5.4 Effects of Electrolytes
139
more gradually albeit over a narrow range. Then other thermodynamic properties also
vary gradually over the narrow range. The question is how to treat such situations.
The Gibbs convention is to define a Gibbs dividing surface so that the thermodynamic properties of one phase continue up to one side of the Gibbs dividing surface
and the thermodynamic properties of the other phase continue from the other side up
to the Gibbs dividing surface [94]. Then, in a two-component system that consists
of a solvent and a solute, the concentration of the solute is constant in each of the
two phases divided by the Gibbs dividing surface. Surface excess, , is defined as
the difference between the total mole in a system and the sum of the moles in each
of the two phases divided by the Gibbs dividing surface [93]. The Gibbs convention
of selecting the position of the Gibbs dividing surface is such that the surface excess
of the solvent becomes zero.
The Gibbs adsorption isotherm relates the surface excess to the change in the
surface tension as [94]
dγ = −Γ dμ
(5.4.7)
where γ is the surface tension, is the surface excess and μ is the chemical potential
of a solute. Practically, it is convenient to express the chemical potential in terms of
the bulk solute concentration, C, in the case of an ideal solution [91]
dγ = −Γ kT d(ln C)
(5.4.8)
where k is the Boltzmann constant and T is the absolute temperature. The Gibbs
adsorption isotherm shows that (1) the surface excess is positive when the surface
tension decreases with increasing solute concentration in the bulk solution phase,
and vice versa, (2) the greater the change in the surface tension for a given change in
the solute concentration the greater the size of the surface excess. For example, the
surface tension of a surfactant solution decreases with the surfactant concentration.
The Gibbs adsorption isotherm shows that surfactants positively adsorb to a water
surface. The greater the reduction in the surface tension for a given amount the more
surface active the surfactant is.
In contrast, the surface tension of a salt solution typically increases with the salt
concentration. The Gibbs adsorption isotherm shows that salts negatively adsorb to a
water surface, that is, less salts are present next to a water surface than they are deep
inside the bulk of the salt solution. In microscopic terms, an electric field is induced
when an electric charge approaches an interface where there is a discontinuity in the
dielectric constant [92]. A graphically convenient way to describe such an induced
electric field by an interface is to imagine that an image charge is induced inside
the medium at the opposite side of the interface to which the real electric charge is
approaching [92]. The consequence of such an image charge force is that an electric
charge such as an ion is repelled from a gas–aqueous interface as it approaches from
the aqueous phase, and the repulsive force becomes progressively stronger the closer
the electric charge approaches the interface. Consequently, the ion concentrations
139
more gradually albeit over a narrow range. Then other thermodynamic properties also
vary gradually over the narrow range. The question is how to treat such situations.
The Gibbs convention is to define a Gibbs dividing surface so that the thermodynamic properties of one phase continue up to one side of the Gibbs dividing surface
and the thermodynamic properties of the other phase continue from the other side up
to the Gibbs dividing surface [94]. Then, in a two-component system that consists
of a solvent and a solute, the concentration of the solute is constant in each of the
two phases divided by the Gibbs dividing surface. Surface excess, , is defined as
the difference between the total mole in a system and the sum of the moles in each
of the two phases divided by the Gibbs dividing surface [93]. The Gibbs convention
of selecting the position of the Gibbs dividing surface is such that the surface excess
of the solvent becomes zero.
The Gibbs adsorption isotherm relates the surface excess to the change in the
surface tension as [94]
dγ = −Γ dμ
(5.4.7)
where γ is the surface tension, is the surface excess and μ is the chemical potential
of a solute. Practically, it is convenient to express the chemical potential in terms of
the bulk solute concentration, C, in the case of an ideal solution [91]
dγ = −Γ kT d(ln C)
(5.4.8)
where k is the Boltzmann constant and T is the absolute temperature. The Gibbs
adsorption isotherm shows that (1) the surface excess is positive when the surface
tension decreases with increasing solute concentration in the bulk solution phase,
and vice versa, (2) the greater the change in the surface tension for a given change in
the solute concentration the greater the size of the surface excess. For example, the
surface tension of a surfactant solution decreases with the surfactant concentration.
The Gibbs adsorption isotherm shows that surfactants positively adsorb to a water
surface. The greater the reduction in the surface tension for a given amount the more
surface active the surfactant is.
In contrast, the surface tension of a salt solution typically increases with the salt
concentration. The Gibbs adsorption isotherm shows that salts negatively adsorb to a
water surface, that is, less salts are present next to a water surface than they are deep
inside the bulk of the salt solution. In microscopic terms, an electric field is induced
when an electric charge approaches an interface where there is a discontinuity in the
dielectric constant [92]. A graphically convenient way to describe such an induced
electric field by an interface is to imagine that an image charge is induced inside
the medium at the opposite side of the interface to which the real electric charge is
approaching [92]. The consequence of such an image charge force is that an electric
charge such as an ion is repelled from a gas–aqueous interface as it approaches from
the aqueous phase, and the repulsive force becomes progressively stronger the closer
the electric charge approaches the interface. Consequently, the ion concentrations