Applied Chemistery-I
Session 2009-10 , UET Lahore
Colligative properties
Colligative properties are properties of solutions that depend on the number of molecules in a given
volume of solvent and not on the properties (e.g. size or mass) of the molecules. Colligative properties
include: lowering of vapor pressure; elevation of boiling point; depression of freezing point and
osmotic pressure. Measurements of these properties for a dilute aqueous solution of a non-ionized
solute such as urea or glucose can lead to accurate determinations of relative molecular masses.
Alternatively, measurements for ionized solutes can lead to an estimation of the percentage of
ionization taking place.
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Lowering of vapour pressure
Elevation of Boiling Point
Depression of Freezing Point
Osmotic Pressure
Boiling-point elevation
Boiling-point elevation describes the phenomenon that the boiling point of a liquid (a solvent) will be
higher when another compound is added, meaning that a solution has a higher boiling point than a pure
solvent. This happens whenever a non-volatile solute, such as a salt, is added to a pure solvent, such as
water. The boiling point can be measured accurately using an ebullioscope.
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Explanation
The change in chemical potential of a solvent when a solute is added explains why boiling point
elevation takes place.
The boiling point elevation is a colligative property, which means that it is dependent on the presence
of dissolved particles and their number, but not their identity. It is an effect of the dilution of the
solvent in the presence of a solute. It is a phenomenon that happens for all solutes in all solutions, even
in ideal solutions, and does not depend on any specific solute-solvent interactions. The boiling point
elevation happens both when the solute is an electrolyte, such as various salts, and a nonelectrolyte. In
thermodynamic terms, the origin of the boiling point elevation is entropic and can be explained in
terms of the vapor pressure or chemical potential of the solvent. In both cases, the explanation depends
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Hasan Qayyum Chohan , Reg. No. 2009-CH-204
Chemical Engineering
UET Lahore
Applied Chemistery-I
Session 2009-10 , UET Lahore
on the fact that many solutes are only present in the liquid phase and do not enter into
the gas phase (except at extremely high temperatures).
Put in vapor pressure terms, a liquid boils at the temperature when its vapor pressure equals the
surrounding pressure. For the solvent, the presence of the solute decreases its vapor pressure by
dilution. A non-volatile solute has a vapor pressure of zero, so the vapor pressure of the solution is the
same as the vapor pressure of the solvent. Thus, a higher temperature is needed for the vapor pressure
to reach the surrounding pressure, and the boiling point is elevated.
Put in chemical potential terms, at the boiling point, the liquid phase and the gas (or vapor) phase have
the same chemical potential (or vapor pressure) meaning that they are energetically equivalent. The
chemical potential is dependent on the temperature, and at other temperatures either the liquid or the
gas phase has a lower chemical potential and is more energetically favourable than the other phase.
This means that when a non-volatile solute is added, the chemical potential of the solvent in the liquid
phase is decreased by dilution, but the chemical potential of the solvent in the gas phase is not affected.
This means in turn that the equilibrium between the liquid and gas phase is established at another
temperature for a solution than a pure liquid, i.e., the boiling point is elevated.
The phenomenon of freezing-point depression is analogous to boiling point elevation. However, the
magnitude of the freezing point depression is larger than the boiling point elevation for the same
solvent and the same concentration of a solute. Because of these two phenomena, the liquid range of a
solvent is increased in the presence of a solute.
Calculations
The extent of boiling-point elevation can be calculated by applying Clausius-Clapeyron relation and
Raoult's law together with the assumption of the non-volatility of the solute. The result is that in dilute
ideal solutions, the extent of boiling-point elevation is directly proportional to the molal concentration
of the solution according to the equation:
ΔTb = Kb · mB
where
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ΔTb, the boiling point elevation, is defined as Tb (solution) - Tb (pure solvent).
