## Determination of Molecular Weight of Non-Volatile Solute: An Introduction

The **cryoscopic** method is one of the best methods used to determine the molecular mass of a non-volatile solute, as we have, ΔTf=Kf.m where, ΔTf is calculated experimentally and Kf is constant and by using molality we can easily find the **molecular weight **of the solute particle. **Colligative properties** are those properties of solutions that depend on the ratio of the number of solute particles to the number of solvent particles in a solution, and not on the nature of the particles present.

## Determination of Molecular Weight of Non-Volatile Solute

Freezing point depression can be defined as the phenomenon of lowering the freezing point of any solvents after the addition of solutes. From this freezing point depression definition, it must be clear that this is a colligative property of solutions. In most cases, the freezing point formula is usually proportional to the molality of the solute that is added.

With the help of this knowledge, one can also conclude that the freezing point formula is as follows;

\[\Delta {T_f} = i \times {K_f} \times m\]

In this freezing point depression formula, ΔTf is the freezing point depression, i is the Van’t Hoff factor, kf is the Cryoscopic constant, and m is the molality.

Molality can be defined as the moles of solute dissolved in kg of solvent.

\[molality = \dfrac{{moles\;of\;solute}}{{mass\;of\;solvent}}\]

Moles of solutes are calculated by dividing the mass of the solute by the molecular mass of the solute.

Hence, molality becomes-

\[molality = \dfrac{{mass\;of\;solute}}{{molecular\;mass\;of\;solute \times mass\;of\;solvent}}\]

Therefore, the molecular mass of the molecular weight of the solute can be calculated as follows:

\[molecular\;mass\;of\;solute = \dfrac{{mass\;ofsolute}}{{molality \times mass\;of\;solvent}}\]

## Colligative Properties Calculations

There are four types of colligative properties-

1. Relative Lowering in vapour pressure

The relative lowering of vapour pressure is the rate of lowering of vapour pressure to the vapour pressure of the pure solvent.

\[\dfrac{{{P_ \circ } - {P_s}}}{{{P_ \circ }}} = {\chi _{solute}}\]

Where Po is vapor pressure of pure solvent, Ps is vapor pressure of the solution and Xsolute is the mole fraction of the solute.

2. Elevation in Boiling Point (ΔTb)

The boiling point of a liquid is the temperature at which its vapor pressure becomes equal to the atmospheric pressure. When a non-volatile solute is added to the solvent, the result always boils at an advanced temperature than the pure solvent. The difference between the boiling point of the result and the pure solvent is called elevation in boiling point.

ΔTb=Tb’ - Tb

Where \[\Delta {T_b}\]. is the elevation in boiling point, Tb’ is the boiling point of the solution and Tb is the boiling point of the solvent

\[\Delta {T_b} = i \times {K_b} \times m\]

Where i is van’t Hoff factor, M is molality and Kb is the ebullioscopic constant.

3. Depression in Freezing Point (ΔTf)

The freezing point of a solution is less than the freezing point of the pure solvent. This difference between the freezing point of solvent and solution is known as depression in freezing point.

ΔTf = Tf -Tf’

Where \[\Delta {T_f}\] is the depression in freezing point, Tf’ is the freezing point of the solution and Tf is the freezing point of the solvent.

\[\Delta {T_f} = i \times {K_f} \times m\]

ΔTf is the freezing point depression, i is the Van’t Hoff factor, kf is the

Cryoscopic constant, and m is the molality.

4. Osmotic Pressure (π)

Osmotic pressure is the minimum pressure that needs to be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane. The osmotic pressure can be calculated as follow;

\[\Pi = iCRT\]

Where ℼ is the osmotic pressure, i is Van’t Hoff factor C is the concentration of the solution, R is gas constant and T is the absolute temperature.

## Boiling Point and Molecular Weight

The Boiling Point (B.P.) of any organic emulsion depends on its molecular weight, if molecular weight increases, B.P. also increases. Generally, B.P. increases by adding the chain length by one carbon. If two compounds have the same molecular weight also there are different factors which determine the boiling point of the organic compounds. In the absence of other intermolecular forces, the more advanced the molecular mass the lesser the boiling point. The longer the alkyl chain like methane, ethane, propane, butane and so on, the more van der Waal force between molecules, and therefore the higher the boiling point.

## How to Find Molar Mass of Unknown Compound?

We can calculate the molar mass of an unknown compound by using its molarity and volume of solution and mass of the unknown compound. First, we have to calculate the moles of the unknown compound by using its molarity and volume of solution by using the following formula;

\[molarity = \dfrac{{moles\;of\;solute}}{{volume\;of\;solution}}\]

Hence,

\[moles\;of\;solute = molarity \times volume\;of\;solution\]

Now, we know that the number of moles is equal to the fraction of mass and molar mass. So, the molar mass of an unknown compound can be calculated as follow;

\[molar\;mass = \dfrac{{mass\;of\;unknown\;compound}}{{moles\;of\;unknown\;compound}}\]

Therefore, by using these formulas we can find out the molar mass of unknown compounds.

## Interesting Facts

Molecular weight can be determined by colligative properties calculation methods.

The boiling point of a compound increases with an increase in molecular weight.

## Key Features of Determination of Molecular Weight

As the molecular weight increases, mechanical properties increase.

The osmotic pressure method is the most suitable method for determining the molar mass of a polymer.

Molecular weight can be determined by different methods including cryoscopy, ebulliometry, viscometry etc.

## FAQs on Determination of Molecular Weight of Non-Volatile Solute

1. What are the molecular weight determination methods for polymers?

Molecular weight of polymers can be determined by chemical or physical methods of functional group analysis. They are measurements of colligative properties, light scattering, or ultracentrifugation.

2. Which is the most suitable method for determining molecular weights of proteins?

The method most frequently used to determine the molecular weight of the protein is ultracentrifugation.

3. What is molarity?

Molarity is defined as the moles of solute dissolved per litre of solution. The unit of molarity is g/mol.