Solutions

1
Chapter 9

• Solutions

2
Physical Chemistry
Solutions
Ideal Solutions
A solution where the molecules of the various
species are so similar to one another that
replacing molecules of one species with molecules
of another species will not change the spatial
structure or the intermolecular interaction
energy in the solution.
To prevent change on mixing B and C, the size and
shape of B molecules ? those of C
B at T, P
C at T, P
B-B, C-C
The intermolecular interaction energies should be
essentially the same for B-B, B-C, and C-C pairs
of molecules.
B-B, C-C, B-C
B C at T, P
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Physical Chemistry
Solutions
Ideal Solutions
When two liquids B and C whose molecules resemble
each other closely are mixed at constant T and P,
the experimental ?mixG is
From the molecular definition, the formation of
an ideal solution from pure components at
constant T and P
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Physical Chemistry
Solutions
Ideal Solutions
For ideal gases
(3.32)
For ideal solutions
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Physical Chemistry
Solutions
Ideal Solutions
For ideal solutions
For ideal solutions (ideal liquid or solid
mixtures) containing the gas constant R?
R applies not only to the zero-pressure limit of
a gas
But also to entropy
Avogadro constant
Boltzmanns constant
And other fundamental equations of statistical
mechanics!
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Physical Chemistry
Solutions
Ideal Solutions
For ideal solutions
Thermodynamic definition of an ideal solution
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Physical Chemistry
Solutions
Ideal Solutions
Thermodynamic definition of an ideal solution A
solution is ideal if the chemical potential of
every component in the solution obeys (9.41) for
all solution compositions and for a range of T
and P.
Molecular definition of an ideal solution A
solution where the molecules of the various
species are so similar to one another that
replacing molecules of one species with molecules
of another species will not change the spatial
structure or the intermolecular interaction
energy in the solution.
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Physical Chemistry
Solutions
Thermodynamic Properties of Ideal solutions
Standard States
For an ideal liquid solution, pure liquid i at T
and P
For an ideal solid solution, pure solid i at T
and P
The degree superscript denotes the standard state
and the star superscript indicates a pure
substance.
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Physical Chemistry
Solutions
Mixing Quantities
ideal solution
(9.44)
Same as
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Physical Chemistry
Solutions
Thermodynamic Properties of Ideal Solutions
Mixing Quantities
Since
We have
(9.41)
An irreversible (spontaneous) process at constant
T, P.
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Physical Chemistry
Solutions
Thermodynamic Properties of Ideal Solutions
Mixing Quantities
Since
We have
(9.41)
An irreversible (spontaneous) process at constant
T, P.
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Physical Chemistry
Solutions
Thermodynamic Properties of Ideal Solutions
Mixing Quantities
There is no heat of mixing on formation of an
ideal solution at constant T and P.
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Physical Chemistry
Solutions
Thermodynamic Properties of Ideal Solutions
Mixing Quantities
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Physical Chemistry
Solutions
Thermodynamic Properties of Ideal Solutions
Mixing Quantities in Summary
For an ideal solution, const. T, P
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Physical Chemistry
Solutions
Thermodynamic Properties of Solutions
Chemical Potential (?)
Raoults Law Henrys Law
Ideal Solutions Ideal Dilute Solutions
Ideal Solutions Non-ideal Solutions
departures
Activity
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Physical Chemistry
Solutions
Thermodynamic Properties of Ideal Solutions
Vapor Pressure
Two-phase system of solution in equilibrium with
its vapor.
(4.88)
(9.48)
(6.4)
(9.49)
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Physical Chemistry
Solutions
Thermodynamic Properties of Ideal Solutions
Vapor Pressure
Two-phase system of solution in equilibrium with
its vapor.
(9.48)
(9.49)
(9.50)
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Physical Chemistry
Solutions
Thermodynamic Properties of Ideal Solutions
Raoults law
(9.51)
ideal solution, ideal vapor, P is not very high
The partial pressure of substance i in the vapor
in equilibrium with an ideal liquid solution at T
The vapor pressure of pure liquid i at the same T
The mole fraction of i in the ideal solution
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Physical Chemistry
Solutions
Thermodynamic Properties of Ideal Solutions
Raoults law
ideal solution, ideal vapor, P is not very high
The (total) vapor pressure of the ideal solution
The sum of the partial pressure
For two-component solution,
(9.53)
(9.54)
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Physical Chemistry
Solutions
Thermodynamic Properties of Ideal Solutions
(9.54)
At fixed T
(pure C)
(pure B)
Fig. 9.18 (a)
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Physical Chemistry
Solutions
Thermodynamic Properties of Ideal Solutions
Some mixtures obey Raoults law very well,
especially when the components are chemically
similar.
Fig. 9.18 (a)
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Physical Chemistry
Solutions
Thermodynamic Properties of Ideal Solutions
Mixtures that obey Raoults law throughout the
composition range from pure A to pure B are
called ideal solutions.
Fig. 9.18 (a)
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Physical Chemistry
Solutions
Molecular Interpretation
The origin of Raoults law can be understood in
molecular terms by considering the rates at which
molecules leave and return to the liquid.
The law reflects that fact that the presence of a
second component reduces the rate at which A
molecules leave the surface of the liquid but
does not inhibit the rate at which they return.
blocked
Solute molecules
Solvent molecules
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Physical Chemistry
Solutions
Molecular Interpretation
The rate at which A molecules leave the surface
is proportional to the number of them at the
