Isothermal adsorption data for many gases and vapors on charcoal and other adsorbents have been shown by various investigators (1), (2), (3), (4), to agree satisfactorily with the Langmuir adsorption isotherm, except for deviations, possibly due to multilayer adsorption, as the pressure of the saturated vapor is approached. The Langmuir equation is derived on the hypothesis of a unimolecular adsorbed layer. The rate of adsorption, assumed proportional to the pressure p and the fraction of the surface unoccupied, (1 - ϑ), is equated to the rate of desorption which is assumed proportional to the fraction of the surface covered, ϑ, giving the equation below

Innes, W. B.

Rowley, H. H.

English

University of Northern Iowa

Proceedings of the Iowa Academy of Science Volume 47 Annual Issue Article 28 1940 Application of the Van't Hoff Equation to Adsorption Equilibria H. H. Rowley State University of Iowa W. B. Innes State University of Iowa Copyright ©1940 Iowa Academy of Science, Inc. Follow this and additional works at: https://scholarworks.uni.edu/pias Recommended Citation Rowley, H. H. and Innes, W. B. (1940) "Application of the Van't Hoff Equation to Adsorption Equilibria," Proceedings of the Iowa Academy of Science, 47(1), 165-170. Available at: https://scholarworks.uni.edu/pias/vol47/iss1/28 This Research is brought to you for free and open access by the Iowa Academy of Science at UNI ScholarWorks. It has been accepted for inclusion in Proceedings of the Iowa Academy of Science by an authorized editor of UNI ScholarWorks. For more information, please contact scholarworks@uni.edu. APPLICATION OF THE VAN'T HOFF EQUATION TO ADSORPTION EQUILIBRIA1 H. H. Rowu:v AND W. B. INNES Isothermal adsorption data for many gases and vapors on char-coal and other adsorbents have been shown by various investiga-tors ( 1), (2), ( 3), ( 4), to agree satisfactorily with the Langmuir adsorption isotherm, except for deviations, possibly due to multi-layer adsorption, as the pressure of the saturated vapor is ap-proached. The Langmuir equation is derived on the hypothesis of a uni-molecular adsorbed layer. The rate of adsorption, assumed pro-portional to the pressure p and the fraction of the surface unoc-cupied, ( 1 - {}), is equated to the rate of desorption which is as-sumed proportional to the fraction of the surface covered, {}, giving the equation below: C1p(l -.ft) = C2.ft (1) This can be rearranged to give: C2 _ p ( 1 - {}) _ k cl - .ft - (2) Plots of this equation for different values of k are given in Fig. 1. If the amount adsorbed at equilibrium per gram of adsorbent is v and the amount adsorbed per gram of adsorbent when the surface is completely covered is <p ; {} = 2- and k = p (IP - v) ( 3) <p v The reaction of desorption can be represented by the equation below: adsorbate µ adsorbent + gas According to the Langmuir conception, ( 1 - {}) can be interpreted as a measure of the concentration of the adsorbent at the surface, {} as a measure of the concentration of the adsorbate, and the pres-sure as a measure of the concentration of the gas. The constant k thus identifies itself as the mass law equilibrium constant for this reaction. From another viewpoint, k can be considered as the vapor pressure of the adsorbate when the fraction of the surface 1 For a more nearly complete work on the subject see Master's Thesis of W. B. Innes, State University of Iowa, 1939. 165 1Rowley and Innes: Application of the Van't Hoff Equation to Adsorption EquilibriaPublished by UNI ScholarWorks, 1940166 IOWA ACADEMY OF SCIENCE [VoL. XL VII 1.0.....