Colligative properties are properties of solutions that depend on the number of molecules in a given volume of solvent and not on the properties/identity (e.g. size or mass) of the molecules. Colligative properties include: relative lowering of
vapor pressureVapor pressure or equilibrium vapor pressure is the pressure of a vapor in thermodynamic equilibrium with its condensed phases in a closed system. All liquids have a tendency to evaporate, and some solids can sublimate into a gaseous form...
;
elevation of boiling pointBoiling-point elevation describes the phenomenon that the boiling point of a liquid 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...
;
depression of freezing pointFreezing-point depression describes the phenomenon in which the freezing point of a liquid is depressed when another compound is added, meaning that a solution has a lower freezing point than a pure solvent. This happens whenever a non-volatile solute is added to a pure solvent, such as water...
and
osmotic pressureOsmotic pressure is the pressure which needs to be applied to a solution to prevent the inward flow of water across a semipermeable membrane....
. Measurements of these properties for a dilute
aqueous solutionAn aqueous solution is a solution in which the solvent is water. It is usually shown in chemical equations by appending aq to the relevant formula, such as NaCl. The word aqueous means pertaining to, related to, similar to, or dissolved in water...
of a non-ionized solute such as
ureaUrea or carbamide is an organic compound with the chemical formula CO2. The molecule has two —NH2 groups joined by a carbonyl functional group....
or
glucoseGlucose is a simple sugar and an important carbohydrate in biology. Cells use it as the primary source of energy and a metabolic intermediate...
can lead to accurate determinations of relative molecular masses. Alternatively, measurements for ionized solutes can lead to an estimation of the percentage of
ionizationIonization is the process of converting an atom or molecule into an ion by adding or removing charged particles such as electrons or other ions. This is often confused with dissociation. A substance may dissociate without necessarily producing ions. As an example, the molecules of table sugar...
taking place.
Vapor pressure
The relationship between the vapour pressure and concentration is given by
Raoult's law, which states that:
- The vapour pressure of an ideal solution
In chemistry, an ideal solution or ideal mixture is a solution with thermodynamic properties analogous to those of a mixture of ideal gases. The enthalpy of solution is zero as is the volume change on mixing; the closer to zero the enthalpy of solution is, the more "ideal" the behavior of the...
is dependent on the vapour pressure of each chemical component and the mole fraction of the component present in the solution.
(For details, see the article on
Raoult's law.) Colligative properties are mostly studied for dilute solutions.
Boiling point and freezing point
Both the boiling point elevation and the freezing point depression are proportional to the lowering of vapor pressure in a dilute solution
Boiling point elevation
- Boiling Pointtotal = Boiling Pointsolvent + ΔTb
where
- ΔTb = molality * Kb * i, (Kb = ebullioscopic constant
In thermodynamics, the ebullioscopic constant, Kb, allows one to relate molality to boiling point elevation. It is the ratio of the latter to the former:\Delta T = i\cdot K_b \cdot mi is the Vant Hoff factor...
, which is 0.512°C kg/mol for the boiling point of water; i = Van 't Hoff factorThe van 't Hoff factor i is a measure of the effect of a solute upon colligative properties, such as vapor pressure, osmotic pressure and freezing point depression. The van 't Hoff factor is the ratio between the actual concentration of particles produced when the substance is dissolved, and the...
)
Boiling point is achieved in the establishment of equilibrium between liquid and gas phase. At the boiling point, the number of gas molecules condensing to liquid equals the number of liquid molecules evaporating to gas. Adding any solute effectively dilutes the concentration of the liquid molecules, slowing the liquid to gas portion of this equilibrium. To compensate for this and re-attain the equilibrium, boiling point is achieved at higher temperature.
Any description of a colligative property which includes steric occlusion, or blocking of the surface to reduce the vapor pressure has no basis in reality, despite the fact that this explanation is frequently taught. This is also why vapor pressure and boiling point are independent of a liquid's accessible surface area.
