SURFACE TENSION INTERFACIAL TENSION SURFACE FREE ENERGY DETERMINATION OF SURFACE TENSION ADSORPTION ISOTHERM SPREADING COEFFICIENT DETERGENCY SOLUBILIZATION

1. Surface and interfacial phenomenon
Liquid interfaces
Surface & Interfacial tensions
Surface free energy
Measurement of surface &
interfacial tensions
Spreading coefficient
Adsorption at liquid interfaces
Surface active agents
HLB Scale
Solubilization
Detergency
Adsorption at solid interface
NABEELA MOOSAKUTTY
ASST. PROFESSOR
DEPT. OF PHARMACEUTICS
KTN COLLEGE OF PHARMACY

2. � Interfacial phase is a term used to describe molecules forming
the interface between two phases which have different
properties from molecules in the bulk of each phase
Interface is the boundary between two phases
Surface is a term used to describe either a gas-solid or a
gas- liquid interface

3. Air-Liquid interface
� The air-liquid interface is that between air (phase α) and liquid (phase β)
� The liquid-liquid interface is that between two immiscible liquids (phase α and phase β)
� The solid-liquid interface is that between a solid (phase α) and a liquid (phase β)
� The solid can be polar (high surface energy solid such as an oxides), semipolar
(intermediate surface energy solid such as cellulose acetate), or nonpolar (low surface
energy solid such as hydrocarbon solid or poly(tetrafluoroethylene)
� The liquid can be polar (such as water or alcohol) or nonpolar (such as hydrocarbon oil)
Liquid-Liquid interface
Solid-Liquid interface

4. Applications
� It helps to understand the molecular interactions of phases
� It helps to select vehicles in dissolving the drugs
� It helps to identifying instability problems associated with manufacturing of
suspensions, emulsions and creams
� Wetting of powders and detergency are based on the principles of interfacial
phenomena
� Coating of tablets
� Drug solubility and stability
� Disintegration and absorption of drugs from tablets
� Spreading of ointments
� Surfactants: as pharmaceutical adjuvants
� It helps to determine physicochemical property such as contact angle, zeta potential
etc
� It helps to understand the binding stoichiometry of Drug-Cyclodextrin complex and
to compare the inclusion complex of various kinds of cyclodextrins
� It helps to standardize and characterize the liposomal products
� It controls the output of aerosol particles from nebulizers and atomizers

5. SURFACE TENSION
� Surface tension is the force per unit length that must be applied
parallel to the surface to counterbalance the net inward pull
� It has the units of dynes/cm or N/m

6. � Molecules in the bulk liquid are surrounded in all directions by other molecules for which they have an
equal attraction (only cohesive forces)
� Molecules at the surface can only develop cohesive forces with other molecules that are below and
adjacent to them; and can develop adhesive forces with molecules of the other phase
� This imbalance in the molecular attraction will lead to an inward force toward the bulk that pulls the
molecules of the interface together and contracts the surface, resulting in a surface tension

7. INTERFACIAL TENSION
� Interfacial tension is the force per unit length existing at the interface between
two immiscible phases (units are dynes/cm or N/m)
� The term interfacial tension is used for the force between: Two liquids / Two
solids / Liquid-solid

8. SURFACE FREE ENERGY
� The surface layer of a liquid possesses additional energy as compared to the bulk liquid
� If the surface of the liquid increases (e.g. when water is broken into a fine spray), the energy of
the liquid also increases
� This energy is proportional to the size of the free surface, it is called a surface free energy
ΔG = γ . ΔA
ΔG: surface free energy (J)
γ : surface tension (N)
ΔA : increase in area (m )
Therefore,
� surface tension can also be defined as the surface free energy per unit area of liquid surface
� Surface free energy is equal to the surface tension
Definition: It is the work required to increase the area of a liquid by 1 square meter