---------------------, k::. lf__-------:=====i .8 e .6 0 4 8 12 16 20 24 28 p Fig. 1. Langmuir isotherms for different values of the adsorption equilibrium constant. covered influences equally the rate at which molecules leave the surface and the rate at which molecules go on the surface, i.e. when the fraction of the surface covered, {}, is one-half. The variation of an equilibrium constant with temperature can be represented by the van't Hoff equation. d ln k + .1H 0 (4) dT RT2 k =equilibrium constant. .1H 0 =The heat content of the products minus the heat con-tent of the reactant, all in standard states. Integrating and assuming .1H 0 constant with temperature: -.1Ho lnk= RT +c (5) Substituting the value of I< from equation (2) in this expression and choosing the standard state for the gas as 1 mm. Hg., for the adsorbate {} = 1, for the adsorbent ( 1 - {}) = 1, a general equa-tion relating the fraction of the surface covered, the temperature, and the pressure of the gas in equilibrium with the surface is obtained: 1 n p ( 1 - {}) = ~ .1H o + C {} RT (6) Using the data of Pearce and associates ( 5-13) this equation has been tested and the constants ~H0 , Ii at 25°C., and C have been 2Proceedings of the Iowa Academy of Science, Vol. 47 [1940], No. 1, Art. 28https://scholarworks.uni.edu/pias/vol47/iss1/281940] APPLICATION OF V AN'T HOFF EQUATION 167 evaluated and are given in Table I. Typical plots for the change of !? with temperature are given in Fig. 2. Agreement was found to be satisfactory in most cases except for deviations as the pres-sure of the saturated vapor was approached. To evaluate /?, it is Table I ~H Cal. +~Ho <I> cc. Temp. Range kin mm. Exp ti. Cal. c (n.t.p.) in t°C. Hg 25° Methyl chloride 9200 7700 17.0 159-.22t -30° - 180° 56.4 Ethyl chloride 11600 8800 16.3 115-.14t 0° - 180° 5.0 Propyl chloride 15000 10000 15.9 98-.14t 0° - 130° 0.5 Methylene chloride 8550 15.3 126-.29t -30° - 100° 2.2 Chloroform 14900 9200 14.1 104-.17t 0° - 100° 0.5 Acetone 13400 10500 15.1 127-.28t 40° - 130° Methyl acetate 10500 6600 10.5 110-.46t 0° -0° 0.5 Dimethyl ether 6000 13.3 124-.24t 0° - 180° 0.3 Diethyl ether 8500 13.1 89-.19t 40° - 180° Ethylene chloride 9800 14.7 119-.33t 40° - 140° Ethylidene chloride 8600 13.7 107-.26t 40° - 140° Methyl alcohol 13700 8000 15.1 225-.48t 60° - 100° Ethyl alcohol 8000 14.6 175-.40t 60° - 100° Methylamine 5500 13.6 187-.54t oo - 80° 128 necessary to know the value of qi, the amount adsorbed when the surface is completely covered. This quantity <p can be evaluated from the slope of the straight line obtained, if the data fits the Langmuir equation, when .E. is plotted against p. Also the value v can be obtained by inspection of the adsorption isotherm if data on the flat portion of the curve are available. The magnitude of <p was found to decrease lineally with the temperature in all cases ex-1-,f r•..-~~~~.....-~~~~-.--~~--~-.,-~~~~--.~~~~----. .3·0 .3·> -=;:x1ff' l{D Fig. 2. Plots of the log of the adsorption equilibrium constant as a function of the re~ ciprocal of the absolute temperature, using the data of Pearce and Taylor. 3Rowley and Innes: Application of the Van't Hoff Equation to Adsorption EquilibriaPublished by UNI ScholarWorks, 1940168 row A ACADEMY OF SCIENCE [VoL. XLVII amined as shown in Fig. 3. The quantity k was evaluated as the equilibrium pressure when the surface was half covered. The general equation ( 6) yields three special cases: the isother-mal case when the temperature is constant, the isobaric case when t.c . .. t' n.t.p. <\l ,,., S'""''' l'l 0 n 0 0 " /$: 11/0 13 0 ,._. 110 IO 0 50 --- -'R -r--.~ -f-----0 r--_ CHJCI--~ ----l~ h!t.L r----- -------C_,#1 ce --n---·----....... .___ ~ ~le_ .,._ t---~ ~ -~ /OO Fig. 3. Variation with the temperature of the amount adsorbed per gram of adsorbent when the surface is completely covered. the pressure is constant, and a third case where the fraction of the surface covered is constant. The isothermal case relates the frac-tion of the surface covered to the equilibrium pressure: it=-P_. k=e (C-~Ho/RT) (7) k+p' When the fraction of the surface covered remains constant an equation relating the equilibrium pressure with the temperature is obtained: -~Ho it ln p= ·RT + b where b-=--= ln l -it+ C (8) In the isobaric case the fraction of the surface covered 1s related to the temperature: {t ~Ho ln l-it =RT -d where d=C- ln p (9) The case when the fraction of the surface