Title: Nonideal Solutions
1Chapter 10
Physical Chemistry
2Physical Chemistry
Solutions
Ideal Solutions
B-B, C-C
B-B, C-C, B-C
If B-B, C-C and B-C interactions are all different
3Physical Chemistry
Solutions
Nonideal Solutions
If B-B, C-C and B-C interactions are all different
The molecules of one type cluster together
Reorganization of the molecules orderly mixture
Separation is spontaneous
Liquids become immiscible or partially miscible
4Physical Chemistry
Nonideal Solutions
The Wide Significance of Chemical Potential
The chemical potential (?) does more than show
how G varies with composition.
A general infinitesimal change in U for a system
of variable composition can be written
At constant V and S
5Physical Chemistry
Nonideal Solutions
The Wide Significance of Chemical Potential
hence
In the same way, it is easy to deduce
6Physical Chemistry
Nonideal Solutions
Activity and Activity Coefficients
(10.1)
ideal or ideally dilute solution
(10.2)
ideal or ideally dilute solution
7Physical Chemistry
Nonideal Solutions
Activity and Activity Coefficients
When the solution is neither ideal nor ideally
dilute solution,
(10.3)
every solution
ai is defined as activity, a kind of effective
mole fraction.
(10.4)
every solution
8Physical Chemistry
Nonideal Solutions
Activity and Activity Coefficients
activity coefficient
The activity coefficient ?i measures the degree
of departure of substance is behavior from ideal
or ideally dilute behavior. The activity ai is
obtained from the mole fraction xi by correcting
for nonideality.
9Physical Chemistry
Nonideal Solutions
Activity and Activity Coefficients
Since ?i depends on T and P, and the mole
fraction xi, the activity ai and the activity
coefficient ?i depend on these variables
Note from (10.3) and (10.5) that ai and ?i are
dimensionless and nonnegative.
The task of thermodynamics show how ai and ?i
can be obtained from experimental data.
The task of statistical mechanics show how ai
and ?i can be found from the intermolecular
interactions in the solution.
10Physical Chemistry
Nonideal Solutions
Activity and Activity Coefficients
The activity ai is a measure of the chemical
potential ?i in the solution.
Like the chemical potential, ai is a measure of
the escaping tendency of i from the solution.
The activity ai is more convenient to use in
numerical calculations than ?i
11Physical Chemistry
Nonideal Solutions
Activity and Activity Coefficients
The activity ai is more convenient to use in
numerical calculations than ?i.
(a) we can not determine absolute value of ?i
(more relative values).
(c) ai can be compared with xi (and ?i with 1) to
judge the degree of nonideality.
12Physical Chemistry
Nonideal Solutions
Standard States for Nonideal-Solution Components
Convention I
(10.7)
for all components
Convention I is the same convention as that used
for ideal solutions.
is independent of the choice of standard state
depends on the choice of standard state
depends on the choice of standard state
13Physical Chemistry
Nonideal Solutions
Standard States for Nonideal-Solution Components
Convention I
(10.7)
for all components
depends on the choice of standard state
depends on the choice of standard state
depends on the choice of standard state
14Physical Chemistry
Nonideal Solutions
Standard States for Nonideal-Solution Components
Convention I
15Physical Chemistry
Nonideal Solutions
Standard States for Nonideal-Solution Components
Convention I
Since the Convention I standard state of each
solution is the pure substance, the Convention I
standard state thermodynamic properties of i
equal the corresponding properties of pure i.
Convention I puts all the components on the same
footing and does not single out one component as
the solvent.
Convention I is often called the symmetrical
convention.
16Physical Chemistry
Nonideal Solutions
Standard States for Nonideal-Solution Components
Convention II
Convention II is often called the unsymmetrical
convention.
Convention II is chosen when one wants to treat
one solution component (the solvent A)
differently from the other components (the
solutes i).
Common cases are solid or gases solutions in a
liquid solvent
The Convention II standard state of the solvent A
is pure liquid A at the T and P of the solution.
17Physical Chemistry
Nonideal Solutions
Standard States for Nonideal-Solution Components
Convention II
(10.9)
For each solute i?A, Convention II chooses the
standard state so that ?II,i goes to 1 in the
limit of infinite dilution
(10.10)
18Physical Chemistry
Nonideal Solutions
Standard States for Nonideal-Solution Components
in the standard state
When xA is near 1 and the solute mole fractions
are small, then by (10.10) the activity
coefficient ?II,i, is close to 1.
