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Colligative Properties

Colligative properties are properties that depend only on the number (concentration) of solute particles present in a solution. These properties do not depend on the identity of the solute. As an example let's talk about two aqueous solutions; one containing glucose and the other containing urea. As far as the colligative properties are concerned, the two solutions are not different as long as the number of glucose and urea particles are the same. In other words, if the concentration of the given samples of urea and glucose are the same, the colligative properties of both solutions will be the same.

The colligative properties that you have to be familiar with for the MCAT are:
  1. vapor-pressure lowering
  2. boiling-point elevation
  3. freezing-point depression
  4. osmotic pressure generating

A simple solution is a mixture of a solute and a solvent.


Vapor-pressure Lowering

When a solvent contains impurities (solutes), there will be a reduction in its vapor pressure. This means the vapor pressure shown by a solvent when it is pure is lowered by the addition of solutes. The change in vapor pressure is proportional to the quantity of the dissolved solute. Raoult's law explains this relationship.
According to Raoult's law, the mole fraction of the solvent times the vapor pressure of the pure solvent is numerically equal to the vapor pressure of the solution. This is mathematically represented as shown below:


Here, PAis the vapor pressure of the solution (impure solvent),

XA is the mole fraction of the solvent, and

PA is the vapor pressure of the pure solvent.


Example 7-1

Calculate the mole fractions of sodium chloride and water in a solution containing 11.7 g of sodium chloride and 9 g of water.


In this solution, we have 11.7 grams of NaCl and 9 grams of H2O. First, you have to find the number of moles of NaCl and H2O.




The total number of moles in the solution = 0.2 + 0.5 = 0.7 mol



Boiling-point Elevation 

The boiling point of a liquid is defined as the temperature at which its vapor pressure equals the prevailing pressure. The prevailing pressure is normally the atmospheric pressure, provided that the container in which the liquid is present is kept open while boiling. When a nonvolatile solute is added to a pure solvent, the boiling point increases. The increase is proportional to the number of moles of the solute added to the solvent. The relationship is mathematically represented as shown below:

ΔTb = i Kb Cm


Here, ΔTbis the boiling-point elevation,


i is the ionization factor,


Kbis the boiling-point elevation constant, and


Cmis the molal concentration of the solution.




Calculate the boiling point of 0.2 m aqueous solution of glucose. (Kbof water is 0.512oC/m.)



The formula for finding the boiling-point elevation is:


ΔTb = i Kb Cm


In this problem, we have all the necessary values to find the boiling-point elevation. Here, the ionization factor is 1, since glucose doesn't ionize. Let's substitute the values into the formula.


ΔTb = Kb Cm= 0.512o C/m x 0.2 m≈ 0.1oC


The boiling point of 0.2 m solution of glucose is 100 + 0.1 = 100.1oC

Freezing-point Depression

The solute concentration affects the freezing point of a solvent. The freezing point of a pure solvent is decreased when solutes are added to it. Just like the boiling-point elevation, freezing-point depression is proportional to the molal concentration. The relationship is shown:

ΔTf = i Kf Cm


Here, ΔTfis the freezing-point depression,


i is the ionization factor,


Kfis the freezing-point depression constant, and


Cm is the molal concentration of the solution.




Calculate the freezing point of 2 m aqueous solution of glucose. (Kf of water is 1.86oC/m)



The formula for finding the freezing-point depression is:


ΔTf i Kf Cm


In this problem, we have all the necessary values to find the freezing-point depression. The ionization factor is 1.


ΔTf =Kf Cm = 1.86o C/m x 2 m 3.7oC


So the freezing point of 2m solution of glucose is 0.0 – 3.7 = – 3.7oC

Osmotic Pressure

Osmotic pressure is also a colligative property. Before we talk about osmotic pressure let's turn our attention to the process of osmosis. Consider two solutions that are made out of the same solvent with different concentrations of solute separated by a semipermeable membrane. The solvent will flow through the semipermeable membrane from the solution of lower concentration to the solution of higher concentration. Thus, osmosis is defined as the flow of solvent through a semipermeable membrane resulting in the equilibrium of concentrations on both sides of the semipermeable membrane.
We will explore the process of osmosis with an experiment. A dilute solution of sodium chloride is taken in a funnel. The mouth of the funnel is covered by a semipermeable membrane. The funnel is then placed upside down into a beaker which is filled with pure distilled water. The set up is done according to the diagram shown :


image\24821 Ch 7.png

Osmosis experiment

The arrow indicates the direction of flow of the solvent (H2O).
Water will flow into the funnel through the semipermeable membrane, and the liquid level of the funnel will gradually increase. The osmotic pressure is the pressure required or applied to the solution to stop the flow of the solvent, or in other words, to stop the process of osmosis. The osmotic pressure and concentration are related by the following equation:

Osmotic pressure, π = M R T


Here, M is the molar concentration of the solute,


R is the gas constant, and


T is the absolute temperature.


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