covered is constant has the form of the Clapeyron equation. The isobaric equation is a new expression which is compared with the adsorption data for ethyl chloride in Fig. 4. The shape of these plots appear characteristic for all isobaric adsorption data examined. As shown by the work of Pearce and associates ( 5-13), applica-4Proceedings of the Iowa Academy of Science, Vol. 47 [1940], No. 1, Art. 28https://scholarworks.uni.edu/pias/vol47/iss1/281940] .9 .t 7 e .6 .s .II .3 .2 .J APPLICATION OF V AN'T HOFF EQUATION 169 T Fig. 4. Isobaric adsorption of ethyl chloride on charcoal. Theoretical curves using equa· tion 9, and experimental points. Upper curve calculated for a pressure of 100 mm. Hg. and lower curve for 10- mm. Hg. 0 adsorption data at 100 mm, Hg. EB adsorption data at 10 mm. Hg. tion of the Clapeyron equation to the isosteric data when the amount adsorbed remains constant gives lower values for the heat of adsorption than does direct measurement. The l'iH 0 values ob-tained by applying the van't Hoff equation to these data are even lower. The explanation of this discrepancy perhaps lies in the fact that the calculated l'iH 0 values correspond to the heat effect if the adsorption took place at a constant value of {}, whereas {} actually increases in the course of an experimental measurement. The dis-crepancy would then be clue to the heat effect involved in the in-crease of l't. The calculated heat effect, l'iH 0 obtained from equa-tion ( 4) would appear to be due wholly to interaction of the ad-sorbent with the adsorbate if k is governed only by the reaction of the gas with the adsorbent. The second heat effect could be ex-plained as being due to interaction between the adsorbed molecules, i.e. the heat effect due to crowding adsorbate molecules together as {} is increased. The decrease of <I> with temperature is a mani-festation of this heat effect. Measured values of heat of adsorption are included with calculated values in Table I. These data were obtained by Pearce and associates on the same charcoal on which adsorption measurements were made. Values of Po (Po= saturated vapor pressure of the liquid) and k qi have been used ( 14) in qualitatively predicting which com-ponents will be selectively adsorbed from a solution. Large values of Po and of qi in comparison with the values for other components k would favor the selective adsorption of this component. 5Rowley and Innes: Application of the Van't Hoff Equation to Adsorption EquilibriaPublished by UNI ScholarWorks, 1940170 row A ACADEMY OF SCIENCE [VoL. XL VII Plots of isobaric equation 9 for each gas should be useful m qualitatively determining the best temperature and pressure to effect separation of gases or vapors by adsorption. BIBLIOGRAPHY 1. H. ZEISE, Z. physik Chem., 136, 409 (1910). 2. A TrTOFF, Z. physik Chem., 74, 129 ( 1910). 3. KAUTSKY AND BLINOFF, z. physik Chem., A 139, 498 (1925). 4. BENTON AND WHITE, J. Am. Chem. Soc., 54, 1373 (1932). 5. PEARCE AND KNUDSON, Proc. Iowa Acad. Sci., (1928). 6. PEARCE AND JOHNSTONE, J. Phys. Chem., 34, 1260 (1930). 7. PEARCE AND TAYLOR, J. Phys. Chem., 35, 1091 (1931). 8. PEARCE AND PETERS, Proc. Iowa Acad. Sci., 37, 223 (1930). 9. PEARCE AND EvERsoLE, J. Phys. Chem., 38, 383 (1934). JO. PEARCE AND HANSON, Proc. Iowa Aca<l. Sci., 41, 140-1 (1934). J. Phys. Chem., 39, 697 (1935). 11. PEARCE AND REED, J. Phys. Chem., 39, 293 (1935). 12. PEARCE AND McKINLEY, J. Phys. Chem., 32, 360 (1928). 13. PEARCE AND TRrMnLE, S. U. I. Master's Thesis (1933). 14. W. B. INNES, S. U. I. Master's Thesis ( 1939). PHYSICAL CHEMISTRY LABORATORY, STATE UNIVERSITY oF IowA, IowA CITY, IowA. 6Proceedings of the Iowa Academy of Science, Vol. 47 [1940], No. 1, Art. 28https://scholarworks.uni.edu/pias/vol47/iss1/28

Application of the Van\u27t Hoff Equation to Adsorption Equilibria

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Application of the Van\u27t Hoff Equation to Adsorption Equilibria

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