Assignment 4. Adsorption Isotherms

Transcription

1 Insttute of Process Engneerng Assgnment 4. Adsorpton Isotherms Part A: Compettve adsorpton of methane and ethane In large scale adsorpton processes, more than one compound from a mxture of gases get adsorbed, leadng to compettve adsorpton: The dfferent compounds compete for the empty adsorpton stes of the adsorbent. The purpose of ths exercse s to show how also the classcal Langmur sotherm, bascally vald only for one-component adsorpton, can be extended to mult-component adsorpton, and to compare to the Ideal Adsorbed Soluton (IAS) theory. Exercse A1 Determne the parameters NA, NB, ka und kb of the Langmur sotherm equaton for the gven data for pure methane (A) and ethane (B) on actvated carbon, e.g. by usng the sotherm n ts nverse form and performng a lnear regresson: Data for methane (A) on actvated carbon: na (mol/g) pa (kpa) E E E E E E E E E E Data for ethane (B) on actvated carbon: nb (mol/g) pb (kpa) E E E E E E E E E E Source: Adsorpton of Bnary and Ternary Hydrocarbons on Actvated Carbon: Expermental Determnaton and Theoretcal Predcton of the Ternary Equlbrum Data, E. Costa, J.L. Sotelo, G. Calleja, AIChE Journal Vol.27, p. 5-12, (1981) Exercse A2 Put up the bnary Langmur adsorpton sotherm from the determned parameters of the two Langmur adsorpton sotherms for the pure components. MM 9 November Assgnment3_Adsorpton_Isotherms.docx

2 Insttute of Process Engneerng Exercse A3 Draw the followng dagrams: a) Amount adsorbed (na respectvely nb) vs. partal pressure (pa respectvely pb) for the pure components A and B (Langmur sotherm and data ponts). b) Amount adsorbed (n ) vs. partal pressure (pa) usng the bnary Langmur sotherm for 80% methane / 20% ethane and 70% methane / 30% ethane. c) Mole fracton n the adsorbed phase (xa) vs. partal pressure (pa) usng the bnary Langmur sotherm and the data gven below. The total pressure s P = kpa. The followng lst contans equlbrum data for the adsorbed and gas phase. xa s the mole fracton of component A n the adsorbed phase: xa = na(pa) / ntotal(pa). On the other hand, ya s the mole fracton of component A n the gas phase: pa = ya P. xa ya Source: Adsorpton of Bnary and Ternary Hydrocarbons on Actvated Carbon: Expermental Determnaton and Theoretcal Predcton of the Ternary Equlbrum Data, E. Costa, J.L. Sotelo, G. Calleja, AIChE Journal Vol.27, p. 5-12, (1981) Exercse A4 Determne the bnary adsorpton sotherm of methane and ethane on actvated carbon usng the Ideal Adsorbed Soluton (IAS) theory. For the pure adsorpton sotherms, the Langmur sotherms calculated n exercse A1 should be taken. Compare the predcton of bnary adsorpton by the IAS theory wth the bnary Langmur sotherm by addng another curve to the correspondng dagram of exercse A3. Agan the total pressure s P = kpa. Exercse A5 Besdes the Langmur sotherm, whch has been used up to ths pont, there are many other adsorpton sotherms found n the lterature. Another frequently used sotherm represents the Ant-Langmur sotherm, whose equaton s shown below: n Nk p Langmur 1 kp Nk p Ant-Langmur 1 kp Usng the Ideal Adsorbed Soluton theory, analytcally derve the expressons for the bnary sotherms usng the followng combnaton of pure adsorpton sotherms of the two components: Component A: Ant-Langmur n Component B: Ant-Langmur Assume that the saturaton capactes are equal for both components (N = NA = NB) and that kb > ka. MM 9 November Assgnment3_Adsorpton_Isotherms.docx

