\(100 \mathrm{~mL}\) of \(1 \times 10^{-2} M\) aqueous solution of an organic compound were shaken with \(50 \mathrm{~mL}\) of an organic solvent till equilibrium is attained. Calculate the concentration of organic compound in organic solvent. Given that distribution coefficient of organic compound for the given solvent is 50 in favour of organic solvent.

The partition coefficient, denoted as K_d, is vital when studying how a compound divides itself between two immiscible liquids at equilibrium. It is a ratio expressing how, given a compound and two solvents, the compound prefers one solvent over the other. Mathematically, it's represented by \( K_d = \frac{[S]_{\text{organic}}}{[S]_{\text{aqueous}}} \), where \( [S]_{\text{organic}} \) is the solute's concentration in the organic solvent and \( [S]_{\text{aqueous}} \) is its concentration in the aqueous layer.

In a practical scenario, such as solvent extraction processes in laboratories, this value provides insight into where most of the solute will end up after the extraction. A higher partition coefficient means the solute is more soluble in the organic layer compared to the aqueous layer, which guides chemists in choosing suitable solvents for their extractions. Understanding this concept is crucial for efficiently separating compounds and is frequently used for drug development and environmental monitoring.

Calculating the equilibrium concentration requires an understanding of the system's initial conditions and the conservation of mass within the system. In our example, we aimed to calculate the concentration of an organic compound in an organic solvent after equilibrium using the initial concentration and volumes of the reacting liquids. The equation that relates the initial and final concentrations and volumes is \( V_{\text{aqueous}} \times [S]_{\text{initial aqueous}} = V_{\text{aqueous}} \times [S]_{\text{final aqueous}} + V_{\text{organic}} \times [S]_{\text{organic}} \).

A precise calculation helps us predict where the compound will predominantly reside after equilibrium. The process involves algebraically finding the final concentrations after considering the volume of both solvents and partition coefficient.

Solvent extraction is a method to separate compounds based on their relative solubilities in two immiscible liquids, usually water and an organic solvent. The principle hinges on the differing affinities of the solute for the two solvents, quantified by the partition coefficient. It is a widely-used technique in industrial processes, analytical chemistry, and the manufacturing of pharmaceuticals. By shaking an aqueous solution with an organic solvent until equilibrium is reached, the solute will distribute between the phases accordingly, allowing for separation and purification.

For instance, during drug purification, solvent extraction can be used to remove impurities based on selective solubility. This technique hinges not just on the partition coefficient but also on the proper choice of an organic solvent, the volumes used, and the system's temperature.

The law of mass conservation states that mass can neither be created nor destroyed in a closed system through ordinary physical or chemical processes. Applying this to chemical equilibria, particularly in systems undergoing solvent extraction, means that the total mass of solutes and solvents remains constant throughout the process. When an organic compound is dissolved in an aqueous solution and then comes into contact with an organic solvent, the substance's total amount remains unaltered, even as it redistributes between the two layers.

When calculating concentrations after solvent extraction, keeping track of the total amount of solute is crucial to find the equilibrium concentration in each of the phases. The mass balance equation used in our solution reflects this principle, which ensures that the calculated concentrations respect the conservation of mass.