State the principles involved in the following methods used to separate the components of mixtures.

(a) Solvent extraction

(b) Gravity separation

(c) Fractional crystallisation

(d) Fractional distillation

Also give one example of a mixture separated by employing the above methods.

(a) Solvent extraction — Solvent extraction is based on the difference in solubility of components in a solvent. A solvent is chosen in which one or more components of the mixture dissolve, while others do not. The soluble component is then separated from the insoluble ones.
Example: A mixture of sodium chloride and calcium carbonate can be separated by this method.

(b) Gravity separation — Gravity separation works on the principle of differences in the densities of components. Heavier particles settle at the bottom due to gravity, while lighter particles remain on top or are separated by other means.
Example: A mixture of sand and sawdust can be separated by this method.

(c) Fractional crystallisation — Fractional crystallisation relies on the difference in solubility of components in the same solvent. When a mixture of solids is dissolved in a solvent and the solution is heated, the components may have different solubilities. As the solution cools, the less soluble component crystallizes first, while the more soluble component remains dissolved. Repeating this process allows for the separation of the components.
Example: A mixture of common salt and potassium nitrate can be separated by this method.

(d) Fractional distillation — Fractional distillation is used to separate liquid-liquid homogeneous mixtures (miscible liquids) that have different boiling points. When the mixture is heated, the liquid with the lower boiling point vapourizes first, and its vapour is condensed and collected in a separate receiver. The process is repeated, and the second liquid vapourizes once the temperature rises to its boiling point.
Example: Water and alcohol are separated by this method.