylene-CG - - Ethylene-Ethane-CG - - Ethylene-Propylene-CG - Ethylene-Propane-CG - - Propane-Propylene-CG - Propane-Propylene-GLC - Methane-Ethylene-SG - - Ethane-Ethylene-SG - - Ethane-Propane-SG - - - Isobutane-Butene-l-SG Acetylene-Ethylene-SG - Propane-Ethylene-SG - - Ethylene-Propylene-SG - Propane-Propylene-SG - AXL. Ethylene-Ethane-SG - - - 66 - - - 66 - - - 66 - - - 66 - - - 67 - - - 67 - - - 69 - - - 67 - - - 68 - - - 68 - - - 68 - - - 68 - - - 69 - - - 69 - - - 69 - - - 69 - - - 70 - - - 70 - - - 70 - - - 70 AI. AII. AIII. AIV. AV. AVI. AVII. AVIII. AIX. AX. AXI. AXII. AXIII. AXIV. AXV. AXVI. AXVII. AXVIII. AXIX. AXX. Solid Fugacities AXLI. AXLII. AXLIII. AXLIV. AXLV. AXLVI. AXLVII. AXLVIII. AXLIX. AL. Ethane-Propane-PCC - - Isobutane-Butene-l-PCC Acetylene-Ethylene-PCC Methane-Ethylene-CG - - Ethylene-Ethane-CG - - Propane-Propylene-GLC - Isobutane-Butene-l-SG - Propane-Ethylene-SG - - Ethylene-Propylene-SG - Propane-Propylene-SG - 71 71 72 72 73 73 74 74 75 75 vi FIGURES / Functions Page 1. Ethane-Propane-PCC - - - - - - - - - - - - - - - 7 2. Isobutane-Butene-1-PCC - - - - - - - - - - - - - 8 3. Acetylene-Ethylene-PCC - - - - - - - - - - - - - 9 4. Ethylene-Propane-PCC - - - - - - - - - - - - -- 10 5. Methane-Ethylene-CG - - - - - - - - - --- - - - 11 6. Ethylene-Ethane-CG - - - - - - - - - - - - - - - 12 7. Ethylene-Propylene-CG - - - - - - - - - - - - - 13 8. Propane-Propylene-GLC - - - - - - - - - - - - - 14 9; Ethane-Ethylene-SG - - - - - - - - - - - - - - - 15 10. Ethane-Propane-SG - - - - - - - - - - - - - - - 16 11. Isobutane-Butene-1-SG - - - - - - - - - - - - - 17 12. Aoetylene-Ethylene-SG - - - - - - - - - - - - - 18 13. Propane-Ethylene-SG - - - - - - - - - - - - - - 19 14. Ethylene-Propylene-SG - - - - - - - - - - - - - 20 15. Propane-Propylene-SG - - - - - - - - - - - - -- 21 16. Ethylene-Ethane-SG - - - - - - - - - - - - - - - 22 Solid Fugacities vs. Pressure 17. Ethane-Propane-PCC - - - - - - - - - - - - - - - 28 18. Acetylene-Ethylene-PCC - - - - - - - - - - - - - 29 19. Methane-Ethylene-CG - - - - - - - - - - - - - - 30 20. Ethylene-Ethane-CG- - - - - - - - - - - - - -- 31 21. Isobutane-Butene-1-SG----- - ------- 32 22. Ethylene-Propylene-SG - - - - - - - - - - - - - 33 23. ropne-Popyene-G -- - - - - - - - - - - - -AA23. Propane-Propylene-6O -- -- -- -- -3 Solid Fugacities vs. N 24. than-PrpanePCC- -------------- 324. Etha e- ropane-PCC --------------3 25. Acetylene-Ethylene-PCC - - - - - - - - - - --- 36 26. Methane- Ethylene-CG - - - - - - - - - - - - - - 37 27. Ethylene-Ethane-CG - - - - - - - - - - - - - - - 38 28. Isobutane-Butene-1-SG - - - - - - - - - - - - - 39 29. Ethylene-Propylene-SG - - - - - - - - - - - - - 40 30. Propane-Propylene-SG - - - - - - - - - - - - - - 41 vii Solid Fugacities vs. N for Mixture Adsorption Only Page Ethane-Propane-POC - - Acetylene-Ethylene-PCC Methane-Ethylene-CG Ethylene-Ethane-CG - - Isobutane-Butene-l-SG Ethylene-Propylene-SG Propane-Propylene-SG - 42 43 44 45 46 47 48 Solid Fugacities vs. P for Mixture Adsorption Only 38. Adsorption on Carbon - - 39. Adsorption on Silica Gel - - - - - - - - - - - - 49 - - - - - - - - - - - - 50 31. 32. 33. 34. 35. 36. 37. viii SUMMARY The object of this work was to find correlations based on sound thermodynamic principles which would permit prediction of the adsorption of binary gaseous mixtures on a solid from the adsorption isotherms of the pure gases only. Data concerning the adsorption of twenty hydrocarbon mixtures were examined first by utilizing the thermodynamic requirements proposed by Broughton and then by considering the solid as a component of the system and calculating the variation in its fugacity. Neither of these methods of analysis yielded a general correlation of the data. This was primarily due to the fact that both require extremely accurate data as the pressure of the gas being adsorbed approaches zero, and such data were not available. It was concluded that the LangmWir and the Magnus equations as extended to gaseous mixtures are not generally applicable, that the Broughton criterion cannot be used for testing data or as a possible means of general correlation unless the data are extremely accurate at very low pressures, that there is no general correlation for the variation in the fugacity of the solid adsorbent, and that the Van Laar type of equation cannot be applied in the form proposed by Cadogan and Chertow since the fugacity of the solid varies with the composition of the gaseous mixture. For many years there has been much interest in the nature of the adsorption of gases on solids. Not only is adsorption of primary concern in many catalytic reaction processes, but also it may prove to be of conrsid'rable importance in the separation of petroleum refinery gases. It is the latter consideration that prompted this work. The normal method of separating the hydrocarbons of petroleum is the distillation and rectification of the crude petroleum. Naturally this method depends on differences in the boiling points of the various com- ponents present. However, when the molecular weights of the compounds are nearly equal, these differences become too small to afford a practical separation in this manner. In addition, the very low molecular weight compounds are gases at normal temperatures and pressures, and special high pressure or low temperature equipment would be required to use the distillation procedure at all. A reliable method of predicting the characteristics of selective adsorption would be of great value in judging whether or not the distillation process could be replaced by an adsorption process. The purpose of this work then was to analyze and correlate previously published data in such a manner that the adsorption of binary gaseous mixtures on a solid could be predicted from data on the separate adsorption of the pure gases on the solid. In addition, it was proposed to derive these correlations from sound thermodynamic bases rather than from purely empirical considerations. Most of the previous work done has been concerned with the adsorption of a single pure gas on a solid. Various empirical and semi-theoretical correlations have been presented for predicting the adsorption iso- therms of specific systems, but no entirely general correlation has been found. Attempts to extend these theories to gaseous mixtures have not met with much success. One of the main difficulties encountered in these extensions has been the lack of experimental data for mixture adsorption. Such data are now available and show the lack of general applicability of these extensions, the most important of which are the Langmuir j2, the Magnus (?, and the Hill (5 equations . Broughton jLhas also provided a thermodynamic means of testing such equations and he has shown that the Langmuir equation is correct only in a very special instance. Likewise, the Magnus equation proved to be generally inapplicable by this test. The Hill equation is at present in such an impractical form that it could not be tested either by the Broughton criterion or by actual data. LITERATURE SURVEY Since the main interest in mixed adsorption lies in the possibilities of separation of hydrocarbons, it was thought desirable to confine the examination to hydrocarbon mixtures. A search of the literature revealed that the only signifigant data were to be found in work recently done at the Massachusetts Institute of Technology. Most of this work was done by Cadogan (3) and Chertow (4 and their coworkers, and all of the data were summarized and presented by one or the other of these men. These two references were the only sources of data used for this analysis. Since the majority of the investigations were carried out at a temperature of 25*C