Equilibrium Biosorption Performance

7/27/2019 Equilibrium Biosorption Performance

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SECTION 6.1

6.1.1 Single-Sorbate Isotherms

6.1.2 Comparison of Sorption

Performance

6.1.3 Equilibrium Constants6.1.4 Experimental Sorption Isotherm

6.1.5 REFERENCES

6.1.6 Ion Exchange Isotherms 6EQUILIBRIUM

EEQQUUIILLIIBBRRIIUUMM BBIIOOSSOORRPPTTIIOONN PPEERRFFOORRMMAANNCCEE

SORPTION EQUILIBRIUM 6.1

The case of a sorption processconsidered here involves a solid phase

(sorbent) and a liquid phase (solvent,normally water) containing a dissolvedspecies to be sorbed (sorbate, e.g. metalions). Due to the higher affinity of thesorbent for the sorbate species the latter isattracted into the solid and bound there bydifferent mechanisms. This process takes

place until an equilibrium is establishedbetween the amount of solid-bound sorbatespecies and its portion remaining insolution (at a residual, final or equilibriumconcentration Cf ). The degree of thesorbent affinity for the sorbate determines

its distribution between the solid and liquidphases.

METAL

ION IN

PROTON

OUT

METAL

ION IN

ADSORPTIONADSORPTION ION EXCHANGEION EXCHANGE

Langmuir

Model

IonEx

Model

Figure 6.1-1Adsorption is different from ion exchange

The quality of the sorbent material is judged according to howmuch sorbate it can attract and retain in an immobilized form. For this

purpose it is customary to determine the metal uptake (q) by the biosorbentas the amount of sorbate bound by the unit of solid phase (by weight,volume, etc.).

The calculation of the metal uptake [mgMet /g (dry!) sorbent] isbased on the material balance of the sorption system:

103sorbate which disappeared from the solution must be in the solid.


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/ CHAPTER 6 Evaluation of Biosorption Performance104

Correspondingly, the amount of metal bound by the sorbent whichdisappeared from the solution can be calculated based on the mass

balance for the sorbent in the system:

V[L] (Ci) [mg/L] = all the sorbate in the system [mg]

V[L] (Cf) [mg/L] = the sorbate left over in the solution [mg]The uptake (sorbate in the solid phase) will be the difference:

q = V[L] (Ci - Cf)[mg/L]/S[g] [in weight units mg/g]

where (metal sorbate example):

V (C - C )

Sq

fi=

METALMETAL

UPTAKEUPTAKE

[mg/g][mg/g]

EQUILIBRIUM SORPTIONEQUILIBRIUM SORPTION

Ci initial

solid

sorbent

contactenough

time

metal

solutionanalyze

filtrate[mg/L][mg/L]

FINALFINAL

METALMETAL

CONCENTRATIONCONCENTRATION

Cf

filterResidual sorbate in solution:

S[mg]

V[mL]

VCf

VCi

ALL sorbate inthe system

MASS

BALANCE:

Figure 6.1-2The sorbate uptake is obtained from its mass balance

V is the volume of the metal-bearingsolution contacted (batch) with the sorbent[L];Ci and Cf are the initial and equilibrium

(residual) concentrations of the metal in thesolution, respectively. They have to be

analytically determined [mg/L];S is the amount of the added (bio)sorbenton the dry basis [g].

The sorption uptake q can be expressed in different units depending on thepurpose of the exercise:

1) For practical and engineering process evaluation purposes whichare eventually concerned with process mass balances it is customary to useweight per (dry) weight [e.g. mg of metal sorbed per gram of the (dry)

sorbent material].2) Ultimately, mainly because of the reactor volume considerations

(e.g. a packed-bed column), the uptake may also be expressed on a pervolume basis [e.g. mg/L]. However, the volume porosity (voids) may

present a complication in quantitative comparison of biosorptionperformance.

3) Only when working on the stoichiometry of the process and whenstudying the functional groups and metal-binding mechanisms it may beuseful to express q on a molar orcharge equivalent basis - again, per unitweight or volume of the sorbent [e.g. mmol/g ormeq/g].

All these units are relatively easilyinterconvertible. The only problem may arise with thesorbent weight-volume conversions. For scientificinterpretations, the sorbent material dry weight basis isthus preferred.

