SORPTION EQUILIBRIUM 6.1

Transcription

1 SECTION Single-Sorbate Isotherms Comparison o Sorption Perormance Euilibrium Constants Experimental Sorption Isotherm REFERENCES Ion Exchange Isotherms EQUILIBRIUM 6 EQUILIBRIUM BIOSORPTION PERFORMANCE SORPTION EQUILIBRIUM 6.1 The case o a sorption process considered here involves a solid phase (sorbent) and a liuid phase (solvent, normally water) containing a dissolved species to be sorbed (sorbate, e.g. metal ions). Due to the higher ainity o the sorbent or the sorbate species the latter is attracted into the solid and bound there by dierent mechanisms. This process takes place until an euilibrium is established between the amount o solid-bound sorbate species and its portion remaining in solution (at a residual, inal or euilibrium concentration C ). The degree o the sorbent ainity or the sorbate determines its distribution between the solid and liuid phases. ADSORPTION ION IN Langmuir Model ION EXCHANGE Figure Adsorption is dierent rom ion exchange The uality o the sorbent material is judged according to how much sorbate it can attract and retain in an immobilized orm. For this purpose it is customary to determine the metal uptake ( ) by the biosorbent as the amount o sorbate bound by the unit o solid phase (by weight, volume, etc.). The calculation o the metal uptake [mgmet /g (dry!) sorbent] is based on the material balance o the sorption system: sorbate which disappeared rom the solution must be in the solid. ION IN PROTON OUT IonEx Model 103

2 104 / CHAPTER 6 Evaluation o Biosorption Perormance Correspondingly, the amount o metal bound by the sorbent which disappeared rom the solution can be calculated based on the mass balance or the sorbent in the system: V [L] (C i ) [mg/l] = all the sorbate in the system [mg] V [L] (C ) [mg/l] = the sorbate let over in the solution [mg] The uptake (sorbate in the solid phase) will be the dierence: = V [L] (C i - C )[mg/l] / S [g] [in weight units mg/g] V [ml] metal solution C i initial solid S[mg] sorbent contact enough time ilter VC i ALL sorbate in the system EQUILIBRIUM SORPTION MASS BALANCE: V (C i - C ) = S analyze Residual sorbate in solution: iltrate C [mg/l] FINAL VC CONCENTRATION Figure The sorbate uptake is obtained rom its mass balance where (metal sorbate example): V is the volume o the metal-bearing solution contacted (batch) with the sorbent [L]; C i and C are the initial and euilibrium (residual) concentrations o the metal in the solution, respectively. They have to be analytically determined [mg/l]; S is the amount o the added (bio)sorbent on the dry basis [g]. SORPTION : mmol/g = me/g = The sorption uptake can be expressed in dierent units depending on the purpose o the exercise: 1) For practical and engineering process evaluation purposes which are eventually concerned with process mass balances it is customary to use weight per (dry) weight [e.g. mg o metal sorbed per gram o the (dry) sorbent material]. 2) Ultimately, mainly because o the reactor volume considerations (e.g. a packed-bed column), the uptake may also be expressed on a per volume basis [e.g. mg/l]. However, the volume porosity (voids) may present a complication in uantitative comparison o biosorption perormance. 3) Only when working on the stoichiometry o the process and when studying the unctional groups and metal-binding mechanisms it may be useul to express on a molar or charge euivalent basis - again, per unit weight or volume o the sorbent [e.g. mmol/g or me/g]. Sorption Uptake [ mg / g] Molecular ( Atomic) Weight Sorption Uptake [ mmol / g] Ion Valence All these units are relatively easily interconvertible. The only problem may arise with the sorbent weight-volume conversions. For scientiic interpretations, the sorbent material dry weight basis is thus preerred. The use o "wet biomass weight", unless the (wetweight / dry-weight) conversion well speciied should be discouraged. Dierent biomass types are likely to retain dierent moisture contents, intracellular as well as that trapped in the interstitial space between the cells or tissue particles (e.g. seaweed particles). Dierent types o biomass obviously compact in a dierent way.