and a pressure of one atmosphere, it was decided to further restrict the examination to data obtained under these conditions. All the data used in this work as original data were obtained from the smoothed curves presented in the references. Table I presents the systems considered and Tables AI through AXX give the original data for them. Table I Hydrocarbon Systems Analyzed Hydrocarbons Adsorbent Reference Ethylene-Propane PCC+ (3) Ethane-Propane it Isobutane-Butene-1 " Acetylene-Ethylene (4) Ethylene-Propane "t Methane-Ethylene CG++ (3) Ethylene-Ethane It Ethylene-Propylene "t Ethylene-Propane "1 Propane-Propylene It Propane-Propylene GLC (4) Methane-Ethylene SG++++ (3) Ethane-Ethylene it I" Ethane-Propane " " Isobutane-Butene-1 t Acetylene-Ethylene (4) Propane-Ethylene It Ethylene-Propylene "t Propane-Propylene I Ethylene-Ethane " + Pittsburgh Coke and Chemical Co. Activated Carbon, 28/60 mesh. ++ Columbia G Activated Carbon, 8/14 mesh. +++ Godfrey L. Cabot Carbon Black. ++++ Davison Silica Gel, Refrigeration Grade, 14/20 mesh. THERMODYNAMIC TEST OF DATA Broughton (1) presented a thermodynamic basis for the examination of binary mixture data but at the time of presentation, not enough data were available to test it adequately. The initial step in the analysis then was the testing of the data for thermodynamic validity. Broughton showed that for a binary gas mixture maintained at constant temperature and at equilibrium at all times fN,, Me 0 f Pa where: N = the number of moles of gas adsorbed per unit weight of solid. P* = the pressure of pure gas over the solid. P = the partial pressure of the gas in the binary mixture over the solid. This equation can be further simplified to NO i-Vr /;7?4. where: N* = the number of moles of pure gas adsorbed per unit weight of solid under a total pressure equal to the mixture pressure. = the ratio P/P*. r = the ratio N/N*. Thus, the graphical integration of ln ( = $(r) for the two gases in a binary mixture should provide a means of determining the validity of the reported data, i. e., the ratio of the areas under the curves should be equal to the reciprocal of the ratio of the NO's. &Figures 1 through 16 show these "L" functions for sixteen of the systems. Four of the systems so obviously violated this condition that the _ funtions were not plotted. Tables AXXI through AXL give the calculated values of l and r for all twenty systems. Fiur 1.4l F7 -4-444-4 ~4~L ~ I. _ I~L444- LJ4~_ L A-A, _+_J I- 4 - 44-i e- .... ._ .-4 .4- .+. m~ I- li p , -~ T - -44-~-z r--4t f f- A ~ -4- t~ 7 -- , I I - 1* 1- t .. .... '-i 54F--i - T4 3-I 0. 0.+. . 0.1 0. lz 0.,3 0.,v 0.!s 0.4, 0.7 0. If 0. rf /0 Figure 1. r1c e -4 a -n P_ o"l-60--oRkne -t S --- - -6 - -- Figure 2. 2 - - -t- - I -I-- -4--- 4-- Li: -t --I-- - 4- LLLIJJW~1~ -j~J -t - 0.3 .-. u olr c :Af I I U I I rt~T -I---7t10.1 c -- - t -4-- -- -- - - I CO-&~t T - -t I- -1-4 r~$ +- - -A -a- IITIII-VbIzhIi tI~fl-LW - i - Inow 77 77- I- -4 t- I - 4 -4j - - -- - - 4 t - - 4 -7 - - - -4- = - - -4 i 0I .. ~ .il .. . . - . ' - - - - 14 ITI 4+ O D ~-- F K ~4''4 ~ - 11 lid;t~ 11i ; 0 1 + IT I!,.~i Ir Fii~--' W!H- Hl k t++ Fi w 'i' IjI i 4 I~i th C4-- IsI * !-4-~ IL 4.- 4 -1 i44- T4 C , 1- - - - - - - - KI)i I-ttt E i) V ~ ~iF~j r, 17 1 F III:t ITIT N 11111 1!I 1 kI iI i tT ii I I~~ J~ W ilI 111111 + . I A + 4~+ l.44 t4 4 11 141i r+i + I I r 4lII 47VH- T- 0 1-T ;!Ii f :if T Ip !! , , , I ~ it I I M w II I* ** I t I I I f1 I 1!k 11 1 it - t-4 H -- r t t ~ ~ If 10 -44 I t WA~L I I go Tt~ !tajjj i l 4-4 1 * + 1 1 L l 1 it~ _ 01111 -4t v W i W 11 w N1J ' 0 Iw_ Is w 91 w ul V 1 % % - Figure 7. 1 -U - - - AR -; 7 -7:t -* V 74~ 3a I -44 + -IT 3a 0CD.5. iI . ~ I_ I 111 44-. itI ,iI I ,I II .1r 2 - % it I t 1111111t KrI I IK t if if 1 '31~C'IN. f% Figure 9. 10 tt -4-3- F ET 4- -4-- 4- 4- - :T: 2 4. 4~I f t 4 - - E i ::_ - + - I -4 t 040 Z. . 4- '- - 065 /0 0 LS Figure 10.1 al0 -4 - -- 4A 44--1 ------ -4 .---- 4 4 1-r4 - -- - - - - - O 0.3 0. 4 0.5 .6 Or 0. 0r rf/,Ieor' l I--:1,VJ 47+7- r 77' I4- N 1- -I 0.1 ~ k T fi- .- - --- - -1 I- 4- Figure 11. I -t 4EE t o.3 --4 -$ 14 -4- T - -4 I 'i ~- I - t- I -- Wi- t trl I a, t - ------------- 0. *f or I-iuteie-I _________ ~ --- ----i I 0.5 0.4 - ~- 4 - - -I- -A- - t TI- - --- - - T_ - - -V --4 -A- -i -- t + - 4 -- + 4 4 - -~ 44 4-4-4-444 -I- 4-- --I 4- -i-- ~ t 7 ----1-- 441 * It -~ 14- - 4- --4 J, 111t f IfiI i pi LVVt T t- T; 141.4z -I. 1+ I+ I l.lT ; f , A4 '4'.r I . I I IlI I 4+4~~ t . . L4 ~ ~ + I t 1,H li l l ' l lii- I ' I! II L iI i I i + 0i Figure 13.* I 0.1 aq~ 19 I' j 1. U~ 0 -+ - - - - - -* ---------- 6I 3 - 3:7 -O -4 9 -O o-3 10 -. Figure 14.0 -------------. .. + . .J I-~-- -- -- - -- - f-44 H- -4 -L 0,4 05 MEN. - . - - To, O -it, " -471iH j11I~i I Itji ~ 4.$-* V V 4 I I I- I~ IL 101!HT id Hl I-, 'pE00'I 0) 116111 w I I w 1111 vi % 14 W N % , I - I itI T II II. . t f Ii- 4 l it l 11 1W l W , li Ii I h ~l111 !1 P I l~ ~ 1lIIII i II N i Ii l , h 1 :1 1 11 111 111 '1 jllii I 1111H 1 1 tI 11 1il !k 1 ll I 1 H I I! I it H I: i , I I Ii I Il t I I i I I i i 11 ;il Il , 1 I 1 1111 , -4-- I i tt F LLf, v1 i 4~~i ttr' i+t+4~ 1 _ _7 Ip*40 23 Table II presents the results of the graphical integration of the L functions. Table II Broughton's Test of Data System Component A Component B Ads. Ethylene Ethane Isobutane Acetylene Ethylene Methane Ethylene Ethylene Ethylene Propane Propane Methane Ethane Ethane Isobutane Acetylene Propane Ethylene Propane Ethylene Propane Propane Butene-1 Ethylene Propane Ethylene Ethane Propylene Propane Propylene Pro pylene Ethylene Ethylene Propane Butene-1 Ethylene Ethylene Propylene Propylene Ethane PCC " " " " CG it tI it t GLC SG if it ift"I "t " " % Diff. o ~j NjOlnies 4(-J2+oo 7 A ->100 1.375 1.151 -16.3 3.56 4.20 18.0 0.786 0.593 -24.6 1.235 2.39 -93.5 0.413 0.276 -33.2 1.81 1.74 - 3.90 2.75 1.24 -55.0 ->100 Insufficient data. 1.759 1.823 Unreliable data. 0.1445 0.170 1.012 0.389 0.230 0.358 0.445 0.0566 0.0814 0.106 1.043 0.267 0.1825 0.3875 0.402 0.1315 - 3.6 -42.4 -37.6 3.06 -31.4 -20.6 9.08 - 9.67 132 It can be seen that, according to this test, few of the data seem to be consistent with the thermodynamic requirements. This is due to the fact that the test requires high precision of the data in regions where this is usually not obtainable. Most of the area under each curve is to be found at the end at which r approaches zero. At this end, the pressure is also approaching zero and as this happens, the precision of the original data becomes very poor. In order to obtain values of Y at low r's, it was necessary to extrapolate the original data to such low values of pressure that errors of 50% or more could easily be made. Even with careful ex- trapolation of the original data as far as possible, it was still necessary to extrapolate the ffunctions to zero r. With these extrapolations, which occur at such critical regions, it is not surprising that the correct area ratios are not obtained. It seems unlikely therefore, that this test can be used for more than a qualitative check unless extremely precise data for the critical regions are available. It can be used for this however, and on this basis the following systems seemed doubtful enough to be neglected in subsequent examinations. Ethylene-Propane-PCC (3) Ethylene-Propane-PCC (4) Ethylene-Propylene-CG Ethylene-Propane-CG Propane-Propylene-'CG Methane-Ethylene-SG Ethane-Ethylene-SG (3) Ethane-Pr opane-SG Acetylene-Ethylene-SG Ethylene-Ethane-SG (4) In spite of the difficulties ino lved in using this test, attempts were made to find simple empirical equations for the )'functions,.and in doing so, impose the condition of correct area ratios. It was thought that these functions might possibly be correlated by such means. Such