SORPTION UPTAKE :

mmol/g =WeightAtomicMolecular

gmgUptakeSorption

)(

]/[

meq/g =ValenceIon

gmmolUptakeSorption ]/[

The use of "wet biomass weight", unless the (wet-weight / dry-weight) conversion well specified should

be discouraged. Different biomass types are likely toretain different moisture contents, intracellular as wellas that trapped in the interstitial space between the cellsor tissue particles (e.g. seaweed particles). Differenttypes of biomass obviously compact in a different way.


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6.1 Sorption Equilibrium / 105

When centrifuging the biomass, the g-force and time need to be specifiedand even then any comparison is difficult to make. All this makes the wet

biomass weight citation very approximate at best and generallyundesirable.

6.1-1 Single-Sorbate Isotherms

Since sorption processes tend to beexothermic and since the sorption performancemay vary with temperature, constanttemperature during the sorption process is a

basic requirement. Sorption isotherms areplots between the sorption uptake (q ) and thefinal equilibrium concentration of the residualsorbate remaining in the solution (Cf ). Thissimple relationship can be expressed in slightlydifferent variations.

METALMETAL

UPTAKEUPTAKE

[mg/g][mg/g]

FINAL METAL CONCENTRATION [mg/L]FINAL METAL CONCENTRATION [mg/L]

q

Cf

EQUILIBRIUM

SORPTION ISOTHERM

q

q

max

max

Figure 6.1-3Typical single-sorbate isotherms.Which sorbent here is better ? Yellow or blue ?

Biosorption is not necessarily so stronglyexothermic as other physical adsorptionreactions. The temperature range for

biosorption applications is consideredrelatively narrow, roughly between (10 -70)

oC, diminishing thus the temperature

sensitivity issue to a large degree.

Simple Sorption Models

The (q ) vs (Cf ) sorption isotherm relationship can also be

mathematically expressed. This was done already in the early 1900s inthe classical work of Langmuir [9] and Freundlich [5] who studiedactivated carbon adsorption.

a TheLangmuir isotherm relationship is of a hyperbolic form:

Langmuir: q qbC

bC

f

f

=+

max1

The Langmuir relationship can be linearized by plotting either (1/q ) vs (1/ Cf)

or (Cf/q) vs Cf

where: qmax is the maximum sorbate

uptake under the givenconditions; e.g. [mg/g]; b C

1 + b Cq q

maxf

f=

METALMETAL

UPTAKEUPTAKE

[mg/g][mg/g]


EQUILIBRIUM SORPTION ISOTHERM

qmax

q max

LANGMUIR

model

b - related to initial slopeit indicates the sorbent affinity

Cf

Figure 6.1-4Lan muir model for the sor tion isotherm

b is a coefficient related to the

affinity between the sorbentand sorbate (the relationship

between b and the affinityconstantKis developed laterin this section).

TheScatchard linearization of Langmuir is:

. (q/Cf) = b qmax - b q


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The Langmuir isotherm (1918) considers sorption as a chemical

phenomenon. It was first theoretically examined in the adsorption of gaseson solid surfaces. Langmuir constant b = 1/K which is related to the

energy of adsorption through the Arrhenius equation. The higherb and thesmallerK, the higher is the affinity of the sorbent for the sorbate. qmax canalso be interpreted as the total number of binding sites that are available for

biosorption, and q as the number of binding sites that are in fact occupiedby the sorbate at the concentration Cf.

Although the Langmuir model sheds no light on the mechanisticaspects of sorption, it provides information on uptake capabilities and iscapable of reflecting the usual equilibrium sorption process behavior.Langmuir assumed that the forces that are exerted by chemicallyunsaturated surface atoms (total number of binding sites) do not extendfurther than the diameter of one sorbed molecule and therefore sorption isrestricted to a monolayer.

In the simplest case the following assumptions were made:

a) fixed number of adsorption sites; at equilibrium, at anytemperature and gas pressure a fraction of the surface sites is

occupied by adsorbed molecules, and the fraction 1- is free.b) all sorption sites are uniform (i.e. constant heat of adsorption)c) only one sorbated) one sorbate molecule reacts with one active sitee) no interaction between sorbed species

Assumption of a value for the surface area covered per moleculethen could allow computation of the active specic surface area of thesorbent using Avogadros number. However, the concept of surface areacannot be used in gel-like sorbents that most biosorbents may be.As long as its restrictions and limitations are clearly recognized, theLangmuir equation can be used for describing equilibrium conditions for

sorption behavior in different sorbate-sorbent systems, or for variedconditions within any given system.