9. Sphere!
� Each molecule of the liquid has a tendency to move inside the liquid
from the surface; therefore, when the surface is increased, the liquid
takes the form with minimal surface and as a result, minimal surface
energy

10. Measurement of surface & interfacial tensions
● Capillary rise method
● Drop method
● Maximum bubble pressure method
● Wilhelmy plate method
● Du Nouy ring tensiometer method

11. Capillary rise method
When a capillary tube is placed
in a liquid contained in a
beaker, the liquid rises up in
the tube to a certain distance
The rise in the tube continue
Until the upward movement is
balanced by the downward
force of gravity due to the
weight of the liquid

12. DERIVATION
Upward Component
Force: Surface tension of liquid at any point
Upward Component: a = 𝜸 . cos ø
𝜸 = surface tension of the liquid
ø = contact angle between the surface of the liquid
and capillary wall
Total upward force around the inside circumference of
the tube
Upward Component: a = 𝜸 . 2 π r. cos ø
r = inside diameter of the capillary tube
for water ø= 0 then cos ø = 1 then,
Upward Component: a = 2 π r 𝜸
Downward Component
Counteracting Force: Gravity
Downward Component:
b= mass of the liquid in capillary x acceleration
b=(mass upto lower meniscus+w)xacceleration
w = additional mass of water present above the lower
meniscus
b= mass x acceleration
b= volume x density x acceleration
b= cross sectional area x height x density x
acceleration
b = π r2 x h x ρ x g
At equilibrium, a=b
2 π r 𝜸 = π r2 x h x ρ x g

13. DROP METHOD / STALAGMOMETRIC METHOD
Instrument Used: STALAGMOMETER /STACTOMETER/ STALOGOMETER

14. PRINCIPLE
LIQUID IS ALLOWED TO FALL THROUGH A CAPILLARY
TUBE
FORMS A DROP
INCREASES IN SIZE (DEPENDENT ON THE
CHARACTERISTICS OF THE SOLUTION)
WEIGHT OF THE DROP OF THE LIQUID = TOTAL
SURFACE TENSION (EQUILIBRIUM)
DROP FALLS
TATE’S LAW
mg = 2 π r 𝜸

15. Drop Weight Method
It consists of a glass tube with a bulb in the middle of the tube
Two markings X and Y
The liquid is sucked up to X
then the liquid is allowed to drop into a vessel
About 20 to 30 drops are collected
Weight of single drop is determined using
mg = 2 π r 𝜸

16. Drop Count Method
The liquid is sucked up to the upper mark
The number of drops falling from A to B is counted
The procedure is repeated with water having known surface tension
Then, the surface tension of liquid is determined by
𝜸₂ = 𝜸₁n₁ρ₂ / n₂ρ₁

17. Wilhelmy Plate Method
A Method for measuring the surface tension of a liquid
Interfacial tension between two liquids and
contact angle between a liquid and a solid

18. Principle: When a vertically suspended plate touches a
liquid surface or interface, then a force F, which correlates
with the surface tension or interfacial tension 𝜸 and with
the contact angle θ according to the following equation,
acts on this plate:
L = 2 [ w + D ] where, w is the plate width and D is the plate thickness
𝜸 = F / L cos ø

19. ★ Platinum is chosen as the plate material when measuring the SFT or IFT as;
It is chemically inert
Easy to clean, and
It can be optimally wetted on account of its very high surface free energy
therefore, generally forms a contact angle θ of 0° (cos θ = 1) with liquids
★ To measure the force F, the plate is attached to a force sensor of a tensiometer
★ The required variable σ can be calculated directly from the measured force

20. Maximum Bubble
Pressure Method
Air-pressure is applied slowly through a capillary tube dipping in the experimental liquid
A bubble is formed at the end of the capillary
Slowly the bubble grows and becomes hemispherical
Then it breaks away and the pressure recorded by the manometer is noted
This is the maximum pressure required to make a bubble at the end of the capillary

