CHE 102 Lecture Notes - Lecture 5: Freezing-Point Depression, Colligative Properties, Osmotic Pressure

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30 Oct 2017
Department
Course
Professor
Colligative properties
CH102 General Chemistry, Spring 2014, Boston University
There are four colligative properties.
• vapor-pressure lowering
• boiling-point elevation
• freezing-point depression
• osmotic pressure
Each of these properties is due to the effect of solute on entropy changes and so spontaneity. We will see that the cause of
each of the properties is changes necessary to keep free energy in balance.
à
Vapor-pressure lowering
Provided the amount of solute is small, that is, the mole fraction of the solvent is close to 1, the vapor pressure decreases
linearly with the solvent mole fraction
X1
,
P1=X1P°1
This is known as Raoult's law. If there is no solute at all, so that
X1=1
(pure solvent), then the vapor pressure
is
P°1
,
the vapor pressure of the pure solvent. We can rewrite this expression in terms of the solute mole fraction,
X2=1-X1
, as
P°1-P1=X2P°1
This relations shows that the solute mole fraction is the fractional change in pressure of the solvent.
X2=HP°1-P1LP°1.
That is, the reduction in solvent vapor pressure is proportional to the mole fraction.
-DP1=X2P°1
Entropy change
Vapor pressure is due to equilibrium between a solvent and its vapor. This equilibrium means that the free energy of the
solvent and vapor are equal,
Gvapor
0=Hvapor -T Svapor
0=Gsolvent =Hsolvent -T Ssolvent
We can rearrange this equality to see that the entropy of the vapor above the pure solvent,
Svapor
0
, exceeds the entropy of the
solvent by is
+DHvap T
,
Svapor
0=Ssolvent +Hvapor -Hsolvent
T=Ssolvent +DHvap
T
A way to understand this additional entropy is that it is due to the corresponding lowering of the entropy of the
surroundings by
-DHvap T
, because of the heat
DHvap
removed from the surroundings, necessary to provide the energy
for the vaporization.
Copyright © 2014 Dan Dill (dan@bu.edu). All rights reserved
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Adding solute to the pure solvent results in a solution with more arrangements than the pure solvent. This means that
adding solute to the pure solvent raises the entropy of the solution relative to that of the pure solvent. If we assume that the
concentration of the solute is very small so that its overall interaction with the solvent molecules is negligible, then the
enthalpy of the solvent is unaffected by the presence of the solute,
Hsolution =Hsolvent
This means that the entropy of the vapor over the solution must increase by the same amount as does the entropy of the
vapor over the solvent,
Svapor =Ssolution +Hvapor -Hsolution
T=Ssolution +Hvapor -Hsolvent
T=Ssolution +DHvap
T
Adding
DHvap T
to this higher initial entropy value means the entropy of the vapor is raised. This is illustrated in the
following diagram.
Adding non-volatile solute raises the entropy of the solvent vapor.
Increased vapor entropy corresponds to lower vapor pressure, that is, fewer particles in a given volume and so a greater
number of arrangements
W
.
Examples: Oxtoby and Nachtrieb, 3e, problem 4-44
The vapor pressure of diethyl ether (molar mass, 74.12 g/mol) at
30 °C
is 0.8517 atm. Suppose 1.800 g of maleic acid,
C4H4O4
, is dissolved in 100.0 g of diethyl ether at
30 °C
. Calculate the vapor pressure of diethyl ether above the resulting
solution.
Calculate that there are 1.349 mol ether and 0.01551 mol acid, and so that the ether mole fraction is 0.9886.
Calculate the ether vapor pressure. Answer: 0.8420 atm.
à
Boiling-point elevation
If we are at the boiling point, then
P°1=1
atm. This means that if we add any solute at all, boiling will stop, since
P
will
then be less than 1 atm. For boiling to resume, we must increase the temperature enough to offset the reduction in vapor
pressure from 1 atm. The text shows that the change in temperature needed to restore boiling is proportional to the solute
molality,
Tb¢-Tb=Kbm.
Here
Tb¢
is the new boiling point and
is the boiling point of the pure solvent;
is known as the boiling-point elevation
constant, and it must be determined experimentally for each solvent.
Colligative properties, CH102 General Chemistry, Spring 2014, Boston University 2
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