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 will determine molar mass from colligative properties. One such colligative property is freezing point depression. According to Raoult’s law, when in a solvent, a non-volatile solid is added, its vapour pressure decreases. After that, it would come to be equal to that solid solvent at a lower temperature. Therefore, the disparity between the pure solvent’s freezing point and its solution is known as the depression in freezing point.

Depression In Freezing Point

The depression of  freezing point is a colligative property due to the addition of solute molecules to any solvent. So, to be very precise, depression of freezing point is a term that refers to lowering of the freezing point of solvents due to the addition of solute molecules to it. Due to a decrease in temperature, a substance starts freezing and its intermolecular forces take over, arranging themselves in a pattern and eventually turning into solid. Let us take an example to have a better understanding when we keep water to cool whether the temperature is below the freezing point of water -the hydrogen bonding begins to stick more and thus result in the formula for depression of freezing point:

△Tf  = i  x Kf x m

Here, 

△Tf stands for depression of freezing point,

 i  stands for Van’t Hoff Factor,

 Kf stands for cryoscopic constant and,

 m represents molality.

In all cases, the solute is the material that has been added or is present in smaller amounts, whereas the solvent is the original component that is present in larger amounts. As a result, the freezing point temperature of a mixed solution or solid-solid combination is lower than that of a pure solvent or solid. In addition, the mixture’s solvent has a lower chemical potential than the pure solvent, which is proportional to the mole fraction.

A comparable phenomenon occurs when the chemical potential of vapour over a solution is lesser than that of vapour above a pure solvent, increasing to the boiling point. At temperatures below 0 °C (32 °F), the freezing point of pure water, freezing-point depression causes seawater (a combination of salt and other chemicals in water) to remain liquid.

The Freezing Point Constant (Kf)

The concentration of the solute determines the freezing point depression. The concentration of a solution is measured by its molality, which is defined as:

molality=  Moles of solute / kilograms of solvent 

The molal concentration of the solution is denoted by the letter m. The amount of moles of solute per kg of a solvent is known as molality. However, we now understand that molality is determined by:

M = (1000 × w2) ÷ (w1 × M2)

In this scenario,

The molar mass of the solute is M2, and its weight is w2.

The solvent weighs w1.

Hence,

The term “freezing point depression” is defined as follows:

ΔTf = (Kf × 1000 × w2) ÷ (w1 × M2)

As a result, the equation becomes:

M2 = (Kf × 1000 × w2) ÷ (w1 × ΔTf)

The molecular weight of the solute is calculated in this way.

The calculation for dilute solutions

When the solution is viewed as an ideal solution, the amount of the freezing-point depression is only determined by the solute concentration, which can be evaluated using a simple linear connection with the cryoscopic constant (“Blagden’s Law”):

ΔTf = Kf · b · i

where,

• The freezing-point depression is defined as Tf (pure solvent).
• The cryoscopic constant, Kf, is determined by the solvent’s characteristics rather than the solute’s. (Note: A higher KF number makes it easier to see bigger reductions in the freezing point while doing tests.) Kf = 1.853 Kg/mol for water.] ).
• The molality is denoted by the letter b. (moles solute per kilogramme of solvent).

freezing point depression importance:

1. In cold areas where the temperature drops below 0°C, sodium chloride (NaCl) is spread over the roads to prevent ice formation. NaCl lowers the freezing point of water. Hence, ice doesn’t accumulate over the road.
2. In areas where the atmospheric temperature drops to 18° C, Calcium Chloride (CaCl2) is used instead of sodium chloride. Calcium chloride Associates into three ions, which causes more depression in the freezing point of water and helps to melt ice on roads. 
3. During cold seasons, there is a chance of the radiator getting frozen. We use radiator fluids in automobiles. These fluids are generally made of ethylene glycol and water and help prevent the freezing of radiators.
4. It is used as a purity analysis tool. It is analysed by differential scanning calorimetry. This method is very effective and gives pure results.
5. It is used in the dairy industry. This property makes sure that extra water is not there in the milk. Milk with a freezing point depression of 0.509° is considered pure.
6. This property is also used in making ice cream. It helps to make a freezing mixture by adding NaCl or another salt to lower its melting point.

Conclusion

The Depression of Freezing Point is a decrease in the temperature at which a material freezes, when a lesser amount of another non-volatile chemical is added to the mixture. The addition of salt to water (used in ice cream makers and to de-ice roads), the addition of alcohol to water, the addition of ethylene or propylene glycol to water (used in antifreeze in automobiles), the addition of copper to molten silver (used to form solder that flows at a lower temperature than the silver pieces being connected), and the blending of two substances, such as contaminants into a finely powdered medicine are all examples.