3 6.1 Sorption Euilibrium / 105 When centriuging the biomass, the g-orce and time need to be speciied and even then any comparison is diicult to make. All this makes the wet biomass weight citation very approximate at best and generally undesirable Single-Sorbate Isotherms Since sorption processes tend to be exothermic and since the sorption perormance may vary with temperature, constant temperature during the sorption process is a basic reuirement. Sorption isotherms are plots between the sorption uptake ( ) and the inal euilibrium concentration o the residual sorbate remaining in the solution (C ). This simple relationship can be expressed in slightly dierent variations. Biosorption is not necessarily so strongly exothermic as other physical adsorption reactions. The temperature range or biosorption applications is considered relatively narrow, roughly between (10-70) o C, diminishing thus the temperature sensitivity issue to a large degree. EQUILIBRIUM SORPTION ISOTHERM C FINAL CONCENTRATION [mg/l] Figure Typical single-sorbate isotherms. Which sorbent here is better? Yellow or blue? Simple Sorption Models The ( ) vs (C ) sorption isotherm relationship can also be mathematically expressed. This was done already in the early 1900 s in the classical work o Langmuir [9] and Freundlich [5] who studied activated carbon adsorption. a The Langmuir isotherm relationship is o a hyperbolic orm: The Langmuir relationship can be linearized by plotting either (1/ ) vs (1/ C ) bc Langmuir: = 1 + bc where: is the imum sorbate uptake under the given conditions; e.g. ; b is a coeicient related to the ainity between the sorbent and sorbate (the relationship between b and the ainity constant K is developed later in this section). or (C /) vs C b C 1 + b C = LANGMUIR model b - related to initial slope it indicates the sorbent ainity The Scatchard linearization o Langmuir is:. (/C ) = b - b C FINAL CONCENTRATION [mg/l] Figure Langmuir model or the sorption isotherm

4 106 / CHAPTER 6 Evaluation o Biosorption Perormance b The Langmuir isotherm (1918) considers sorption as a chemical phenomenon. It was irst theoretically examined in the adsorption o gases on solid suraces. Langmuir constant b = 1/K which is related to the energy o adsorption through the Arrhenius euation. The higher b and the smaller K, the higher is the ainity o the sorbent or the sorbate. can also be interpreted as the total number o binding sites that are available or biosorption, and as the number o binding sites that are in act occupied by the sorbate at the concentration C. Although the Langmuir model sheds no light on the mechanistic aspects o sorption, it provides inormation on uptake capabilities and is capable o relecting the usual euilibrium sorption process behavior. Langmuir assumed that the orces that are exerted by chemically unsaturated surace atoms (total number o binding sites) do not extend urther than the diameter o one sorbed molecule and thereore sorption is restricted to a monolayer. In the simplest case the ollowing assumptions were made: a) ixed number o adsorption sites; at euilibrium, at any temperature and gas pressure a raction o the surace sites θ is occupied by adsorbed molecules, and the raction 1-θ is ree. b) all sorption sites are uniorm (i.e. constant heat o adsorption) c) only one sorbate d) one sorbate molecule reacts with one active site e) no interaction between sorbed species Assumption o a value or the surace area covered per molecule then could allow computation o the active specic surace area o the sorbent using Avogadro s number. However, the concept o surace area cannot be used in gel-like sorbents that most biosorbents may be. As long as its restrictions and limitations are clearly recognized, the Langmuir euation can be used or describing euilibrium conditions or sorption behavior in dierent sorbate-sorbent systems, or or varied conditions within any given system. The Freundlich isotherm relationship is exponential: Freundlich: ( 1/n) = k C where: k and n are Freundlich constants. The Freundlich relationship is an empirical euation. It does not indicate a inite uptake capacity o the sorbent and can thus only be reasonably applied in the low to intermediate concentration ranges (C!). However, it is easier to handle mathematically in more complex calculations (e.g. in modeling the dynamic column behavior) where it may appear uite reuently. Freundlich model can be easily linearized by plotting it in a (log-log) ormat. The Langmuir model has eventually been empirically most oten used since it contains the two useul and easily imaginable parameters ( and b) which are more easily understandable since they relect the two important characteristics o the sorption system [6,7,12-14]. Note the assumptions taken or the development o these original relationships which originated rom the work done with activated carbon as a solid-phase sorbent or molecular species. Monomolecular layer considered or deposition o sorbates implies the surace-based adsorption which is not the case or biosorption.

