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SURFACE CHEMISTRY Contact: By: Muhammad Asif Phone: +92-303-7807073 Lecturer (Physical Chemistry) E-mail: masif33pk@yahoo.com Govt. College Sahiwal, Pakistan 6.1 Introduction ………………………………………………………………………. 02 6.2 Adsorption ………………………………………………………………………... 02 6.3 Types of Adsorption ……………………………………………………………… 03 6.4 Factors Affecting Adsorption …………………………………………………….. 05 6.5 Adsorption Isotherms …………………………………………………………….. 06 6.6 Various Equations of Adsorption Isotherms ……………………………………... 07

6.6.1 Freundlich Isotherm ……………………………………………………… 07 6.6.2 Langmuir Isotherm ……………………………………………………….. 08 6.6.3 BET Isotherm …………………………………………………………….. 10 6.6.4 Temkin Isotherm …………………………………………………………. 13 6.6.5 DR Isotherm ……………………………………………………………… 13

6.7 Thermodynamics of Adsorption …………………………………………………. 14 6.8 Kinetics of Heterogeneous Reactions ……………………………………………. 16 6.9 Applications of Adsorption ………………………………………………………. 20 Dated | Sunday, 20 March 2011

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6.1 INTRODUCTION

The part of system throughout which all the physical properties of a material are

essentially uniform is called phase. Distinct phases may be described as different states of

matter such as gas, liquid, solid and plasma.

“Surface chemistry is the branch of chemistry that generally studies the processes

occurring at the interfaces between two phases”.

The surface forming a common boundary between two immiscible phases is known as

interface. An interface may be spherical or flat. It may involve the same or different states of

matter. There are five possible types of interfaces:

1. Liquid-Liquid (oil/water)

2. Gas-Liquid (air/water)

3. Gas-Solid (air/smoke)

4. Liquid-Solid (water/clay)

5. Solid-Solid (rubber/carbon black)

Interfaces may cause various optical phenomena, such as refraction. Optical lenses serve as

an example of a practical application of the interface between glass and air. Surface tension is

the function which rules interface processes.

6.2 ADSORPTION

In liquids and solids, the molecules which are present in the bulk are attracted from all

sides so the forces are mutually balanced, whereas, the molecules which are present at the

surface are attracted only from below and the sides so the forces are unbalanced. These

unbalanced or residual forces have tendency to attract and retain the molecular species with

which it comes in contact at the surface.

“The process in which a substance accumulates or concentrates at the surface of a

liquid or a solid is known as adsorption”.

The substance that sticks or adheres to the surface is called adsorbate, and the surface

on which the adsorbate settles is called adsorbent. Gases and ions are good adsorbates, while

solid surfaces are good adsorbents.

The phenomenon of adsorption should not be confused with absorption where the

substance is not only retained on the surface but also passes through the surface (interface), to

become distributed throughout the body of a solid or liquid. Sucking of water by a sponge

when put it into the water, is an example of absorption.

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Where doubt exists as to whether a process is true adsorption or absorption, the non

committable term sorption is sometime used to include both the processes (adsorption and

absorption). Hence sorption is a process in which both adsorption and absorption take place

simultaneously. Dying of cotton fibers is an example of sorption, where dyestuff is adsorbed,

as well as absorbed by cotton fibers.

The reverse of adsorption i.e., the removal of an adsorbate from the surface on which

it is adsorbed is known as desorption.

If there is an increase in the concentration of a substance (adsorbate) at the interface,

the adsorption is called positive adsorption. If there is a decrease in the concentration of the

adsorbate at the interface, the adsorption is said to be negative adsorption.

6.3 TYPES OF ADSORPTION

Depending upon the type of interaction between adsorbate and the adsorbent, there are two

types of adsorption: Physical Adsorption or Chemical Adsorption.

Physical Adsorption (Physisorption)

When the force of attraction existing between adsorbate and adsorbent are weak Van

der Waal forces of attraction, the process is called Physical Adsorption or Physisorption. For

example, adsorption of hydrogen on charcoal, adsorption of nitrogen on iron at 190°C, etc.

