Lecture 3 Sorption equilibrium - CHERIC

1 Lecture 3. Sorption equilibrium Pure Gas adsorption -Linear isotherm-Freundlichisotherm-Langmuir isotherm-Other adsorption isotherms-BET isotherm Gas Mixtures and Extended Isotherms Liquid adsorption Ion-Exchange EquilibriaAdsorption equilibrium Dynamic equilibrium in adsorption : solute distribution between fluid and solid surface-[concentration (if the fluid is a liquid) or partial pressure (if the fluid is a gas) of the adsorbatein the fluid] vs. [solute loading on the adsorbent (mass, moles, or volume of adsorbateper unit mass or surface area)] adsorption isotherm: equilibrium data at a constant temperature-A limit on the extent to which a solute is adsorbed from a specific fluid mixture on a given adsorbent for one set of conditionsClassification of adsorption Isotherms (1) Type I isotherm-Typical of adsorbents with a predominantly microporousstructure-Corresponds to unimolecularadsorption-Maximum limit in the amount adsorbed-Gases at temperatures above their critical temperature-Example.

2 Nitrogen on carbon at 77K and ammonia on charcoal at 273 KStandard classification developed by IUPACC lassification of adsorption Isotherms (2) Type II isotherm-Physical adsorption of gases by non-porous solids-Corresponds to multimolecularBET adsorption (monolayer coverage followed by multilayeringat high relative pressures)-Gases at temperatures below their critical temperature and pressures below, but approaching, the saturation pressure-The heat of adsorption for the first adsorbed layer is greater than that for the succeeding layers-Example: carbons with mixed micro-and meso-porosity Type III isotherm-Convex and undesirable (extent of adsorption is low except at high P) -Characteristic of weak adsorbate-adsorbent interactions -Corresponds to multimolecularadsorption -The heat of adsorption of the first adsorbed layer is less than that of succeeding layers-Example: adsorption of iodine vapor on silica gelClassification of adsorption Isotherms (3) Type IV isotherm-The maximum extent of adsorption occurs before the saturation pressure is reached-A hysteresis loop, which is commonly associated with the presence of mesoporosity-Capillary condensation gives rise to a hysteresis loop Type V isotherm-Convex to the relative pressure axis-Characteristic of weak adsorbate-adsorbent interactions at low relative pressures-Microporousor mesoporoussolids-Hysteresis in multimolecularadsorption regions-Capillary condensation version of Type IIIC lassification of adsorption Isotherms (4) Type VI isotherm-Complete formation of monomolecular layers before progression to a subsequent layer- adsorption on extremely homogeneous, non-porous surfaces where the monolayer capacity corresponds to the step height-Example.

3 adsorption of krypton on carbon black at 90 KClassification of adsorption Isotherms (5) Hysteresis loop-Occurs due to capillary condensation (gas adsorption in the pores at a low density after a sufficient amount of gas has been supplied, it spontaneously condenses into a liquid-like state inside the pores)-Change of geometry during adsorption and desorption processchannels with uniform sizes and shapeschannels with a pore mouth smaller than pore body (ink-bottle-shaped pores)solids with a very wide distribution of pore sizelimited amounts of mesoporeslimited by microporesPure-Gas adsorption Linear isotherm: a form of Henry s lawq kp=q: equilibrium loadingk: empirical, temperature-dependent constant for the componentp: partial pressure of the species-As temperature increases, the amount adsorbed decreases because of Le Chatelier sprinciple for an exothermic processAdsorption isothermsAdsorption isobarsIsostericHeat of AdsorptionAdsorption isosteresIsostericheats of adsorptionconstant amount adsorbed Clausius-ClapeyronequationlnDads2Hd pdTRT-=log( / ).