5 6.1 Sorption Euilibrium / 107 Other sorption isotherm relationships : Table 6-1 c Some sorption isotherm relationships Other sorption isotherm relationships listed in Table 6-1 are commonly appearing in the Brunauer-Emmett-Teller (BET) [1938]: biosorption literature. It is necessary to realize BQC that these relationships basically do not relect the = physico-chemical underlying principles o the ( C s C )[1 + ( B 1)( C / C s )] sorption process which, in most cases, may not C s is the saturation constant o the solute; even be well understood. For all practical B is a constant relating to the energy o purposes they are just mathematical models o the interaction with the surace; phenomenon capable o describing the ( ) vs (C ) Q is the number o moles o solute adsorbed relationship as experimentally observed. In this per unit weight o adsorbent in orming a complete monolayer on the surace; capacity, neither can any o these models oer any important clues as to the sorption mechanism nor could they be sensitive to external process variables (such as e.g. ph, ionic strength, etc.). While the Langmuir adsorption model is valid or a single-layer adsorption, the BET model represents sorption isotherms relecting apparent multi-layer adsorption (Figure 6.1-5). Both euations are limited by the suumption o uniorm energies o adsorption on the surace. The BET isotherm, the more generally applicable o the two, reduces to the Langmuir model when the limit o adsorption is a mono-layer. Both models may be deduced rom either kinetic considerations or the thermodynamics o adsorption [9,2,1]. The latter derivations are somewhat more sophisticated, though less intuitive, than the kinetic treatments since ewer assumptions are involved (e.g. the balancing o orward and reverse rate processes according to some assumed mechanism). Dubinin-Radushkevich (DR) [1947]: ln = ln m - B E 2 B is a constant related to the sorption energy E is Polanyi potential E = RT ln(1+ 1/C ) Radke-Prausnitz [1972]: = + β ac bc Reddlich-Peterson [Jossens et al.,1978]: ac = 1+ bc Combination: bmc = 1 + bc n (1/ n) (1/ n) (Langmuir-Freundlich) [Sips, 1948] The BET model assumes that a number o layers o adsorbate molecules orm at the surace and that the Langmuir euations applies to each layer. A urther assumption o the BET model is that a given layer need not complete ormation prior to initiation o subseuent layers; the euilibrium condition will thereore involve several types o suraces in the sense o number o layers o molecules on each surace site. For adsorption rom solution with the additional assumption that layers beyond the irst have eual energies o adsorption, the BET euation takes the simpliied orm as in Table 6-1. C BET model = BQC (C S -C )[1+ (B-1)( C S /C )] FINAL CONCENTRATION [mg/l] Figure Brunauer-Emmett-Teller sorption isotherm model

6 108 / CHAPTER 6 Evaluation o Biosorption Perormance The use o simple isotherm models is not much more than curve itting The surace area concept is NOT applicable or gellike biosorbents Needless to say, or dierent sorption systems and mechanisms outside o the scope o these assumptions the application and it o the model euations is a matter o chance. They become just mathematical relationships which happen to be capable o ollowing the experimental data. The problem with biosorption is that usually not very much speciic inormation is available on the sorption mechanism(s) involved. The usual concept o the solid-phase sorbent with physical pores and surace area etc. may not be so close to the real structure, appearance and behavior o biosorbent materials. Particularly in conjunction with metallic ions as sorbate species, biosorbents may appear as gels, very transparent or the minute ions and protons. Actually, when it comes to an ion exchange process, which apparently plays a very important role in biosorption, at least one ion rom within the molecular structure o the sorbent is exchanged or another one coming rom outside. This leads to ever-changing conditions in the sorption system due to the stream o exchanged ions also leaving the sorbent into the liuid environment. That is until the sorption euilibrium is established Comparison o Sorption Perormance Perormance o sorbing materials oten needs to be compared. The simplest case is when there is only one sorbate species in the system. The comparison o single-sorbate sorption perormance is best based on a complete single-sorbate sorption isotherm curve. In order or the comparison o two or more sorbents to be air it must always be done under the same conditions. These may be restricted by the environmental actors under which sorption may have to take place (ph, temperature, ionic strength, etc.). EFFECT o ph FINAL CONCENTRATION [mg/l] Figure As an external actor, ph has to become a parameter or the conventional sorption isotherm plot They may not necessarily be widely adjustable. It is important to compare sorption perormance e.g. under the same ph since isotherms could vary with ph. By perormance o the sorbent is usually meant its uptake ( ). The sorbents can be compared by their respective values which are calculated e.g. rom itting the Langmuir isotherm model to the actual experimental data (i it its). This approach is easible i there exists the characteristic sorption perormance plateau (the imum sorbent saturation). A good sorbent that one always looks or would eature a high sorption uptake capacity. However, also desirable is a high ainity between the sobent and sorbate relected in good uptake values at low concentrations (C ). This is characterized by a steep rise o the isotherm curve close to its origin. Perormance in this region is relected in the Langmuir coeicient b.