21. A, B:
A bubble appears on the end of the capillary
As the size increases, the radius of curvature of the bubble decreases
C:
At the point of the maximum bubble pressure, the bubble has a complete
hemispherical shape whose radius is identical to the radius of the capillary
Its denoted by Rcap
The surface tension can be determined using the Young–Laplace equation
(σ: surface tension, ΔPmax: maximum pressure drop, Rcap: radius of
capillary)
D, E:
After the maximum pressure, the pressure of the bubble decreases and the radius of the bubble increases until the bubble is
detached from the end of a capillary and a new cycle begins
Change of pressure during bubble formation plotted as a function of time

22. The method involves slowly lifting a ring often
made of platinum from the surface of a liquid
The Force F, required to raise the ring from the
liquid’s surface
F = w + 2 π (rⅰ + rₐ) 𝜸
ri = radius of the inner ring of the liquid film pulled
ra = radius of the outer ring of the liquid film
w = weight of the ring - the buoyant force due to the part of the ring below the liquid surface
DuNouy Ring Method

23. 1. The ring is above the surface and the force is
zeroed
2. The ring hits the surface and there a slight positive
force due to the adhesive force between the ring and
the surface
3. The ring must be pushed through the surface (due
to surface tension) which causes a small negative
force
4. The ring breaks the surface and a small positive
force is measured due to the supporting wires of the
ring
5. When lifted through the surface the measured
force starts to increase
6. The force keeps increasing until
7. The maximum force is reached
8. After the maximum, there is a small decrease of
the force until the lamella breaks (or the ring is
pushed back below the surface)

24. SPREADING COEFFICIENT
The spreading coefficient or parameter is a
measure of the tendency of a liquid phase to
spread (complete wetting) on a second, liquid or
solid phase.
The spreading coefficient S is the difference
between the work of adhesion Wa between the
phases and the work of cohesion Wс of the phase
under consideration:
S = Wa - Wс

25. Work of Cohesion
It is the energy required to separate the molecules of the spreading liquid
There is no interfacial tension
Consider 2 drops of liquid having same cross sectional area of 1 sqm
A A

26. Wс = 𝜸🇱 . ΔА + 𝜸🇱 . ΔА
𝜸🇱 = surface tension of the liquid
ΔА = 1 cm²
Wс = 2𝜸🇱
A
A
𝜸🇱 . ΔА
𝜸🇱 . ΔА

27. Work of Adhesion
It is the energy required to bring out the adhesion between the liquids
Consider 2 drops having area of 1 cm²
A
B
𝜸🇱 . ΔА
𝜸s . ΔА
𝜸🇱 = surface tension of the spreading liquid
𝜸s = surface tension of the sublayer liquid
𝜸LS = Interfacial tension between liquids
ΔА = 1 cm²
Wa = 𝜸🇱 . ΔА + 𝜸s . ΔА - 𝜸🇱s . ΔА
Wa = 𝜸🇱 + 𝜸s - 𝜸🇱s

28. When the adhesive forces are stronger than the cohesive forces,
then the spreading occurs
S = Wa - Wс
S = 𝜸🇱 + 𝜸s - 𝜸🇱s - 2𝜸🇱
S = 𝜸s - 𝜸🇱s - 𝜸🇱
s = 𝜸s - [𝜸🇱 + 𝜸🇱s]
If 𝜸s > [𝜸🇱 + 𝜸🇱s] then S is positive indicates Spreading
If 𝜸s < [𝜸🇱 + 𝜸🇱s] then S is negative indicates no Spreading

29. LENS
There may be saturation of the liquid with the other , and leads to changes in surface
tension of liquids. Such changes reduce the initially obtained S value and even
make it negative. This situation is indicated by the formation of lens due to
coalescence of excess spreading liquid
Spreading coefficient of a substance can be increased by
presence of polar functional groups ex: Propanoic acid and Ethyl alcohol
reducing the non-polar chain length ex: Petrolatum and Oleic acid
Applications
Absorption of medicament from creams lotions etc
Stabilization of emulsions
Evaluation of binder in tablet manufacture
Coating of tablets