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Physisorption takes place with formation of multilayer of adsorbate on adsorbent. It

has low enthalpy of adsorption i.e. ΔHadsorption

Chemical Adsorption (Chemisorption)

is 20-40 kJ/mol. It takes place at low

temperature below the boiling point of adsorbate.

When the force of attraction existing between adsorbate and adsorbent are chemical

forces of attraction or chemical bond, the process is called Chemical Adsorption or

Chemisorption. For example, adsorption of hydrogen on nickel, adsorption of nitrogen on

iron at 500°C, etc.

Chemisorption takes place with formation of unilayer of adsorbate on adsorbent. It

has high enthalpy of adsorption i.e. ΔHadsorption is 40-400 kJ/mol. It can take place at all

temperature.

In many cases, it has been observed that adsorption is neither physical nor chemical but a

combination of the two. Some systems show physical adsorption at low temperatures but as

the temperature is raised, physical adsorption changes into chemical adsorption.

Difference between Physisorption and Chemisorption

Physisorption Chemisorption

1 It involves physical bond forces It involves strong chemical bond forces

2 Heat of adsorption is less than

40 kJ/mole

Heat of adsorption is greater than

40 kJ/mole

3 It takes place at ordinary temperature It occurs at high temperature

4 The rate of adsorption increases with

increase in pressure of the adsorbate

The rate of adsorption decreases with

increase in the pressure of the adsorbate

5 It is a reversible process It is an irreversible process

6 It leads to multilayer formation It leads to monolayer formation

7 Energy of activation is low for this

process

Energy of activation is high for this

process

8 It is more a function of adsorbate

than the adsorbent

It is a function of both adsorbate and

adsorbent

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6.4 FACTORS AFFECTING ADSORPTION

The extent of adsorption depends upon the following factors:

1. Nature of adsorbate and adsorbent

2. The surface area of adsorbent

3. Activation of adsorbent

4. Experimental conditions, e.g., temperature, pressure, etc.

1. Nature of Adsorbate and Adsorbent

The extent of adsorption depends upon the nature of adsorbate and adsorbent. Gases like

SO2, NH3, HCl and CO2 which liquefy more easily are adsorbed more readily than the

elemental gases like H2, N2 and O2

2. The Surface Area of Adsorbent

which do not liquefy easily; because the easily

liquefiable gases have greater Van der Waal’s forces of attraction or cohesive forces. The

excellent adsorbents are highly porous in nature. Larger pores give greater adsorption.

The silica gel, alumina and charcoal are the good examples of porous material.

The magnitude (or extent) of adsorption also depends upon the surface area. Greater the

surface area of adsorbent, greater the amount of the gas adsorbed. Surface area of a

powdered solid adsorbent depends upon its particle size. Smaller the particle size, greater

is its surface area. For example, if nickel and platinum metals are finally divided, then

they adsorb the hydrogen gas to greater extent.

3. Activation of Adsorbent

The adsorption power of an adsorbent can further be enhanced by a process called

activation. The activation of adsorbent provides more number of vacant sites on the

surface of the adsorbent and it can be done by breaking solid crystal in small pieces,

heating charcoal at high temperature, breaking lump of solid into powder or other

methods suitable for a particular adsorbent. For example, charcoal adsorbs 0.01gms of

CCl4

4. Effect of Temperature

at 24°C but when activated it adsorbs 1.48gms at 24°C.

Low temperatures favour the physical adsorption while chemisorption generally increases

with the temperature. For example, nitrogen shows physical adsorption on iron at 190°C

and chemisorbed to form a nitride at 500°C.

5. Effect of Pressure

As depicted by Adsorption Isotherms, with the increases in pressure, adsorption increases

up to a certain extent till saturation level is achieved. After saturation level is achieved no

more adsorption takes place no matter how high the pressure is applied.

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6.5 ADSORPTION ISOTHERMS

The process of Adsorption is usually studied through graphs know as adsorption

isotherm. It is the graph between the amounts of adsorbate (x) adsorbed on the surface of

adsorbent (m) and pressure (if adsorbate is gas) or concentration (if adsorbate is liquid) at

constant temperature. Five general types of isotherms have been observed in the case of

adsorption of gases on solids as shown in figure below,

Type I Type II Type III Type IV Type V

In case of chemisorption, only Type I curves are observed while in case of physisorption all

the five types of isotherm occur.

