Physical Chemistry
Lecture 32
Ideal and Nonideal Solutions
Activities and ideal solutions
Activity and concentration
of a liquid solution related
by activity coefficient
Ideal solution properties
sensitive to concentration
as they change
statistically
For ideal solutions
γi
= 1
ai , liq
= γ X ,i X i
ai , liq
= γ c ,i
ci
ciθ
= γ m ,i
mi
miθ
ai , liq
Raoult’s law in the idealsolution limit
Activity determined by
statistics
No differential energies
of interaction between
components
Activities in the solution
and the gas are related

Gives a relation between
solution concentration
and gas partial pressure
Total pressure linear in
mole fraction
P1
=
X 1,liq P1•
P2
=
X 2,liq P2•
P = P1
= P1•
+ P2
+ ( P2• − P1• ) X 2
Ideal-solution example:
SiCl4 and CCl4
Almost ideal solution

Comes close to obeying
Raoult’s law for an ideal
solution
Molecules are quite
similar in structure

Replacing SiCl4 by CCl4
does not change the
energy structure
significantly
To be nearly ideal, the
partners must be very
similar in structure and
intermolecular
interactions
Negative deviations:
Acetone-chloroform solutions
Deviation from the ideal
Raoult law is negative
Molecules prefer to be
in solution
ΔmixingGexcess < 0
Strong attractive forces
between components
γ<1
Positive deviations:
CCl4-CH3OH solutions
Deviations from ideal
Raoult’s law are positive
Molecules prefer to be in
the gas phase above what
is expected statistically
ΔmixingGexcess > 0
Strong repulsive forces
between the components
γ<1
Regular-solution theory
Attempt to model deviations from
ideal solution
Additional chemical-potential
term proportional to X2
Deviations determined by
interaction energy, due to
differences in coupling between
like and unlike molecules
Activity coefficients determined
by interaction energy and
concentration
µ1 (T , X 1 ) = µ1ideal (T ) + wX 22
µ 2 (T , X 2 ) = µ 2ideal (T ) + wX 12
w = 2ε12
 wX 22 

γ 1 ( X 1 , T ) = exp

 RT 
 wX 12 

γ 2 ( X 2 , T ) = exp
 RT 
2
γ ( X ) 1.5
1
0
0.2
0.4
0.6
X
0.8
− ε11 − ε 22
1
Regular-solution interaction
energies
Interaction energies
range from positive to
negative values
Typical magnitude of
100-1000 joules
w is temperaturedependent
Only approximates real
behavior
Solution
T/K
w/J
CCl4-Benzene
298
324
Cyclohexane-Benzene
293
1275
Cyclohexane-CCl4
313
267
Benzene-toluene
353
-41
Carbon disulfide- acetone
308
4175
Summary
Raoult’s law (based on mole fractions) applies
to an ideal solution
Ideal solutions result from mixing two similar
materials
Most solutions are not ideal
Positive and negative deviations from Raoult’s
law determined by the nature of interactions
Regular-solution theory – attempt to model the
deviations from Raoult’s law with a simple
correction term in the chemical potential