If the adsorbent and

adsorbate are contacted long

enough, an equilibrium will

be established between the

amount of adsorbate

adsorbed and the amount of

adsorbate in solution. The

equilibrium relationship is

described by adsorption

isotherms.

Adsorption Equilibria Ref: faculty.washington.edu/.../Adsorption%20...

Adsorption Equil Principles_483

An adsorption isotherm is a curve relating the

equilibrium concentration of a solute on the surface of an

adsorbent, qe, to the concentration of the solute in the

liquid, Ce, with which it is in contact.

Adsorption Equilibria

The adsorption isotherm is also an equation relating the

amount of solute adsorbed onto the solid and the

equilibrium concentration of the solute in solution at a

given temperature.

Adsorption Equilibria

The adsorption capacity of activated carbon may be

determined by the use of an adsorption isotherm

which can take multiple forms.

Isotherms are found by doing lab tests.

Adsorption Isotherms

Add same initial target chemical concentration, Cinit, in each

Different activated carbon dosage, Csolid, in each

Control

o e o eC -C mg/L C -C .Vmg g mass=

g g g/L mass

e

solid

q or orC X

An adsorption ‘isotherm’ is a qe vs. Ce relationship at

equilibrium.

Isotherm models

There are several models for predicting the

equilibrium distribution.

However, the following four models are most

commonly observed.

Commonly Reported Adsorption Isotherms

max1

L

L

K cq q

K c

linq k c

n

fq k c

Linear: Langmuir:

Freundlich:

Adsorption Equilibria

i. Linear

ii. Langmuir

iii. Freundlich

iv. Brunauer, Emmet, and Teller (BET)

The most commonly used isotherms for the application

of activated carbon in water and wastewater treatment

are the Freundlich and Langmuir isotherms.

Freundlich isotherm is an empirical equation.

Langmuir isotherm has a rational basis.

Linear Isotherm

qe = K. Ce

Langmuir Isotherm

It assumes

1. Monolayer coverage,

2. Equilibrium model,

3. All adsorption sites are equally probable,

4. A second order reaction.

QM

v

[S.A]

[S ][A]

At equilibrium Kad =

ST = [Sv] + [S.A] (moles/m2) Eq’n 2

Combining Eq’n.s 1 & 2

ad

[S.A]+[S.A]

K [A]

Eq’n 1

Consider total number of sites, ST, to be fixed :

(possible if monolayer coverage is assumed)

ST =

Solve for [S.A] and use CA = [A]

[S.A] = ad A TT

ad A

ad A

K .C .SS=

1 1+K .C1+

K .C

Need expression for qA, which is mg adsorbate

g adsorbent

A ad Aq =[S.A].A .MW

M ad AA

ad A

Q .K .Cq =

1+K .C

0

eA

e

b.C .Qq =

1+ b.C

or

QM or Qo = maximum adsorption capacity for

forming single layer.

Ce has units of mg/L.

Kad or b has units of L/mg.

where

Freundlich Isotherm

n and KF are system specific constants.

n1

eFe CKq

It is emprical and very widely

used.

11

n

KF is an indicator of adsorption capacity.

Higher the maximum capacity, higher the KF.

1/n is a measure of intensity of adsorption.

Higher the 1/n value, more favorable is the adsorption.

Generally, n < 1

This is a more general,

multi-layer model. It

assumes that a

Langmuir isotherm

applies to each layer

BET (Brunauer, Emmett and Teller) Isotherm

and that no transmigration occurs between layers.

It also assumes that there is equal energy of

adsorption for each layer except for the first layer.

Qo or QM

0

( ){1 ( 1)( / )}

B ee

S e B e S

K C Qq

C C K C C

BET (Brunauer, Emmett and Teller) Isotherm

CS =saturation (solubility limit) concentration of the

solute. (mg/liter)

KB = a parameter related to the binding intensity for all

layers.

Note: when Ce << CS and KB >> 1 and Kad = KB/Cs

BET isotherm approaches Langmuir isotherm.

qe

Ce

Most favorable one because

even at low concentrations

you can load your surface

with high amounts of material.

The concept of the adsorption isotherm is

very important, because how much you load

the surface at equilibrium depends on how

much is left in water.

Shape of Freundlich Isotherm

n1

eFe CKq

To determine which model to use to describe the

adsorption for a particular adsorbent/adsorbate

isotherms experiments are usually run. Data from

these isotherm experiments are then analyzed

using the following methods that are based on

linearization of the models.

Determination of appropriate model

For the Langmuir model linearization gives:

0 0

1e e

e

C C

q K Q Q

A plot of Ce/qe versus Ce should give a straight line

with intercept :

0

1

K Q

0

1

Q

and slope:

If you obtain a straight line, determine constants

from slope and intercept.

or:

0 0

1 1 1 1

e eq CQ K Q

Here a plot of 1/qe versus 1/Ce should give a

straight line with intercept : 1/Qo

0

1

K Qand slope :

If you obtain a straight line, determine constants

from slope and intercept.

For the Freundlich isotherm use the log-log version :

Clogn

1Klogqlog Fe

A log-log plot should yield an intercept of log KF

and a slope of 1/n.

0 0

1 1

( )

e eB

S e e SB B

C CK

C C q CK Q K Q

0

1

BK Q

B

0

B s

K 1

K Q C

For the BET isotherm we can arrange the isotherm

equation to get:

Intercept =

Slope =