30. Adsorption at Liquid Interfaces
Positive Adsorption
[Partitioned in the favour of the
interface]
When the added molecules
move on their own accord to
interface
Surface free energy and Surface
tension get decreased
Ex: Surfactants: Sodium lauryl
sulphate, Tweens and
Triethanolamine
Negative Adsorption
[Partitioned in the favour of
the bulk]
When the added molecules
prefer to remain in the bulk
of solution
Enhances surface tension
Ex: Inorganic electrolytes:
sodium chloride

31. Certain molecules / ions when added to a liquid, they may modify the interface in
different ways
Some substances do not affect the interfacial tension when they are added to water
Ex: Sugars, Carbohydrates and Cellulose derivatives

32. ❖ These are compounds that lower the surface tension (or interfacial tension) between two liquids, between a
gas and a liquid, or between a liquid and a solid
❖ Surfactants may act as detergents, wetting agents, emulsifiers, foaming agents, or dispersants
SURFACTANTS

33. ★ These are organic compounds
★ They are amphiphilic in nature meaning they contain both
❏ hydrophobic groups (tails) - long carbon chain - little affinity for aqueous solvents
❏ hydrophilic groups (heads) - polar groups (ex: COOH, OH etc) - high affinity for
aqueous solvents

34. ANIONIC SURFACTANTS
● Have a negative charge on their hydrophilic end (head) Ex: Sodium dodecyl sulphate
● Used frequently in soaps and detergents
● Create a lot of foam when mixed
● Have unpleasant taste and not suitable for internal use due to irritant action on intestinal mucosa
NON-IONIC SURFACTANTS
● These are neutral, they do not have any charge on their hydrophilic end
● They are resistant to pH change
● Ex: Glycerol, Glycol esters (glyceryl monostearate), Macrogol esters ( poloxyl stearate), Spans and Tweens
● These have a unique property called a cloud point
The cloud point is the temperature at which the nonionic surfactant begins to separate from the cleaning solution,
called phase separation
When this occurs, the cleaning solution becomes cloudy. This is considered the temperature for optimal detergency
The temperature of the cloud point depends upon the ratio of the hydrophobic and hydrophilic portions of the nonionic
surfactant
Some cloud points are at room temperature while others are very high
Some nonionics don’t have a cloud point because they have a very high ratio of hydrophilic to hydrophobic moieties
Classification (Based on their ionization in aqueous solutions)

35. CATIONIC SURFACTANTS
● Have a positive charge on their hydrophilic end (HEAD)
● The positive charge makes them useful in anti-static products, like fabric softeners
● Cationic surfactants can also serve as antimicrobial agents, so they are often used in disinfectants
● Ex: Cetrimide, Benzalkonium chloride, Benzethonium chloride
AMPHOTERIC SURFACTANTS
● Amphoteric surfactants have a dual charge on their hydrophilic end, both positive and negative
● The dual charges cancel each other out creating a net charge of zero, referred to as zwitterionic
● The pH of any given solution will determine how the amphoteric surfactants react
● In acidic solutions, the amphoteric surfactants become positively charged and behave similarly to cationic
surfactants. In alkaline solutions, they develop a negative charge, similar to anionic surfactants.
● Amphoteric surfactants are often used in personal care products such as shampoos and cosmetics
● Ex: Lecithin, N-dodecyl alanine, Betaines
ClassifiCation Continue……...