investigations showed that the wide diversity of the shapes of the curves prevented the use of the (tfunctions as a means of general correlation. SOLID FUGACITY FUNCTIONS In a further attempt to find a sound thermodynamic correlation, the possibility of a relation between the fugacity of the solid adsorbent when the pure gases are separately adsorbed and the fugacity of the solid adsor- bent when the gaseous mixture is adsorbed was investigated. Consider the system of pure gas and solid as a binary one, i. e., include the normally neglected solid as a component. If s-~ 2~ ,TtNg P,T,Ns where: N is the number of moles adsorbed. F is the molal free energy. F is the partial molal free energy. s refers to the solid. g refers to the gas. then, from basic thermodynamic relations N'ds + NgdFg = PT - - - - - - - -(1) If, during the adsorption process, the total pressure is assumed to be held constant by a non-adsorbable gas that has a negligible effect on Fs and Fg, then the restriction of constant pressure may be neglected. Since dFsR RTdlnfs, where f is the fugacity, equation (1) becomes Nsdlnfs + Ngdlnfg = OIT. Since the moles of 26 solid remain constant, dlnfNs = -N dlnf T - - - - - - - - - (2) For the gas mixtures, i. e., ternary systems, similar reasoning shows that dlnf = -NAdlnfA -NBdlnfBP,T - - - - (3). Here one does not require the hypothetical non-adsorbable gas to maintain constant pressure. Since the pressures in question are all atmospheric or less, partial pres- sures may be substituted for the fugacities of the gases. Also, dlnP = d and dPA = -dPB' Upon substi- P tution in equations (2) and (3), one obtains the final equations dlnfNs = - dPs:n ~~J--------------(4) dlnfjs -(N, - NM dPA T - - - - - - - - - - (5) Equation (4) applies to the binary system and equation (5) applies to the ternary system. Graphical integration should then reveal ln fgs or f N as a function of Pg for the binary systems and as a function of PA for the ternary systems. If the fugacity functions of the solid in the ternary systems could be related to the fugacity functions of the solid in the binary systems and if the empirical relation that NA is linear in NB be assumed (4), then the character- istics of mixture adsorption could be predicted from data on pure gas adsorption alone. Figures 17 through 23 show fs= (Pg) for pure gases and fI = '(PA) for the mixtures. Figures 24 through 30 show the fugacities of the solid as functions of N. Figures 31 through 37 show the fugacities of the solid in the mixtures as functions of N on a larger scale and Figures 38 and 39 diow ln f s = ( The numerical values from which these curves were plotted may be found in Tables AXL through AL. The basis for all calculations was the assumption that the fugacity of the pure solid is 1.0. In three cases the functions i N for the pure gases were so lacking in precision at g low pressures that the fugacity of the solid for pure gas adsorption could not be calculated. For these cases the fugacities of the solid in the ternary systems were calculated by arbitrarily assigning a fugacity of 1.0 to the solid when one of the pure gases is adsorbed under a pressure of one atmosphere. Since the basis of calculation in now different from the original one, the numerical values of the fugacity of the solid are incorrect. However, the shapes of the curves are cor- rect and are shown in Figures 38 and 39. - -. Figure 17. v~ i*-~~ -Md~dL +1 I mm t, pet F -- -j A i 4 .4 .4/4-t ~ 4~4$& + -~Th4~.-W4T-J F4iI- +-4~A- -I-i 4 4++ A+ 4-4-4 -[-LJ4-44H+14-1 i IA iF-lt + -4- -4 J .- t- 4-4 4 44~4~ 4-44- 4-i+4+ 44- If - Ii f4 H, 4 T _v t r-i I. -, y_ _ i4 -1 -1- 4-.,- 4. 441 ; -- H'44" 0 c1I fOb 4T44H+"It I I - t 0 4-! o.q 0. b 7I 4- LL .. . 1.4 77-1 7 2 :4H 14 P-41 1 i 1 i 1 P -++* + t-t+ Ct2 A,4. 4,4 4r+ wwmj 7H4 -~I - I 4 4 -f 4- -I-- -4-A- ~ ## - 4-h -+ -4-4-L4 :t, ]A- f-ti 4- 4 f4i rr/~e9~v TW Figure 19. 4 I- A- 14- -~ I. 4- J-4 4- + + -4+ -.-L -44 4- 4-'4 44 T 11 - 7-t 4@ U +4 -t t- - 'a- 7 - 1jTi 4 4 71 "--4 -----1 -Ii~I4. i 4t/1 1 4 * - 4 . * ~ ..~ ~ I~.4-1-4 L-4-t 1 id rPu - L4-4..LLL.A..iLZ~~iJA.74jLLV7 4: 7 Vi ~- -. t- - 4 ~ ______ l T TTITYT4 t t1 4i 4--+ -t-~ 1t IT 4#44 4T 44 i - - -4- 44-444 I4,----4- 4 ~- I... . .-... . I - .4. IJ.L244-. 1 LW 7V T 1 -A - 4- - ~-'~~~~1 L 1 4t-14 I i-t~v 4 .'44- I 4-4-~ -~.4- I ~ -.-.--,-.-I----. -- ~ I ~ ... 4 4 .4-J .~LJ4 .L LLL4. I LI. 41 i 4- - I - _ 7]~ 14 - 4T I4 I -4 ~T. ft+ -T 141 *1- rt , HL -4-_0 -- f 4 4-~424F-T E LU. 74.5 7T1 1 T7~7 V 4. t 11 4.4.11 Ill T4 11 4. * I 4-,-rt-t.-4-44 4+4---/ 4 ~ 4 4-~ 4 -'-44 ..- 4-9-4 4 ~ 4 s-.-.. ~ J&.4-..4I~.....LL...LLL~...LLLLLLLLL 4.. V" - -tt r*. Ti4f -4 - AFI _i J _4 _ 4t 1-t 7. .4 +4 . -WI _ 4 + JIlT 1~-'-~~ ~44~,. F t ~- 21 TI -44-,- I 4-"-" 7. -4. - ~ tr ~ i -f- 44 : -t4-4--t-r1--t-4-$-+4-t4*4 rt-I~h.FH-+4.-41- IJ44,444I44LL 0.8 -T t__ _ .A : 4 o.2af. o-6 petylneor / &vf hia-FE) a " 1W I I- tt 4-. #14 K I : r 4- J t ft 12p,+ L 4 41 - 4Th~t -4-,---- -. -i-i-Hi 3 0 ~72~ 14 - U,4 I 1 11 4- + /0 47 tTt ll Ha -4 4-4-4-+-4-F 4 44 4. - :It~.tTji -'I F - ~ #4h 7444- , 4- 4 . .. 7 +T + 7- 4 Xhl - _H_ iff f -4i 4 U 4J, TT 4: 4+ + LIJ. 9f 11 j44- aa777 44 4__ 'tt_ Jj :t t_+-t-+ - . . 4,j Ah -4 i Tj . 11 T 17 '-*-I- '_ '! IT_. t -4. i+H- 4L,-; 1. rttt,+ f 7I -T, =7 4L 7 T d -7 474 ihi -44T -7, + T-1 T, 1, 7-T I-, ETTT-T7-1 _44 47: _11 7 11 _L1 _LL i I 4 Ji 4+ 4-, i + 4-4,' -07 TFT 4:rlI T , , 1- -1 ii-, - I I . 1 -1-11 -T Jrt H-HI, Figure 20. tf 4-~ 31 *1~-~*~~~ 4, 4 -, -j44 T-h1.4... ..4. . A -4 T- :-f 1 -I - 1~ L~ }~ iL1]~Th7 441441H r-oM 04444TP1 A 1 i;4 J-~ '-A- 4 4 It -A45 - 77 4 14- -- TH4 t 1. +-IT -- rf +-1 RlItj- -1~. -- 4----I t -.- R~-~ -H f7 I I IWqiit{ 1- 41 :.4 40 th + Lq - Jj . I~~~ Lt . f+l -! '-i-~r i IL P 11YtF$~4~tI~44--4 Hlu~tu f. 0 ~K 41 ~ 4Th: -4-4-4- 4 LLt.2T 4144ftj [2~ II ~ rV +T~fd~~~W I- o-Z 1 erica 2e 0.or Aky/e, pe -1 ThT 44 j 4- -IN A 41 4- 0 -- - - 10.7- 0 .9 T 1131T p 4-4, j -14 Figure 21. 5- -l -4 14 -4- +lTjt14Y~b4 ~ 74.1 ., 32 lft4U4 4 D ! r3 '4 4 ffl~ t1 J t 1 2 T mLH-4 ~. I,. 4 - -- T7 f t t-I 14 ---rTo j T H IT - HF--I f - -- Ip til- T-Hr T 1_ 7 t Tt n+ bTr -- t t d~- +' T * -11~ V4- I.- 27::l -- ... 1 T-i' ~2I: 114 ~- 1- i '41- 14H H44.&.LLL~......4. 11~ J.. ,...Lin..L A .-..-.....-.--&-. 4. ~ I ~4 44-4-4.4 ..-.4--. 4. .- 4.4~4. 4 4......4 4. 4.-4 4 - 4 4 ~..... 4 ~+4.4444 4. 4~44* I ~44 4. ~-+4 44 4.-- t7T -1: I + s?- .4a.r . ..... i.... . .... . . +74 - _ * 1- V. L~. I - T -7f-;: I _______________________________________ . 0, f 0.64 0-.5 -li .4 t l- 0 or |-c m. I K * _the6 IQIr 1. _T 4fri . K 1j jTA~ 4- hl- I T I I I T i l l 74 4 -H _T_ --i 7 T44:1 Ir4-r- T j!I L Tri rr aun a r - I F. - 44!tL- fill 4-f. If I ~TL 44 4i 4-4 1-1144-'+414. . . ... ft ttt-ttt t -J I A Ll I-1. TER t Figure 22. 4-'- .17 4H -1+44IT i + t U 4~~~~ L r ~ 44 El-i I-- 0. If 0.4 0.6 '.0 ,Perpykwre ooP IfPehyl/., aem.r I - F, -C 145~ I lid t7 at m~. s. 4- 1 4- tit 7, 1 1 , 14- -4 ! !! I A 7j. 11-4; _44!1+1 Hit: fi,VH--I -L4pJ- I . I. 1 1 1 1 T-, TZ-f Tt LL +L f4. - 4 ;4 4 - Ir~rr~i 17Et'r K -4 4 ,; 7jKl trr!L 4- 4 1 ~ iN I 434 * - ~H 4 4-1 IL L 4.~~2? h~4fTh+ 4 4' 1 4[+1A 4~t 4 ~+444 - ~ Vt~jT~tth~4it~t~VB4d+ 4 #thd T IT Ij + 41 t Ft t- f _ _J i- A ~kf11t K 4 ft4t~ Fi ~fl irF t. I 4 2 ; IT ftJ I~~~~ tA Ttdt-4 4-i-H 41 {' +A K VIU.'t.31 1 4 -1 T-t 4 - - - - - - - - - - - - - I7* T-T . _ _ : i a Ila 1 0.4 0 d ' I 19 F . .1 f I q . - IT t-r r 4-4 4 7- I - f - - T jr - _ " ' -1 7 r 7- tt r I T I f I L44 7 LET "T:j T "g, r t- TF -4 r rj "rt' r t- .A +; 4+ W IT I-F, + .44 44 7 - .2 IT '" -t rl-l- T 4 _H_'l -t'll 1 -1 .4-1 4- L 11 'I-!! f+ t,- 4 r r h -i- r _TT '4 jL 4 J+ t [t + T q' 1-7 t 1-T It- R r+4- 4- ;+ 1 4 - _ _ tU4f f-T 4- il t- rt v 11- -1 11-1 i t .4- tL h+ f T ' T" T r - . _Z 1 4- L j I tT.