Type I Adsorption Isotherm

This type of curve is obtained in such cases where monolayer is formed on the surface

of the adsorbent. This type of curve is rare. Example is the adsorption of Nitrogen on

charcoal at -183°C.

Type II Adsorption Isotherm

This type of curve has a transition point B which represents the pressure at which the

formation of monolayer is complete and that of multilayer is being started. Example is the

adsorption of Nitrogen on silica gel at -195°C.

Type III Adsorption Isotherm

In this type of isotherm there is no transition point. Multilayer formation starts even

before the formation of monolayer is complete. This type seems to be characterized by a heat

of adsorption equal to or less than the heat of liquefaction of the adsorbate. Example is the

adsorption of Bromine or Iodine vapours on silica gel at 79°C.

Type IV Adsorption Isotherm

At lower pressure region of graph is quite similar to Type II. This indicates that there

is a tendency for saturation state to be reached in the multilayer region. Example is the

adsorption of Benzene vapours on ferric oxide gel at 50°C.

Type V Adsorption Isotherm

It represents the case of physical adsorption on porous material. Example is the

adsorption of water vapours on charcoal at 100°C.

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6.6 VARIOUS EQUATIONS OF ADSORPTION ISOTHERMS

The various equations of adsorption isotherms are:

1. Freundlich Isotherm

2. Langmuir Isotherm

3. Brunauer-Emmett-Teller Isotherm

4. Temkin Isotherm

5. Dubinin-Radushkevich Isotherm

6.6.1 FREUNDLICH ISOTHERM [1909]

In 1909, Freundlich proposed the following equation to show the variation of amount gas

adsorbed per unit mass of the adsorbent with pressure at constant temperature,

n/1kPmx= ………. (1)

Where x = Mass of the adsorbate

m = Mass of the adsorbent

P = Equilibrium pressure of the adsorbate

k & n = Constants depending upon the nature of adsorbate and adsorbent and on the

temperature.

The equation (1) is known as Freundlich Adsorption equation or Freundlich Adsorption

Isotherm or simply Freundlich Isotherm.

In order to test Freundlich isotherm, take the logarithm on both sides of the equation (1),

klogPlogn1

mxlog +=

This Equation is similar to the equation for a straight line. Thus, if we plot a graph of

log(x/m) against logP, we should get a straight line with slope 1/n and intercept logk as

shown in figure.

However, it was found that the actual plots were straight lines only at low pressures and

showed a slight curvature at high pressure, especially at low temperatures. This indicates that

Freundlich isotherm is approximate and cannot be applied to adsorption of gases by solids at

high pressure. It successfully explain the Type I isotherm.

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Limitations of Freundlich Isotherm

1. It is valid over a certain range of pressure only

2. The constants k and n vary with temperature

3. It is purely empirical formula without theoretical foundation

6.6.2 LANGMUIR ISOTHERM [1916]

In 1916, Irving Langmuir developed another equation for the adsorption process known as

Langmuir isotherm. This equation is based on the following assumptions,

1) The layer of the gas adsorbed on the solid adsorbent is monolayer (one molecule thick)

2) All the sites over the surface are equivalent and can accommodate at most one molecule

3) There is no interaction between the adjacent molecules of the adsorbed layer

Langmuir considered that the gas molecules strike the solid surface and are thus adsorbed.

Some of these molecules then evaporate and are desorbed fairly rapidly. A dynamic

equilibrium is eventually established between the two opposing processes, adsorption and

desorption.

If θ is the fraction the total surface covered by the adsorbed molecules, and the

fraction of the uncovered surface is (1-θ). Then,

θ∝ desorption of Rate

θ= dkdesorption of Rate

Where, Kd

is constant for the desorption process.

P)1( adsorption of Rate θ−∝

P)1(kadsorption of Rate a θ−=

Where, Ka

At the stage of dynamic equilibrium, these two rates are equal, so

is constant for the adsorption process and P is the pressure of the adsorbate.