The Freundlich isotherm relationship is exponential:

Freundlich: where: k and n are Freundlich constants.q k Cf( /n)= 1

b

The Freundlich relationship is an empirical equation. It does notindicate a finite uptake capacity of the sorbent and can thus only bereasonably applied in the low to intermediate concentration ranges (Cf !).However, it is easier to handle mathematically in more complexcalculations (e.g. in modeling the dynamic column behavior) where it mayappear quite frequently. Freundlich model can be easily linearized by

plotting it in a (log-log) format.

The Langmuir model has eventually been empirically most oftenused since it contains the two useful and easily imaginable parameters (qmax

and b) which are more easily understandable since they reflect the twoimportant characteristics of the sorption system [6,7,12-14].

Note the assumptions taken for the development of these originalrelationships which originated from the work done with activated carbon asa solid-phase sorbent for molecular species. Monomolecular layerconsidered for deposition of sorbates implies the surface-based adsorptionwhich is not the case for biosorption.


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Other sorption isotherm relationships : Table 6-1

Some sorption isotherm relationships

Brunauer-Emmett-Teller(BET) [1938]:

)]/)(1(1)[(s

Cf

CBf

Cs

C

fBQC

q+

=

Cs is the saturation constant of the solute;

B is a constant relating to the energy ofinteraction with the surface;Q is the number of moles of solute adsorbed

per unit weight of adsorbent in forming acomplete monolayer on the surface;

Dubinin-Radushkevich (DR) [1947]:lnq = lnqm -B E

2

B is a constant related to the sorption energyE is Polanyi potential

E = RT ln(1+ 1/Cf)

Radke-Prausnitz[1972]:

+=

ff bCaCq

111

Reddlich-Peterson [Jossens et al.,1978]:

n

f

f

bC

aCq

+=

1

Combination:

)/1(

)/1(

1n

f

nfm

bC

Cbqq+

=

(Langmuir-Freundlich) [Sips, 1948]

Other sorption isotherm relationships

listed in Table 6-1 are commonly appearing in thebiosorption literature. It is necessary to realizethat these relationships basically do not reflect the

physico-chemical underlying principles of thesorption process which, in most cases, may noteven be well understood. For all practical

purposes they are just mathematical models of thephenomenon capable of describing the (q) vs (Cf)relationship as experimentally observed. In thiscapacity, neither can any of these models offerany important clues as to the sorption mechanismnor could they be sensitive to external processvariables (such as e.g. pH, ionic strength, etc.).

c

While the Langmuir adsorption model isvalid for a single-layer adsorption, the BET modelrepresents sorption isotherms reflecting apparentmulti-layer adsorption (Figure 6.1-5). Bothequations are limited by the suumption of uniform

energies of adsorption on the surface. The BETisotherm, the more generally applicable of thetwo, reduces to the Langmuir model when thelimit of adsorption is a mono-layer. Both modelsmay be deduced from either kinetic considerationsor the thermodynamics of adsorption [9,2,1]. Thelatter derivations are somewhat moresophisticated, though less intuitive, than the

kinetic treatments since fewer assumptions areinvolved (e.g. the balancing of forward andreverse rate processes according to some assumedmechanism).

q = BQCf(CS-Cf)[1+ (B-1)( CS/Cf )]f

METALMETAL

UPTAKEUPTAKE

[mg/g][mg/g]



qmax

BET

model

Cf

Figure 6.1-5Brunauer-Emmett-Teller sorption isotherm model

The BET model assumes that anumber of layers of adsorbate moleculesform at the surface and that the Langmuirequations applies to each layer. A furtherassumption of the BET model is that agiven layer need not complete formation

prior to initiation of subsequent layers; the

equilibrium condition will thereforeinvolve several types of surfaces in thesense of number of layers of molecules oneach surface site. For adsorption fromsolution with the additional assumptionthat layers beyond the first have equal

energies of adsorption, the BET equationtakes the simplified form as in Table 6-1.


6/14


Needless to say, for different sorption systems and mechanismsoutside of the scope of these assumptions the application and fit of the

model equations is a matter of chance. They become just mathematicalrelationships which happen to be capable of following the experimentaldata. The problem with biosorption is that usually not very much specificinformation is available on the sorption mechanism(s) involved.