surface, which is in turn is proportional to the
mole fraction of A
A constant of proportionality
Rate of vaporization k xA
The rate at which molecules condense is
proportional to their concentration in the gas
phase, which in turn is proportional to their
partial pressure
Rate of condensation k PA
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Physical Chemistry
Solutions
Molecular Interpretation
At equilibrium, the rates of vaporization and
condensation are equal, hence
k xA k PA
It follows that
For the pure liquid, xA1, so
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Physical Chemistry
Solutions
Partial Molar Properties
(9.55)
These are consistent with
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Physical Chemistry
Solutions
Ideally Dilute Solutions
In ideal solutions the solute, as well as
solvent, obeys Raoults law. However, an ideal
solution occurs in the limit where the molecules
of the different species resemble one another
very closely.
A different kind of limit is where the solvent
mole fraction approaches 1, so that all solutes
are present in very low concentrations ? ideally
dilute solution.
In an ideally dilute solution, solute molecules
interact essentially only with solvent molecules
because of the high dilution of the solutes.
Fig. 9.19
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Physical Chemistry
Solutions
Ideally Dilute Solutions
(9.56)
solute in ideally dilute solution
(9.57)
solvent in ideally dilute solution
Thermodynamic definition
An ideally dilute solution is one in which the
solute and solvent chemical potentials are given
by (9.56) and (9.57) for a range of composition
with xA close to 1 and for a range of T and P.
As a real solution becomes more dilute, the
chemical potentials approach (9.56) and (9.57)
more closely.
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Physical Chemistry
Solutions
Thermodynamic Properties of Ideally Dilute
Solutions
Standard States
Solvent A pure A at T and P of the solution
Solutes
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Physical Chemistry
Solutions
Thermodynamic Properties of Ideally Dilute
Solutions
Solutes
The fictitious state at T and P of the solution
that arises by supposing that
holds for all values of xi and setting xi1.
The solution is essentially ideally dilute and
follows (9.58)
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Physical Chemistry
Solutions
Thermodynamic Properties of Ideally Dilute
Solutions
Since the properties of i in the dilute solution
depend very strongly on the solvent, the
fictitious standard state of solute i depends
on what the solvent is.
The fictitious standard state of solute i is a
state in which i is pure, but by some magical
means, each i molecule experiences the same
intermolecular forces it experiences in the
ideally dilute solution, where it is surrounded
by solvent molecules.
(9.59)
ideally dilute solution
(9.60)
ideally dilute solution
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Physical Chemistry
Solutions
Thermodynamic Properties of Ideally Dilute
Solutions
Standard states
Solvent pure liquid A at T and P of the solution
Solute i the fictitious state at T and P
obtained by taking the limit xi ? 1 while
pretending that (9.59) holds for all
concentrations.
Ideally dilute solutions and ideal solutions are
not the same!
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Physical Chemistry
Solutions
Thermodynamic Properties of Ideally Dilute
Solutions
Equations (9.59) and (9.60) hold only for high
dilution, whereas (9.42) holds for all solution
compositions.
The standard state for every component of an
ideal solution is the actual state of the pure
component at T and P of the solution, whereas the
standard state of each solute in ideally dilute
solution is fictitious.
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Physical Chemistry
Solutions
Thermodynamic Properties of Ideally Dilute
Solutions
Vapor Pressure
Two-phase system of solution in equilibrium with
its vapor.
(9.61)
Defining Ki as
(9.62)
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Physical Chemistry
Solutions
Thermodynamic Properties of Ideally Dilute
Solutions
Vapor Pressure
Equation (9.61) becomes
(9.63)
Solute in ideally dilute solution, ideal vapor
Henrys law states that the vapor partial
pressure of solute i above an ideally dilute
solution is proportional to the fraction of i in
the solution.
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Physical Chemistry
Solutions
Thermodynamic Properties of Ideally Dilute
Solutions
Raoults law (9.51) and Henrys law (9.63)
comparison
In both laws, the vapor-phase partial pressure of
the species is proportional to its mole fraction
in the solution.
Molecules of solute i in the ideally dilute
solution are in an environment different from
their environment in pure i.
In an ideal solution, the environment surrounding
a molecule is similar to that in the pure
substance.
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Physical Chemistry
Solutions
Thermodynamic Properties of Ideally Dilute
Solutions
P
Ideal/dilute solution (Henrys law)
When it is the minor component (the solute), its
vapor pressure is still proportional to mole
fraction, but the constant of proportionality is
now KA (Henrys law).
Ideal solution (Raoults law)
0
1
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Physical Chemistry
Solutions
Thermodynamic Properties of Ideally Dilute
Solutions
In an ideally dilute solution, the solvent obeys
Raoults law and the solutes obey Henrys law.
Fig. 9.21 (see next slide) shows large deviation
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Physical Chemistry
Solutions
Fig. 9.21
Deviations from Raoults law and Henrys law
(a) acetone-chloroform at 35oC
(b) acetone-CS2 at 29oC
Negative deviation
Positive deviation
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Physical Chemistry
Solutions
Solubility of Gases in Liquids
(9.65)
P not very high
The gas solubility is proportional to Pi above
the solution, provided that the solution is
ideally dilute.
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Physical Chemistry
Solutions
Partial Molar Quantities
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Physical Chemistry
Solutions
Homework
P277
Section 9.5 9.31, 9.32
P278
Section 9.6 9.39, 9.43, 9.44
P279
Section 9.8 9.48, 9.50
P279-280
General 9.62, 9.63, 9.67, 9.69