Kb, the ebullioscopic constant, which is dependent on the properties of the solvent. It can be
calculated as Kb = RTb2M/ΔHv, where R is the gas constant, and Tb is the boiling temperature
of the pure solvent [in K], M is the molar mass of the solvent, and ΔHv is the heat of
vaporization per mole of the solvent.
mB is the molality of the solution, calculated by taking dissociation into account since the
boiling point elevation is a colligative property, dependent on the number of particles in
solution. This is most easily done by using the van 't Hoff factor i as mB = msolute · i. The factor
i accounts for the number of individual particles (typically ions) formed by a compound in
solution. Examples:
o i = 1 for sugar in water
o i = 2 for sodium chloride in water, due to the full dissociation of NaCl into Na+ and
Clo i = 3 for calcium chloride in water, due to dissociation of CaCl2 into Ca2+ and 2Cl-
At high concentrations, the above formula is less precise due to nonideality of the solution. If the solute
is also volatile, one of the key the assumptions used in deriving the formula is not true, since it derived
for solutions of non-volatile solutes in a volatile solvent. In the case of volatile solutes it is more
relevant to talk of a mixture of volatile compounds and the effect of the solute on the boiling point must
be determined from the phase diagram of the mixture. In such cases, the mixture can sometimes have a
boiling point that is lower than either of the pure components; a mixture with a minimum boiling point
is a type of azeotrope.
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Hasan Qayyum Chohan , Reg. No. 2009-CH-204
Chemical Engineering
UET Lahore
Applied Chemistery-I
Session 2009-10 , UET Lahore
Ebullioscopic constants
Values of the ebullioscopic constants Kb for selected solvents:
Compound
Boiling point in
°C
Ebullioscopic constant Kb in units of [(K·kg)/mol] or
[K/molal]
Acetic acid
118.1
3.07
Benzene
80.1
2.53
Carbon disulfide
46.2
2.37
Carbon
tetrachloride
76.8
4.95
Naphthalene
217.9
5.8
Phenol
181.75
3.04
Water
100
0.512
Uses
Together with the formula above, the boiling-point elevation can in principle be used to measure the
degree of dissociation or the molar mass of the solute. This kind of measurement is called ebullioscopy
(Greek "boiling-viewing"). However, since superheating is difficult to avoid, precise ΔTb
measurements are difficult to carry out,[1] which was partly overcome by the invention of the
Beckmann thermometer. Furthermore, the cryoscopic constant that determine freezing-point depression
is larger than the ebullioscopic constant, and since the freezing point is often easier to measure with
precision, it is more common to use cryoscopy.
A common misuse of the effect of ebullioscopic increase leads to add salt when cooking pasta, only
after water has started boiling. The misconception is that otherwise it would take longer for water to
boil to elevate the temperature of the water before it boils. However, at the approximate dosage of
salting water for cooking (10 g of salt per 1 kg of water, or 1 teaspoon per quart), ebullioscopic
increase is approximately 0.17 C (0.31 F), but it is counteracted by the fact that at that concentration
salted water absorbs heat faster.
Freezing-point depression
Freezing-point depression describes the phenomenon that the freezing point of a liquid (a solvent) is
depressed when another compound is added, meaning that a solution has a lower freezing point than a
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Hasan Qayyum Chohan , Reg. No. 2009-CH-204
Chemical Engineering
UET Lahore
Applied Chemistery-I
Session 2009-10 , UET Lahore
pure solvent. This happens whenever a solute is added to a pure solvent, such as water.
The phenomenon may be observed in sea water, which due to its salt content remains
liquid at temperatures below 0°C, the freezing point of pure water.

Explanation
The change in chemical potential of a solvent when a solute is added explains why freezing point
depression takes place.
The freezing point depression is a colligative property, which means that it is dependent on the
presence of dissolved particles and their number, but not their identity. It is an effect of the dilution of
the solvent in the presence of a solute. It is a phenomenon that happens for all solutes in all solutions,
even in ideal solutions, and does not depend on any specific solute-solvent interactions. The freezing
point depression happens both when the solute is an electrolyte, such as various salts, and a
nonelectrolyte. In thermodynamic terms, the origin of the freezing point depression is entropic and is
most easily explained in terms of the chemical potential of the solvent.
At the freezing (or melting) point, the solid phase and the liquid phase have the same chemical
potential meaning that they are energetically equivalent. The chemical potential is dependent on the
temperature, and at other temperatures either the solid or the liquid phase has a lower chemical
potential and is more energetically favourable than the other phase. In many cases, a solute does only
dissolve in the liquid solvent and not in the solid solvent. This means that when such a solute is added,
the chemical potential in the liquid phase is decreased by dilution, but the chemical potential of the
solvent in the solid phase is not affected. This means in turn that the equilibrium between the solid and
liquid phase is established at another temperature for a solution than a pure liquid; i.e., the freezing
point is depressed.[1]
The phenomenon of boiling point elevation is analogous to freezing point depression. However, the
magnitude of the freezing point depression is larger than the boiling point elevation for the same
solvent and the same concentration of a solute. Because of these two phenomena, the liquid range of a
solvent is increased in the presence of a solute.