36. HLB SCALE
Hydrophilic-Lipophilic
Balance
It's also known as Griffin’s Method / Griffin scale
It’s an arbitrary scale in which values are assigned to different
surfactants according to their nature (polar and nonpolar)
HLB value 1 indicates Surfactants are soluble in oil lipophilic
HLB value 20 indicates Surfactants are soluble in water
hydrophilic
A higher HLB number indicates that the emulsifier has more
hydrophilic groups on the molecule and therefore is more
hydrophilic
Ex: Tweens
Because of their water-soluble character, Tweens will cause the
water phase to predominate and form an o/w emulsion
An emulsifier having a low HLB number indicates that the number
of hydrophilic groups present in the molecule is less and it has a
lipophilic character
Ex: Spans
Because of their oil-soluble character, spans cause the oil phase to
predominate and form a w/o emulsion

39. METHOD OF ESTIMATION
HLB = ∑ (Hydrophilic group number) − ∑ (Lipophilic group number) + 7
1. The chemical structure of a molecule is split into different component groups. Each group assigned a number.
The algebraic sum of these numbers permits the calculation of it’s HLB value (David Formula)
2. Each atom or group has been assigned a constant and used in the calculation of HLB.
For example, if surfactant contains Polyoxyethylene chains, the HLB is calculated by the
equation;
where, E and P are percents by weight of oxyethylene chains and polyhydric alcoholic
groups, respectively in the surfactant molecule.
When the molecule contains only oxyethylene groups then, HLB is calculated by the
equation:
3. HLB values of surfactants such as glyceryl monostearate that contain fatty acid esters
and polyhydric alcohols are calculated by the equation:
where S is saponification number and A is acid number.

40. Drawbacks of HLB System:
HLB system provides only information about the hydrophilic and lipophilic nature of the
surfactants but the concentration of these surfactants is not considered. For optimum stability
and therapeutic safety concentrations of the surfactant are equally important.
It does not consider the effect of temperature as well as the presence of other additives.
Other methods:
● Titration
● Dielectric constant method
● Spreading
● Cloud point data
● Dispersion
● Gas Chromatography
● Heat of hydration method

41. RHLB (Required HLB) / CRITICAL HLB
It’s a hydrophilic-lipophilic value that is desired in order to prepare a stable emulsion of o/w or
w/o type
The RHLB value is calculated based on the oil phase and the type of emulsion
Ex:
OIL PHASE O/W W/O
Cotton seed oil 6-7 -
Mineral oil 10-12 5-6
Beeswax 9-11 5
Paraffin wax 10 4
HLB of Mixture of 2 surfactants
HLBmixture = f. HLB🇦 + (1-f) HLB🇧

42. SOLUBILIZATION
Definition:
The property of surface active agents to cause an increase in the solubility of organic compounds in aqueous system
This property is exhibited at or above CMC that is critical micellar concentration
MICELLES
Micelles are colloidal particles formed from the aggregation of
amphiphilic molecules
The term “micelle” describes a system that exists in aqueous
solvent, in which the amphiphile’s hydrophilic zone is oriented
outwards while the hydrophobic zone is oriented towards the
particle’s core
“Reverse/inverse micelle” describes the opposite orientation
that arises in bulk non-polar solvent

43. The CMC is an important characteristic of a surfactant.
Before reaching the CMC, the surface tension changes strongly with the
concentration of the surfactant.
After reaching the CMC, the surface tension remains relatively constant
The value of the CMC for a given dispersant in a given medium depends on
temperature, pressure, concentration of other surface active substances and
electrolytes.
Micelles only form above critical micelle temperature (Krafft temperature)
● It is defined as the minimum temperature from which the micelle formation
takes place.
● It is named after German chemist Friedrich Krafft.
● It has been found that Solubility at the Krafft point is nearly equal to Critical
micelle concentration (CMC).
For example, the value of CMC for sodium dodecyl sulfate in water (without
other additives or salts) at 25 °C, atmospheric pressure, is 8x10−3 mol/L
Definition: CMC is defined as the concentration of surfactants above which
micelles form and all additional surfactants added to the system will form micelles
Critical Micelle Concentration