The use of simpleisotherm models

is not much morethan curve fitting

The usual concept of the solid-phase sorbent with physical poresand surface area etc. may not be so close to the real structure, appearanceand behavior of biosorbent materials. Particularly in conjunction withmetallic ions as sorbate species, biosorbents may appear as gels, verytransparent for the minute ions and protons. Actually, when it comes to anion exchange process, which apparently plays a very important role in

biosorption, at least one ion from within the molecular structure of thesorbent is exchanged for another one coming from outside. This leads toever-changing conditions in the sorption system due to the stream ofexchanged ions also leaving the sorbent into the liquid environment. That

is until the sorption equilibrium is established.

The surface areaconcept is NOTapplicable for gel-

like biosorbents

6.1-2 Comparison of Sorption Performance

Performance of sorbing materials often needs to be compared.The simplest case is when there is only one sorbate species in the system.The comparison of single-sorbate sorption performance is best based on acomplete single-sorbate sorption isotherm curve.

METALMETAL

UPTAKEUPTAKE

[mg/g][mg/g]


q

q

200

200

10


q

EFFECT ofpH6 - 7

4 - 6

3 - 4

2 - 3

max

10

Figure 6.1-6As an external factor, pH has to become a parameterfor the conventional sorption isotherm plot

In order for the comparison of two or more sorbents to be fair itmust always be done under the same conditions. These may be restricted

by the environmental factors under which sorption may have to take place(pH, temperature, ionic strength, etc.).They may not necessarily be widely

adjustable. It is important to comparesorption performance e.g. under thesame pH since isotherms could varywith pH.

By performance of thesorbent is usually meant its uptake (q ).The sorbents can be compared by theirrespective qmax values which arecalculated e.g. from fitting the Langmuirisotherm model to the actualexperimental data (if it fits). Thisapproach is feasible if there exists thecharacteristic qmax sorption performance

plateau (the maximum sorbentsaturation). A good sorbent that onealways looks for would feature a highsorption uptake capacity qmax .

However, also desirable is a high affinity between the sobent and sorbatereflected in good uptake values at low concentrations (Cf). This ischaracterized by a steep rise of the isotherm curve close to its origin.Performance in this region is reflected in the Langmuir coefficient b.


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Which sorbent is better??

METALMETAL

UPTAKEUPTAKE

[mg/g][mg/g]

FINALFINAL METAL CONCENTRATION [mg/L]METAL CONCENTRATION [mg/L]

q

q


q

q

max

max

A

>AB

B

A

B

Figure 6.1-7At low Cfs A is better than B

There is no direct answer to thatuntil this question is qualified: under

what conditions? The sorption isothermdiagram depicts the experimentallydetermined performance of sorbents Aand B. Given the same experimental(environmental) conditions, as requiredfor comparison, the independent variablein the sorption system is the Cf . Bothcurves intersect - obviously, at that pointthe performance of both sorbents is thesame (in terms ofq ).

However, sorbent A wouldexhibit higherqs for the same Cf s inthe range of lowerCf values (left from

the curve intersect): sorbent A isbetter than sorbent B in that range.This is important, for instance, when thesorbent is supposed to work at lowresidual sorbate concentrations as may bethe case e.g. the when regulatory agencylimits the maximum concentration of a

pollutant (sorbate, toxic metal, etc.)allowable in the discharged effluent.

METALMETAL

UPTAKEUPTAKE

[mg/g][mg/g]


q

q


q

q

max

max

A

B

>B A

Figure 6.1-8At high Cfs B is better than A

When the limitation of themaximum residual sorbate concentrationis not of a concern and the purpose is tosaturate the sorbent as much as possible(no matter how much of the sorbate maystill be left over in the solution), sorbentB is better because it accumulatesmore sorbate at higher residual sorbateconcentrations (higher Cf range). Thismay be of importance when the eventualrecovery of the sorbate from the

biosorbent is desired. A biosorbent"better" at low concentrations may be"inferior" at higher ones, and vice versa.

METALMETAL

UPTAKEUPTAKE

[mg/g][mg/g]


q

q

200

10 200

10


q

q

max

max

Figure 6.1-9qmax indicates the ultimate performance

This is the reason why onecomparison at "low" Cf (e.g. 10 mg/L)and also another one at "high" Cf (e.g.200 mg/L) was made in some biosorption

screening work [6,7]. Another aspect of afair comparison is to compare, forinstance, the best with the best: theoptimal pH value for the best performanceof one sorbent may not be the same one asfor the best performance of anothersorbent. If the operating parameter is assimple as pH, which can perhaps easily beadjusted in the process, the feasibility of


8/14


this adjustment should be considered. Inall comparisons it is extremely importantto make certain that all the external

sorption system parameters remainindeed comparable.