-4 j 4. -fjrL Lr -r - L It - " ; 4 E T T _ _ 7_7 Afl p '4 4-4j- T tt j so -T4- fF 4_ 7_ _ijL L t + t Figure 24. 3 + -. -t I $4 4 Rp~~ f4t44-i 4- 4 il 4-11 di4r~ 14~ g tT~t Tit S T#T Hi - -t ~IT~m 4 14 1 - -4i-2! I 1t .- - - I T, T- n di 4i Kwp KI 1~ .1-jr 4. -I--.- I K; 'j41 -d 11 + 44 4--i tP- 1 4:2 4- I - 4 t j- J fi ud t T+J J-IL '' '4- 1-I 1+i ~tr A -71 14-+ I r- 4- .- , I Taii: T1 4 i4 r; T TT -~ -t . - 4,N 0.8 I' 32 -I-A 4 7 ' 4 {4 -v J. onUr LIM-&Q -H'T 4- lii- .i~:~-ltj =-,T ? ~-- -- t 4- - H-i L--I t ;4 1 1 4 ff4 - I I . I I I I . I I . .. I I I -444-4+! 44 -4- ki c "0 .9 z (0 -12 N;N wI It aI-rs Figure 25. 3 itti ty- I ~ EtaA ~ b414- 1- t 14~ &~ i'or~b~e ~t~7I J m -I4 Y.4c Li b 4-. 11 1 1 ---j---,-IT EF 4 S 44 4L-- 4- It - -1 T4 4 P, It i4 - - A - -- 4ft- .....- + T i + Z-4 4 -, 4 F$ K.A - - T t f:- :t.-i 4 - - It A i A T7 14-~ _ i 1- 7 - r 4-,4 I~ 1-4 -4 4 _ I Figure 26. - I ~ .. 1 h 1.6 2.4- 3.20 I~.7 ~Au T' '4 = I -T 44 -6 t 41 - 7nK t4 T- T 21 + 4-i tH-IIHHH-H H Hi+dtH++HH PmtIH H H+1HY HH d tVH F H Ih H Ii+ Th444414~ F~LH4l4~44 -1- $ ~-+++I -H-I-H-H-t-t-H-+9 -4 ++-++t- I-+-,--i-i+H-H-1-t ++4-1 4+1 A-4-4-1-1+t-~ r 444-!'1 14 14 4444-4-P f4 _4 _ $p 1 $1 + t 11ttfh+ + ti+i tt ~t1444$$$b4$$$14$4 ---'it; 77* 7L- ~4~i41AI~ +j~ftjj4~r'At~t H tttr ~ ~!t~frH H ThtI ii ft HI hclttrlti'+: Ij h1 ~tt I rrr- 1T--rlrrrrrnrTrr'F~T rrrr.-rrrr rvr lrr 'urrrmr t1 4- K T Z 4 -L T $ t$$-$$ $4$$$$4$$$ $$$ $$ F 1T " . r-t +- ] .T s++ 4 P - 4TT r I - 4T 7 :th1 W + i 4 4 -1 1 +1 1 + + 4-i -'1 4 +1 +7-4 i+ i i _7 F A- + - 7 P~t4tPT II ~~1~.. 1 T -17 L 4tj T-i.44 i- 4, - N, mf/iree/es #1 -4., ii 4 'K'] 14 I go 1- L 't t t-, LL 4- 4- .A1-~44444-~144+I-.4 [-4 4 '-I4- 4t 7 VP 4 +-I --7 4-4 -~ -4- 1- 'I-.-.,- fl+441++ IfH+LJVIH Fl H +W&r+1 t4tl V4 -.1.1 tffitL iAt tA tiJ ii I~ ti ff t fttLI d1lit~ I I L PH+r~i H+tWH tt S-4 TI-,- 4-It 4- pi -xl I I7 4-. + ~-+ ~. I I-f S -1 0.8 - t -4- L' t4 ... ()0 t~t~ 4 4 IT~ LIIlLJI- tI IA Ii 11 tL-" 4 t . . . ..... . .. 1 1 J i l l, -t v -L 4 11 ia a ss ~ s + 1 11144 14 ;I mJ. 11-1. _TH 4 .+g AS J, tI J i i i P i i i I'Pq11111 H -I j i i i i i i 1 j T$ $$$$$144$t4V M$4i; $$$$$$$1$?+$$ 3.2 2.114 p 44 4 ... .......... i .. .... .. . I + H #H$$4- $ $$j$,$$$$$$$$t$$$ .7 1 .7-- n t ST. r-r 44 W -- :- L44 L 1 * _ _I L I 141 4 -4 1-4k H - If t it+- 441 jtq. TI 0 r- $ - - I-7;7 I II 7 3' .4 4: 4ftV r% AD -T-r Lt - . 1 .7 * ~ 4V - 'L-.. 4-4 T'-A I - -7 Figure 28. 3 14 R j4 41- -4-F I La 24 -u-4 -144- 4H 474 +-4. -L ,4 7HA -4 -4 T-444~ 4 4 t -4 TT7j -lill1 442 .4 V -- =4~ _ -hr Vi.?4 IT Cq ~ $IW4 A-4 7 .. . +< 41 I414~1- 4.-I :1.1 -1 Mt T-4 4 +i;7t- 4, 4F 4 -1-4-1 -4, 7 - T .x 1 f 4- IT 4 - :i? f , n J ++ iT 4-4+4 , :4 p 4+i I+ -714- T t-rt-4- 4T 4-, -4T.- 1 T .14 -4- + 4- -i-+ T #-4-T: TIT -4 4-. HR t l T I . i 1 1: 4- 4 A Li .4 -t4+.-r 14 7171 __l L 1 7 ___i L; TTr 1# 4+ -4 44 4+ 7 T-rl 4:4 T7 4 4 _r 7- 4 44, + A+ th 11 -FT :4F- . T. _T .4 -LILL IAL A~ -rr L1L j47- ~ 1 1 .4 _: 4 l++4WM4 I -4. fh - t~~ir~rn~ '-rtI4 - r-2 4r#to 4 ~A: 0.8 /6 H- +41 LT 2.41 4(o NV wlfiwe 0 S 4 H '44 jJ4 4 T U,4. T _j 44 4"ot R 4H 4 + 4 L4-t AI Y TL A .4t i4_ -4 i( t4 I 4t1 4 T- -how"" Ll .. ... ... 1.. 4 + al4;44 Figure 29. 40 t p Mo 4 A'4 I IT 7~ 04d r~~ :44~ T'i 71 Jt~ i t 4 t t~ Lt -- I- I I~~ ~ I rW I 4- 114 Al~t -- 2+t p r4 +_- - 4 ~ 4-- -147771~~ - 7 --1. t 4 1-44 4K 444:q -WI .:1 7 77 H 4 ,11 - r L_ 7. TT -I T ~ , - I r -I,-, J 42- - ~ 44 +__ __ __ __ ___ __ __ __ _ - L % m,/,4~.e 1~ Figure 30. S a T- -r -I- -.4 -IT t4 --t T t 4 ;4 is -F T - - +t 4 7, Tl~ -j + t- -7- V-414 I ~ ~ - . T - - TT 44- + 4 ti + T __T .4+ - }-- - - 4 4 ~ 4 -4 - -_q -- 0.0 /. N,wsee 4f 4) 1+4 U11 v 24 jJ~- 4-"}~ 4 44H 44i -n't -4 .4- - - o0. Yo 4-~ -- - -14 41 In I T -- =t 7H - -14- + T# 4- + I + 4 -4 -4 --- I - -+ -- - -1 I -- z ALl I.I It - - - 4 T 14, -L4 4 - ~t4 4 444- m44 4- r _11 14 410 -11 TI: 7- 7- 7- A 61 1d ' u g acdI1 _ yp 6 A o a s a o r~c b dl G . #_ j 1 -4 -T 1~1+ 4T -L -I- .-- ~ti + :-T f2 4 1 t~~A M7tt . .4, -t igure 31.' 4F L 44- S T4 7144 T i 4 2 14+ 1 ~T .44 14 4 TV tNA ~i -4 4-m T I' - 14 '4 ;+ ~ ~ Z-8 fa, Y?'//o/s tt t 4 ~ 4-14-44-1 1 1 1 .-. 1.1...1. --.....- 3.z Tp_ 7 + 4-44 4-: 4LE-4 T-4 VT,. Ii -L-i pitt .4- V. 44 t I -I Ii+ t4 iT4 ' TB tt iii t, F T7 I iii I ii I!! ii ii~ fJ T IL 1 1 1T 1i7 L iK ,'' !I 7 T- T IT i H i ll 111 111 1 IM ; :!J 0 11 11 1 L L 1 1 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ~ iiii UI IfW hi liii III ! ~i[~ ;II I I ~ I I I lii i II I Iii II M H . . . . I ; I I 111P HIE" i, _ ;I T 7 1 T !' - TI T1 ii If i-~. ~ 7 I~4 K ii 1. 1 1.4 A F"I T I i I I I i I I I I I I I I i I It j;tj q: HI M : ilM iN iT M W 1W H I - T, a,; 1 , h '1111 - T L I If I fi t 1 1 1 1 J i ll 11 1: i; _ T 'it : I H ill M , 1: 1 i ili il; 1M II II II I f it II I[ I!. . . . . . . . 0 - 11 - . . . . 1 1 1 1 i I J FT F IT H I 1 1 1 1 1 9 1 f F il l 1%) (0) 4 L4 01 % J O D 0 d Is _ j a 0 0 11 - - TH T I I . . l i i .41 1-~ 4- 1444-1 7 11 jJ1 4 , IA- T 1 - -trt ,ili itI!,m - - . , - - i---- 5L22~H _4 - . A '''I ~ 4 T it IT"/ +f44 I 2 7L4 ri 4 14- . . . . . . ~ . . .4 t +l, f'! ; -T t - - it~4 till (, - 0 1 (D 111, 0 ri I m N it) N - 0) (ID r1_ 0 if) I m 0 a 0 1,- v In 14 0) N N 51 Unfortunately, no correlation could be found for predicting the fugacity of the solid in ternary systems from pure gas isotherms only. This may be due to the enormous difference in the range of values for the solid fugacity when under the pure gases and when under the mixture. This can be easily seen in Figures 24 through 30. If, for example, the fugacity of the solid when NA moles of A and NB moles of B were adsorbed at one time (ternary system) were some function of the fugacities of the solid when NA moles of A and NB moles of B were adsorbed separately (binary systems), the fugacities in the binary systems would have to be extremely accurate as they would be so much larger than those in the ternary system. It may be possible to find a correlation similar to this but involving only those portions of the curves for the binary systems which lie in the same range of fugacity values as those for the ternary system. For example, the fugacity of.the solid in the ternary system may be a function of the fugacities-of the solid in the binary systems at points where the moles adsorbed in the binary systems are equal to the total moles ad- sorbed in the ternary system. This would require that the data for one of the binary systems extend to pres- sures higher than one atmosphere. Lacking a correlation between the adsorption of the pure gases and the adsorption of the mixtures, considerable aid could still be obtained if the shapes of the solid fugacity functions for various ternary systems could be related to one another. If the shapes of these functions could be accurately predicted, then the slopes of these curves at various points could be used to find 1A A) if the empirical relation that NA is linear in NB could still be assumed. Chertow has shown that this relation is within engineering accuracy in most cases. Here again, no such relation could be found. These solid fugacity functions are not of the types generally foiund in engineering work since all attempts to rectify the curves failed completely. It might be well to mention here that the Van Laar type of relation proposed by both Chertow and Cadogan should not be correct, if the solid is to be considered as a component of the system as it certainly should be. The tacit assumption which must be made in order to apply their equation correctly is that the fugacity of the solid in ternary systems at constant pressure is not affected by changes in the composition of the gaseous mixtures. This is clearly not the case. An attempt was made to apply a similar type of equation to the adsorption