P)1(kk ad θ−=θ

PkPkk aad θ−=θ

PkPkk aad =θ+θ

Pk)Pkk( aad =+θ

Pkk

Pk

ad

a

+=θ

Pk/kk/k

Pk/k

dadd

da

+=θ

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KP1KP+

=θ

Where, K=ka/kd

KP1KP

mx

+∝

(the ratio of two constants), is a type of equilibrium constant and is referred

as adsorption coefficient.

Since, the amount of the gas (adsorbate) adsorbed per gram of the adsorbent is proportional to

θ. Hence,

KP1KPk

mx

+′= ………. (1)

Where, k′ is another constant.

The Equation (1) is known as Langmuir Isotherm. It gives the relation between the amount of

a gas adsorbed to the pressure of the gas at constant temperature.

In order to test the Langmuir isotherm, rearrange the equation (1) so that,

)KP1(k1

m/xKP

+′

=

kP

Kk1

m/xP

′+

′=

k1P

k1

m/xP

′′+

′=

Where, Kkk ′=′′ is also a constant.

When a graph is plotted between P/x/m

k′ on y-axis and P on x-axis, a straight line is obtained as

shown in figure. From the slope of the line, we get the value of 1/ and intercept of the

straight line gives the value of 1/ k ′′ . Langmuir Isotherm holds good at low pressures but fails

at high pressures. It successfully explain the Type I isotherm.

Limitations of Langmuir Theory

1. According to this theory, the saturation value of adsorption is independent of

temperature. But experiments show that the saturation value decreases with rise of

temperature.

2. This theory assumes that the surface is capable of adsorbing a layer one molecule

thick and no more. But in actual practice much thicker layers have been reported.

3. This theory cannot explain all the five types of adsorption isotherms.

4. This theory holds good at low pressures only.

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6.6.3 BRUNAUER-EMMETT-TELLER (BET) ISOTHERM [1938]

In 1938, Stephan Brunauer, Paul Emmett and Edward Teller expanded the Langmuir theory

from monolayer to multilayer adsorption by assuming that,

1) Gas molecules physically adsorb on a solid in infinite number of layers

2) There is no interaction between each layer

3) The Langmuir theory can be applied to each layer.

The following figure gives an example of multilayer adsorption on surface,

Let S0, S1, S2, …, Si represent the surface area of adsorbent covered by 0, 1, 2, 3, …, ith

layers of the adsorbed molecules. As S0

must remain constant at equilibrium, the rate of

condensation on the bare surface is equal to the rate of evaporation from the first layer. Thus, RT/E

11011eSbPSa −= ……... (1)

Where, a1 and b1 are constants, E1

Similarly, for equilibrium in successive layers,

is the heat of adsorption of the first layer, T is the

temperature and P is the pressure.

RT/E2212

2eSbPSa −= ……… (2)

RT/E3323

3eSbPSa −=

RT/Eii1ii

ieSbPSa −− =

Hence, total surface area A of the adsorbent can be written as,

∑∞

=

=0i

iSA ……… (3)

And total volume of the gas adsorbed is given by,

∑∞

=

=0i

i0 iSVV ……… (4)

Where, V0 denotes the volume of the gas adsorbed on one cm2

of the adsorbent surface when

it is covered with a unimolecular layer. From Equation (3) and Equation (4), we get

∑

∑∞

=

∞

==

0ii

0ii0

S

iSV

AV

Figure: Multilayer Formation

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∑

∑∞

=

∞

===

0ii

0ii

m0 S

iS

VV

AVV

……… (5)

Where, Vm

Brunauer, Emmett and Teller assumed that,

is the volume of the gas adsorbed when the entire surface is covered by a

unimolecular layer.

(i) Li432 EE...EEE ===== ……… (6)

(ii) gab...

ab

ab

i

i

3

3

2

2 ==== ……… (7)

Where EL

Now, S

is the heat of liquefaction, and g is constant.