METALMETAL

UPTAKEUPTAKE

[mg/g][mg/g]


q


qmax

b

Figure 6.1-10Langmuirian b relates to affinity between the sorbentand the sorbate (often metal ion considered here)

The above consideration leadsto another important characteristic of thesorption isotherm curve and this is itsinitial slope. A curve with a steep initialslope indicates a sorbent which has acapacity for the sorbate in the lowresidual (final, Cf ) concentration range.That means that the sorbent has a highaffinity for the sorbed species. Thisaffinity is indicated by the coefficient bin the Langmuir equation. The lower the

value ofb the higher the affinity.In conclusion, for good sorbents in general, one is looking for a

high qmax and a steep initial sorption isotherm slope as indicated by lowvalues of Langmuir parameter b [9,13]. It is advisable to base thecomparison of sorption performance on whole sorption isotherm plotswhich are in turn derived experimentally.

6.1-3 Equilibrium Constants

Langmuir model assumes that all the binding sites on the sorbentare free sites, ready to accept the sorbate from solution. Therefore, anadsorption reaction is taking place that can be described as :

(6-1) B + M BM

B represents the free binding sites, M is the sorbate in the solution (metal),and BM denotes the adsorbed sorbate Mboundon B.

The adsorption equilibrium constant is defined from the massconservation law:

K=[B][M]

[BM](6-2)

METAL

ION IN

PROTON

OUT

METAL

ION IN


Langmuir

Model

ADSORPTIONADSORPTION

Adsorption

Langmuir Model

Parameter :

IonEx

Model

reaction :

B+M BMIonEx

Model[BM]

K = [B][M]

b = 1/K

equilibrium affinity:

Figure 6.1-11Relationship between Langmuirian b and theequilibrium affinity constant K

it represents the affinity of sorbate forthe binding site.[ ] denotes the concentration.According to the mass conservation of

binding sites, the total binding capacityBT is:

[BT

]= [B] + [BM] (6-3)

By combining equations (2) and (3) thefollowing is obtained:

[BM] =[M]1

[M]][BT

K

K

+(6-4)

where [BM] also represents the sorbateuptake q, then:


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q =[C]1

[C]][BT

K

K

+(6-5)

Equation (6-5) is one of the conventional forms of Langmuir equation. K

represents the affinity of sorbateM

to siteB

.Another form of Langmuir equation could be derived from the aboveequation (6-5) by dividing the whole fraction in equation (6-5) with Kandwe obtain:

q =[C])(1/

[C]][BT

+K(6-6)

Making b = 1/K (6-7)then K= 1/b (6-8)

ReplacingKin equation (6-6) with equation (6-8) we obtain:

q =[C]

[C]][BT

+b(6-9)

Equation (6-9) is another form of Langmuir equation where b is a constant.Its physical meaning could be illustrated by combining equations (6-2) and (6-7):

b= 1/K=[BC]

[B][C](6-10)

Therefore, b represents the reverse of the affinity.

Langmuir or Freundlich typebinding assumes free sites, not an (ion)exchange. In the mathematicalmodeling of the phenomenon theLangmuir equation and the ion exchangeconstant for the binding of a metal ionM (for simplicity here a monovalent ion)

replacing a proton H on a complexingsite B are related as seen in therelationships in the left column:


IonEx

Model

reaction :

B+M BM

BMK =

B[M]

reaction :

BH+M BM+H

KK* =

[H]LangmuirModel

Figure 6.1-12Relationship of Langmuirian and Ion-Exchangeequilibrium constants

The differences between the two modelsmay be especially pronounced at lowmetal ion concentrations [3].

(affinities)

The ion exchange approach is probablysomewhat closer to the reality than thesimple Langmuir model, but it is notcompletely satisfying either. Theassumption of the constant number of free sites may be reasonable for aconstant pH system. It may not hold for systems with changing pH values.The cation exchange capacity tends to increase with increasing pH above

the isoelectric point. Modeling the competitive binding of metals andprotons using only a metal-proton ion exchange constant is simplistic. Itshould include at least one reaction where a cation reacts with a free site.

