Physical Chemistry
Lecture 31
Raoult’s Law, Henry’s Law, Ideal and
Nonideal Solutions
Activity in solution
θ
µ liq (aliq , T ) = µ liq
(T ) + RT ln aliq
For any liquid system
The activity in the gas
phase is easily defined
Equilibrium solution
activity determined by
µ liq (aliq , T ) = µ gas (a gas , T )
phase equilibrium with
the vapor phase
Solution activity is
aliquid
θ
determined relative to
= exp(− (µ liq
− µ θgas ) / RT ) = K (T )
a
the activity of the vapor gas
at equilibrium
Phase equilibrium with an
ideal-gas phase
Generally activities in
aliq
phases are related by
equilibrium condition
Vapor pressure is a
measure of the gas’s
a gas
activity in ideal limit
Ideal-gas-limit activity
depends on the
ideal gas limit
aliq
definition of the gasphase standard state
= K a gas
=
P
θ
P
 P 
= K θ
P 
Raoult’s law
Pure-liquid standard state
Vapor pressure over pure
liquid P•
Determines the solution
activity relative to that of a
molecule in the pure liquid
Standard state: molecule’s
energy is dominated by
interactions with like
molecules
P
θ
RL
liq
a
= P
=
•
 P
 •
P 
Henry’s law
Dilute-solution case
derived from studies of
sparingly soluble gases
Imaginary standard state:
solute’s energy is
dominated by interactions
with solvent molecules
only
Henry’-law constant
obtained from solubility
HL
liq
K HL a
=
P
Pθ
Ideal solution
An imaginary solution in which the properties
are sensitive to the amount of material, but
only insofar as they change statistically with
composition
Activity changes mirror concentration
∆ mixing G ideal = n1 RT ln X 1 + n2 RT ln X 2
∆ mixing S ideal
= − n1 R ln X 1
∆ mixing H ideal
= 0
No enthalpy of mixing
These are statistical results
− n2 R ln X 2
Free energies of mixing in
nonideal solutions
A solution with negative
deviation of free energy of
mixing from that of ideal
solution
Molecules gain “stability” by
being in solution over what
they gain just by random
chance
A solution that deviates
positively has a higher free
energy of mixing than an ideal
solution

Molecules require more free
energy to be in solution than if
they were there by chance
Indications of interactions
between molecules
0
-200
-400
∆ G (joule/mole)

Deviation from Ideal Solution
-600
-800
-1000
-1200
-1400
-1600
-1800
-2000
0
0.2
0.4
0.6
0.8
1
Mole Fraction
Ideal Solution
Negative Deviation
Positive Deviation
Raoult’s law in the idealsolution limit
Activity determined by random statistics
Does not depend on differential energies of
interaction between components
•
1
P1 = X 1,liq P
P2 = X 2,liq P2•
P = P1 + P2
•
1
= P
•
2
•
1
+ (P − P ) X 2
Summary
Raoult’s law: activity relative to the situation in
a pure material
Henry’s law: activity relative to a dilute-solution
environment (imaginary state)
Ideal solution


No enthalpy of solution
All properties determined by statistics
Deviations from ideality are indicative of
molecular interactions in solution

Excess free energy