of the pure gas with the intention of extending it to the ternary system by analogy to the original Van Laar extension. However, no satisfactory equation could be found, the difficulty lying in the fact that ln P approaches-oo as P approaches zero. No means could be found to make this an indeterminate ratio as the original Van Laar equation does. PRECISION Basically, the investigations carried out in this work were done in the light of the thermodynamic equilibria requirements of the systems. Both the ori- ginal Broughton proposal and the idea of solid fugacity are seriously hampered by the lack of precision of the data in the most critical regions, viz. when the pres- sure approaches zero. This is probably the primary reason for the failure of the two methods of attack. As mentioned before, at pressures lower than 50 or 60 millimeters of mercury, an error of five millimeters would be magnified enormously when the Y or functions are integrated. The last type of curve is not quite so bad as the first in this respect, since the total area under the curve is distributed more evenly over the entire curve. RESULTS The results of the work done are mainly negative and may be summed up as follows: 1. It was found that the extension of Langmuir's for- mula is sound only when the moles of pure materials adsorbed in a complete monomolecular layer are equal. 2. The Magnus mixture equation is generally inapplicable. 3. The Hill equation is not in a usable form. 4. Logically, the Van Laar type equation applied in the form proposed by Chertow and Cadogan is incor- rect since the fugacity of the solid changes with mixture composition. 5. It is unlikely that the Broughton equation can be used to test data, though it is of great value in testing proposed correlation formulae. 6. It is unlikely that a relation can be found between the fugacity of the solid under the pure gases and the fugacity of the solid under the gaseous mixtures. 7. It may be possible to relate the variation in the fugacity of the solid under mixtures to various types of systems. .56 Table AI. Original Data for the System Ethylene-Propane-PCC Carbon at 25*C (Cadagon) Pure Ethylene Pure Propane Mixture (P* 1 atm.) Ps mI. Hg. 13 60 100 203 300 356 500 645 760 N, mmols. 0.301 0.667 1*25 1.90 20275 2.48 2.67 2.79 2.88 2.96 3.08 3.20 3.30 3.38 m . Hg., 4 19.5 50 100 150 200 250 300 350 400 500 600 700 800 N, mmols. 3.15 3.03 2.79 2.79 2.52 2.37 Xe Ye 0.067 0.110 0.239 00239 0.439 0.601 Table AII. Original Data for the System Ethane-Propane-PCC Carbon at 25*C (Cadagon) Pure Ethane N, mmo ls. 00167 0.381 0.625 0.925 1.16 1.35 1.62 1.82 2.06 2.21 2.41 P, . mm. Hg. 12.5 37.0 69.5 128 180 230 312 399.5 512 59705 751.5 Pure Propane N, P, mmols. mm. Hg. 0.301 0.667 1.25 1.90 2.275 2o48 2067 2.79 2.88 2.96 3.08 3020 3.30 3.38 4 19.5 50 100 150 200 250 300 350 400 500 600 700 800 Mixture (P= 1 atm.) N, Mmols. 3.23 3.19 3.12 3.06 3.00 2.95 2.85 2.77 2.71 2064 2057 2049 2.45 X, Et. 0.050 0.100 0.150 0*200 0.250 0.300 0.400 0.500 00600 0.700 0.800 0.900 0.950 Y,9 Et. 0.385 0.505 0.570 0.615 0.653 00683 0.735 0.785 0.840 0.883 0.938 0.967 0.984 N, Mmo 1s. 0.187 0.639 0.82 1.198 1.42 1.555 1.79 2.004 2.14 00409 0.553 0.782 0.786 0.914 0.949 Table AIII. Original Data for the System Isobutane-Butene-l-PCC Carbon at 2500 (Cadagon) Pure Isobutane N, P, nmiols. mm. Hg. 0.312 1.46 2.27 2.46 2.67 2.79 2.87 2.93 3.05 3.14 3.23 3.31 3.33 2.5 23.5 70.5 100 150 200 250 300 400 500 600 700 747 Pure Butene-1 N, mmols. 2.08 2.40 2.73 2.95 3.10 3.22 3.30 3*47 3.59 3*69 3,78 3.83 P, mm. Hg. 21 50 100 150 200 250 300 400 500 600 700 748.5 Mixture (P= 1 atm.) N, mmols. 3.82 3.80 3.75 3.70 3*66 3*60 3.55 3*50 3.45 X,9 Iso. 0.070 0.100 0.200 0.300 0.400 0.500- 0*600 0.700 0.800 Y,9 Iso. 0.140 0.174 0.305 0.408 0.505 0*600 0*693 0.773 0.862 Table AIV. OrigLnal Data for the System Acetylene-Ethylene-PCC Carbon at 25*C (Chertow) Acetylene Pressure, mm. Hg. Pure 760 723 690 645 580 458 363 274 200 135 83 45 30 20 10 Mixture 760, 744 734 717 688 632 572 513 453 383 308 218 165 113 55 Ethylene N, Pressure, mm. Hg. mmols. Pure Mixture 2.14 2.05 2.00 1.95 1.90 1.80 1.60 1.40 1*20 1.00 0.80 0.60 0.40 0.30 0*20 0.10 760 682 645 605 570 505 385 290 213 150 103 69 41 29 20 10 760 715 693 670 645 578 518 440 372 305 243 183 120 89 60 32 N, mmols. 2.04 2.00 1.96 1.90 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.30 0.20 0.10 Table AV. Original Data for the System Ethylene-Propane-MC Carbon at 25*0 (Chertow) Propane Ethylene Pressure, mm. Hg. Pure Mixture 760 608 508 425 280 190 133 93 64 45 33 25 18 15 N, mmols. 3.35 3.20 3.10 3.00 2.80 2.60 2.40 2.20 2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.10 N, mmols. 2.15 2.00 1.80 1.60 1.40 1020 1.00 0.80 0.60 0.40 0.20 0.10 Pressure, mm. Hg. Pure Mixture 760 633 493 378 285 203 143 95 60 33 15 760 700 648 610 575 548 523 485 430 362 246 160 Table AVI. Original Data for the System Methane-Ethylene-CG Carbon at 2500 (Cadagon) Pure Methane N, P mmols . mm. Hp,. 0.066 0.180 0.230 0.435 0.600 0 .750 0.880 0.990 1.10 1.13 30.5 72 *100 200 300 400 500 600 700 755 Pure Ethylene N, P, mmols. mm. Hg. 1.04 1.53 2.13 2.52 2.83 3.07 3.29 3047 3.57 46 100 200 300 400 500 600 700 757 Mixture (P = 1 atm.) N, X,9 Mmols. Me. 3.20 2.88 2.60 2,38 2.23 2010 1.98 1.85 1.70 1053 1.42 1.35 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.500 0*600 0.700 0.800 760 655 595 538 450 388 343 308 280 255 236 210 200 180 155 128 93 53 33 Y, Me. 0.375 0.585 0.700 0.775 0.823 0.860 0.880 0.910 0.938 0.960 0.970 0.983 Table AVII. Original Data for the System Ethylene-Ethane-CG Carbon at 2500 (Cadagon) Pure Ethylene_ N, P, mmols. mm. Hg. 1.04 1.53 2.13 2.52 2.83 3.07 3.29 3.47 3.57 46 100 200 300 400 500 600 700 757 Pure Ethane N, mmols. 0.888 1.32 1.83 2.43 2*83 3.15 3.42 3.63 3.80 3.90 P, m. Hg. 23.5 50 100 200 300 400 500 600 700 761.5 Mixture (P= 1 atm.) N, mmols. 3.88 3.87 3.85 3.79 3.75 3.71 3.67 3.65 X,. Y,. Ethy. Ethy. 0.150 0.200 00300 0.500 0.600 0.700 0.800 0.835 0.195 00255 0.375 0.600 0.700 0.785 0.865 0.893 Table AVIII. Original Data for the System Ethylene-Propylene-CG Carbon at 25*C (Cadagon) Pure Ethylene N, P mmols. mm. Hg. 1.04 1053 2.13 2052 2.83 3.07 3029 3.47 3.57 46 100 200 300 400 500 600 700 757 Pure Propylene N, P, mmols. mm. Hg. 2.56 3.28 3.99 4035 4.56 4.72 4.86 4.96 5.03 53.5 100 200 300 400 500 600 700 761.5 Mixture (P = 1 atm.) N, X,9 mmols. Et. 4.80 4.62 4.46 4.34 4.24 4015 4.07 4.00 3.88 3.80 3.72 3.67 3.64 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 00500 00600 0.700 0.800 0.833 Y, Et. 0.345 0.550 0.670 0.743 0.800 0.838 0.870 0.890 0.923 0.944 0.960 0.972 0.975 rot Table AIX. Ori4nal Data for the System Ethylene-Propane-OG Carbon at 250C (Cadagon) Pure Ethylene N, mmols. 1.04 1.53 2.13 2.52 2.83 3.07 3.29 3.47 3.57 P, mm. Hg. 46 100 200 300 400 500 600 700 757 Pure Propane N, mmols. 2.46 3.10 3.76 4.00 4.16 4.28 4.37 4.45 4.50 P, mm. Hg. 53 100 200 300 400 500 600 700 800 Mixture (P = 1 atm.) N, mmols. 4.45 4035 4.22 4.12 4004 3.96 3.89 3.83 3.78 3.74 3.66 3.62 X, Et. 0.070 0.100 0.15u 00200 00250 00300 0.350 0.400 0.450 0.500 0.600 0.714 Y, Et. 0.380 0.501 0.635 0.724 0.787 0.833 0.873 0.900 0.918 0.931 0.953 0.970 Table AX. Original Data for the System Propane-Propylene-CG Carbon at 2500 (Cadogan) Pure Propane N, P mmols. mm. Hg. 2.46 3.10 3.76 4.00 4.16 4.28 4.37 4.45 4050 53 100 200 300 400 500 600 700 800 Pure Propylene Mixture (P = 1 Atm.) N, P, N, X, mmols. mm. Hg. mmols. C3HA 2.56 3.28 3.99 4.35 4.56 4.72 4.86 4.96 5.03 53.5 100 200 300 400 500 600 700 761.5 4.79 4.70 4.70 4060 0.264 0.501 0.502 0.742 0.260 0.511 0.507 0.749 61 Table AXI. Original Data for the System Propane- Propylene-GLC Carbon at 25*C (Chertow) Propylene Pro pane Pressure, mm. Hg. Pure Mixture 760 675 5751. 