Chemistry 2402 - Thermodynamics

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Chemistry 2402 - Thermodynamics
Lecture 12 Kinetic coefficients and Linear
response Lecture 13 Non Ideal Solutions and
Activity Lecture 14 Chemical Equilibria
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Chemical 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
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Osmotic 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

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Osmotic 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.
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Example 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 !
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Flash Quiz!

• Why do your hands go wrinkly after a long time in
  the water?
• Is it better or worse in salty water?

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Answer

• 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.

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Non-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

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Introducing 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.

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The 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.
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Activity 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.
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Phase 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.
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T-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
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Sample 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?

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Summary

• 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

Next Lecture

• Chemical Equilibria