Ion exchange: BH + M BM + H (6-11)

BH[M]

BM[H]BM=K and [B]t = [BH] + [BM]

therefore: BMK* = BMK/ [H] (6-12)


10/14


V (C - C )

Sq

fi=

METALMETAL

UPTAKEUPTAKE

[mg/g][mg/g]


contact

Ci initial

solid

sorbent

enough

time

metal

solution

analyze

filtrate[mg/L][mg/L]

FINALFINAL

METALMETAL

CONCENTRATIONCONCENTRATION

Cf

filter plotsorption isotherm

S[mg]

V[mL]

Figure 6.1-13

Experimental procedure for deriving the sorptionisotherm

6.1-4 Experimental Sorption Isotherm

It is relatively simple and easyto obtain laboratory equilibrium

sorption data for a single sorbate. Asmall amount of the sorbent tested is

brought into contact with solutioncontaining the given sorbate. However,the environmental parameters in thesorption system (particularly pH) haveto be carefully controlled at the givenvalue over the entire period of contactuntil the sorption equilibrium isreached. It may take a few hours ormuch longer depending on the size ofsorption particles and the time it takesuntil they attain sorption equilibrium. A

simple preliminary sorption kinetics testwill establish the exposure timenecessary for the given sorbent particles to reach the equilibrium statecharacterized by the unchanging sorbate concentration in the solution. Thatis determined by time-based analyses.

Preliminarydynamics of thesorption process(uptake-timerelationship)must bea roximatel

Safely enough time will be allowed for the sorption system toreach equilibrium. The following procedure provides an example forobtaining the experimental sorption equilibrium data points for the isothermas seen also in the procedure schematic flowchart:

1) Prepare the sorbate in solution at the highest concentration of interest.

2) Make dilutions to cover the entire concentration range (from 0 -blank, tothe max.).

3) Adjust the environmental parameters (e.g. pH, ionic strength, etc.).

4) Determine the sorbate initial concentrations (Ci in all the liquidsamples.

It is convenientto vary Ci

5) Distribute the samples into appropriate-volume containers (record V=30-150 mL of liquid) such as flasks or test tubes (in duplicate, triplicate oras required).

6) Weigh accurately each (approximate) amount of the (bio)sorbent solidsto be used in each contact test and record each amount (S mg).

The sorbentweight Scanfluctuate but mustbe preciselyknown for eachsample

It may help to be able to roughly estimate the anticipated sorption uptake sothat there is a well detectable sorbate final concentration left in the solution

at equilibrium in each sample. If there is too much solids added there maybe virtually no sorbate left in the solution for a reliable analysis.

7) Add the sorbent solids into each sample solution and provide for rathergentle mixing over the contact period (enough time!).

8) Make sure the environmental parameters (pH!) are controlled at aconstant value during the contact period (use appropriate acid or base forthe purpose; do not dilute the sorption system by adding excessivevolume).


11/14


METALMETAL

UPTAKEUPTAKE

[mg/g][mg/g]


q

q

200

200

10


q

EFFECT ofpH

6 - 7

4 - 6

3 - 4

2 - 3

max

10

Figure 6.1-6(repeated)pH is an external factor and it has to be controlled forstandard isotherm experiments the final, equilibrium

H is the one that matters !

9) At the end of the contact period,separate the solids from the liquid

(decantation, filtration, centrifugation, etc.)

10) Analyze the liquid portion for theresidual, final, equilibrium sorbateconcentration (Cf).

11) Calculate the sorbate uptake:q = V[L] (Ci- Cf)[mg/L] /S[g]

Note that q could also be determineddirectly by analyzing the separatedsolids and thus closing the material

balance on the sorbate in the system.However, this usually presents

analytical difficulties (digestion-liquefaction of solids and/or very sophisticated analytical methods may berequired).A variation of this approach is the tea-bag experiment, described below,whereby Cf= Ci and only the solids are analyzed.

There is nocontrol overCf,it happens inthe experiment

In either case, the Cf in the liquid must be known for the sorption isothermplotting:

12) Plot the sorption isotherm q vs (Cf).

Note that for all practical purposes the choice of experimentalvariables narrows usually down to two: concentration Ci and the amount ofsorbent solidsS contacted. One or the other or both can be varied. In the

above procedure it was the concentration of sorbate dilutions Ci.

Experimentalvariables could

be eitherCi or S

Metal depletion in thesolution has to beavoided since it renderssuch samples useless(unreliable or impossibleCfdetermination)

The key point is to obtain measurable and different values ofCf at the endof the contact experiment.