7 6.1 Sorption Euilibrium / 109 Which sorbent is better?? There is no direct answer to that until this uestion is ualiied: under what conditions? The sorption isotherm diagram depicts the experimentally determined perormance o sorbents A and B. Given the same experimental (environmental) conditions, as reuired or comparison, the independent variable in the sorption system is the C. Both curves intersect - obviously, at that point the perormance o both sorbents is the same (in terms o ). However, sorbent A would exhibit higher s or the same C s in the range o lower C values (let rom the curve intersect): sorbent A is better than sorbent B in that range. This is important, or instance, when the sorbent is supposed to work at low residual sorbate concentrations as may be the case e.g. the when regulatory agency limits the imum concentration o a pollutant (sorbate, toxic metal, etc.) allowable in the discharged eluent. When the limitation o the imum residual sorbate concentration is not o a concern and the purpose is to saturate the sorbent as much as possible (no matter how much o the sorbate may still be let over in the solution), sorbent B is better because it accumulates more sorbate at higher residual sorbate concentrations (higher C range). This may be o importance when the eventual recovery o the sorbate rom the biosorbent is desired. A biosorbent "better" at low concentrations may be "inerior" at higher ones, and vice versa. This is the reason why one comparison at "low" C (e.g. 10 mg/l) and also another one at "high" C (e.g. 200 mg/l) was made in some biosorption screening work [6,7]. Another aspect o a air comparison is to compare, or instance, the best with the best : the optimal ph value or the best perormance o one sorbent may not be the same one as or the best perormance o another sorbent. I the operating parameter is as simple as ph, which can perhaps easily be adjusted in the process, the easibility o A B A > B FINAL CONCENTRATION [mg/l] Figure At low C s A is better than B B > A FINAL CONCENTRATION [mg/l] Figure At high C s B is better than A FINAL CONCENTRATION [mg/l] B A B A Figure indicates the ultimate perormance

8 110 / CHAPTER 6 Evaluation o Biosorption Perormance b FINAL CONCENTRATION [mg/l] Figure Langmuirian b relates to ainity between the sorbent and the sorbate (oten metal ion considered here) (6-1) B + M BM ADSORPTION ION IN reaction : B+M IonEx Model Adsorption Langmuir Model Parameter Langmuir : Model BM this adjustment should be considered. In all comparisons it is extremely important to make certain that all the external sorption system parameters remain indeed comparable. The above consideration leads to another important characteristic o the sorption isotherm curve and this is its initial slope. A curve with a steep initial slope indicates a sorbent which has a capacity or the sorbate in the low residual (inal, C ) concentration range. That means that the sorbent has a high ainity or the sorbed species. This ainity is indicated by the coeicient b in the Langmuir euation. The lower the value o b the higher the ainity. In conclusion, or good sorbents in general, one is looking or a high and a steep initial sorption isotherm slope as indicated by low values o Langmuir parameter b [9,13]. It is advisable to base the comparison o sorption perormance on whole sorption isotherm plots which are in turn derived experimentally Euilibrium Constants Langmuir model assumes that all the binding sites on the sorbent are ree sites, ready to accept the sorbate rom solution. Thereore, an adsorption reaction is taking place that can be described as : B represents the ree binding sites, M is the sorbate in the solution (metal), and BM denotes the adsorbed sorbate M bound on B. The adsorption euilibrium constant is deined rom the mass conservation law: b = 1/K ION EXCHANGE ION IN euilibrium ainity: IonExPROTON [BM] Model OUT K = [B][M] Figure Relationship between Langmuirian b and the euilibrium ainity constant K [BM] K = [B][M] (6-2) it represents the ainity o sorbate or the binding site. [ ] denotes the concentration. According to the mass conservation o binding sites, the total binding capacity B T is: [B T ]= [B] + [BM] (6-3) By combining euations (2) and (3) the ollowing is obtained: [B T ] [M] [BM] = (6-4) 1+ KK [M] where [BM] also represents the sorbate uptake, then:

9 6.1 Sorption Euilibrium / 111 [B T ] [C] = 1 + KK [C] Euation (6-5) is one o the conventional orms o Langmuir euation. K represents the ainity o sorbate M to site B. Another orm o Langmuir euation could be derived rom the above euation (6-5) by dividing the whole raction in euation (6-5) with K and we obtain: (6-5) [B T ] [C] = (1/ K) + [C] (6-6) Making b = 1/K (6-7) then K = 1/b (6-8) Replacing K in euation (6-6) with euation (6-8) we obtain: = [B T [C] b +] [C] Euation (6-9) is another orm o Langmuir euation where b is a constant. Its physical meaning could be illustrated by combining euations (6-2) and (6-7): Thereore, b represents the reverse o the ainity. Langmuir or Freundlich type binding assumes ree sites, not an (ion) exchange. In the mathematical modeling o the phenomenon the Langmuir euation and the ion exchange constant or the binding o a metal ion M (or simplicity here a monovalent ion) replacing a proton H on a complexing site B are related as seen in the relationships in the let column: The dierences between the two models may be especially pronounced at low metal ion concentrations [3]. The ion exchange approach is probably somewhat closer to the reality than the simple Langmuir model, but it is not completely satisying either. The ADSORPTION reaction : B+M Langmuir Model BM BM K = B[M] b = 1/K = [B][C] [BC] (6-9) (6-10) ION EXCHANGE reaction : BH+M K K* = [H] Figure Relationship o Langmuirian and Ion-Exchange euilibrium constants (ainities) assumption o the constant number o ree sites may be reasonable or a constant ph system. It may not hold or systems with changing ph values. The cation exchange capacity tends to increase with increasing ph above the isoelectric point. Modeling the competitive binding o metals and protons using only a metal-proton ion exchange constant is simplistic. It should include at least one reaction where a cation reacts with a ree site. BM+H IonEx Model Ion exchange: BH + M BM + H (6-11) BM BM[H] K = BH[M] and [B]t = [BH] + [BM] thereore: BM K * = BM K / [H] (6-12)

10 112 / CHAPTER 6 Evaluation o Biosorption Perormance V [ml] metal solution C i initial solid sorbent S[mg] contact enough time ilter EQUILIBRIUM SORPTION V (C i - C ) = S plot analyze sorption isotherm iltrate C [mg/l] FINAL CONCENTRATION Figure Experimental procedure or deriving the sorption isotherm Preliminary dynamics o the sorption process (uptake-time relationship) must be approximately Experimental Sorption Isotherm It is relatively simple and easy to obtain laboratory euilibrium sorption data or a single sorbate. A small amount o the sorbent tested is brought into contact with solution containing the given sorbate. However, the environmental parameters in the sorption system (particularly ph) have to be careully controlled at the given value over the entire period o contact until the sorption euilibrium is reached. It may take a ew hours or much longer depending on the size o sorption particles and the time it takes until they attain sorption euilibrium. A simple preliminary sorption kinetics test will establish the exposure time necessary or the given sorbent particles to reach the euilibrium state characterized by the unchanging sorbate concentration in the solution. That is determined by time-based analyses. Saely enough time will be allowed or the sorption system to reach euilibrium. The ollowing procedure provides an example or obtaining the experimental sorption euilibrium data points or the isotherm as seen also in the procedure schematic lowchart: 1) Prepare the sorbate in solution at the highest concentration o interest. 2) Make dilutions to cover the entire concentration range (rom 0 -blank, to the.). 3) Adjust the environmental parameters (e.g. ph, ionic strength, etc.). It is convenient to vary C i 4) Determine the sorbate initial concentrations (C i in all the liuid samples. 5) Distribute the samples into appropriate-volume containers (record V = ml o liuid) such as lasks or test tubes (in duplicate, triplicate or as reuired). The sorbent weight S can luctuate but must be precisely known or each sample 6) Weigh accurately each (approximate) amount o the (bio)sorbent solids to be used in each contact test and record each amount (S mg). It may help to be able to roughly estimate the anticipated sorption uptake so that there is a well detectable sorbate inal concentration let in the solution at euilibrium in each sample. I there is too much solids added there may be virtually no sorbate let in the solution or a reliable analysis. 7) Add the sorbent solids into each sample solution and provide or rather gentle mixing over the contact period ( enough time!). 8) Make sure the environmental parameters (ph!) are controlled at a constant value during the contact period (use appropriate acid or base or the purpose; do not dilute the sorption system by adding excessive volume).