Alternatively, measurements for ionized solutes can lead to an estimation of the percentage of ionization taking place.
Freezing point depression (cryoscopy)
Freezing Point
solution = Freezing Point
solvent - ΔT
f
where
- ΔTf = molality * Kf * i, (Kf = cryoscopic constant
In thermodynamics, the cryoscopic constant, Kf, allows one to relate molality to freezing point depression. It is the ratio of the latter to the former:\triangle T_f = K_f \cdot m \cdot i...
, which is 1.86°C kg/mol for the freezing point of water,; i = Van 't Hoff factorThe van 't Hoff factor i is a measure of the effect of a solute upon colligative properties, such as vapor pressure, osmotic pressure and freezing point depression. The van 't Hoff factor is the ratio between the actual concentration of particles produced when the substance is dissolved, and the...
)
Freezing point, or the equilibrium between a liquid and solid phase is generally lowered in the presence of a solute compared to a pure solvent. The solute particles cannot enter the solid phase, hence, fewer molecules participate in the equilibrium. Again, re-establishment of equilibrium is achieved at a lower temperature at which the rate of freezing becomes equal to the rate of liquefying.
The freezing point of a substance is defined as the temperature at which the vapor pressure of its liquid is equal to the vapor pressure of the corresponding solid. Since the addition of a non-volantile solute always lowers the vapor pressure of solvent, therefore, it will be in equilibrium with solid phase at a lower pressure and hence at a lower temperature. The difference between the freezing points of the pure solvent and the solution is called depression in freezing point or cryoscopy.
Osmotic pressure
Two laws governing the osmotic pressure of a dilute solution were discovered by the German botanist
W. F. P. PfefferWilhelm Friedrich Philipp Pfeffer was a German botanist and plant physiologist who was born in Grebenstein.- Academic career :...
and the Dutch chemist
J. H. van’t HoffJacobus Henricus van 't Hoff, Jr. was a Dutch physical and organic chemist and the first winner of the Nobel Prize in chemistry. He is best known for his discoveries in chemical kinetics, chemical equilibrium, osmotic pressure, and stereochemistry...
:
- The osmotic pressure
Osmotic pressure is the pressure which needs to be applied to a solution to prevent the inward flow of water across a semipermeable membrane....
of a dilute solution at constant temperature is directly proportional to its concentration.
- The osmotic pressure
Osmotic pressure is the pressure which needs to be applied to a solution to prevent the inward flow of water across a semipermeable membrane....
of a solution is directly proportional to its absolute temperature.
These are analogous to
Boyle's lawBoyle's law is one of many gas laws and a special case of the ideal gas law. Boyle's law describes the inversely proportional relationship between the absolute pressure and volume of a gas, if the temperature is kept constant within a closed system...
and
Charles's LawCharles' law is an experimental gas law which describes how gases tend to expand when heated. It was first published by French natural philosopher Joseph Louis Gay-Lussac in 1802, although he credited the discovery to unpublished work from the 1780s by Jacques Charles...
for gases. Similarly, the combined
ideal gas lawThe ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behavior of many gases under many conditions, although it has several limitations. It was first stated by Émile Clapeyron in 1834 as a combination of Boyle's law and Charles's law...
, PV = nRT, has an analog for ideal solutions:
- πV = nRTi
where: π = osmotic pressure; V is the volume; n is the number of moles of solute; R = .08206 L atm mol-1 K-1, the molar
gas constantThe gas constant is a physical constant which is featured in many fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation. It is equivalent to the Boltzmann constant, but expressed in units of energy The gas constant (also known as the molar, universal,...
; T is absolute temperature;
i =
Van 't Hoff factorThe van 't Hoff factor i is a measure of the effect of a solute upon colligative properties, such as vapor pressure, osmotic pressure and freezing point depression. The van 't Hoff factor is the ratio between the actual concentration of particles produced when the substance is dissolved, and the...
.
This can be simplified to π = "i"MRT (M = Molarity).