W (metal)

Sq =

METALMETAL

UPTAKEUPTAKE

[mg/g][mg/g]


contact

Ci initial

solid

sorbent

enough

time

metalsolution

analyze

SOLIDS DIFFICULTDIFFICULTTO DETERMINETO DETERMINE

METALMETAL

in SOLIDSin SOLIDS

filter

S[mg]

V[mL]

plot

sorption isotherm

!!!Figure 6.1-14For checking, the loaded sorbent solids can beanalyzed too but it is usually more complicated. If theycould be completely eluted, the desorption liquid couldthen be analyzed to make sure that the sorbate massbalance closes

From the equilibriumprinciples it is easily seen that the initialconcentration of sorbate (Ci) is of littlerelevance in these kinds of sorptiontests. It can assist in identifying thefinal concentration range which, ofcourse, depends on the amount ofsorbent solids (S) in the system. Alsonote that one has no control over the

value ofCf, it sort of happens duringthe experiment.


12/14


The tea-bag experiment

W (metal)

Sq =

METALMETAL

UPTAKEUPTAKE

[mg/g][mg/g]

TEA-BAG EQUILIBRIUM

SORPTION

contact

solid

sorbent

enough

time

metal

solution

analyze

SOLIDS DIFFICULTDIFFICULT

TO DETERMINETO DETERMINE

METALMETAL

in SOLIDSin SOLIDS

separate

solids

S[mg]

V[mL]

plot

sorption isotherm

!!!

SMALL

LARGE

!!Ci initial ~ Cf final

Figure 6.1-15In the tea-bag experiment Ci= Cf

In this approach there is a

possibility of chosing and maintainingthe Cf . For this purpose the liquidvolume is solarge and the amount ofsorbent solids added to it so relativelysmall that there is practically no changein the sorbate concentration and thus Ci= Cf . When the solids are isolatedfrom this special sorption system, theyare analyzed for the sorbate content.This analysis of solids is usually muchmore demanding than the analysis ofliquid. Consequently, this kind ofapproach may be used in special cases

only.

Sorbent

Comparison Based on % Removal


EQUILIBRIUM SORPTION ISOTHERMEQUILIBRIUM SORPTION ISOTHERM

sorbent comparison

Cf

q

METALMETAL

UPTAKEUPTAKE

[mg/g][mg/g]

29 mg/L189

% REMOVAL

82%

91%

C = 100 mg/L

V = 100 mL

S = 30 mg

i

AB

C

D71%

88%

Figure 6.1-16Example of % Removal screening

Another criterion forcomparing sorbent materials found inthe literature is based on % removal ofthe sorbate from the solution. This is arather crude and somewhat inaccurateapproach as will be demonstrated inthis section. Using a specific example

may perhaps best serve as ademonstration of the principle:It is desirable to compare the sorption

performance of (bio)sorbents A, B, C,and D. This could be done in a fewequilibrium tests carried out by thesame procedure using the same V(100mL), Ci (100mg/L), and S(30mg) for each of the contact samples

examined. The results recorded were as follows:

Biosorbent A: experimental Cf = 9 mg/L; calculated sorbate removal = 91%.Biosorbent B: experimental Cf = 12 mg/L; calculated sorbate removal = 88%.Biosorbent C: experimental Cf = 18 mg/L; calculated sorbate removal = 82%.

Biosorbent D: experimental Cf = 29 mg/L; calculated sorbate removal = 71%.

It is obvious that there exist four separate sorption isotherms eachcharacterizing one of the sorbent materials. However, available is only one

point for each curve.


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sorbent comparison

Cf

q

METALMETAL

UPTAKEUPTAKE

[mg/g][mg/g]

29 mg/L189

% REMOVAL

82%

91%

C = 100 mg/L

V = 100 mL

S = 30 mg

i

AB

C

D71%

88%

Figure 6.1-17DANGER: The full isotherms do not follow a pattern

For each of the Cf values obtained thereis one (and different!) corresponding q

which can serve as a basis for sorptionperformance comparison. Theinaccuracy inherent in this approach isin the fact that the performancecomparison is NOT done on the same

basis since the Cf s are different. In thefirst case seen in the Figure, theconclusion can be drawn that the sorbent

performance follows this pattern:A>B>C>D.