425 305 215 150 970 32 23 15 10 3 760 723 685 625 573 520 468 363 258 208 155 103 52 N, Mmols. 2059 2.50 2.40 2020 2.00 1.80 1.60 1.40 1.20 1.00 e.80 0060 0.40 0.20 Pressure, mm. Hg. Pure Mixture 760 650 550 390 273 185 125 83 53 35 23 15 10 3 760 708 672 613 555 500 443 388 333 278 222 165 112 55 Table AXII. Original Data for the System Methane-Ethylene-SG at 25*C (Cadogan) Pure Methane N, P, mmols. mm. Hg. 0.0130 0.0295 0.0469 0.0619 0.0629 0.0844 0.108 0.122 72.5 180.5 285.5 369 404.5 529.5 678 766 Pure Ethylene N, P, mmols. mm, Hg., 0.150 0.259 0.425 0.592 0.766 0.993 55.5 107 211.5 336 503.5 758 Mixture (P = 1 atm.) N, X, Mmols. Me. 0.77 0.62 0.51 0.44" 0.38 0.34 0.32. 0028 0.24 0.20 0017 0.16 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 O.500 0.600 0.700 0.750 N, mmols. 2.79 2.70 2.60 2.40 2.20 2.00 1.80 1.40 1.00 0.80 0.60 0.40 0.20 Y, Me. 0.581 0.682 0.750 0.800 0.842 0.878 0.911 0.920 0.948 0.970 0.980 0.985 62s Table AXIII. Ori4nal Data for the System Ethane-Ethylene-SG at 250C (Cadogan) Pure Ethane N, mmols. 0.070 0.120 0.220 0.300 0.370 0.435 0.500 0.610 Ps Mm. Hg. 50 100 200 300 400 500 600 760 Pure Ethylene N, mmols. 0.150 0.259 0.425 0.592 0.766 o.993 P , mm. Hg. 55.5 107 211.5 336 503.5 758 Mixture (P = 1 atm.) N, mmols. 0.94 0.90 0.87 0.84 0.80 0.78 0.73 0.69 0.65 0.63 0*60 X, Y, C 2]'G Coh& 0.060 0.100 0.150 0*200 0.250 0.300 0.400 0*500 0.600 0.700 0.800 0.175 0.253 0.340 0.412 0.475 0.537 0.640 0.730 0.803 0.870 0.921 Table AXIV. Origtnal Data for the System Ethane-Propane-SG at 25*C (Cadogan) Pure Ethane N, P, mmols. mm. Hg. 0.070 0.120 0.220 0.300 0.370 0.435 0.500 0.610 50 100 200 300 400 500 600 760 Pure Propane N, P, mmols. M*. Hg. 0.225 0.390 0*640 0.850 1.025 1.180 1.330 1.55 50 100 200 300 400 500 600 760 Mixture (P = 1 atm.) N, mmols. 1.14 1.08 1.03 0.97 0.88 0.80 0.73 0.724 X. Y. Et. Et. 0.139 0.200 0.250 0.300 0.400 0.500 0.600 0.671 0.503 0 * 600 0.655 0.700 0.770 0.823 0.863 0.896 63 Table AXV. Original Data for the System Isobutane-Butene-l-SG at 25*0 (Cadogan) Pure Isobutane Pure Butene-1 Mixture (P = 1 atm.) P, q mm. Hg. 15.5 62.5 155.5 264 414 605 757.5 N, nmols. 1.09 1.625 2.11 2.43 2.67 2.86 3.05 3.21 3.28 P, mm. Hg. 40 100 200 300 400 500 600 700 749 Table AXVI. Original Data for the Acetylene-Ethylene-SG (Chertow) N, X, mmols. Iso. 3.23 3.16 3.12 3.03 2.95 2.88 2.81 2.74 2668 2.56 0.080 0.150 0.200 0.300 06400 0.500 06600 0.700 0.800 0.843 System at 25*C Acetylene Ethylene Pressure, mm. Hg. Pure Mixture 760 700 663 620 582 505 440 380 325 230 155 95 53 36 22 9 760 725 -, 698 670 642 585 553 483 433 343 257 183 120 88 58 27 N, mmols. 0.96 0.90 0.85 0.0 0670 0660 0.50 0.40 0.30 0.20 0.10 Pressure, mm. Hg. Pure Mixture 760 685 625 565 465 373 290 215 153 95 44 760 720 693 667 615 555 495 425 353 265 160 N, Mmols. 06217 0.574 1.04 1.43 1.84' 2*25 2.53 Yq Iso. 0.215 0.352 0.435 0.565 0.663 0.753 0.828 0.890 0.939 0.958 N, mmols. 1.81 1,75 1.70 1.65 1660 1.50 1.40 1.30 1.20 1.00 0.80 0660 0.40 0.30 0.20 0.10 64 Table AXVII. Original Data for the System Propane-Ethylene-SG at 250C (Chertow) f Ethylene Pressure, mm. Hg. Pure Mixture 760 685 623 569 465 370 285 212 145 90 45 760 725 692 645 590 518 438 357 272 185 90 Propane N, Pressure, mm. hg. Mmols. Pure Mixture 1.54 1.50 1.45 1.40 1.30 1420 1.10 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 760 725 685 650 575 510 445 388 333 282 232 187 148 110 76 48 22 760 748 730 710 655 595 535 480 425 375 325 275 225 180 133 92 49 Table AXVIII. Original Data for the 6ystem Ethylene-Propylene-SG at 25*C (Chertow) Pr opylene Ethylene Pressure, mm. Hg. Pure Mixture 760 675 520 400 310 235 173 118 80 50 28 13 760 710 590 485 390 305 235 175 125 88 53 23 N, Mmols. 0.96 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.05 Pressure, mm. Hg. Pure Mixture 760 685 563 458 365 285 210 146 90 40 18 760 753 725 695 655 605 545 466 365 260 130 N, mmols. 0.96 0.90 0.85 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 N, mmols. 2.29 2.20 2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 Table AXIX. Original Data for the System Propane-Propylene-SG at 25*C (Chertow) Propylene Propane Pressure, Mm. Hg. Pure Mixture 760 678 605 535 418 320 242 173 123 85 53 29 10 760 698 648 595 498 405 330 260 200 140 94 56 26 N, nmols. 1.56 1.50 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.10 Pressure, mm. Hg. Pure Mixture 760 715 635 500 383 280 185 108 46 20 760 746 728 675 603 515 405 280 148 75 Table AXX. Original Data for the System Ethane-Ethylene-SG at 25*C (Chertow) Ethylene Pressure, mm. Hg. Pure Mixture 760 675 563 455 360 275 203 137 80 35 760 695 580 476 385 305 233 162 100 48 Ethane N, Pressure, MM. Hg. nmols. Pure Mixture 0.60 0@i50 0.40 0.30 0.20 0.10 0.05 760 600 450 313 193 85 43 760 680 593 495 375 218 120 N, mmols. 2.30 2020 2.10 2.00 1.80 1.60 1.40 1.20 1.00 0.80 0060 0.40 0.?0 N, Mmols. 0.96 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 Table AXXI. fFunctions for the System Propane-Ethilene-PCC Carbon at 25 C (Cadogan) Table AXAII. rFunctions for the System Ethane-Propane-PCC Carbon at 25 0C (Cadogan) C3H8 C3H8 r . - 0.037 0.075 0.112 0.149 0.224 0.373 0.523 0.597 0.672 0.748 0.821 0.934 0.956 0.986 1.00 4.0 3*85 3.80 3.72 3.71 3.04 2.32 2.04 1.71 1.45 1.21 0.95 0.925 0.951 1.00 Table AXXIII. (Functions for the System Isobutane-Butene-l-PCC Carbon at 25*C (Cadogan) Table AXXIV. (Functions for the System AcetyLene-Ethylene-PCC Carbon at 25*0 (Chertow) Isobutane r r 0.037 0.075 0.150 0.224 0.300 0.450 0.524 0.600 0.674 0.749 0.824 0.861 0.899 0.944 0.974 1.00 56.5 48.0 37.8 30.9 25.1 15.8 12.79 10.39 7.86 5.46 3.50 2.675 1.983 1.510 1.201 1.00 Butene-1 r 0.033 0.065 0.130 0.260 0.391 0.456 0.521 0.651 0.716 0.781 0.847 0.879 0.912 0.936 0.961 0.985 1.00 53.8 53.0 49.7 40.6A 30.5 24.8 18.7 6.69 4.55 3.18 2.16 1.819 1.541 1.36 1.183 1.062 1.00 Acetylene r I 0.049 0.098 0.162 0.196 0.294 0.392 0.491 0.588 0.686 0.784 0.883 0.932 0.962 0.982 1.00 5.5 5.65 5.50 4.8 3.7 2.84 2.26 1.87 1.58 1.38 1.19 1.11 1.063 1.015 1.00 Ethylene r 7 0.047 0.094 0.140 0.187 0.280 0.374 0.467 0.560 0.655 0.748 0.842 0.888 0.912 0.935 0.958 1.00 3.2 3.0 3.07 2.93 2.84 2.36 2.03 1.75 1.52 1.34 1.14 1.13 1.11 1.07 1.05 1.00 66 03H8 r 0.075 0.149 0.224 0.298 0.373 0.448 0.522 0.597 0.671 0.746 0.820 0.895 0.971 1.00 C2H4 r 0.116 0.232 0.349 0.465 0.582 0.698 0.814 0.930 1.00 0.058 0.035 0.024 02H4 17.5 10.8 7.06 4.70 3.19 2.175 1.57 1.173 1.00 26.0 28.9 34.0 1.25 1.309 1.23 1.21 1.22 1.22 1.22 1.275 1.292 1.308 1.275 1.142 1.038 1.00 02H6 r 0.021 0.031 0.041 0.052 0.103 0.206 0.309 0.412 0.515 0.618 0.721 0.824 0.927 1.00 02H6 r - 41.7 34.8 31.6 26.4 16.05 8.36 5,.29 3.79 2.845 2.23 1.792 1.45 1.142 1.00 Table AXXV. /Functions for the System Ethylene-Propane-PCC Carbon at 2500 (Chertow) Propane Ethylene r % r jr 0.299 0.358 0.418 0.477 0.537 0.597 0.657 0.717 0.776 0.836 0.895 0.927 0.956 1.00 12.0 11.10 8.40 7.15 5.66 4.37 3.31. 2.58 2.04 1.61 1.26 1.17 1.08 1.00 0.093 0.186 0.278 0.372 0.465 0.559 0.651 0.744 0.838 0.931 1.00 16.4 11.0 7.16 5.10 3.66 2.70 2.02 1.61 1.32 1.11 1.00 Table AXXVI. (Functions for the System ivethane-Ethylene-CG Carbon at 25*C (Cadogan) Methane r Z 0.044 0.089 0.178 0.267 0.356 0.444 0.534 0.622 0.711 0.800 0.889 1.00 5.0 4.67 3.89 3.39 2.91 2.515 2.14 1.796 1.625 1.411 1.23 1.00 Ethylene r r 0.070 0.140 0.210 0.279 0.349 0.419 0.489 0.559 0.629 0.699 0.769 0.838 0.909 1.00 1.65 1.60 1.47 1.39 1.289 1.263 1.112 1.074 1.040 1.00 0.969 0.942 0.942 1.00 Table AXXVII. (Functions for the System Ethylene-Ethane-CG Carbon at 25*C (Cadogan) Table AXXVIII. (Functions for the System Ethylene-Propylene-CG Carbon at 25*C (Cadogan) Ethylene r y 0.070 0.140 0.196. 