11 6.1 Sorption Euilibrium / 113 9) At the end o the contact period, separate the solids rom the liuid (decantation, iltration, centriugation, etc.) 10) Analyze the liuid portion or the residual, inal, euilibrium sorbate concentration (C ). 11) Calculate the sorbate uptake: = V [L] (C i - C )[mg/l] / S [g] EFFECT o ph FINAL CONCENTRATION [mg/l] Figure (repeated) ph is an external actor and it has to be controlled or standard isotherm experiments the inal, euilibrium ph is the one that matters! Note that could also be determined directly by analyzing the separated solids and thus closing the material balance on the sorbate in the system. However, this usually presents analytical diiculties (digestionliueaction o solids and/or very sophisticated analytical methods may be reuired). A variation o this approach is the tea-bag experiment, described below, whereby C = C i and only the solids are analyzed. In either case, the C in the liuid must be known or the sorption isotherm plotting: 12) Plot the sorption isotherm vs (C ). There is no control over C, it happens in the experiment Note that or all practical purposes the choice o experimental variables narrows usually down to two: concentration C i and the amount o sorbent solids S contacted. One or the other or both can be varied. In the above procedure it was the concentration o sorbate dilutions C i. The key point is to obtain measurable and dierent values o C at the end o the contact experiment. Experimental variables could be either C i or S From the euilibrium principles it is easily seen that the initial concentration o sorbate (C i ) is o little relevance in these kinds o sorption tests. It can assist in identiying the inal concentration range which, o course, depends on the amount o sorbent solids (S ) in the system. Also note that one has no control over the value o C, it sort o happens during the experiment. Metal depletion in the solution has to be avoided since it renders such samples useless (unreliable or impossible C determination) V [ml] metal solution C i initial solid sorbent S[mg] contact enough time ilter EQUILIBRIUM SORPTION analyze SOLIDS =! W (metal) S plot sorption isotherm DIFFICULT TO DETERMINE in SOLIDS Figure For checking, the loaded sorbent solids can be analyzed too but it is usually more complicated. I they could be completely eluted, the desorption liuid could then be analyzed to make sure that the sorbate mass balance closes

12 114 / CHAPTER 6 Evaluation o Biosorption Perormance metal solution solid S[mg] sorbent SMALL LARGE V [ml] contact enough time C i initial ~ C inal separate solids! TEA-BAG EQUILIBRIUM SORPTION analyze SOLIDS Figure In the tea-bag experiment C i = C =! W (metal) S plot sorption isotherm DIFFICULT TO DETERMINE in SOLIDS The tea-bag experiment In this approach there is a possibility o chosing and maintaining the C. For this purpose the liuid volume is solarge and the amount o sorbent solids added to it so relatively small that there is practically no change in the sorbate concentration and thus C i = C. When the solids are isolated rom this special sorption system, they are analyzed or the sorbate content. This analysis o solids is usually much more demanding than the analysis o liuid. Conseuently, this kind o approach may be used in special cases only. 91% 88% 9 sorbent comparison B 18 % REMOVAL 82% 71% 29 mg/l FINAL CONCENTRATION Figure Example o % Removal screening D C A C i = 100 mg/l V = 100 ml S = 30 mg [mg/l] C Sorbent Comparison Based on % Removal Another criterion or comparing sorbent materials ound in the literature is based on % removal o the sorbate rom the solution. This is a rather crude and somewhat inaccurate approach as will be demonstrated in this section. Using a speciic example may perhaps best serve as a demonstration o the principle: It is desirable to compare the sorption perormance o (bio)sorbents A, B, C, and D. This could be done in a ew euilibrium tests carried out by the same procedure using the same V (100mL), C i (100mg/L), and S (30mg) or each o the contact samples examined. The results recorded were as ollows: Biosorbent A: experimental C = 9 mg/l; calculated sorbate removal = 91%. Biosorbent B: experimental C = 12 mg/l; calculated sorbate removal = 88%. Biosorbent C: experimental C = 18 mg/l; calculated sorbate removal = 82%. Biosorbent D: experimental C = 29 mg/l; calculated sorbate removal = 71%. It is obvious that there exist our separate sorption isotherms each characterizing one o the sorbent materials. However, available is only one point or each curve.

