Molecular Weight Determination Using Solution Colligative Properties

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Colligative Properties Definition


Colligative Properties: 

The properties that are dependent on the concentration of the solute ions of solute molecules are called colligative properties. It is important to note that colligative properties are independent of the identity of the solute.


Molecular Weight: 

It is also known as molecular mass. Molecular mass is nothing but the sum of each atomic mass of each atom present in a molecule.


Types of Colligative Properties

  • osmotic pressure

  • lowering of vapor pressure

  • elevation in boiling point

  • depression in freezing point.

In simple terms, colligative properties depend on the number of solute particles and independent of the identity of the solute particles.


Colligative properties of the solution are used to determine the molecular mass of different compounds. As the colligative properties of a solution depend only on the number of molecules of the solute, this method is mainly used to find out the molar masses of proteins, polymers, macromolecules, and complex molecules.


In a solvent, the solution of the given concentration of the substance is made. The freezing point or vapor pressure, or boiling point of that solvent is given to us. The property under calculation is chosen so that its measurement is done pretty conveniently under the allotted conditions, and thus, the variation is minimalistic.


The colligative properties under consideration are looked into in detail. And from this analysis, we will find out how molecular weight is calculated with the help of these properties.


Depression In Freezing Point:

Depression in freezing point is nothing but a lowering of the solvent's freezing point when a particular solute is added to it. The solute must be non-volatile.


Examples:

a. When salt is added to water,

b. When alcohol is added to water.

The resultant solution or mixture possesses a relatively lower freezing point than that of a pure solvent. The depression in freezing point and molal concentration of the solution's solute are directly proportional to each other.

The equation expresses this depression in freezing point-

ΔTf = Kf × m.

In this particular equation

ΔTf = depression in freezing point

Kf = The Freezing Point Constant

m = molal concentration of the solution.

Molality is nothing but the number of moles of solute per kg of solvent.

But, we now know that molality is given by:-

M = (1000 × w2) ÷ (w1 × M2)

In this equation,

weight of solute is w2

the molar mass of solute is M2

The weight of the solvent is w1.

Hence,

Freezing point depression is denoted by:-

ΔTf = (Kf × 1000 × w2) ÷ (w1 × M2)

Thus, the equation becomes

M2 = (Kf × 1000 × w2) ÷ (w1 × ΔTf)

In this way, the molecular weight of the solute is computed.


Elevation in Boiling Point

Elevation in boiling point is nothing but the elevation of the solvent's boiling point when a particular solute is added to it. The solute must be non-volatile. The elevation in boiling point and molal concentration of the solution's solute are directly proportional to each other.

ΔTb = Kbm

⇒m = (1000 × w2) ÷ (w1 × M2)

Hence, elevation in boiling point is expressed by

ΔTb  = (Kb × 1000 × w2) ÷ (w1 × M2)

Hence, the molecular weight of the solute becomes-

M2 = (Kb × 1000 × w2) ÷ (w1 × △Tb)


Osmotic Pressure:

The minimum amount of pressure which is sufficient to prevent the movement of a fluid through a semipermeable membrane. It can also be defined as the measurement of the tendency of a solution to take in pure solvent through osmosis.

π = CRT

In this equation,

π is the osmotic pressure

C is the molar concentration of the solution

R is the Universal gas constant and

T is the Temperature.

Let us consider that the solution contains w2 grams of solute, and the molar mass of the solute is M2. The volume of the solution is V (in liters).

Hence, the molar concentration can now be expressed as-

C = (w2/M2) ÷ V = w2 ÷ (V × M2)

So osmotic pressure is:

Π = (w2RT) ÷ (M2V)

Hence the above equation can be rearranged as-

M2 = (w2RT) ÷ (πV)

Therefore, calculating the molecular weight of a substance using the solution's colligative properties is an easy process.


The three above mentioned processes discussed give us the options applied based on the type of substance and the nature of the solvent, and the extent of accuracy required during the calculation.


Relative Lowering of Vapor Pressure

After the addition of the solute, the resultant solution's vapor pressure is found to be relatively lower than that of a pure liquid at a particular temperature.


This process of lowering in vapor pressure is because after adding the solute to the pure liquid, that is, solvent, the liquid surface now consists of the molecules of the pure fluid and the solute.


The number of solvent molecules escaping into the vapor phase, therefore, gets decreased. As a result of the pressure exerted by the vapor phase is also reduced. This phenomenon is called the relative lowering of vapor pressure.


Let us take a binary solution. In this solution, the mole fraction of the solvent is x, and that of the solute is y, p is the vapor pressure of the solvent

According to Raoult's Law:

p=xq…………………………..(1)

The relative lowering in vapor pressure of the solvent (∆p) is given by:

=> ∆p = q-p

=> ∆p = q-qx        [using equation (1)]

=> ∆p = q (1-x)

But we have taken that the solution is a binary solution, y = 1-x.

=> ∆p = qy

=> y = p/∆p

Thus from this equation, the mole fraction is calculated. And from the mole fraction, the molecular weight of the solute is calculated.

FAQ (Frequently Asked Questions)

Q1: Colligative Properties are Dependent on What?

Ans: The properties that are dependent on the concentration of the solute ions of solute molecules are called colligative properties. It is important to note that colligative properties are independent of the identity of the solute. However Colligative properties of solutions are the properties that are mainly dependent upon the concentration of solute ions or molecules. They are not dependent on the identity of the solute itself.

Q2: What is the Use of Colligative Properties in Daily Life?

Ans: Colligative properties play a very crucial role in freezing point depression. Generally, automobiles use anti-freezers with a very low freezing point, which will help operate automobile engines. The process of Osmosis is very much helpful in the biological system because of the membrane's semipermeability nature. The method of Osmosis is very beneficial in body mechanism as it helps in the absorption of nutrients in different body parts. Removal of waste products from the body is also possible through Osmosis.