44. Examples:
● The fat-soluble vitamin phytonadione is solubilized by the use of polysorbates
● Polyoxyethylene castor oil is used to increase the solubility of an immune expressing drug cyclosporine and anticancer drug
paclitaxel
● Cetomacrogol has been found to show improved solubility of chloramphenicol
● The solubility of volatile and essential oils can be improved by the use of lanolin derivatives. Chloroxylenol which normally has
a solubility of 0.03% in water can be improved by the use of soaps
● Vitamin A, D, E, and K, griseofulvin, aspirin, and phenacetin, etc. are poorly soluble drugs that are solubilized by micellar
solubilization
The solubilization mechanism involves entrapment (adsorbed or dissolved) of molecules in micelles and Increases in the
concentration of micelles lead to increases in drug solubility
For liquid dosage forms of water-insoluble drugs, solubilization is an important tool in preformulation studies for the selection of
surfactants

45. ● Wetting is the ability of a liquid to spread over a solid surface
● The degree of wetting is called wettability
● The shape that a drop takes on a surface depends on the
surface tension of the fluid and the nature of the surface
● It is determined by a force balance between the cohesive forces
of the liquid and the adhesive forces between the surface and
the liquid
● To determine the degree of wetting, the contact angle (q) that is
formed between the liquid and the solid surface is measured
● The smaller the contact angle and the smaller the surface
tension, the greater the degree of wetting.
● Contact angle: It is an angle formed by a liquid at the three-
phase boundary where a liquid, gas and solid intersect
WETTING

46. If the liquid runs evenly on the solid surface, complete wetting is present with a
contact angle of 0 °. If the angle is between 0 ° and 90 °, the surface is
wettable. The surface is called hydrophilic.
An angle between 90 ° and 180 ° means the surface is not wettable. It is
hydrophobic.
If the angle clearly approaches the value of 180 °, it is an ultrahydrophobic
surface that is completely liquid-repellent. This property is described as a
lotus effect
Angle 𝝷 = 0 Ideal wetting
Angle between 0 ° and 90 ° = surface wettable, hydrophilic
Angle between 90 ° and 180 ° = surface not wettable, hydrophobic
Angle is close to 180 ° = ultrahydrophobic surface, completely liquid-repellent,
lotus effect
Applications:
Preparation of suspensions and emulsions
Granulation prior to tabletting - mixing of powders with liquid binding
agents
Film Coating
Disintegration and Dissolution of tablets
Contact angle is an angle between the liquid droplet and surface over which it spreads
It is used as an indicator to evaluate the efficiency of a wetting agent

48. Surfactants in aq. solutions are used to remove
the dirt from substrates such as glass, fabric, skin
etc.
Effective detergents are required for the
cleaning of production equipment, containers
for packing and also in order to maintain
hygiene in the industry.
Detergency is a complex process and a
number of steps are simultaneously involved
● Initial wetting of the dirt from the surface
● Solubilizing of the dirt
● Removing the insoluble dirt as
deflocculation particles
● Suspending the particles in the detergent
solution
● Removing the oil soluble materials and
convert into emulsion
● Converting the dirt into foam so as wash
easily
DETERGENCY

49. Adsorption at solid interfaces
Adsorbate: The substance (gas or liquid) whose molecules
accumulate on the solid surface
Adsorption: It is the addition of atom, ions or molecules from a gas,
liquid, a dissolved solid to a surface
Adsorbent: The solid on the surface of which gas or a liquid
molecules accumulate

50. Types of Adsorption
Physical Adsorption
Example: Adsorption of gases on charcoal
Force: Van der Waals weak intermolecular
interaction
Nature of gas: Easily liquefiable gases are
readily adsorbed
Effect of Pressure: P directly proportional to
the extent of adsorption
Reversible nature: Decrease in Pressure
causes Desorption (reversible)
Effect of Temperature: Favoured at low
temperature [10-40 KJ/mol]
Thickness of adsorbed layer: unimolecular at
low pressure and multi-molecular at higher
pressure
Chemical Adsorption
Example: Adsorption of oxygen on silver or
gold
Force: Chemical bonds
Nature of gas: Highly specific
Effect of Pressure: P directly proportional to
the extent of adsorption until the surface gets
saturated, after that P has no effect
Reversible nature: Decrease in pressure does
not cause desorption (irreversible)
Effect of Temperature: Favoured at high
temperature [ > 40 KJ/mol]
Thickness of adsorbed layer: unimolecular