0.280& 0.350 0.420 0.491 0.561 0*631 0.701 0.771 0.842 0.912 0.981 1.00 8.92 7.85 6.84 5.75 4.75 3.74 3.16 2.66 2.27 1.94 1.65 1.42 1.24 1.05 1.00 Ethane r 0.064 0.128 0.192 0.256 0.320 0.385 0.449 0.514 0.577 0.641 0.706 0.770 0.834 0.899 0.967 1.00 6.96 6.31 5.70 5.06 4.25 3.73 3.05 2.58 2.20 1.96 1.71 1.545 1.38 1.24 1.09 1.00 Ethylene r y 0.035 0.070 0.140 0.210 0.279 0.392 0.449 0.560 0.673 0.785 0.840 0.897 0.953 1.00 18.65 33.4 25.9 19.0 13.85 8.10 6.33 4.06 2.75 1.90 1.61 1.36 1.15 1.00 Propylene r r 0.050 0.099 0.149 0.199 0.298 0.398 0.497 0.596 0.696 0.796 0.895 1.00 2.01 2.01 1.61 1.70 2*23 1.80 1.87 1.98 2.07 1.98 1.58 1.00 57-W& Table AXXIX. )Functions for the System Ethylene-Propane-CG Carbon at 250C (Cadogan) Table AXXX. )/Functions for the System Propane-Propylene-CG Carbon at 250C (Cadogan) Ethylene r r 0.013 0.025 0.038 0.050 0.061 0.074 0.086 0.121 0.177 0.230 0.282 0.332 0.427 0.475 0.615 0.721 0.799 0.900 0.950 0.978 1.00 38.3 37.6 36.9 34.4 33.1 32.6 30.9 28.0 21.8 17.2 13.7 10.84 6.84 5.46 3.29 2.38 1.81 1.33 1.14 1.05 1.00 Propane r / __ 0.040, 0.080 0.163 0.232 0.325 0.416 0.464 0.512 0.564 0.617 0.675 0.800 0.867 0.905 0.919 0.934 0.947 0.964 0.975 0.989 1.00 1013 1.62 1.81 1.78 1.77 1.71 1.68 1.67 1.70 1.79 1.73 1.70 1.55 1.41 1.36 1.32 1.26 1.16 1.16 1.05 1.00 Table AXXXI. (Functions for the System Propane-Propylene-GLC Carbon at 25 C (Chertow) Propylene. r r 0.072 0.143 0.215 0.287 0.359 0.501 0.645 0.716 0.789 0.861 0.932 0.968 1.00 17.30 10.30 10.30 9.04 8.38 5.19 3.12 2.42 1.88 1.47 1.19 1.07 1.00 Propane r _ 0.077 0.155 0.232 0.309 0.387 0.464 0.541 0.619 0.695 0.774 0.850 0.928 0.967 1.00 Table AXXXII. (Functions for the System Meteane-Ethylene-SG at 250C(Cadogan) Data too unreliable to warrant calculation. 18.30 11.20 11.00 9.65 7.95 6.28 4.67 3.54 2.70 2.03 1.57 1.22 1.09 1.00 68%C 0.282 0.525 0.762 11.78 5.94 3.37 0.702 0.466 0.235 4.46 8.40 12.50 Propane r _r -Pro pylene r_ / Table AXXXIII. rFunctions for the System Ethylene-Ethane-SG at 250C (0adogan) Table AXXXIV. KFunctions for the System Ethane-Propane-SG at 250C (Cadogan) Ethane r Ethylene r 9E 2.89 2.80 2.63 2.49 2.37 2.25 2.16 2.06 1.85 1.67 1.53 1.40 1.29 1.23 1.00 0.121 0.151 0.182 0.202 0.252 0.302 0.403 0.454 0.504 0.554 0.605 0.655 0.706 0.756 0.807 0.888 1.00 1.41 1.47 1.40 1.40 1.36 1.34 1.28 1.24 1.21 1.18 1.16 1.12 1.09 M.06 1.03 1.00 1.00 Table AXXXV. YFunctions for the System Isobutane-Butene-l-SG at 25*C (Cadogan) Ethane r r 0.260 0.295 0.328 0.410 0.492 0.574 0.656 0.728 0.770 0.820 1.00 Propane r r 2.96 '2.66 2.44 2.06 1.78 1.58 1.40 1.26 1.21 1.15 1.00 0.146 0 1 1 6 1 0.194 0.226 0.258 0.323 0.355 0.387 0.420 0.451 0.485 0.516 0.550 1.00 1.58 1.50 1.45 1.38 1.31 1.18 1.14 1.10 1.07 1.04 1.02 1.01 1.00 1.00 Table AXXXVI. fFunctions for the System Acetylene-Ethylene-SG at 25*C (Chertow) Isobutane, r r 0.013 0.026 0.039 0.051 0.077 0.101 0.186 0.244 0.356 0.464 0.565 0.661 0.752 0.841 0.846 0.926 0.941 0.965 0.973 0.977 1.00 9.50 9.83 9.65 9.31 8.66 8.51 5.36 4050 3.40 2.61 2014 1.76 1.50 1.30 1.30 1.12 1.09 1.045 1.023 1.018 1.00 Butene-1 r 0.024 0.030 0.040 0.064 0.079 0-1121 0.162 0.248 0.338 0.435 0.532 00641 0.756 0.813 0.897 0.921 0.949 0.961 0.973 0.991 1.00 3.33 3.78 3.44 3.08 2.96 3.44 3.49 3.30 3*11 2.48 2.12 1.65 1.32 1.19 1.06 1.05 1.02 1.01 1.01 1.00 1.00 Ethylene r_ Y 0.104 0.208 0.312 0.416 0.520 0.625 0.729 0.833 0.885 0.937 1.00 3.56 2.79 2.30 1.97 1.71 1.49 1.32 1.18 1.09 1.05 1.00 Acetylene r _ 0.055 0.111 0.166 0.221 0.332 0.442 0.563 0.664 0.719 0.724 0.830 0.885 0.912 0.940 00968 1.00 3.00 2.64 2.44 2.26 1.93 1.66 1049 1.33 1.27 1*21 1.16 1.10 1.08 1.05 1.04 1.00 0.093 0.131 0.164 0.197 0.230 0.262 0.295 0.328 0.410 06492 0.574 0.655 0.738 0.787 1.00 (Cadoizan) Table AXXXVIII. rFunctions for the System Propane-Ethylene-SG at 250C (Chertow) rFunctions for the System Ethylene-Propylene-SG at 25*0 (Chertow) Ethylene r Y 0.104 0.156 0.208 01312 0.416 0.520 0.625 0.729 0.833 0.885 0.937 1.00 2.00 2.00 2.06 1.88 1.73 1.54 1.40 1.27 1.13 1.11 1.06 1.00 Propne r P- 0.065 0.130 00195 0.260 0.324 0.390 0.455 0.520 0.584 0.650 0.715 0.780 0.845 0.910 0.943 0.974 1.00 2.22 1.92 1.75 1.64 1.52 1.47 1.40 1.33 1.275 1.24 1020 1.17 1014 1.09 1.07 1.03 1.00 Propylene r _ 0.087 0.175 0.262 0.350 0.437 0.524 0.611 0.699 0.786 0.874 0.961 1.00 1.78 1.89 1.76 1.56 1.48 1.36 1.30 1.26 1.21 1.13 1.05 1.00 Ethylene r -K 0.052 0.104 0.208 0.313 0.416 0.520 0.625 0.730 0.834 0.939 1.00 7.22 6.50 4.06 3.19 2.60 2.12 1.80 1.52 1.29 1.10 1.00 Table AXXXIX. (Functions for the System Propane-Propylene-SG at 25*C (Chertow) Table AXL. (Functions for the System Ethylene-Ethane-SG at 25*0 (Chertow) Propylene r r 0.087 0.174 0.261 0.348 0.435 0.521 00609 0.695 0.784 0.870 0.914 0.958 1*00 2.60 1493 1.77- 1.65 1.63 1.50 1.36 1.27 1.19 1.11 1.07 1.03 1.00 0.064 0.128 0.256 0.385 0.513 0.642 0.770 0.899 0.962 1.00 3.75 3.22 2.60 2.18 1.84 1.57 1.35 1.15 1.04 1.00 Ethylene r __ 0.104 0.208 0.313 0.416 0.520 0.625 0.730 0.834 0.939 1.00 1.37 1.25 1.18 1.15 1.11 1.07 1.04 1.03 1.03 1.00 Ethane r Y 0.083 0.167 0.333 0.500 0.667 0.834 1.00 2.79 2.56 1.94 1058 1.32 1.13 1.00 Table AXXXVII. Propane r / Table AXLI. Solid Fugacities for the System Ethane-Propane-PCC Carbon at 2500 (From data of Cadogan) Pure Propane P, N, atm. ~ mmol. 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.250 0.300 0.350 0.400 0.500 0.600 0.700 0.800 0.900 1.000 1.0 0.275 0.154 0.094 0.061 0.042 0.0295 0.0215 0.0160 0.0095 0.0059 0.00275 0.00145 0.00085 0.00052 0.00035 0.00024 0.00016 0.000 0.650 1.070 1.380 1.630 Pure Ethane atm. _S_ 0.000 1.0 0.025 0.767 0.050 0.617 0.075 0.510 0.100 0.429 0.125 0.366 0.150C0.315 0.175 2.250 0.200 0.250 2.580 0.300 0.350 2.800 0.400 2.950 0.500 3.060 0.600 3.15 0.700 3.20 0.800 3.33 0.900 3.35 1.000 0.273 0,240 0.1825 0.1490 0.1200 0.0970 0.0660 0.0470 0.034 0.0255 0.0197 0.0153 N, Rmo1. Mixture p , W.5 N, Rtm. _ _ mmol. 0.000 0.000 0.01530 2.43 0.666 0.100 0.0097 1.036 0.200 0.250 1.344 0.300 0.350 1.600 0.400 1.825 0.500 1.988 0.600 2.114 0.700 2.240 0.800 2.340 0.900 2.43 1.000 0 .0059 0.0046 0.0036 0.0028 0.0021 0.0013 0.00078 0.00049 0.00033 0.00024 0.00016 Table AXLII. Solid Fugacities for the System Isobutane-Butene-l-PCC Carbon at 250C (From data of Cadogan) Mixture Only Pb _ f__ atm. -4 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 1.000 0.822 0.691 0.589 0.505 0.434 0.370 0.311 0.256 0.208 0.165 N, mmo1. 3.34 3.413 3.478 3.529 3 * 600 3.665 3.720 3.756 3.788 3.814 3.840 2.609 2.780 2.931 3*088 3.220 3.266 3.274 3.280 3.300 3.350 Table AXLIII. Solid Fugacities for the System Acetylene-Ethylene-PCC Carbon at 25*C (From data of Chertow) Pure Acetylene P N at-M. -RWOl! Pure Ethylene Ptj~ N Mixture Pe.9 N9 0.000 0.000 0.050 0.543 0.100 0.150 0.864 0.200 0.250 1.086 0.300 1.264 0.400 1.425 0.500 1.571 0.600 1.708 0.700 1.832 0.800 1.953 0.900 2.04 1.000 1.00 0.499 0.354 0.261 0.196 0.154 0.124 0.084 0.059 0.044 0.034 0.0262 0.021 0.0167 0.000 0.000 0.0365 2.04 0.640 1.008 1.254 1.444 1.590 1.722 1.834 1.944 2.043 2.14 0.100 0.0345 2.051 0.200 0.0325 2.022 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 0.0310 0 .0285 0.0263 0.0240 0.0220 0.0198 0.0180 0.0167 2.013 2.008 2.015 2.042 2.075 2.116 2.124 2.14 Table AXLIV. Solid Fugacities for the System Methane-Ethylene- CG Carbon at 25*C (From data of Cadogan) . Pure Methane P,~. rgN, ati. O mmol . Pure Ethylene P, HS N, atm. mmol. Mixture p , Ns N, atm. ,mmol 0.000 0.000 0.050 0.178 0.100 0.150 0.340 0.200 0.250 0.486 0.300 0.350 0.616 0.400 0.740 0.500 0.840 0.600 0.924 0.700 1.024 0.800 1.08 0.900 1.125 1.000 0.000 0.050 00100 0.150 0.200 0.250 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 1.00 0.724 0.542 0.420 0.337 0.275 0.228 0.162 0.121 0.092 0.071 0.056 0.045 0.0365 0.000 0.050! 