Calculations
The extent of freezing-point depression can be calculated by applying the Clausius-Clapeyron relation
and Raoult's law together with the assumption of the non-solubility of the solute in the solid solvent.
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Hasan Qayyum Chohan , Reg. No. 2009-CH-204
Chemical Engineering
UET Lahore
Applied Chemistery-I
Session 2009-10 , UET Lahore
The result is that in dilute ideal solutions, the extent of freezing-point depression is
directly proportional to the molal concentration of the solution according to the
equation
ΔTf = Kf · mB
where
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ΔTf, the freezing point depression, is defined as Tf (pure solvent) − Tf (solution), the difference between
the freezing point of the pure solvent and the solution. It is defined to assume positive values
when the freezing point depression takes place.
Kf, the cryoscopic constant, which is dependent on the properties of the solvent. It can be
calculated as Kf = RTm2M/ΔHf, where R is the gas constant, Tm is the melting point of the pure
solvent in kelvin, M is the molar mass of the solvent, and ΔHf is the heat of fusion per mole of
the solvent.
mB is the molality of the solution, calculated by taking dissociation into account since the
freezing point depression is a colligative property, dependent on the number of particles in
solution. This is most easily done by using the van 't Hoff factor i as mB = msolute · i. The factor
i accounts for the number of individual particles (typically ions) formed by a compound in
solution. Examples:
o i = 1 for sugar in water
o i = 2 for sodium chloride in water, due to dissociation of NaCl into Na+ and Clo i = 3 for calcium chloride in water, due to dissociation of CaCl2 into Ca2+ and 2 Clo i = 2 for hydrogen chloride in water, due to complete dissociation of HCl into H + and
Clo i = 1 for hydrogen chloride in benzene, due to no dissociation of HCl in a non-polar
solvent
At high concentrations, the above formula is less precise due to the approximations used in its
derivation and any nonideality of the solution. If the solute is highly soluble in the solid solvent, one of
the key assumptions used in deriving the formula is not true. In this case the effect of the solute on the
freezing point must be determined from the phase diagram of the mixture.
Cryoscopic constants
Values of the cryoscopic constant Kf for selected solvents:
Compound
Acetic acid
Benzene
Camphor
Carbon disulfide
Carbon tetrachloride
Chloroform
Cyclohexane
Ethanol
Ethyl ether
Naphthalene
Phenol
Water
Freezes at °C
16.6
5.5
179.8
−112
−23
−63.5
6.4
−114.6
−116.2
80.2
41
0
Kf at °C/m
3.90
5.12
39.7
3.8
30
4.68
20.2
1.99
1.79
6.9
7.27
1.86
Uses
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Hasan Qayyum Chohan , Reg. No. 2009-CH-204
Chemical Engineering
UET Lahore
Applied Chemistery-I
Session 2009-10 , UET Lahore
The phenomenon of freezing point depression is used in technical applications to avoid
freezing. In the case of water, ethylene glycol or other forms of antifreeze is added to
cooling water in internal combustion engines, making the water stay a liquid at temperatures below its
normal freezing point.
The use of freezing-point depression through "freeze avoidance" has also evolved in some animals that
live in very cold environments. This happens through permanently high concentration of
physiologically rather inert substances such as sorbitol or glycerol to increase the molality of fluids in
cells and tissues, and thus decrease the freezing point. Examples include some species of arctic-living
fish, such as rainbow smelt, which need to be able to survive in freezing temperatures for a long time.
In other animals, such as the spring peeper frog (Pseudacris crucifer), the molality is increased
temporarily as a reaction to cold temperatures. In the case of the peeper frog, this happens by massive
breakdown of glycogen in the frog's liver and subsequent release of massive amounts of glucose.
Together with formula above, freezing-point depression can be used to measure the degree of
dissociation or the molar mass of the solute. This kind of measurement is called cryoscopy (Greek
"freeze-viewing") and relies on exact measurement of the freezing point. The degree of dissociation is
measured by determining the van 't Hoff factor i by first determining mB and then comparing it to
msolute. In this case, the molar mass of the solute must be known. The molar mass of a solute is
determined by comparing mB with the amount of solute dissolved. In this case, i must be known, and
the procedure is primarily useful for organic compounds using a nonpolar solvent. Cryoscopy is no
longer as common a measurement method as it once was. As an example, it was still taught as a useful
analytic procedure in Cohen's Practical Organic Chemistry of 1910, in which the molar mass of
Naphthalene is determined in a so-called Beckmann freezing apparatus.
