Problem 97 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

The degree of dissociation \((\alpha)\) of a weak electrolyte, \(A_{x} B_{y}\), is related to Van't Hoff factor (i) by the expression (a) \(\alpha=\frac{i-1}{x+y-1}\) (b) \(\alpha=\frac{i-1}{x+y+1}\) (c) \(\alpha=\frac{x+y-1}{i-1}\) (d) \(\alpha=\frac{x+y+1}{i-1}\)

Step-by-Step Solution

Answer

The correct relationship between the degree of dissociation (\textbackslash(alpha)) of a weak electrolyte and the Van't Hoff factor (i) is (a) \textbackslash(frac{i-1}{x+y-1}\textbackslash).

Step 1: Understanding the Relation Between Degree of Dissociation and Van't Hoff Factor

The Van't Hoff factor (i) indicates how many particles a solute splits into when dissolved. For weak electrolyte, not all the molecules dissociate into ions, so the degree of dissociation (α) reflects the fraction of dissociated molecules. The formula relating α and i considers the number of ions produced from the electrolyte upon dissociation.

Step 2: Formulating the Correct Expression

The total number of moles of particles after dissociation is given by i, which is the undissociated part plus the dissociated part. For an electrolyte dissociating into x and y parts, the increase in moles due to dissociation is xα + yα - α, as we lose one undissociated molecule and gain x and y parts. Hence, we express the increase as α(x + y - 1) and the Van't Hoff factor becomes i = 1 + α(x + y - 1).

Step 3: Solving for Degree of Dissociation

To find the relationship for α, we isolate it in the previous equation: i = 1 + α(x + y - 1). Solving for α gives α = (i - 1) / (x + y - 1).

Key Concepts

Van't Hoff Factor

The Van't Hoff factor, represented by the symbol 'i', plays a crucial role in understanding the behavior of solutions in chemistry. It is defined as the ratio of the actual number of particles in a solution to the number of particles that would be present if the solute were to dissociate completely.

This factor is particularly vital when dealing with colligative properties, which are the properties of solutions that depend on the number of dissolved particles rather than on the type of particle itself. These properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure. For example, when we add salt to water, it causes the boiling point of the water to increase, a phenomenon affected by the Van't Hoff factor of the salt.

In the context of weak electrolytes, where dissociation into ions is not complete, the Van't Hoff factor provides a quantitative measure of the extent of dissociation. It is important because it helps in calculating the degree of dissociation of the electrolyte in the solution, which otherwise would be difficult since weak electrolytes do not fully ionize.

Weak Electrolyte

Weak electrolytes are substances that partially dissociate into ions when dissolved in a solvent. Unlike strong electrolytes, which dissociate completely, weak electrolytes exist in a dynamic state of equilibrium between the undissociated molecules and the ions produced.

Common examples of weak electrolytes include weak acids like acetic acid and weak bases like ammonia. These substances do not produce a large number of ions in solution, which has implications for the conductivity of the solution and its colligative properties. The degree of dissociation \(\alpha\) of a weak electrolyte signifies the fraction of molecules that have dissociated into ions; it ranges from 0 (no dissociation) to 1 (complete dissociation).

Understanding weak electrolytes is pivotal not only in chemistry but also in various biological processes and industrial applications where control of pH and ion concentration is essential.

Chemical Equilibrium

Chemical equilibrium is a state in which the rate of the forward reaction equals the rate of the reverse reaction, resulting in no observable changes in the amounts of reactants and products over time. At equilibrium, the concentrations of all reactants and products remain constant.

In the context of weak electrolytes, the dynamic equilibrium between the intact molecules and the ions produced ensures that the solution contains both the undissociated form and the dissociated ions. Since the electrolyte is not fully dissociated, this equilibrium is essential for predicting the behavior and properties of the solution.

Chemists use the equilibrium constant to quantify the concentration of the reactants and products at equilibrium. This constant can help determine the degree of dissociation of a weak electrolyte. A deeper understanding of chemical equilibrium is crucial for predicting how changes in conditions, such as temperature or concentration, will shift the equilibrium position and affect the degree of dissociation.