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# Colligative Properties and Determination of Molar Mass

The presence of innumerable elements and substances around us present a unique opportunity to understand their properties. We need to study different properties of such matter because then it becomes easy to comprehend the nature and action of these substances. Determination of molar mass of such matter helps the most in learning the different properties of these substances.

Every matter, whether in solid or liquid or gaseous form, tends to behave in a certain way, which is highly dependent upon its properties. Therefore, all liquid substances can be studied in terms of their colligative properties. This helps in the study of the vapor pressure of the solution. So, let’s understand the colligative properties of matter and the determination of molar mass.

### Suggested Videos        Introduction to Colligative Properties Introduction to Abnormal Colligative Property Numericals on Elevation in Boiling Point ## Colligative Properties of Liquids

Colligative properties are those properties of a liquid which depend on the number of solute particles and not on the concentration of the solution. These properties are studied in liquids. As per these properties, the mixing of a non-volatile solution in a volatile solution shows a decrease in the relative vapour pressure of the solution.

Furthermore, this decrease in the vapour pressure can be further used to quantify and study the properties of all liquid solutions. Specifically, colligative properties are dependent upon the solute particles present in a given solution. Derived from the Latin word ‘Coligare’, the word, colligative refers to ‘binding together’.

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There are four colligative properties namely- relative lowering of vapour pressure, elevation of boiling point, depression of freezing point and osmosis and osmotic pressures. Related to these properties, the following deductions can be made:

### 1) Relative Lowering of Vapour Pressure

When a non-volatile solute is added to a solvent, the vapour pressure gets lower. This phenomenon is the lowering of vapour pressure. A relation between the pressure of the solution, the vapour pressure of the pure solvent and the mole fraction of the solute was discovered by a French Chemist.

It was also observed by him that it is mainly the concentration of the solute particles which was responsible for the lowering of vapour pressure. As per the laws devised by scientists at that time, Decrement in Vapour Pressure = Vapour Pressure of Pure Solvent – Vapour Pressure of Solvent. It is through this equation that we can determine the ultimate molar mass of a solute.

(Psolvent = Xsolvent Posolvent)

### 2) Elevation of Boiling Point

The vapour pressure of a solute tends to decrease as a non-volatile solute is added in a solvent. What is to be noted here is that the boiling point of such solution is always greater than the pure solvent in which it is added. This happens because the pressure of vapour is in direct proportion to the temperature of the solution.

If the solution is to be boiled, the temperature of such a solution has to be raised. This phenomenon comes to be identified as the elevation of boiling point. The solute particles in the solvent, along with the vapour pressure, together play a role in this phenomenon.

Formula: ΔT = iKbm

where ΔT= change in temperature
i = the van’t Hoff factor, which is the number of particles into which the solute dissociates
m = the molality, which is the moles of solute per kilograms of solvent
Kb = the molal boiling point constant (for water, Kb = 0.5121oC/m)

### 3) Depression of Freezing Point

Decreasing the vapor pressure of a solution results in decreasing the freezing of the solution as well. The freezing point of a solution can be identified as a point at which the vapor pressure of a given substance is equal in the liquid and vapor state. As per the law, the freezing point for a given dilute solution also stays directly proportional to molality of the solute, same as the boiling elevation point.

Formula: ΔT = iKfm

ΔT= change in temperature
i = the van’t Hoff factor, which is the number of particles into which the solute dissociates
m = the molality, which is the moles of solute per kilograms of solvent
Kf = the molal freezing point constant (for water, Kf = -1.86 oC/m)

### 4) Osmosis and Osmotic Pressure

You may have observed raw mangoes shriveling when placed in salt water or wilted flowers reviving when placed in fresh water. This happens due to a process called osmosis. Osmosis is the flow of solvent molecules from pure solvent to the solution through a membrane. The flow continues until equilibrium is reached.

The process of osmosis occurs through a membrane that looks continuous but contains small pores that allow small solvent molecules like water to pass through, but not bigger solute molecules. Such membranes are called semipermeable membranes (SPM).

The flow of solvent towards the solution side across the semipermeable membrane can be stopped by applying extra pressure on the solution. This pressure is known as the osmotic pressure of the solution.

Few important things to note –

• During osmosis, the solvent flows from the dilute (lower concentration) to concentrated (high concentration) side across the semipermeable membrane.
• Osmotic pressure depends on the concentration of the solution.

The osmotic pressure of a solution is the excess pressure applied to the solution to prevent osmosis. It is also a colligative property and depends on the number of solute molecules and not their identity.

For dilute solutions, osmotic pressure is directly proportional to the molarity (C) of the solution at a given temperature (T).

Π = C R T =  (n2/V) R T

where, Π – osmotic pressure, C – molarity, R – gas constant, T – temperature, V – a volume of solution in liters, n – the number of moles of solute.

Since n2 = w2/M2, then Π V = w2RT/M2 OR M2= w2RT/Π V

NOTE: The measurement of osmotic pressure is widely used to determine the molar masses of polymers, proteins, and other macromolecules.

## Usually, the measurement of boiling point elevation, freezing point depression or osmotic pressure, is used to calculate the molar mass or the molecular weight of a solute in a solution.

## Some Important Terms

Isotonic solutions are solutions that have the same osmotic pressure at a given temperature.

Hypotonic solutions are those that have a lower osmotic pressure than other solutions.

Hypertonic solutions are those that have a higher osmotic pressure than other other solutions. Isotonic, Hypotonic and Hypertonic solutions [Source: Wikimedia Commons]

## Solved Question for You

Q: Discuss the formula for the determination of molar mass.

Solution: Different aspects are to be considered for the determination of the molar mass of a solute in a solution. Here, let’s take a look at it now.

1. Firstly, change in boiling point –  ΔT = T solution – T pure solvent
2. Secondly, determining the molal concentration – Divide Delta T with constant of boiling point elevation.
3. Finally, determine the molar mass from the mass of an unknown number of moles. Further, for this, divide the mass of unknown with moles of the unknown.

Similarly, the molar mass can be determined from freezing point depression and osmotic pressure point of view. You can determine the moles of the unknown, from the molality of the solution. For this, multiply the molality with the mass of the solvent to determine the same. The same would also be followed in case of freezing point depression and osmotic pressure. Thus, the molar mass can be determined.

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