Molecular Weight Determination by Solution 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 vapour pressure

• elevation in boiling point

• depression in freezing point.

In simple terms, colligative properties depend on the number of solute particles and are 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 vapour 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:

1. When salt is added to water,

2. 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-

\[\Delta T_{f} = K_{f} * M\]

In this particular equation

\[\Delta T_{f} \] = depression in freezing point

\[K_{f}\] = 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:-

\[M = \frac{(1000 \times w_{2})}{w_{1} \times M_{2}}\]

In this equation,

weight of solute is \[w_{2}\]

the molar mass of solute is \[M_{2}\]

The weight of the solvent is \[w_{1}\].

Hence,

Freezing point depression is denoted by:-

\[\Delta T_{f} = \frac{(K_{f} \times 1000 \times w_{2})}{(w_{1} \times M_{2})}\]

Thus, the equation becomes

\[M_{2} = \frac{(K_{f} \times 1000 \times w_{2})}{(w_{1} \times \Delta T_{f})} \]

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.

\[\Delta T_{b} = Kbm \]

\[ \Rightarrow m = \frac{1000 \times w_{2}}{w_{1} \times M_{2}} \]

Hence, elevation in boiling point is expressed by

\[ \Delta Tb = \frac{K_{b} \times 1000 \times w_{2}}{w_{1} \times M_{2}} \]

Hence, the molecular weight of the solute becomes-

\[ M_{2}= \frac{K_{b} \times 1000 \times w_{2}}{w_{1} \times \Delta Tb} \]

Osmotic Pressure

The minimum amount of pressure 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.

\[\pi \] = CRT

In this equation,

\[\pi \] 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 \[w_{2}\] grams of solute, and the molar mass of the solute is \[M_{2}\]. The volume of the solution is V (in litres).

Hence, the molar concentration can now be expressed as-

\[ C = \frac{\frac{w_{2}}{M_{2}}}{V} = \frac{w_{2}} {(V \times M_{2})} \]  

So osmotic pressure is:

\[ \Pi  =  \frac{(w_{2}RT)}{(M_{2}V)}\]  

Hence the above equation can be rearranged as-

\[ M_{2} =  \frac{(w_{2}RT)}{(\pi V)}\]  

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 Vapour Pressure

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

This process of lowering in vapour 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 vapour phase, therefore, gets decreased. As a result, the pressure exerted by the vapour phase is also reduced. This phenomenon is called the relative lowering of vapour 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 vapour pressure of the solvent

According to Raoult's Law:

p=xq…………………………..(1)

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

\[ \Rightarrow  \Delta p = q - p\]

\[ \Rightarrow  \Delta p = q - qx\]

using equation(1)

using equation(1)

\[ \Rightarrow  \Delta p = q (1 - x)\]

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

\[ \Rightarrow \Delta p = qy\]

\[ y = \frac{p}{\Delta p}\]

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

State the Properties of the Polymers that influence their Molecular Weight.

The various properties of polymers that are used for the calculation of the molecular weight are Processability, that is, the suitability of the polymer to physical processing, Glass-transition temperature, that is, the transformation of a glass-forming liquid into a glass, solution viscosity, which refers to the measure of the resistance caused by a fluid when it is being deformed by either shear stress or tensile stress, Hardness, that is, the measure of how resistant a polymer is to various kinds of permanent shape change when a force is applied, Melt viscosity, which refers to the rate of extrusion of thermoplastics at a prescribed temperature and load through an orifice, Tear strength, that is, a measure of the polymers resistance to tearing, Tensile strength, that is, as indicated by the maxima of a stress-strain curve and, in general, is the point when necking occurs upon stretching a sample, Stress-crack resistance, that is, the formation of cracks in a polymer caused by relatively low tensile stress and environmental conditions, Brittleness, that is, the liability of a polymer to fracture when subjected to stress, Impact resistance, that is, the relative susceptibility of polymers to fracture under stresses applied at high speeds, Flex life, that is, the number of cycles required to produce a specified failure in a specimen flexed in a prescribed manner, Stress relaxation, that is, how polymers relieve stress under constant strain, Toughness, that is, the resistance to fracture of a polymer when stressed, Creep strain, that is, the tendency of a polymer to slowly move or deform permanently under the influence of stresses, Drawability, that is, The ability of fibre-forming polymers to undergo several hundred percent permanent deformation, under load, at ambient or increased temperatures, Compression is the result of compressive stress applied on the polymer, Fatigue, that is, the failure by repeated stress, Tackiness, that is, the property of a polymer being adhesive or gummy to the touch, Wear, that is, the erosion of material from the polymer by the action of another surface and Gas permeability, that is,  the permeability of gas through the polymer.