That may be quite correct if theindividual isotherms follow a similar(steadily rising) pattern. Of course, thecorrect comparison can only be done

along the same line of the same Cf for allthe materials. Obviously, this is not

possible when the whole sorptionisotherm plots are not available. Thedanger in using the simplisticmethodology is that the full individualisotherm curves might follow quitedifferent patterns outside of the range ofthe Cfs experimentally obtained. This isseen in the next case Figure where theconclusion on the sorbent performancewould suggest the same pattern:

A>B>C>D.FINAL METAL CONCENTRATION [mg/L]FINAL METAL CONCENTRATION [mg/L]

EQUILIBRIUM SORPTION ISOTHERMEQUILIBRIUM SORPTION ISOTHERMsorbent comparison

Cf

q

METALMETAL

UPTAKEUPTAKE

[mg/g][mg/g]

29 mg/L

A>B >C >DA>B >C >D

189

% REMOVAL

82%

91%

WRONG !

A

B

D71%

OKV (C - C )

Sq

fi=

C = 100 mg/L

V = 100 mL

S = 30 mg

iC

A>C >B >DA>C >B >D

Figure 6.1-18Wrong conclusion about the sorbents !

However, in the higher Cf range, theisotherm for sorbent B is flat and anothertest conducted in the higher finalconcentration range would undoubtedlyindicate a different sorbent performance

pattern: A>C>B>D !



sorbent comparison

Cf

q

METALMETAL

UPTAKEUPTAKE

[mg/g][mg/g]

29 mg/L

correctcorrect

comparisoncomparison

189

V (C - C )

Sq

fi=

% REMOVAL

82%

91%

C = 100 mg/L

V = 100 mL

S = 30 mg

i

approximate !

A

B

CD71%

OK

Figure 6.1-18% Removal is only for crude judgement

The original simple test would neverreveal this fact. Indeed, in some cases,the simplistic % Removal methodcould lead to outright misleadingconclusions on the relative sorption

performance.

It can only serve the purpose of crudeorientation, perhaps adequate only forquick and very approximate screening of(bio)sorbent materials. The %Removal values so often quoted in theliterature also do not offer anyinformation on the concentration rangewhere the removal took place (e.g. rangein the 1,000's, 100's or 10's of mg/L ).


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6.1-5 REFERENCES

1. Adamson, A.W. 1967. Physical Chemistry of Surfaces (2nd ed.). IntersciencePublishers, New York, NY.

2. Brunauer, S., Emmet, P.H. and Teller, E. 1938. Adsorption of gases in multimolecularlayers. J. Am. Chem. Soc. 60, 309-319.

3. Crist, R.H., Martin, J.R., Carr, D., Watson, J.R., Clarke, H.J. and Crist, D.R. 1994.Interaction of metals and protons with algae. 4. Ion exchange vs adsorption modelsand a reassessment of Scatchard plots; ion-exchange rates and equilibria compared

with calcium alginate.Envir. Sci. Technol.28, 1859-1866.

4. Dubinin, M.M. and Radushkevich, L.V. 1947. Equation of the characteristic curve ofactivated charcoal. Chem. Zentr. 1, 875

5. Freundlich, H. 1907. Ueber die Adsorption in Loesungen.Z. physik. Chem.57, 385-470.

6. Holan, Z.R. and Volesky, B. 1994. Biosorption of Pb and Ni by biomass of marine

algae.Biotechnol. Bioeng.43, 1001-9.

7. Holan, Z.R., Volesky, B. and Prasetyo, I. 1993. Biosorption of Cd by biomass of

marine algae.Biotechnol. Bioeng.41, 819-25.

8. Jossens, L., Prausnitz, J.M., Fritz, W., Schlunder, U. and Myers, A.L. 1978.Thermodynamics of multisolute adsorption from dilute aqueous solutions. Chem.

Eng. Sci. 33, 1097-1106.

9. Langmuir, I. 1918. The adsorption of gases on plane surfaces of glass, mica and

platinum.J. Am. Chem. Soc.40, 1361-1403.

10. Radke, C.J. and Prausnitz, J.M. 1972. Thermodynamics of multi-solute adsorptionfrom dilute liquid solutions. J. AIChE, 18, 761.

11. Sips, R. 1948. On the structure of a catalyst surface. J. Chem. Phys. 16, 490-495.

12. Volesky, B. 1994. Advances in biosorption of metals: Selection of biomass types.FEMSMicrobiol. Rev. 14, 291-302.

13. Volesky, B. and Holan, Z.R. 1995. Biosorption of heavy metals. Biotechnol.Progress

11, 235-50..

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Equilibrium Biosorption Performance