1, S2, S3, …, Si are expressed in terms of S0

. From Equation (1),

01RT/E

11 PSaeSb 1 =−

0RT/E

1

11 SPe

baS 1

=

01 ySS = ……… (8)

Where RT/E

1

1 1Pebay

= ……… (9)

And from Equation (2),

12RT/E

22 PSaeSb 2 =−

12RT/E

22 PSaeSb L =− (By Eq.(6))

1RT/E

2

22 SPe

baS L

=

1RT/E

2 SPeg1S L

= (By Eq.(7))

12 xSS =

Where RT/ELPeg1x

= ……… (10)

02 xySS = (By Eq.(8))

Similarly,

02

3 ySxS =

12

03

4 ySxS =

0i

0i

0

i

01i

i cSxSxyxyS

xxySxS =

=== − ……… (10)

Where RT/EE

1

1RT/E

RT/E11 L1

L

1

eb

gaPe)g/1(Pe)b/a(

xyc −=== (By Eq.(9) and Eq.(10))

Form Equation (10), Equation (5) can be written as,

+

===

∑

∑

∑

∑

∑

∑∞

=

∞

=∞

=

∞

=∞

=

∞

=

1i

i0

1i

i0

0i0

i

0i0

i

0ii

0ii

m xc1S

ixcS

cSx

cSix

S

iS

VV

But 21i

i

)x1(xix−

=∑∞

=

and)x1(

xx1i

i

−=∑

∞

=

. Therefore,

[ ]cxx1)x1(cx

x1cx1)x1(

cx

x1xc1

)x1(cx

VV

2

2

m +−−=

−+−

=

−+

−=

)x1(V

xcV

)1c(x1

m −=

−+

mm cV

)1c(xcV

1)x1(V

x −+=

− ……… (11)

Here, x equal to P/Po

can be substituted,

mm cV)1c(P/P

cV1

)P/P1(VP/P −

+=−

cV

1PP

cV1c

)PP(VP

mm

+

−=

−

……… (12)

Where, P and Po

(a) Type II isotherm will follow when E

are the equilibrium and the saturation pressure of the adsorbate respectively.

The Equation (12) is known as BET isotherm. Various types of experimental adsorption

isotherms can be explained on the basis of this theory: Type I isotherm is explained when the

adsorption is monolayer. To explain types II and III isotherms, it has been suggested that:

1 > E

(b) Type III isotherm will follow when EL

1 < E

To explain types IV and V isotherms, it has been suggested that in addition to the multilayer

adsorption, condensation of the gas molecules also takes place in the small pores and

L

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capillaries of the adsorbent even at pressure below Po. The distinction between these two

types is again based on the relative magnitudes of E1 and EL

(a) If E

.

1 > EL

(b) Whereas when E

isotherms of type IV is obtained

1 < EL

Limitations of BET Isotherm

isotherms of type V follow

1. The assumption that adsorbate has liquid properties is not correct.

2. BET equation holds good when P/Po values lie between 0.05 to 0.35. This equation

fails if P/Po

3. When the net heat of adsorption (E

is below 0.05 or above 0.35.

1 - EL

6.6.4 TEMKIN ISOTHERM [1933]

) is low, the constant c is small.

An adsorption isotherm where θ increases logarithmically with P was first found by Slygin

and Frumkin in 1935. However, the pressure-logarithm isotherm is usually associated with

the name of Temkin, who had already proposed such a law on theoretical grounds in 1933.

It

relates the surface coverage θ to the logarithm of the pressure P,

BPlnA=θ

6.6.5 DUBININ-RADUSHKEVICH (DR) ISOTHERM [1947]

Where the constant A is dependent on temperature and B is related to the heat of adsorption.

It can be shown that the Temkin isotherm follows from an assumption that the heat of

adsorption drops linearly with increasing coverage.