4 Dads1 2303Hd pd TRT-=[ adsorption of NH3on charcoal]- Hadsis initially 7,300 cal/mol 6,100 cal/molat 100 cm3/gHeat of vaporization of HN3at 30oC: 4,600 cal/molFreundlichIsotherm Freundlichisotherm: empirical and nonlinear in pressure (Type I)1nq kp=-k and n are temperature-dependent constants-n lies in the range of 1 to 5-In general, with T n but k , approaching a value of 1 at high T-Can be derived by assuming a heterogeneous surface with a nonuniformdistribution of heat of adsorption Fitting of experimental data to the Freundlichequation-By a nonlinear curve fit-By plotting log qvs. log pfor the linear formlog log ( )log1qk n p= +Langmuir Isotherm (1) Basis of Langmuir equation/ ( )q q1addq dt k pk= - --From mass-action kinetics, assuming chemisorption-The surface of adsorbent pores is homogeneous ( Hads= constant)-Negligible interaction forces between adsorbed moleculesq: fraction of surface covered by adsorbed molecules1 -q: fraction of bare surface Net rate of adsorptionAt equilibrium , dq/dt= 0( / )( / )q=1a da dk k pk k p+ka: adsorption kinetic constantkd: desorption kinetic constantK: adsorption - equilibrium constant/q=mq qqm: maximum loading corresponding to complete surface coverage1 KpKp=+Langmuir Isotherm (2)Langmuir adsorption isotherm is restricted to a monomolecular layer=1mKq pqKp+At low pressures (Kp 1), q=Kqmp(linear isotherm)Although originally Langmuir adsorption isotherm is devised for chemisorption, it is widely applied to physical- adsorption data.

5 Fitting of experimental data to the Langmuir equation-By a nonlinear curve fit-By plotting p/qvs. pfor the linear form1=mmppq q K q+ Theoretically, K should change rapidly with T but qmshould notAt high pressures (Kp 1), q=qmOther adsorption Isotherms Tothisotherm()=1ttmpqb p+-m, b, and t are constants for a given adsorbate-adsorbent and T-Obeys Henry s law at low P and reaches a maximum at high P-Reduce to the Langmuir isotherm for t = 1 UNILAN isothermln=2ssn c peqs c pe- + + -n, s, and c are constants for a given adsorbate-adsorbent and T-Based on a model of heterogeneous surfaces assuming a uniform distribution of adsorption energy-Reduce to the Langmuir isotherm for s = 0 BET Isotherm (1) BET theory: physical adsorption of gas molecules on a solid surface to form multilayerNsites: total number of sitesq0: fraction of surface sites unoccupied q1: fraction of surface sites covered by a monolayerq2: fraction of surface sites covered by a bilayer Number of adsorbed molecules()1 2 3q q qsites2 3LN N= + + + First layerRate of adsorption = ,0q0aNk pRate of desorption = ,1q0dNkAt equilibrium , ,,01q q00adk p k=BET Isotherm (2) Second layerRate of adsorption = ,1q1aNk pRate of desorption = ,2q1dNkAt equilibrium , ,,12q q11adk p k= Third layerRate of adsorption = ,q2 2aNk pRate of desorption = ,3q2dNkAt equilibrium , ,,23q q22adk p k=MOnce a monolayer has been formed, all the rate constants involving adsorption and desorption from the physisorbedlayers are assumed to be the same.

6 ,,01q q00adk p k=, ,( )100qq q0 00adk k p K p ==,,12q q11adk p k=, ,( )21qq1 1adk k p =0q20 1K K p=,,23q q22adk p k=, ,( )32qq2 2adk k p =0q2 30 1K K p=, , , ,( )( )0q20 0 1 1adadk k k k p=, , , ,( )( )0q2 30 0 1 1adadk k k k p=BET Isotherm (3)Because0 1 2 3q +q q q1L+ + + =00001=q + qqq22 300 10 1LK p K K pK K p+++{}00=q + q2 20111LK pK p K p+ + +0= 1+ q011K pK p - ()0q =11 011K pK K p-- - Number of adsorbed species00= qq2sites 0sites 0 12L K p K K p++()0= q2 2sites 0111 2 3L K pK p K p+ + +()0q=sites 0211 K pK p-0=q10111K p K pK p - + - BET Isotherm (4)()()=sites 0121 01111 K pK p K K pK p- - --()(){}=sites 011 01 1 K pK pK K p- - -The ratio N/Nsitesis equal to the ratio v/vmonv: total volume adsorbedvmon: volume adsorbed for complete monolayer coverage=10K PP0: vapor pressure of the liquid()(){}0mon00 1 01 1 1K PvvP PK K P P=- - -K1is the equilibrium constant for the reaction in which the reactant is a molecule physisorbedand the product is the molecule in the Mixtures and Extended Isotherms (1) One component can increase, decrease, or have no influence on adsorption of another, depending on interactions of adsorbed molecules.