13 6.1 Sorption Euilibrium / 115 For each o the C values obtained there is one (and dierent!) corresponding which can serve as a basis or sorption perormance comparison. The inaccuracy inherent in this approach is in the act that the perormance comparison is NOT done on the same basis since the C s are dierent. In the irst case seen in the Figure, the conclusion can be drawn that the sorbent perormance ollows this pattern: A>B>C>D. That may be uite correct i the individual isotherms ollow a similar (steadily rising) pattern. O course, the correct comparison can only be done along the same line o the same C or all the materials. Obviously, this is not possible when the whole sorption isotherm plots are not available. The danger in using the simplistic methodology is that the ull individual isotherm curves might ollow uite dierent patterns outside o the range o the C s experimentally obtained. This is seen in the next case Figure where the conclusion on the sorbent perormance would suggest the same pattern: A>B>C>D. However, in the higher C range, the isotherm or sorbent B is lat and another test conducted in the higher inal concentration range would undoubtedly indicate a dierent sorbent perormance pattern: A>C>B>D! The original simple test would never reveal this act. Indeed, in some cases, the simplistic % Removal method could lead to outright misleading conclusions on the relative sorption perormance. It can only serve the purpose o crude orientation, perhaps adeuate only or uick and very approximate screening o (bio)sorbent materials. The % Removal values so oten uoted in the literature also do not oer any inormation on the concentration range where the removal took place (e.g. range in the 1,000's, 100's or 10's o mg/l ). 91% 88% 9 sorbent comparison B 18 % REMOVAL 82% 71% 29 mg/l FINAL CONCENTRATION D C A C i = 100 mg/l V = 100 ml S = 30 mg [mg/l] Figure DANGER: The ull isotherms do not ollow a pattern OK 91% sorbent comparison 9 A>B >C >D 18 % REMOVAL 82% 71% 29 mg/l FINAL CONCENTRATION D A>C >B >D Figure Wrong conclusion about the sorbents! OK 91% B FINAL CONCENTRATION [mg/l] C WRONG! C A C i = 100 mg/l V = 100 ml S = 30 mg V (C i - C ) = S [mg/l] C sorbent comparison correct 9 comparison 18 % REMOVAL 82% 71% 29 mg/l A approximate! Figure % Removal is only or crude judgement C D B C i = 100 mg/l V = 100 ml S = 30 mg V (C i - C ) = S C

14 116 / CHAPTER 6 Evaluation o Biosorption Perormance REFERENCES 1. Adamson, A.W Physical Chemistry o Suraces (2nd ed.). Interscience Publishers, New York, NY. 2. Brunauer, S., Emmet, P.H. and Teller, E Adsorption o gases in multimolecular layers. J. Am. Chem. Soc. 60, Crist, R.H., Martin, J.R., Carr, D., Watson, J.R., Clarke, H.J. and Crist, D.R Interaction o metals and protons with algae. 4. Ion exchange vs adsorption models and a reassessment o Scatchard plots; ion-exchange rates and euilibria compared with calcium alginate. Envir. Sci. Technol. 28, Dubinin, M.M. and Radushkevich, L.V Euation o the characteristic curve o activated charcoal. Chem. Zentr. 1, Freundlich, H Ueber die Adsorption in Loesungen. Z. physik. Chem. 57, Holan, Z.R. and Volesky, B Biosorption o Pb and Ni by biomass o marine algae. Biotechnol. Bioeng. 43, Holan, Z.R., Volesky, B. and Prasetyo, I Biosorption o Cd by biomass o marine algae. Biotechnol. Bioeng. 41, Jossens, L., Prausnitz, J.M., Fritz, W., Schlunder, U. and Myers, A.L Thermodynamics o multisolute adsorption rom dilute aueous solutions. Chem. Eng. Sci. 33, Langmuir, I The adsorption o gases on plane suraces o glass, mica and platinum. J. Am. Chem. Soc. 40, Radke, C.J. and Prausnitz, J.M Thermodynamics o multi-solute adsorption rom dilute liuid solutions. J. AIChE, 18, Sips, R On the structure o a catalyst surace. J. Chem. Phys. 16, Volesky, B Advances in biosorption o metals: Selection o biomass types. FEMS Microbiol. Rev. 14, Volesky, B. and Holan, Z.R Biosorption o heavy metals. Biotechnol.Progress 11,