This isotherm was originally proposed by Dubinin and Radushkevich in 1947 for adsorption

on micro porous solids. The equation is,

−ρ=

b

PPlnRTkexpVM

Where M = Weight of adsorbed material

ρ = Density of the liquid contaminant

k = First structural constant

b = Second structural constant

R = Ideal gas constant

T = Absolute temperature

Vo

P and P

= Micropore volume of the adsorbent

o

= The equilibrium and saturation pressure of the adsorbate respectively

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6.7 THERMODYNAMICS OF ADSORPTION

GIBBS ADSORPTION EQUATION [1878]

When adsorption takes place at an interface, surface tension (γ) changes. The exact

relationship between adsorption and surface tension was first deduced by J. Willard Gibbs

(1878), and independently by J.J. Thomson (1888): it is known as the Gibbs adsorption

equation.

Let the two phases α and β are separated by an interphase of zero thickness σ then

according to first law of thermodynamics for a closed system, the internal

energy of the system is given by,

dWdQdU +=

If A is the area of the interface between phases α and β then the work done

on such a system is given by,

dAPdVdW γ+−=

Therefore,

dAPdVdQdU γ+−=

dAPdVTdSdU γ+−= (By 2nd

For an open system, the arguments suggest that an additional term of chemical potential

should be added according to Gibb’s Duhem Equation i.e.,

Law of thermodynamics)

∑µ+γ+−=i

iidndAPdVTdSdU ……… (1)

Now, according to Gibb’s model system, for α and β phases,

∑ αααα µ+−=i

iidnPdVTdSdU ……… (2)

∑ ββββ µ+−=i

iidnPdVTdSdU ……… (3)

Hence, for interphase σ,

{ }βασ +−= dUdUdUdU

∑ βαβαβασ −−µ+γ+++−−−=i

iiii )dndndn(dA)dVdV(PPdV)dSdSdS(TdU

∑ σσσ µ+γ++−=i

iidndAPdVPdVTdSdU )dVdVdV( =+ βα

∑ σσσ µ+γ+=i

iidndATdSdU ………. (4)

Integrating taking intensive variables T, γ and μi

as constant,

∑ σσσ µ+γ+=i

iinATSU

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Differentiating,

∑∑ µ+µ+γ+γ++= σσσσσ

iii

iii dndnAddAdTSTdSdU ………. (5)

Comparing Equation (4) and Equation (5),

∑∑∑ µ+µ+γ+γ++=µ+γ+ σσσσσσ

iii

iii

iii dndnAddAdTSTdSdndATdS

∑ =µ+γ+ σσ

iii 0dnAddTS

At constant temperature,

∑ µ−=γ σ

iii dnAd

∑ µ−=γσ

ii

i dAn

Ad

∑ µΓ−=γ σ

iii dd ……… (6)

Where, Γ (Capital Gamma) is the surface excess concentration or surface excess. The

equation (6) is known as Gibbs adsorption isotherm.

The simplest application of this equation is a system of two components e.g., a solvent 1 and

a solute 2. In this case we have,

2211 ddd µΓ+µΓ=γ− σσ

Since, the surface excess of the solvent at the interface is zero i.e., 01 =Γσ . Therefore,

22 dd µΓ=γ− σ

Now 22iiiii alnRTddor alnRTddor alnRT =µ=µ+µ=µ Therefore,

alnRTdd 22σΓ=γ−

γ−=Γσ

22 alnd

dRT1

And for ideal solutions ai = ci

γ−=Γσ

22 clnd

dRT1

. Therefore,

……… (7)

This is very important equation. It directly tells us that when a solute is enriched at interface

( 02 >Γσ ), the surface tension decreases when the solution concentration is increased. Such

solutes are said to be surface active and they are called surfactants or surface active agents.

When a solute avoids the interface ( 02 <Γσ ), the surface tension increases by adding the

substance.

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6.8 KINETICS OF HETEROGENEOUS REACTIONS

The chemical reactions in which reactants are present in two or more phases are

known as heterogeneous reactions. For example, a reaction between a gas and a liquid, a gas and

a solid or a liquid and a solid is heterogeneous. Heterogeneous reactions are actually the reactions

that occur at the interface between two phases. The process of adsorption is a type of

heterogeneous reaction that occurs at the surfaces. The heterogeneous reactions may be

unimolecular or bimolecular.

