Question

The Nernst distribution law equation \(\mathrm{C}_{\mathrm{f}} / \mathrm{C}_{2}=K\) applies when (a) the molecular state of the solute is the same in both the solvents (b) the molecular state of the solute is different in both the solute (c) the molecular state of the solute is different in both the solute (d) none of these

Short answer

Option (a) is correct.

Step-by-step solution

Comprehend Nernst distribution law

The Nernst distribution law states that the ratio of the concentration of a solute between two immiscible solvents is constant at constant temperature, and the molecular state of the solute is the same in both solvents. Mathematically, it is defined as \(C_{1} / C_{2} = K\) where \(C_1\) and \(C_2\) are the concentrations of the solute in the first and second solvent respectively and K is a constant.

Identify the underlying conditions

The condition for Nernst distribution law to apply is that the molecular state of the solute is the same in both the solvents which is stated in option (a). Options (b) and (c) both suggest that the molecular state of the solute is different in both the solvents, contradicting the conditions of the law.

Choosing the right option

As per the Nernst distribution law, the molecular state of the solute needs to be same in both solvents for the law to hold true. Therefore, option (a) 'the molecular state of the solute is the same in both the solvents' is the correct choice.

Key concepts

Concentration Ratio

Understanding the concentration ratio is critical when we delve into the principles of the Nernst distribution law. This law describes the behavior of a solute between two immiscible solvents, where the solute distributes itself in a definite proportion, assuming its molecular state remains unchanged. The term 'concentration ratio' essentially refers to the constant ratio of the concentration of the solute in each solvent, denoted by the symbol K in the equation \(C_1 / C_2 = K\). Here, \(C_1\) is the concentration in the first solvent and \(C_2\) the concentration in the second solvent.

For students looking at textbook exercises, remembering the significance of the concentration ratio can be the key to unlocking questions related to the distribution law. It's the expression of chemical equilibrium between the two phases in terms of their concentrations. Maintaining a constant temperature ensures the consistency of this ratio. In practical applications, this principle is vital in fields like pharmaceuticals, where the distribution of drugs between water and oil phases can affect their efficiency and delivery.

Immiscible Solvents

Immiscible solvents are a cornerstone to understanding the Nernst distribution law. 'Immiscible' means the liquids are not miscible in all proportions; they do not dissolve in each other to form a homogeneous solution. A classic example of immiscible liquids is oil and water. When applied to the Nernst distribution law, it is crucial that the two solvents in question do not mix because the law predicts how a solute will share itself between these two distinct phases.

It's fascinating to observe that irrespective of the amount of each solvent used, as long as they are immiscible, the solute will distribute between them according to the concentration ratio, as long as the molecular state in each remains unchanged. This plays a huge role in separating and extracting chemicals in laboratories and industry. The student should visualize the solute 'choosing' a partition between two non-mixing layers, symbolizing its preference based on the chemical environment presented by the solvents.

Chemical Equilibrium

An understanding of chemical equilibrium is essential when discussing the Nernst distribution law. Chemical equilibrium occurs when the rate of the forward reaction equals the rate of the reverse reaction, and the concentrations of the products and reactants remain unchanged over time. In the context of the Nernst law, equilibrium is attained when the solute is evenly distributed between the two immiscible solvents to the extent defined by its concentration ratio.

When working through textbook problems, consider equilibrium as the point where all the dynamic processes involved balance out. It's important to remember that reaching equilibrium does not mean the molecules stop moving; rather they do so in a way that their overall concentrations in each solvent do not change. The Nernst law allows students to predict the point of equilibrium for a solute between two solvents. This concept is pivotal in various scientific processes, including pharmaceutical formulation and environmental science, where the distribution of substances between different mediums can influence biological activity or pollution.