Title: Chemistry 2402 - Thermodynamics
1Chemistry 2402 - Thermodynamics
Lecture 12 Kinetic coefficients and Linear
response Lecture 13 Non Ideal Solutions and
Activity Lecture 14 Chemical Equilibria
2Chemical Potential and Semi-Permeable Membranes
- A membrane that only allow passage of solvent
molecules only can result in a cell, when placed
in a dilute solution, swelling till it ruptures.
Or, when placed in a concentrated solution,
shrinking dramatically
3Osmotic Pressure
- Consider a solution and the pure solvent,
separated by a rigid semi-permeable membranes
that permits only the solvent to pass through.
Solution
Pure Solvent
Rigid semi-permeable membrane
Pressure
4Osmotic Pressure (cont.)
the volume per solvent molecule
So at equilibrium
Or
When x1 lt 1, we need to apply an additional
pressure ?P (or ?, the osmotic pressure) to
establish equilibrium and stop the flow of
solvent into the solution. Note that the chemical
nature of the solute is irrelevant (again) in the
ideal solution.
5Example Problem
- Calculate the osmotic pressure at 300K of an
aqueous sucrose solution at a sucrose mole
fraction of xsucrose 0.01. The volume per
molecule of water is 3.0 10-29 m3.
kB 1.381 10-23 JK-1
? 1.39 103 kPa or 13.7 atm !
6Flash Quiz!
- Why do your hands go wrinkly after a long time in
the water? - Is it better or worse in salty water?
7Answer
- Why do your hands go wrinkly after a long time in
the water? - Once any oil washes off the surface of your
hands, they become permeable to water. - Skin cells have a higher concentration of solutes
(e.g. salt) than the water outside. - Water flows osmotically into these cells, which
expand. - The skin wrinkles to accommodate the extra
surface area. - Is it better or worse in salty water?
- Salty water means the osmotic pressure inside and
out are more similar. The process occurs more
slowly.
8Non-Ideal Solutions
Acetone Chloroform (dashed lines indicate
Raoults Law predictions)
P Pacetone Pchloroform
Pacetone
Pchloroform
- a negative deviation from Raoults Law
- the result of additional attraction between the
different molecules
9Introducing the Activity of a Species
- For many solutions, Pi ? xi(liq) Pi.
- To describe these non-ideal solutions while
retaining the form of the ideal solution
equations, we define a new quantity called the
activity ai of species i as - ai(liq) Pi/Pi so that Pi ai(liq) Pi is
always true (by definition). - The activity can be thought of as the effective
mole fraction. - We define the activity coefficient ?i ai/xi.
- For an ideal solution, all ?i 1. In a
non-ideal solution ?i maybe greater or less than
1. For the case of acetone chloroform both ?is
are less than 1. -
10The Chemical Potential for a Non-Ideal Solution
- Replacing the mole fraction by the activity, we
have
We can take this, rather than ai Pi/Pi, as the
definition of the activity ai but we need to
understand that this means the definition of
activity depends on our choice of reference
state. For aqueous solutions we need to choose a
new reference state because many of the solutes
are not liquids at 1 atm in the temperature range
for liquid water
Where the reference state is a 1 molar solution
of the solute in water.
11Activity Coefficient depends on the Other
Molecules Present
The activity coefficient ?i depends on the
concentration of species i and what other species
are present.
In the case of chloroform, ?chloroform 1 at
chloroform mole fractions of 0 and 1 but is less
than one in between. Replace acetone by hexane
and the activity coefficient becomes closer to 1
over the whole concentration range.
12Phase Diagrams for Non-Ideal Solutions
Acetone Chloroform
A point where gas and liquid have the same
composition is called an azeotrope. Distillation
cannot work when the system is exactly at the
azeotrope.
13T-x Phase Diagrams
Azeotropes can arise from positive and negative
deviations from Raoults Law.
negative azeotrope
positive azeotrope
vapour
vapour
T
T
Toby Hudson
liquid
liquid
1
0
1
0
xA
xA
14Sample exam questions from previous years
- Consider a gas mixture at equilibrium with a
solution of the same species. - What is the relationship between chemical
potential and concentration in an non-ideal
solution?
15Summary
- You should now
- Understand the connection between the solubility
of a solid into an ideal solution, and the free
energy of melting that solid - Be able to explain the concept of osmosis and
osmotic pressure - Be able to calculate the osmotic pressure of a
solution - Understand the concept of activity, and the
activity coefficient - Qualitatively predict the deviations from ideal
behaviour in solutions with non-zero DHmix - Be able to explain the concept of an azeotrope,
and its role in distillation
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