A) UNIMOLECULAR REACTIONS ON SURFACES

If there is a single reactant, it is first chemisorbed and subsequently, on activation,

breaks up into products. If A is the reactant molecule and S the surface atom of the solid, the

elementary process may be depicted as follows,

A + S AS

Product AS 2k→

Where, AS refers to the adsorbed molecule.

Suppose θ be the fraction of the surface covered by A at any instant t and pressure P.

According to Langmuir-Hinshelwood the reaction rate should be,

θ== 2krRate ……… (1)

If we assume steady state approximation for [AS], we get

0]AS[k]AS[k]S][A[kdt

d[AS]211 =−−= −

21

1

kk]S][A[k]AS[

+=

−

……… (2)

Now let concentration of vacant sites )1(C]S[ s θ−=

And concentration of occupied sites θ= sC]AS[

Where, Cs

On substituting the values of [S] and [AS] in Equation (2),

refers to the total concentration of the surface sites of the catalyst.

21

s1s kk

)1(C]A[kC+

θ−=θ

−

11]A[kkk1

]A[kkk

kk)1](A[k

1

21

1

21

21

1 −θ

=+

⇒θθ−

=+

⇒+

θ−=θ −−

−

]A[k

]A[kkk11]A[kkk1

1

121

1

21 ++=

θ⇒+

+=

θ−−

k -1

k 1

17

211

1

kk]A[k]A[k++

=θ−

……… (3)

Therefore, Equation (1) becomes,

211

12

kk]A[k]A[kkr++

=−

……… (4)

For gaseous reactions, concentration term [A] can be replaced by partial pressures and

Equation (4) can be modified to,

21A1

A12

kkPkPkkr++

=−

……… (5)

Usually it is more convenient to use limiting cases as follows:

Case (I): If )kPk(k 1A12 −+>> then

A12

A12 Pkk

Pkkr ==

Case (II): If )kPk(k 1A12 −+<< then

1KP

KPk1P)k/k(

Pk)k/k(kPk

PkkrA

A2

A11

A211

1A1

A12

+=

+=

+=

−

−

−

Where, K refers to adsorption equilibrium constant.

(a) At Low Pressure, KPA A2KPkr =<<1. Therefore and the reaction would be of first order

with respect to A.

(b) At High Pressure, KPA 2kr =>>1. Therefore and the reaction rate would be independent

of pressure and the reaction is of zero order with respect to A.

B) BIMOLECULAR REACTIONS ON SURFACES

Consider a reaction in which two molecules A and B react on a surface and get

adsorbed on neighboring sites. The process may take place in two ways,

A + S AS

B + S BS

2SProduct BS AS 3k +→+

Suppose θ1 and θ2

)1( 21 θ−θ−

be the fractions of surface covered by adsorption of A and B respectively.

The fraction of the surface which is vacant is .

The rate of formation of products is given as follows,

213kr θθ= ……… (1)

On applying the steady state approximation to [AS] and [BS], we obtain

k -1

k 1

k -2

k 2

18

0]BS][AS[k]AS[k]S][A[kdt

d[AS]311 =−−= − ……… (2)

0]BS][AS[k]BS[k]S][B[kdt

d[AS]322 =−−= − ……… (3)

If Cs

refers to the total concentration of the surface sites then we have,

1sC]AS[ θ=

2sC]BS[ θ=

)1(C]S[ 21s θ−θ−=

On inserting [AS], [BS] and [S] in Equation (2) and Equation (3), we get

0CkCk)1(C]A[k 212s31s121s1 =θθ−θ−θ−θ− − ……… (4)

0CkCk)1(C]B[k 212s32s221s2 =θθ−θ−θ−θ− − ……… (5)

These equations are having two unknown variables θ1 and θ2 hence, can be solved for θ1 and

θ2

0k 3 →

. If it is assumed that the rate determining step is the chemical reaction between the

adsorbed molecules, then and Equation (4) and Equation (5) becomes as follows,

11211 k)1](A[k θ=θ−θ− −

22212 k)1](B[k θ=θ−θ− −

)1](A[kk

211

11 θ−θ−=θ

−

)1](A[K 2111 θ−θ−=θ ……… (6)

