The correct answer for the solubility parameter determination is option 'C' which is the Hildebrand equation. The solubility parameter is a concept used to predict the solubility of one substance in another based on their compatibility and intermolecular forces. It is an important parameter in fields such as polymer science, pharmaceuticals, and coatings.

The Hildebrand equation, named after the American chemist Joel H. Hildebrand, is an empirical equation used to estimate the solubility parameter. It relates the solubility parameter (δ) to the heat of vaporization (ΔHv) of a substance.

The Hildebrand equation can be represented as follows:

δ = (ΔHv/V)^(1/2)

where δ is the solubility parameter, ΔHv is the heat of vaporization, and V is the molar volume of the substance.

The equation suggests that the solubility parameter is determined by the ratio of the heat of vaporization to the molar volume. This implies that substances with similar solubility parameters are likely to be soluble in each other, while substances with different solubility parameters are likely to be insoluble.

The solubility parameter is a measure of the cohesive energy density of a substance, which reflects the strength of intermolecular forces. It is calculated in units of (J/cm^3)^(1/2) or (MPa)^(1/2). Substances with similar solubility parameters have similar intermolecular forces and are likely to be compatible.

The Hildebrand equation is widely used in the field of polymer science to predict the compatibility of polymers with solvents. It is also used in the formulation of pharmaceuticals and coatings, where solubility and compatibility are important factors.

In conclusion, the solubility parameter is determined using the Hildebrand equation, which relates the solubility parameter to the heat of vaporization and molar volume of a substance. The solubility parameter is a measure of the compatibility and intermolecular forces between substances and is widely used in various fields.