51. Adsorption Isotherm
Definition: The variation in the amount of gas adsorbed by the adsorbent per
unit area or unit mass of solid with different pressures of the gas at constant
temperature can be expressed by means of a curve termed as Adsorption
isotherm
Types
1. Langmuir Isotherm
2. Freundlich Isotherm
3. BET (Brunauer, Emmett and Teller) Isotherm

52. Freundlich Adsorption Isotherm
In 1909, German scientist Freundlich provided an empirical relationship between
the amount of gas adsorbed by a unit mass of solid adsorbent and pressure at a
particular temperature
It is expressed using the following equation –
x/m = k.P1/n (n > 1)
where,
‘x’ is the mass of the gas adsorbed on mass ‘m’ of the adsorbent at pressure ‘P’
‘k’ and ‘n’ are constants that depend on the nature of the adsorbent and the
gas at a particular temperature

53. The mass of the gas adsorbed per gram of the
adsorbent is plotted against pressure
The curve reaches saturation at high pressure,
then 1/n = 0 hence, extent of adsorption becomes
independent of pressure (It fails at higher pressure)
x/m = k.P1/n log x/m = log k + 1/n log P
Plot of log x/m on the y-axis and log P on the x-axis
If the plot shows a straight line, then the Freundlich
isotherm is valid, otherwise, it is not
The slope of the straight line gives the value of 1/n,
while the intercept on the y-axis gives the value of log
k

54. Langmuir Adsorption Isotherm
1916 Langmuir proposed this isotherm based on different assumptions
Assumptions
❏ Dynamic equilibrium exists between adsorbed gaseous molecules and the free gaseous
molecules
❏ The surface of solid possess fixed number of active sites for the adsorption of gases
❏ All the vacant sites are of equal size and shape on the surface of adsorbent
❏ At max. adsorption, the gas layer that is found around the solid is only one molecule thick
❏ The rate of adsorption is proportional to the number of sites unoccupied
❏ The rate of evaporation (desorption) is proportional to the number of occupied sites

55. The Langmuir adsorption isotherm has the form:
Where
θ is the fraction of surface covered by the adsorbed molecule
K is an equilibrium constant known as adsorption coefficient
{ K= ka/kd = rate constant for adsorption/ rate constant for
desorption}
p is the pressure

56. Derivation
of
Equilibrium
constant

59. Substitute theta = y/ym
y = amount of gas adsorbed on solid
ym = amount of gas adsorbed on 1g of solid
Substitute Ka / Kd = b
Ө = Ka/Kd . P / Kd/Kd + Ka/Kd . P
y/ym = bP / (1 + bP)
y = (ym bP) / (1+bP)
Then taking the inverse,
1/y = (1+bP) / (ym bP)
1/y = (1/ym bP) + (bP/ym bP)
1/y = (1/ ym bP) + (1/ym)
Multiplying the equation by Pressure P
P/y = (P/ym bP) + (P/ym)
P/y = (1/ym b) + (P/ym)
Slope
Intercept

61. Under the conditions of high pressure and low temperature, thermal energy of gaseous molecules decreases and more
and more gaseous molecules would be available per unit surface area
Due to this multi-layer adsorption would occur
P
y(Po-P)
1
ym b
b-P
ym b
P
Po
= + .
P = Pressure of the adsorbate
Po = Vapour pressure at saturation
y = mass of the vapour per gram
ym = amount of vapour adsorbed per unit
mass of adsorbent
b = BET constant