The underlying principle based on which fractional distillation is carried out is the different boiling points of each fraction.

Fractional distillation is a technique used to separate a mixture of liquids based on their different boiling points. It is a process that involves heating a mixture of liquids to a specific temperature and collecting the vapors that are produced. These vapors are then condensed back into liquid form and collected as separate fractions.

Here is a detailed explanation of how fractional distillation works based on the different boiling points of each fraction:

1. Introduction to Fractional Distillation:
- Fractional distillation is a type of distillation that is used to separate a mixture of liquids with similar boiling points.
- It is based on the principle that different liquids have different boiling points, and by carefully controlling the temperature, it is possible to separate them.

2. Differences in Boiling Points:
- Each liquid in a mixture has a specific boiling point, which is the temperature at which it changes from a liquid to a vapor.
- The boiling point is determined by the intermolecular forces between the molecules of the liquid.
- Liquids with stronger intermolecular forces have higher boiling points, while liquids with weaker intermolecular forces have lower boiling points.

3. Heating and Vaporization:
- In fractional distillation, the mixture of liquids is heated in a distillation flask.
- As the temperature increases, the liquid with the lowest boiling point begins to vaporize first.
- The vapor rises up through a fractionating column, which provides a large surface area for the vapors to cool and condense.

4. Condensation and Collection:
- As the vapor rises through the fractionating column, it cools and condenses.
- The condensed liquid is collected in separate fractions as it drips down the column.
- Each fraction contains a different liquid with a specific boiling point.

5. Separation and Purification:
- The collected fractions can be further purified by repeating the distillation process.
- Each distillation step increases the purity of the fractions by removing impurities and separating the components with closer boiling points.

6. Applications of Fractional Distillation:
- Fractional distillation is widely used in industries such as petroleum refining, where crude oil is separated into various fractions like gasoline, diesel, and kerosene based on their boiling points.
- It is also used in the production of alcoholic beverages, essential oils, and many other chemical processes.

In conclusion, fractional distillation is carried out based on the different boiling points of each fraction. By carefully controlling the temperature and using a fractionating column, the mixture of liquids can be separated into individual fractions with specific boiling points.