Colligative Properties and Determination of Molar Mass

Colligative properties are those properties of any solution that doesn’t depend on the nature of solute but a total number of solute particles only. Colligative is a term derived from coligare, which is a Latin word. The meaning of coligare is to bind together. We can classify the colligative properties into four, or in other words, there are four kinds of colligative properties such as:

• Osmotic and osmosis pressure
• Elevation in the boiling point
• Relative lowering of the vapor pressure
• Freezing point depression

We will now look into colligative properties and the determination of molar mass in detail.

Osmotic and osmosis pressure

Osmosis can be described as a process that allows liquid to flow via a semipermeable membrane. It allows only solvents to pass through the semipermeable membrane. Some examples would help in understanding the meaning of the term membrane-like blood cells are destroyed when they are kept in a solution of salt and water and raw mangoes when kept in a brine solution to make pickles they get shrined. Thus you might have understood by now that a membrane is nothing but a film or a sheet that allows only some substance to pass through it. The membrane could also be found naturally, for instance, in the bladder of a pig, and it can also be artificial, for instance, cellophane.

A semipermeable membrane allows solvent molecules to pass  through it. It does not allow bigger molecules to pass through it.

Osmotic pressure is the extra pressure added which stops the solvents from flowing. In other words, osmotic pressure is the pressure exerted to prevent the process of osmosis via a semipermeable membrane. 

Mathematically we can write it as follows:

π=CRT

In this equation

π is used to denote osmotic pressure

C is used to denote molar concentration of solution

R represents the universal gas constant

T is used to denote the temperature 

Let us now derive molar mass from colligative properties.

A solution has w2 grams of solute, the molar mass of this solute is M2, the volume of this solution is V. Now we can write the molar concentration of this solution as:

C = w2/m2 / V = w2/ v.m2

Therefore the osmotic pressure will be 

π = w2RT/ m2V

Once this equation is rearranged we will get the following:

M2 = w2RT/πV

Elevation in the boiling point

Adding non volatile solute in the solvent decreases the vapor pressure of the solvent. But the solution’s boiling point will be higher as compared to the pure solvent. This is because the vapor pressure is in direct proportion with the temperature. We all know that to boil any solution it is important to bring the solution to a certain temperature. The increase in temperature is known as the Elevation in the boiling point. Let us now see colligative properties and determination of molar mass.

Mathematical representation of Elevation in the boiling point which is proportional to the molar concentration can be written as:

ΔTb = Kbm

In this equation,

ΔTb is used to denote Elevation in the boiling point

Kb is used to denote the constant of the boiling point elevation

M is used to denote the solution’s molar concentration

Let us assume that:

Weight of the solute = w2

Molar mass of the solute = m2

Weight of the solvent = w1

Thus we can write morality as follows:

m = moles of solute/ mass of solvent (expressed in kg) = w2/m2 / w1/1000

m = 1000 x w2 / w1 x m2 

Thus we can write boiling point elevation as follows:

ΔTb = Kb x 1000 x w2 / w1 x ΔM2

 On rearranging this equation we will get the following :

M2 = Kb x 1000 x w2 / w1 x ΔTb

This equation gives us the relationship between this colligative property and molecular weight.

Relative lowering of the vapor pressure

We will now look at the third colligative property in detail.

When a non volatile solute is added to the solvent the vapor pressure is reduced. This is known as the Relative lowering of the vapor pressure. The solute particles are generally responsible for Relative lowering of the vapor pressure.

If we assume that the solution’s vapor pressure to be P1 and solvent’s vapor pressure to be P10. Let the solvent’s mole fraction be x1 then 

P1 = p10 x1 (according to the raoult’s law)

The reduction in solvent’s vapor pressure Δp2 can be written as:

Reduction in vapor pressure = pure solvent’s vapor pressure – solvent’s vapor pressure 

Thus,

Δ P10 = P10 – P1

When we will substitute P1 = P10 x1 we will get the following:

Δ P1 = P10 – P10 x1

Δ P1 = P1 (1 – x1)

We know that the sum of solven’s mole fraction (x2) and solute’s mole fraction is 1 therefore we can write:

1 – x1 = x2

Δ P1 = P10 x2

Thus, we can say that lowering of vapor pressure is dependent on the solute’s mole fraction.

We can rewrite the equation as follows:

ΔP1/ P10 = X2

ΔP1/ P10 is known as the relative lowering of the vapor pressure which is equal to the solute’s mole fraction.

Freezing point depression

Another colligative property is freezing point depression. We will again determine molar mass from colligative properties.

We all know that freezing point depression can be expressed as follows:

ΔTb = Kfm

In this equation,

ΔTf is used to denote the freezing point depression

Kf is used to denote the constant of the freezing point.

m denotes the molar concentration 

We also know that molarity can be expressed as follows:

m = 1000 x w2/ w1 x m2

Thus, we can express freezing point depression as follows:

ΔTf = Kf x 1000 x w2/ w1 x ΔTf

Thus we can calculate molar mass using this property also.

This was all about colligative properties and determination of molar mass. You now know about all the colligative properties i.e Osmotic and osmosis pressure, Elevation in the boiling point, Relative lowering of the vapor pressure and Freezing point depression. To know more about other related topics make sure to check our website.

Conclusion

Colligative properties are those properties of any solution that doesn’t depend on the nature of solute but a total number of solute particles only. Colligative is a term derived from coligare, which is a Latin word. Osmosis can be described as a process that allows liquid to flow via a semipermeable membrane. It allows only solvents to pass through the semipermeable membrane.