7 Extended Langmuir isotherm-Neglect interactions-Assume the only effect is the reduction of the vacant surface area-For a binary gas mixture of A and B( ) () ( )q q = qA A A BA1aA dk pk- -( ) () ( )q q = qB B A B B B1adk pk- -/( )q =iii mq q(qi)m: maximum amount of adsorption of species ifor coverage of the entire surface Data for binary and multi-component gas-solid adsorbent equilibriaare scarce and less accurate than corresponding pure-gas : fraction of surface covered by AqB: fraction of surface covered by B1 -qA-qB: fraction of vacant surfaceGas Mixtures and Extended Isotherms (2)( )A A AAA A B B1mq K pqK p K p=+ +( )B B BBA A B B1mq K pqK p K p=+ +( )1i m i iij jjq K pqK p=+ For a mixture of jcomponents Extended Langmuir-Freundlichequation( )1011ijnii iinj jjq k pqk p=+ Represents data for nonpolar, multicomponent mixtures in molecular sieves reasonably well Separation factor (selectivity),ai ji jijq qp p=( )( )i m ij m jq Kq K=Liquid adsorption (1) Assumptions in a homogeneous binary liquid mixture adsorption -The composition change of the bulk liquid in contact with the porous solid is due entirely to adsorption of the solute-Solventadsorption does not occur From a solute material balance( )0 01 11en x xqm-=n0: total moles of binary liquid contacting the adsorbentm: mass of adsorbentx10: mole fraction of solute before contact with adsorbentx1.

8 Mole fraction of solute after adsorption equilibrium is achievedq1e: apparent moles of solute adsorbed per unit mass of adsorbentAssuming negligible change in the total moles of liquid mixture Isotherms in the dilute region-Solvent adsorption , if any, may be constant-All changes in total amount adsorbed are due to solute1nq kc==1mKq cqKc+Liquid adsorption (2) Isotherms over entire concentration rangeNegative adsorption Origin of various types of composite isotherms-Composite isotherms or isotherms of concentration change -q1e: surface excess -When the solvent is not adsorbed, a composite curve without negative adsorption is obtainedA: solute, B: solventIon-Exchange Equilibria(1) Ion exchange-One sorbate(a counterion) is exchanged for a solute ion, the process being governed by a reversible, stoichiometric, chemical-reaction equation-Selectivity of the ion exchanger for one counterionover another may be just as important as the ion-exchanger capacity-The law of mass action is used to obtain an equilibrium ratio(1) Case 1.

9 The counterioninitially in the ion exchanger is exchanged with a counterionfrom an acid or base solution( )( )( )( )( )aqaqss 2 lNa OH HR NaR H O+-+ + +(2) Case 2. The counterionbeing transferred from exchanger to fluid remains as an ion( )( )( ) ( )lsslA BR AR Bnnnn + +Leaving no counterionARBA,BBRA=nnnnq cKq c Molar selectivity coefficient for A displacing BIon-Exchange Equilibria(2) The total concentrations, C and Q, in equivalents of counterionsin the solution and the resin, remain constant during exchangeii ic = C x zii iq = Q y zxiandyi: equivalent fractions (xA+ xB=1, yA+ yB=1)zi: valence of counterioni For counterionsA and B of equal chargeA BA,BB A=y xKy x For counterionsA and B of unequal charge( )( )1 AAA,BAA1=1nnnyxCKQ xy- - - ( )( )AAAA1=1yxxy--Ion-Exchange Equilibria(3) Estimation of KA,B=ijijK K KKiandKi: relative selectivities Separation factor, SP (ignoring the valence of the exchange ions)( )( )AAA,BAA1=1yxSxy-- Isotherms for ion exchange of Cu2+and Na+Total normality in the bulk solutionAt low total-solution concentration, the resin is highly selective for Cu2+, whereas at high total-solution concentration, the selectivity is reversed to slightly favor Na+