Freezing-point depression can also be used as a purity analysis tool when analysed by Differential
scanning calorimetry. The results obtained are in mol%, but the method has its place, where other
methods of analysis fail.
This is also the same principle acting in the melting-point depression observed when the melting point
of an impure solid mixture is measured with a melting point apparatus, since melting and freezing
points both refer to the liquid-solid phase transition (albeit in different directions).
In principle, the boiling point elevation and the freezing point depression could be used
interchangeably for this purpose. However, the cryoscopic constant is larger than the ebullioscopic
constant and the freezing point is often easier to measure with precision, which means measurements
using the freezing point depression are more precise
Osmotic pressure
Osmotic pressure on red blood cells
Osmotic pressure is the pressure that must be applied to a solution to prevent the inward flow of water
across a semipermeable membrane.
Jacobus Henricus van 't Hoff first proposed a formula for calculating the osmotic pressure, but this was
later improved upon by Harmon Northrop Morse.[citation needed]
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Hasan Qayyum Chohan , Reg. No. 2009-CH-204
Chemical Engineering
UET Lahore
Applied Chemistery-I
Session 2009-10 , UET Lahore
A related notion, osmotic potential is the opposite of water potential, is the degree to
which a solvent tends to stay in a liquid.
Morse equation
The osmotic pressure Π of a dilute solution can be approximated using the Morse equation (named
after Harmon Northrop Morse):
Π = iMRT,
where
i is the dimensionless van 't Hoff factor
M is the molarity
R=0.08206 L · atm · mol-1 · K-1 is the gas constant
T is the thermodynamic (absolute) temperature
This equation gives the pressure on one side of the membrane; the total pressure on the membrane is
given by the difference between the pressures on the two sides. Note the similarity of the above
formula to the ideal gas law and also that osmotic pressure is not dependent on particle charge. This
equation was derived by van 't Hoff.
Osmotic pressure is an important factor affecting cells. Osmoregulation is the homeostasis mechanism
of an organism to reach balance in osmotic pressure.
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Hypertonicity is the presence of a solution that causes cells to shrink. The solution may or
may not have a higher osmotic pressure than the cell interior since the rate of water entry will
depend upon the permeability of the cell membrane.
Hypotonicity is the presence of a solution that causes cells to swell. The solution may or may
not have a lower osmotic pressure than the cell interior, since the rate of water entry will
depend upon the permeability of the cell membrane.
Isotonic is the presence of a solution that produces no change in cell volume.
When a biological cell is in a hypotonic environment, the cell interior accumulates water, water flows
across the cell membrane into the cell, causing it to expand. In plant cells, the cell wall restricts the
expansion, resulting in pressure on the cell wall from within called turgor pressure.
Applications
Osmotic pressure is the basis of filtering ("reverse osmosis"), a process commonly used to purify water.
The water to be purified is placed in a chamber and put under an amount of pressure greater than the
osmotic pressure exerted by the water and the solutes dissolved in it. Part of the chamber opens to a
differentially permeable membrane that lets water molecules through, but not the solute particles. The
osmotic pressure of ocean water is about 27 atm. Reverse osmosis desalinators use pressures around 70
atm to produce fresh water from ocean salt water.
Osmotic pressure is necessary for many plant functions. It is the resulting turgor pressure on the cell
wall that allows herbaceous plants to stand upright, and how plants regulate the aperture of their
stomata. In animal cells which lack a cell wall however, excessive osmotic pressure can result in
cytolysis.
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Cell wall
Cytolysis
Gibbs-Donnan effect
Osmosis
Hasan Qayyum Chohan , Reg. No. 2009-CH-204
Chemical Engineering
UET Lahore
Applied Chemistery-I
Session 2009-10 , UET Lahore

 Pfeffer cell
 Plasmolysis
Turgor pressure
For the calculation of molecular weight by using colligative properties, osmotic pressure is the most
preferred property.
Potential osmotic pressure
Potential osmotic pressure is the maximum osmotic pressure that could develop in a solution if it were
separated from distilled water by a selectively permeable membrane. It is the number of solute particles
in a unit volume of the solution that directly determines its potential osmotic pressure. If one waits for
equilibrium, osmotic pressure reaches potential osmotic pressure.
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Hasan Qayyum Chohan , Reg. No. 2009-CH-204
Chemical Engineering
UET Lahore