3 Insttute of Process Engneerng Hnt: one can prove that IAS leads to: a) b) Nkp n = A, B Nkp n = A, B c) but not Nkp n = A, B Part B: Determnaton of Specfc Surface Area of a Slca Gel For many materals, the surface to volume rato s an mportant qualty-ated parameter (adsorbents, catalysts). Adsorpton accordng to the BET sotherm s the bass for an mportant analytcal technque for the measurement of the specfc surface area of materals. Ths s shown n the followng example, where Langmur and BET sotherm are compared. Exercse B1 Ntrogen adsorpton s used to determne the surface area of a slca gel sample (mass: 30 g): The temperature used n the experment s the normal bolng pont of N2 (77 K). In the followng lst, the adsorbed volume of N2 s gven at dfferent pressures: p (kpa) Vads (ml) Wrte down a one-component Langmur sotherm usng volumetrc nstead of molar unts (we assume mplctly a constant densty of the adsorbed phase). In partcular, use as maxmal loadng (saturaton capacty) a volume Vmono that represents the volume of a fully occuped monolayer of adsorbed N2 molecules on the surface of the gven sample. Use the data presented above to determne the parameters k and Vmono by lnear regresson. It s assumed that the densty of the adsorbed phase corresponds to that of lqud N2 at 77K (0.808 g/cm 3 ), and that one N2 molecule occupes a specfc surface area of m 2. Calculate the surface of the sample correspondng to Vmono as derved from the Langmur sotherm. Also gve the specfc surface area of the slca gel sample n [m 2 /g]. MM 9 November Assgnment3_Adsorpton_Isotherms.docx

4 Insttute of Process Engneerng Exercse B2 For comparson to the Langmur sotherm, we use a BET sotherm wth the followng functonal form: n 1 p 1 ( c 1) p c N p As n the case of the Langmur sotherm, n s the adsorbed amount of gas, N s the saturaton capacty and p s the pressure atve to the vapor pressure: p = (p / p V ). At 77K, the vapor pressure p V of ntrogen equals the atmospherc pressure,.e kpa. Also ths sotherm may be wrtten n ts nverse form, and usng volumetrc nstead of molar parameters. Hence, we obtan: p 1 c 1 V 1 p cv cv ads mono mono As n the prevous case, Vads s the adsorbed volume of ntrogen, and Vmono s the volume of the fully occuped N2 monolayer on the surface of the gven sample. Use the data presented n B1 together wth ths lnearzed equaton and extract the parameters c and Vmono by lnear regresson. It s agan assumed that the densty of the adsorbed phase corresponds to that of lqud N2 at 77K (0.808 g/cm 3 ), and that one N2 molecule occupes a surface area of m 2. Calculate the surface of the sample correspondng to Vmono as derved from the BET sotherm. Also gve the correspondng specfc surface area of the slca gel sample n [m 2 /g]. p Exercse B3 Draw a dagram of the adsorbed volume vs. the pressure. Include expermental data ponts and curves accordng to the Langmur sotherm and the BET sotherm. Compare the two sotherms wth respect to ther ablty to descrbe the expermental data. MM 9 November Assgnment3_Adsorpton_Isotherms.docx

5 Insttute of Process Engneerng Part C: mult-component BET sotherm In the scope of ths lecture, we have descrbed how a sngle speces can undergo multlayer adsorpton on a sold surface, we have wrtten equatons that descrbe nteractons of the adsorbed molecules wth the sold surface and wth each other, and we have eventually derved from ths the BET sotherm for a sngle adsorbng speces. Exercse C1 Optonal project assgnment As an optonal project assgnment, you may repeat the study that leads to the dervaton of the BET sotherm, now descrbng the case of multlayer adsorpton for two speces that adsorb smultaneously on a sold surface. Extend the set of equatons requred and explore the possblty of dervng the bnary adsorpton sotherm accordngly. MM 9 November Assgnment3_Adsorpton_Isotherms.docx