Physical Chemistry
Lecture 29
Solution Thermodynamics,
Concentrations, and Molar Quantities
Components, solutions and mixtures
Component

A substance added to form a solution or mixture
that can be independently varied
Solution


Material containing multiple components
interacting at the molecular level
Example: NaCl dissolved in water
Physical mixture


Material containing multiple components not
intermingled at the molecular level
Example: NaCl (s) + SiO2 (s)
Types of solutions
Liquid solutions

Usually the kind thought of when the phrase
arises
Solid solutions

Very important kind of solution because many
useful materials are solid solutions
 Example: brass
Gas mixtures are always solutions because
the interactions are molecule-molecule
Thermodynamic properties of
solutions
Thermodynamic properties depend on two intensive variables
and the amount of each material
H
= H (T , P, n1 , n2 )
Changes in thermodynamic properties depend on three variables
dH
 ∂H 
dT
= 

T
∂
 P ,n1 ,n2

= C P dT
 ∂H 
 ∂H 

dP + 
dn1
+ 

P
n
∂
∂

T ,n1 ,n2
 1 T , P , n2
+ V dP + H m1 dn1
 ∂H 

dn2
+ 
n
∂
 2 T , P ,n1
+ H m 2 dn2
Molar quantities are determined by the way in which
thermodynamic quantities change with addition of material

Molar quantities are related by the Maxwell relationship
 ∂H m1 


 ∂n2 T , P ,n1
 ∂H 
=  m 2 
 ∂n1 T , P ,n2
Relative amounts: concentration
descriptions of binary solutions
Mole ratio, r

Useful when the amount
of one component
relative to the second
affects the property
r
=
n1
n2
Mole fraction, X

Useful when the
fractional amount of one
component determines a
property, as in random
interactions
X2
=
n2
n1 + n2
Concentration measures for
liquid solutions
Solvent: the major component, usually
labeled “1”
Solute: the minor component, usually labeled
“2”
Molality, m

Number of moles of solute per kilogram of solvent
Molarity, c

Number of moles of solute per cubic decimeter of
solution
Relationships of concentration
measures
All measures of concentration describe
the same situation and are related
X2
1000 X 2
m =
M1 1 − X 2
1
=
1+ r
1000 ρ m
c =
1000 + ( M 2 − M 1 + 1) m
Mi is the molar mass of substance i, in
grams/mole
ρ is the density of the solution, in
grams/dm3
Partial Molar Quantities
Mixing process
nA + mB →
(n A
+ m B)
Change in a thermodynamic variable
such as volume
∆Vmixing
= Vsolution
− VA•
− VB•
•
= (n AV mA + nB V mB ) − (n AVmA
(
•
= n A V mA − VmA
)
(
•
+ nB V mB − VmB
)
•
+ nBVmB
)
Molar volumes in ethanolwater mixtures
Volume of aqueous sodium
chloride solutions
Volume of Aqueous Sodium Chloride Solutions
1140
1120
3
Volume (cm )
1100
1080
1060
1040
Lever rule
1020
1000
980
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
XNaCl
Solution volume changes with concentration
Lever rule gives the partial molar volumes
Determining partial molar
volumes from fits
Take derivative to find molar
volume of solute at each point
Find molar volume of solvent at
each point by
V
= nsolvent V solvent
+ nsolute V solute
Can be done in a computer easily
y = 0.4577x2 + 18.74x + 1002.6
R2 = 1
3
Volume (cm )
1150
1100
1050
1000
2
0
4
6
Molality
Molar Volumes in Sodium Chloride Solutions
3
V solute
 ∂V 

= 
 ∂nsolute  nsolvent
Volume of Sodium Chloride Solutions
Partial Molar Volume (cm )
Using the lever rule can be difficult
at times
Use the dependence of volume
(for a specific amount of solvent)
on number of moles of solute to
determine the partial molar
volume
Definition of partial molar volume
of the solute
22
21
20
19
18
0
2
4
Molality
6
Summary
Solutions more complicated than pure materials
Define the state of a solution by relative amount
of each component present


Several definitions of concentration
Choice of unit depends on the situation
Thermodynamic quantities depend on
concentration



Expressed by partial molar quantities
Partial molar quantities depend on relative amount of
each component
Related to differences in interactions at the molecular
level