10
The pressure-composition phase diagram of acetone and CS2 at
45ºC.
Note:
The dashed lines represent the vapor pressures of acetone
and CS2 as well as the total vapor pressure if Raoult’s law is
obeyed.
Note:
both CS2 and acetone closely obey Raoult’s law only when
the mole fraction of the other component is very low.
Note:
This is an example of positive deviation from Raoult’s law
for both CS2 and acetone.
Why?
The ideal dilute solution and its relevance to real solutions 11
The ideal dilute solution is a limiting law for dilute real solutions.
1.
Consider an ideal dilute solution of liquid A as solvent (it is the
liquid present in the largest amount) and liquid B as solute (mole
fraction X of B is small).
μAsolvent = μA* + RT ln (PA/PA*) where PA = XAPA* as Raoult’s law is
obeyed.
2.
Consider a real dilute solution of liquid A as solvent and liquid B
as solute.
μAsolvent = μA* + RT ln (PA/PA*) where PA ≠ XAPA* as Raoult’s law is not
obeyed.
Define the activity a of the solvent
asolvent = Psolvent/P*solvent
Then, μsolvent = μ* + RT ln (asolvent)
In an ideal solution,
The activity of the solvent, asolvent = Xsolvent
Define the activity coefficient  of the solvent
solvent = asolvent / Xsolvent
Note: The activity co-efficient  quantifies the degree to which the
solution is non-ideal. As  values go to 1, the solution behaves more
ideally.
For all components “i” of a real solution,
μi = μi* + RT ln ai
In an ideal dilute solution, As Xsolvent → 1, the asolvent → 1
12
Consider a real solution of acetone and CS2 (See page 10)
Acetone obeys Raoult’s law in the limit that acetone → 1 and
→
0 In such a dilute solution, the average acetone molecule on the
surface is surrounded by other acetone molecules. Hence acetone
behaves nearly ideally.
General rule: Raoult’s law is closely obeyed by the solvent in a dilute
solution.
This limiting behaviour is also observed for CS2 in the limit that it is
the solvent. See figure on page 10.
Consider acetone in the limit that acetone → 0 i.e. acetone is the
solute The average acetone molecule at the surface of the solution is
surrounded by CS2 molecules and experience very different
interactions than when it is surrounded by acetone molecules.
As acetone → 0 Pacetone = Xacetone KHacetone
In general, Pi = Xi KHi (Henry’s law) – applies to solute in a dilute
solution. KH is called Henry’s law constant.
As the solution approaches ideal behaviour, KHi → Pi* for the solute
13
Definition of an ideal dilute solution (model). An ideal dilute solution
is a solution in which the solvent is described by Raoult’s law and the
solute is described using Henry’s law.
Important: Activities are defined with respect to Standard States.
Premise:
Activities are defined so that the solution components
approaches ideal behaviour in the limit of interest,
Either XA → 0 or XA → 1
The Raoult’s law standard state
Define
∗
They work best for solvent in a dilute
solution
∗
=
∗
=
∗
+ RT ln a solvent i
+ RT ln
∗
= the chemical potential of pure solvent (component i)
The Henry’s Law Standard State:
Henry’s law activity aiH
aiH =
Henry’s law activity co-efficient iH
 iH =
Note: The equations for the Henry’s law activity and the Henry’s law activity
co-efficient are only are only obeyed well for the solute in dilute solutions.
14
The Henry’s law standard state: A state in which the pure solute has a
vapor pressure equal to its Henry’s law constant KiH rather than its actual
value, P*solute. For a given solution component, KiH is determined by
extrapolation of the vapor pressure vs. mole fraction curve in the low mole
fraction range where Henry’s law is obeyed.
Note: The Henry’s law standard state is defined in this way to ensure that
asolute → 1 as Xsolute →0
It is a hypothetical standard state (i.e. it does not exist)!
Raoult’s law activity and activity co-efficient for CS2 in a CS2acetone solution
As Χ
→1
→ 1
→1
This shows that CS2 closely obeys Raoult’s law as a solvent in a
dilute solution.
15
Henry’s law activity and activity co-efficient for CS2 in a CS2acetone solution.
Note: Henry’s law activity co-efficient for CS2  → 1 as Χ
→0
This shows that CS2 clearly obeys Henry’s law in a dilute solution.
15(b)
Consider a CS2-acetone solution in which the mole fraction of CS2 is
0.0711 and the vapor pressures of CS2 and acetone above the
solution are 123.1 torr and 328.8 torr respectively.
Determine the activity and activity co-efficients for both CS2 and
acetone in the solution according to the definitions for Raoult’s law
and Henry’s law.
Relevant data follows:
P* CS2 = 512.3 torr P* acetone = 348.3 torr KH CS2 = 2010 torr KH
acetone = 1950 torr
Note: In this solution, CS2 is the _______and acetone is the ______
.