)1](B[kk

212

22 θ−θ−=θ

−

)1](B[K 2122 θ−θ−=θ ……… (7)

Where 1

11 k

kK−

= and 2

22 k

kK−

=

Combining Equation (6) and Equation (7),

]B[K]A[K 2

2

1

1 θ=

θ

11

22 ]A[K

]B[Kθ=θ

Putting this value in Equation (6),

)]A[K]B[K1](A[K 1

1

2111 θ−θ−=θ

19

11

211111 ]A[K

]B[K]A[K]A[K]A[K θ−θ−=θ

121111 ]B[K]A[K]A[K θ−θ−=θ

]B[K]A[K]A[K1 211

1 −−θ

=

1

121

]A[K]B[K]A[K1θ

=++

]B[K]A[K1

]A[K

21

11 ++=θ ……… (8)

Similarly, we obtain

]B[K]A[K1

]B[K

21

22 ++=θ ……… (9)

Inserting the values of θ1 and θ2

in from Equation (8) and (9) in Equation (1),

]B[K]A[K1]B[K.

]B[K]A[K1]A[Kkr

21

2

21

13 ++++

=

{ }2

21

213 ]B[K]A[K1

]B][A[KKkr++

= ……… (10)

For gaseous reactions, if PA and PB

denote the partial pressures of A and B then Equation

(10) changes to,

{ }2B2A1

BA213 PKPK1

PPKKkr++

= ……… (11)

Usually it is more convenient to use limiting cases as follows:

Case (I): If each gas (A and B) gets adsorbed very slightly then K1PA << 1 and also

K2PB

<<1 Therefore

BA213 PPKKkr =

This implies that the reaction will be second order and first order each with respect to A and

B. Example of this type include the reaction between NO and O2

Case (II): If one reactant A is relatively more strongly adsorbed than B then K

on glass.

1PA >> K2PB

Therefore

{ }2A1

BA213

PK1PPKKk

r+

=

The rate would be first order with respect to B. Such complicated kinetics has been followed

in the reaction between CO2 and H2 on platinum.

20

Case (III): When one reactant A is very strongly adsorbed then K1PA >> K2PB and K1PA

>>1 Therefore

{ } A1

B232

A1

BA213

PKPKk

PKPPKKk

r ==

Thus the rate is dependent strongly on the concentration of strongly adsorbed component.

The reaction between CO and O2

6.9 APPLICATIONS OF ADSORPTION

on platinum follows such kinetics.

Adsorption finds a large number of applications both in laboratory and industry. Some of the

important applications are:

1. A large number of industrial processes like synthesis of ammonia, manufacture of

sulphuric acid, synthetic petrol, alcohols etc., are catalyzed reactions where the reactants

are adsorbed on the surface of the catalysts.

2. Animal charcoal removes colours of solutions by adsorbing coloured impurities. Thus in

the manufacture of cane-sugar, the coloured solution is clarified by treating with animal

charcoal or activated charcoal.

3. Activated charcoal is used in gas masks as it adsorbs all the toxic gases and vapours and

purifies the air for breathing.

4. Silica and alumina gels possess the property to absorb moisture. Hence, they are used to

remove moisture and controlling humidity of rooms. Silica gel is also used in desiccators.

5. Various dyes, which work on the principle of adsorption, have been introduced as

indicators, particularly in precipitation titrations. For example, KBr is easily titrated with

AgNO3

6. Chromatography, a powerful and versatile technique used in separating and analyzing

minute quantities of various components from a mixture, is based on adsorption.

using eosin as an indicator.

7. In order to retard the evaporation of water, a monolayer of a suitable substance is

deposited on the surface of water in a lake.

8. Dying of fabrics with the help of mordants, tanning of leather, electroplating, etc. are

examples where adsorption finds immense applications.

9. The phenomenon of adsorption now a days is extensively employed for the recovery of

vitamins and other biological substances.

10. Most of the drugs function through adsorption on the body tissues and germs.

11. Softening of hard water by ion exchangers is based on adsorption of cations.

12. Surface active agents are widely used in washing, paints, lubricants, etc.