The document discusses adsorption and the Gibbs adsorption equation. It defines adsorption as molecules of a gas or liquid being attracted to and retained on the surface of a solid. Absorption occurs when a substance is uniformly distributed throughout a solid or liquid. The Gibbs adsorption equation relates changes in surface tension to changes in solute concentration at an interface. It shows that the surface excess concentration of a solute is proportional to the negative of the derivative of surface tension with respect to solute activity. The document also lists factors that affect adsorption and describes adsorption isotherms.

2. Introduction
Characteristics and factors affecting adsorption
Adsorption isotherm
Gibbs adsorption equation
Discussions of gibbs adsorption equation
Experimental results
Conclusion
References

3.  “Adsorption is a technical term coined to denote the taking up of gas,
vapour, liquid by a surface or interface”.
 Adsorption is a surface phenomenon where the surface of a solid has a
tendency to attract and to retain molecules of other species(gas or
liquid) with which such surfaces come in contact.
 Absorption is a bulk phenomenon in which the substance assimilated is
uniformly distributed throughout the body of a solid or liquid to form a
solution or a compound.
 When adsorption and absorption takes place simultaneously is
generally termed as sorption.
 Water vapour is absorbed by anhydrous calcium chloride while it is
absorbed by silica gel.
 Ammonia is adsorbed by charcoal while it is adsorbed by water to form
ammonium hydroxide.

4. Characteristics
• It is a spontaneous process
and takes place in no time.
• The phenomenon of
adsorption can occur at all
surfaces.
• It is accompanied by a
decrease in the free energy
of the system.
Factors Affecting
• Nature of the adsorbent
and adsorbate.
• Surface area of the
adsorbent.
• The partial pressure of
the gas in the phase.
• Effect of temperature.

5.  Adsorption isotherm (also A sorption isotherm) describes
the equilibrium of the sorption of a material at a surface
(more general at a surface boundary) at constant
temperature.
 It represents the amount of material bound at the surface
(the sorbate) as a function of the material present in the
gas phase and/or in the solution.
 If the temperature is kept constant and pressure is
changed, the curve between a and b is known adsorption
isotherm.
Where,
a = amount of adsorbed
p = pressure
T = temperature
a = f (P, T)

6. This equation represents an exact relationship between the
adsorption and change in surface tension of a solvent due to
presence of a solute. This equation was derived by J. Willard Gibbs
(1878) and afterwards independently by J.J Thomson , 1888.
The dG for 2 comonent system is given by:
dG = -SdT + Vdp + µ1dn1 + µ2dn2 + ϒdA ①
Where,
ϒ = Surface tension
dA = Increase in surface area
S = Entropy
p= Pressure
V = Volume

7. dG = Change in Gibbs free energy Integrating equation no. ① at
a constant temperature, pressure, surface tension and chemical
potential of the component we obtain the expression
G = µ1 n1 + µ2 n2 + ϒA ②
Where,
n1 = Number of moles of solvent.
n2 = Number of moles of solute.
Complete differential of Eq. ②
dG = µ1 n1 + µ2 n2 + n1dµ1 + n2d µ2 + µdA + Adϒ ③
Comparing eq. no. ① & ③ the result is:
SdT - Vdp + n1dµ1 + n2d µ2 + µdA + Adϒ = 0 ④

8. At constant temperature and pressure equation no. ④
simplifies to
n1dµ1 + n2d µ2 + Adϒ = 0 ⑤
We can imagine the system under consideration made of 2
portion:
• Surface phase – It involves the portion of system affected
by the surface process and therefore equation no. ⑤ holds
true only for it.
• Bulk Phase – The remainder of the solution which s
unaffected by surface forces is known as bulk phase and
therefore Gibbs Duehem equation holds for this only.
This Equation is
n1
0dµ1 + n2
0d µ2 = 0 ⑥

9. Where
On multiplying equation ⑥ by n1/n1
0 and subtracting from
equation no. ⑤ we obtain the expression
Adϒ + (n2 – n1n2
0/n1
0) dµ2 = 0
“Or”
-dϒ/dµ = [n2 - n1n2
0/n1
0]/A ⑦
Where,
n2 Represents no. of moles of solute associated with n1 moles of
solvent in the surface phase and n1n2
0/ n1
0 is the corresponding
quantity in the bulk phase. It therefore, follows that the quantity [n2
- n1n2
0/n1
0]/A is the excess concentration of the solute per unit area
of the surface and is usually designated by the symbol ‘ᴦ’
Thus equation no. 7 becomes as
ᴦ = -dϒ/ dµ2 ⑧

10. Where ᴦ is independent of n1 and is dependent only on the nature of surface phase
and not on its amount.
ᴦ is also called the surface concentration of solute per unit area of interface .
For a solution :
µ2 = µ2
0 + RT ln a2 ⑨
Where,
a2 is the activity of solute
By differentiating equation no. ⑨ we get:
dµ= RT d ln a2 ⑩
Assuming µ2
0 as a constant
On substituting eq. no. ⑩ in eq. no. ⑧ we get,
ᴦ= 1/ RT ₓ dϒ/d ln a2
or
ᴦ= -a2/ RT ₓ dϒ/da2 [Since d ln a2 = da2/a2 ] ⑪
Equation no. ⑪ is known as Gibbs Adsorption Equation.

11. Gibbs adsorption isotherm for multi component system is an
equation used to relate the changes in concentration of a
component in contact with a surface with changes in the
surface tension. This equation represents exact relationship
between adsorption and change in surface tension of a solvent
due to the presence of solute. This equation is corresponds to
relatively solute solutions, highly hydrated organic
compounds, amphipathic species.

12. Source:
• Advanced physical chemistry Gurdeep Raj, Krishna Prakashan Media,
2012.
• Advanced physical chemistry Gurtu-Gurtu, Pragati Prakashan, Meerut,
2011.
Net Source:
•www.wikipedia.com