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.500 0.600 0.700 0.800 0.900 1.000 1.000 0.8355 0.703 0.595 0.509 0.438 0.379 0.330 0.290 0.256 0.225 1.000 0.205 0.095 0.053 0.032 0.021 0.014 0.0097 0.0070 0.0039 0.0023 0.0014 0.00093 0.00063 0.00044 0.000 0.810 1.315 1.874 2.265 2.552 2.775 2.958 3.115 30280 3.429 3*575 0.000 0.050 0.100 0.150 0.200 0.250 0.300 0.350 00400 0.500 0*600 0.700 0.800 0.900 1.000 0.225 0.109 0.066 0.036 0.023 0.0158 0.0110 0.0079 0.0058 0.0033 0.0020 0.0013 0.00089 0.00061 0.00044 1.125 1.601 1.928 2.320 2.603 2.850 3.010 3.16 3.302 3.414 30504 3.575 Table AXLV. Solid Fugacities for the System Ethylene-Ethane-CG Carbon at 25*0 (From data of Cadogan) Pure Ethylene atm. _ _ Pure Ethar N, P .9 mmol. atm. A e Mixture N, PCH ps N, mnol. atm .6 f mS o 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.250 0.300 0.350 0.400 0.450 0.500 0.600 0.700 0.800 0.900 1.000 1.000 0.435 0.234 0.140 0.0910 0.0630 0.0440 0.0325 0.0245 0 .0150 0 .0095 0.0064 0.0044 0.00315 0.00235 0.00130 0.00075 0.00047 0.00031 0.00015 0.000 0.000 0.831 0.100 1.125 0.107 0.135 1.620 0.200 0.215 0.300 0.400 2.170 0.500 0.600 2.520 0.625 0.700 2.840 0.745 0.800 3.100 0.805 3.300 0.900 3.430 0.950 3.600 1.000 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.250 0.300 0.350 0.400 0.450 0.500 0.600 0.700 0.800 0.900 1.000 0.00067 0.00061 0.00061 01.00059 0.00054 0.00054 0.00049 0.00043 0.00038 0.00033 0.00031 0.00028 0.00026 0.00024 0.00023 0.00019 0.00017 0.00015 3057 3.65 3.67 3.71 3.75 3.79 3o85 3.87 3.88 3.90 Table AXLVI. Solid Fugacities for the System Propane-Propylene-GLC Carbon at 25*0 (From data of Chertow) Mixture Only C3H6 As N, at _. __ mmol. 0.000 1.000 2.59 0.050 0.969 0.100 0.944 2.729 0.150 0.923 0.200 0.904 2.780 0.300 0.887 2.802 0.400 0.870 2.821 0.500 0.854 2.840 0.600 0.838 2.856 0.700 0.822 2.871 0.800 0.808 2.886 0.900 0.796 2.867 0.950 0.785 2.837 1.000 0.780 2.790 1.000 0.532 0.321 0.230 0.162 0.096 0.080 0.0625 0.0490 0.0315 0.0215 0.0150 0.0110 0.0079 0 .0059 0.0035 0.0022 0.00145 0.00095 0.00067 0.000 0.625 0.918 1.34 1.86 2*25 2.52 2.80 3.00 3.15 3.320 3.42 3.57 3.780 3.900 Table AXLVII. Solid Fugacities for the System Isobutane-Butene-1-SG at 25*C (From data of Cadogan) Pure Isobutane P, Ns atm. f_ 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.250 0.300 0.350 0.400 0.450 0.500 0.600 0.700 0.800 0.900 1.000 1.000 0.780 0.585 0.484 0.408 0.349 0.301 0.262 0.230 0.181 0.144 0.116 0.096 0.080 0.066 0.0474 0.0350 0.0260 0.0200 0.0152 N,- Mmol. Pure Butene-1 P, S N,2 atm. Mmol. 0.000 0.000 0.025 0.409 0.050 0.075 0.655 0.100 0.125 0.150 0.175 1.018 0.200 0.250 1.296 0.300 0.350 1.540 0.400 0.450 1.755 0.500 1.950 0.600 2.100 0.700 2.240 0.800 2.421 0.900 2.550 1.000 1.000 0.320 0.169 0.108 0 .0745 0.0540 0.0410 0.0315 0.0250 0 .0160 0.0110 0.00?7 0.0056 0.00425 0.00320 0.00195 0.00130 0.00085 0.00058 0.00042 0.000 1.035 1.360 1.850 2.175 2.420 2.650 2.820 2.940 3.040 3.204 3.310 Mixture P , e s N, X .mmol. 0.00k 0.0152 2.550 0.025 0.061 0.075 0.110 0.150 0.172 0.200 0.247 0.300 0.337 0*400 0.435 0.500 0.565 0.600 0.648 0.718 0.894 1.000 0.0121 0.00965 0.0084 0.00685 0.0056 0.00505 0.00455 0.00378 0.0030 0.00275 0.00215 0.00197 0.00160 0.00130 0.00120 0.00101 0.00083 0.00055 0.00042 2 * 680 2.740 2.810 2.88 2.95 3.03 3.12 3.16 3*23 3.27 3.31 Table AXLVIII. Solid Fugacities for the System Propane-Ethylene-SG at 250C (From data of Chertow) Pp, atn 0.0 0.1 0.2 0.3~ 0.4 O.c 0.7 O.8 0.9 1.C Mixture Only A($ 1. _ _ _ mI 00 1.000 0 00 0.926 1 00 0.856 1 00 0.790 1 00 0.729 1 00 0.670 1 00 0.624 1 00 0.579 1 00 0.538 1 00 0.505 1 00 0.470 1 N, rol. .960 .007 .062 .124 .181 .240 .296 .341 .381 .437 .54 75 Table AXLIX. Solid Fugacities for the System Ethylene-Propylene-SG At 25*0 (From data of Chertow) Pure Propylene P, A/, N, atm. ___ Mmol. Pure Ethylene P, Ns N, atm. mmol. Mixture p ,qS_ N, aUm. s mpol . 1.000 0.947 0.900 0.821 0.755 0.702 0.652 0.606 0.530 0.466 0.414 0.368 0.331 0.298 0.270 0.000 0.000 0.025 0.098 0.050 0.174 0.100 0.150 0.304 0.200 0.250 0.420 0.300( 0.528 0.400 0.620 0.500 0.696 0.600 0.770 .0.700 0.840 0.800 0.900 0.900 0.960 1.000 0.270 0.235 0.205 0.160 0.129 0.105 0.0875 0.0740 0.0540 0 .0400 0.0305 0.0240 0.0190 0.0155 0.0128 0.960 1.039 1.103 1.221 1.293 1.369 1.442 1.516 1.667 1.810 1.934 2.044 2.145 2.219 2*290 Table AL. Solid Fugacities for the System Propane-Propylene-SG at 250C (From data of Chertow) Pure Propane P, N. N, atm. ts Mmol. Pure-Propylene P, N, atm. _O_ Mmol. Mixture pH6 [As N, a. nmol. 0.000 0.000 0.025 0.050 0.304 0.100 0.150 0.518 0.200 0.250 0.696 0.300 0.856 0.400 1.000 0.500 1.128 0.600 1.253 0.700 1.360 0.800 1.458 0.900 1.560 1.000 1.000 0.627 0.483 0.316 0.224 0.170 0.131 0.104 0.068 0.0475 0.0340 0.0253 0.0195 0.0150 0.0118 0.000 0.000 0.300 0.025 0.482 0.050 0.753 0.100 0.150 1.116 0.200 0.250 1.359 0.300 1.560 0.400 1.735 0.500 1.872 0.600 1.988 0.700 2.088 0.800 2.214 0.900 2.300 1.000 0.000 0.025 0.050 0.100 0.150 0.200 0.250 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 1.000 0.741 0.568 0.364 0.253 0.186 0.1425 0.114 0.0745 0.051 0.037 0.0275 0.0208 0.0160 0.0128 0.000 0.300 0.500 0.800 1.130 1.356 1.564 1.744 1.890 2.023 2.120 2.232 2.290 0.000 0.025 0.050 0.100 041150 0.200 0.250 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 0.000 0.025 0.050 0 * 100 0.150 0.200 0.250 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 1.000 0.835 0.705 0.610 0.534 0.470 0.417 0.335 0.2725 0.225 0.186 0.157 0.133 0.114 0.114 0.091 0.074 0.062 0.053 0.046 0.040 0.032 0.026 0.022 0.0182 0 .0158 0.0138 0.0118 1.56 1.737 1.848 1.938 2.012 2.080 2.142 2.198 2.238 2.269 2.300 76 SAMPLE CALCULATIONS The following examples are for the system Ethane-Propane- PCC Carbon at 2500. 1. Calculation of r for propane: First plot N vs. P from origtnal data for both pure adsorption and for mixture adsorption. Then, at N = 0.125 mmols./gm. read Ppure = 3 mm. Hg. and Pmix = 12 mm. Hg. =2 = 4.0 N52. Calculation of fNs for pure adsorption of propane: First plot i vs. P from the original data. Graphical P integration from 0 to P = 0.025 atm. gives an area of 1.2872 = -t&ln fNs. Assume the fugacity of the solid is 1.0 for pure solid. - ln fis = 1.2872 f~s = 0.275 3. Calculation of fNs for mixture adsorption: N First plot y vs. Ppropane for both ethane and propane from the original data. Then, read ( )propane ei. at constant Ppropane from these curvus and plot vs. Ppropane. Graphical integration from 0 to P = 0.10 atm. gives an area of 0.4500 = -Aln fs. Calculation of the adsorption of ethane shows that -ln fNB= 4.1882 at Ppropane =" 0.0 atm. 4.1882 -+ 0.4500 4.6382 f = 0.0097 NOMENCLATURE F - Molal free energy, cal./g.mol. r - Partial molal free energy, cal./g.mol. f - Fugacity N - Millimols of gas adsorbed from mixture or millimols of solid. N*- Millimols of gas adsorbed frxm pure gas at P = 7T. P-- Partial pressure of gas in mixture in mm. Hg. or atm. P*- Pressure of pure gas in mm. Hg. or atm. r - The ratio ._ Greek Letters 1'- The ratio p0. #- Any mathematical function. 7r- Total pressure in mm. Hg. or atm. Subscripts A - First component in a binary gaseous mixture. B - Second component in a binary gaseous mixture. g - Gas. s - Solid. 78 LITERATURE CITATIONS (1) Broughton, D.B., Ind. Eng. Chem. 40, 1506-8 (1948). (2) Brunauer, S., "The Adsorption of Gases and Vapors," pp. 474-94, Princeton, Princeton Univ. Press, 1943. (3) Cadogan, W.P., "Adsorption of Hydrocarbon Gases and Their Mixtures", Sc. D. thesis, Chem. Eng. (1948). (4) Chertow, B., "Adsorption of Binary Mixtures of Gaseoiks Hydrocarbons - Equilibria and Kinetics," Sc. D. thesis, Chem. Eng. (1948). (5) Hill, T.L., J. Chem. Phys. 14, 268 (1946).