LECTURE NOTE ON
GIBBS ADSORPTION ISOTHERM
TOPIC- ADSORPTION
- Dr S P Singh
Dept of Chemistry, A N College, Patna
J. Williard Gibbs (1878) derived an exact relationship between the adsorption and change in
surface tension of a solution due to the presence of solute. This relationship was further
supported by the independent work of J.J. Thomson (1888). It is generally known as Gibbs
adsorption isotherm based on the use of thermodynamic potentials.
The Helmholtz Free Energy (F) of a system of two components is given by
=
+
-------------------------------------- (1)
where and
are the respective number of molecules and and are the
chemical potentials of the two species.
If is the interfacial tension, i.e. interfacial energy per cm2 and A is the area of the surface,
may be added in calculating the free energy (F).
=
+
+
-----------
------------
---------- (2)
On differentiating equation (2)
=
+
+
+
+
+
-------- (3)
The value for
is also obtained by the use of thermodynamic functions, by adding the term
for an increase in surface area so that
=−
+
+
+
+
----------- (4)
where S is entropy, p is pressure and V is volume.
By comparing equations (3) and (4) we get
∴
+
+
+
+
1
+
=−
1
+
2
+
+
2
+
+
= 0 ---------
+
+
+
----------
(5)
At constant temperature and pressure equation (5) takes the form
+
+
= 0 ------- -------- (6)
Now let us imagine the system under consideration to be made up of two portions
(i)
Surface phase – It involves the portion of the system affected by surface process and
therefore, equation (6) holds good for it.
(ii)
Bulk Phase – The remainder of the solution, which is unaffected by surface forces is
known as the bulk phase and therefore, Gibbs – Duhem equation holds for this only.
This equation is
+
= 0 -------- -------- -------- (7)
where
&
represent the number of moles of solvent and solute in
the bulk phase respectively.
Multiplying equation (7) by
or,
+
∴−
+
+
=
and subtracting from equation (6), it leads to be
−
−
=0
×
−
---------
where,
×
---------
=0
---------
---------
represents the number of moles of solute associated with
moles of
is the corresponding quantity in the bulk phase.
solvent in the surface phase and
It, therefore, follows that the quantity [
(8)
−
/ ] is the excess concentration of the solute
per unit area of the surface and is usually designated by the symbol, Γ.
Thus equation (8) becomes
Γ=−
----------
----------
where, Γ is independent of
--------- (9)
and is dependent only on the
nature of the surface phase and on its amount. Γ is also called the surface concentration of solute
per unit area of interface.
For a solution,
=
+
ln
where,
----------
----------
-------- (10)
is the activity of the solute.
Upon differentiating equation (10),
Assuming
=
+
ln
----------
----------
--------- (11)
as constant in equations (9) & (11),
Γ=−
∴Γ = −
∙
-----------
(12)
ln
=
Equation (12) is known as Gibbs adsorption equation. For more dilute solutions, the activity may
be replaced by concentration ‘c’ and the above equation takes the form
Γ=−
----------
----------
Thus equation (12) & (13) are known as Gibbs adsorption equation.
--------- (13)
Discussions
It is evident from equation (13) that
(i) When
is –ve the adsorption in positive. It means that further adsorption of the solute
lowers the surface tension of the solution.
(ii) When
is positive, the adsorption is –ve. It means that further addition of the solute
increases the surface tension of solution.
Experimental Results
Surface tension for the interface between air and aqueous solutions generally display one of the
three forms indicated schematically in fig.1.
Fig-1
i. Curve (1) in fig.1 is the type of behavior characteristic of most unionized organic
compounds. It indicates positive adsorption of the solute. Since
and
are negative,
Γ must be positive. The curve (1) corresponds to relatively dilute solutions.
ii. Curve (2) is typical of inorganic electrolytes and highly hydrated organic compounds.
iii. The type of behavior indicated by curve (3) is shown by soluble amphipathic species,
especially ionic ones. The break in curve (3) is typical of these compounds, however, this
degree of sharpness is observed only for highly purified compounds. If impurities are
present, the curve will display a slight dip at this point.
Amphiphilic molecules
Amphiphilic molecules consists of both hydrophobic groups (e.g. hydrocarbon) and hydrophilic
groups. The interaction of the hydrophilic group with water ensures the stability of compound. The
surface free energy of a surface covered with hydrophobic groups is much lower than that of
water. Therefore, there is a strong tendency of amphiphilic molecules to adsorb at the surface of
water in order to lower its free energy. Ethanol is an example of a weakly amphiphilic molecule.
More strongly amphiphilic molecules are soaps and detergents.
Verification of Gibbs Equation
Mc Lewis made the first attempt to verify Gibbs equation with aqueous solvent having low
surface tension. A drop of oil was passed through the aqueous solution and the bulk
concentration was determined at the beginning and end. The difference in these two readings
gave the amount of solute adsorbed at the surface of the drops. If the dimensions of the drop and
the total quantity of the solute are known, the total area can be calculated and thus the
concentration per unit area may be determined.
Application
Gibbs Adsorption Isotherm is one of the cornerstones of interface science. Gibbs adsorption
equation is an equation used to relate the change in concentration of a component in contact with
a surface with a change in surface tension. It possesses many applications. A few are mentioned
hereunder;
i.
Gibbs adsorption equation corresponds to relatively solute solution, highly hydrated
organic compounds and amphipathic species.
ii.
It is used to estimate the surface excess concentration for surfactants (nonionic and
ionic surfactants) with and without added salt and other compounds in aqueous
solution, from surface tension measurements.
iii.
The Gibbs isotherm method has a very solid agreement with experiments. It estimates
accurately the surface excess concentration for surfactant concentrations smaller than
the critical micellar concentration.
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