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T. Y. Tan
1
6. BINARY SOLUTIONS OF CONDENSED MATTER
A solution is a singlephase material containing more than one component, which may be a
gas, a liquid, or a solid. Gases are in general miscible in all proportions so that practically all
gases, at equilibrium, are solutions. Liquids can often dissolve a wide variety of gases, solids, or
other liquids. The composition of these liquid solutions can be varied over a wide or narrow
range, depending on the solubility relationships in the particular system. Solid solutions are
formed when a gas, a liquid, or another solid dissolves in a solid. They are often characterized by
having a limited concentration range, although pairs of solids, e.g., Cu/Ni and Si/Ge, are known
to be mutually soluble in all proportions.
The behavior of gaseous solutions are approximated well by that of ideal gases, for which a
sufficiently accurate description is given by Dalton's law of partial pressures: in the
same
volume
V, for n
i
moles of each gas with
partial
pressure P
i
,
P
i
V = n
i
RT ,
the total pressure of the solution or gas mixture is
P =
P
i
∑
i
.
The behavior of condensed matter solutions is considerably more complicated than that of
ideal gases. In this chapter the behavior, models, and Gibbs free energy curves of binary con
densed matter solutions are discussed.
6.1
Raoult's Law and the Ideal Solution Model
From experimental point of view, a condensed matter solution is ideal if its external vapor
pressure of each component is proportional to the concentration of that component in the solu
tion, since then the solution behavior is a direct analogy to that of a mixture of ideal gases. It will
be discussed in the next chapter that, in thermal equilibrium, a condensed matter cannot exist
alone but can only coexist with vapor phases of its constituent components. The equilibrium va
por pressures of the components of a solution of condensed matter are important measures of the
state of affairs in the solution. From studies of the properties of these vapor phases we can obtain
a description of the properties of the solution.
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View Full DocumentT. Y. Tan
2
The law of behavior of an ideal solution was first described, based on experimental vapor
pressure data, by Francois Marie Raoult in 1886. It is expressed as
P
i
= x
i
P
i
o
.
(6.1)
Here P
i
is the partial vapor pressure of component i whose fractional concentration in the solu
tion is x
i
, and
P
i
o
is P
i
when x
i
=1 holds. Equation (6.1) is known as the Raoult's law. All solutions
containing different isotopes of the same atomic species follow Raoult's law perfectly. However,
when containing components differing chemically, there are very few solutions follows Raoult's
law even just closely. An example of such a rare case, the solution composed of ethylene
bromide (C
2
H
4
Br
2
) and propylenebromide (C
3
H
6
Br
3
), is shown in Fig. 8.1.
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 Fall '11
 DR.TAN

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