We choose the standard state of each solute i as
the fictitious state.
19Physical Chemistry
Nonideal Solutions
Standard States for Nonideal-Solution Components
The Convention II solute standard state is the
same as that used for solutes in an ideally
dilute solution.
The deviations of ?II,A and ?II,i from 1 measure
the deviation of the solutions behavior from
ideally dilute behavior.
20Physical Chemistry
Nonideal Solutions
Excess Functions
The thermodynamic properties of nonideal (real)
solutions may be expressed in terms of the excess
functions, the difference between the observed
thermodynamic function of solution and the
function for a hypothetical ideal solution.
(10.11)
(10.12)
21Physical Chemistry
Nonideal Solutions
Excess Functions
Excess functions are found from mixing quantities.
22Physical Chemistry
Nonideal Solutions
Regular Solution
Deviations of the excess functions from zero
indicate the extent to which the solutions are
non-ideal. In this connection, a useful model
system is the regular solution.
when
or
then
Regular solution
A regular solution can be thought of as one in
which the two kinds of molecules are distributed
randomly (as in an ideal solution) but have
different energies of interaction with each other.
23Physical Chemistry
Nonideal Solutions
Regular Solution
note
excess chemical potential
In a regular solution, ln?i is proportional to
the inverse of T.
24Physical Chemistry
Nonideal Solutions
Athermal Solution
when
or
then
Athermal solution
The nonideality of regular solution is caused by
the enthalpy effect (due to HE ? 0).
The nonideality of athermal solution is caused by
the entropy effect (due to SE ? 0).
25Physical Chemistry
Nonideal Solutions
Athermal Solution
then
In an athermal solution, ln?i is independent of
T.
26Physical Chemistry
Nonideal Solutions
Determination of activities and activity
coefficients
From data on phase equilibriua
From vapor-pressure measurements
Convention I
27Physical Chemistry
Nonideal Solutions
Determination of activities and activity
coefficients
ideally dilute solution
nonideal solution
Convention II
(10.15)
for i ? A, ideal vapor
(10.16)
ideal vapor, P not very high
Vapor measurements find Ki since ?II,i1 in very
dilute solution
and
28Physical Chemistry
Nonideal Solutions
The Gibbs-Duhem Equation
The use of
29Physical Chemistry
Nonideal Solutions
The Gibbs-Duhem Equation
The Gibbs-Duhem equation
The significance of Gibbs-Duhem equation is that
the chemical potentials of a mixture cannot
change independently in a binary mixture, if one
increases the other must decreases. The same
applies to all partial molar quantities.
30Physical Chemistry
Nonideal Solutions
Activity Coefficients
On the Molality Scale
(10.23)
The molality of solute i
mo ? 1 mol/kg
31Physical Chemistry
Nonideal Solutions
Activity Coefficients
mo ? 1 mol/kg
dimensionless
define
(10.24)
(10.25)
(10.26)
The molality-scale activity coefficient of solute
i
The molality-scale standard state chemical
potential of i
32Physical Chemistry
Nonideal Solutions
Activity Coefficients
extrapolation
Ideally dilute solution
33Physical Chemistry
Nonideal Solutions
Standard States for Nonideal-Solution Components
Similarly, solute molality-scale standard-state
properties
The mole-fraction scale for solvent A
34Physical Chemistry
Nonideal Solutions
Activity Coefficients
On the Molar Concentration Scale
(10.23)
(10.29)
co ? 1 mol/dm3
The mole-fraction scale is used for solvent.
(10.30)
35Physical Chemistry
Nonideal Solutions
Activity Coefficients
Henrys-law activity coefficients
measure deviations from Henrys law
Raoults-law activity coefficient
measure deviations from Raoults law
Fig. 10.6
36Physical Chemistry
Nonideal Solutions
Summary of Standard States Chemical Potentials
Table 11.1 (P. 333, part)
37Physical Chemistry
Nonideal Solutions
Homework
P314, Section 10.1
10.2, 10.3
P315, Section 10.2
10.4
P315, Section 10.3
10.6, 10.8
P315, Section 10.4
10.12, 10.13