Problem 77 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

Van't Hoff's factor for a dilute solution of \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) is (a) \(4.0\) (b) \(0.25\) (c) \(5.0\) (d) \(3.0\)

Step-by-Step Solution

Answer

The Van't Hoff's factor (i) for \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) is 5.0.

Step 1 - Understand Van't Hoff's factor

Van't Hoff's factor, denoted as 'i', is a measure of the effect of solute particles on various colligative properties. For electrolytes, it corresponds to the number of particles the compound dissociates into in solution.

Step 2 - Determine the dissociation of the compound

The given compound, \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\), dissociates into four potassium ions (\(\mathrm{K}^{+}\)) and one complex iron cyanide ion (\(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\)) in a dilute solution.

Step 3 - Calculate Van't Hoff's factor

The compound dissociates into a total of 4 (potassium ions) + 1 (complex ion) = 5 particles. Hence, Van't Hoff's factor for \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) is 5.0.

Key Concepts

Colligative Properties

Colligative properties are characteristics of solutions that depend on the number of dissolved particles in the solution, not on the identity of those particles. These properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure. For example, when a solute is dissolved in a solvent, the boiling point of the resulting solution is typically higher than that of the pure solvent, and the freezing point is lower.

Understanding colligative properties is vital when exploring the behavior of solutions in various fields, such as chemistry, biology, and engineering. In the context of the exercise, Van't Hoff's factor plays a crucial role in quantitatively describing the effect of solute particles on these properties. For the compound in question, knowing that its Van't Hoff's factor is 5.0 allows us to predict that it would have a more significant impact on the solution's colligative properties compared to a solute that does not dissociate into as many ions.

Chemical Dissociation

Chemical dissociation is the process by which a compound separates into smaller components, such as ions or simpler molecules, when dissolved in a solvent. Dissociation is particularly important when dealing with electrolytes, substances that conduct electricity in solution due to the movement of ions.

In the problem at hand, the given compound, \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\), dissociates in water to form multiple ions. Knowledge of the extent of dissociation is essential for accurately calculating colligative properties. The provided step-by-step solution implies that each molecule of the compound dissociates into a total of five ions, which is crucial for determining the solution's behavior.

Understanding the specific pattern of chemical dissociation for various substances helps predict their interactions and the resulting changes in the solution's properties.

Electrolyte Solution

An electrolyte solution is formed when electrolytes dissolve in a solvent and produce charged ions. These ions are essential for the conductivity of electricity through the solution. Electrolytes can be strong or weak, based on their ability to dissociate in solution. Strong electrolytes dissociate completely, providing a higher concentration of ions, while weak electrolytes only partially dissociate.

The overall conductivity and the influence on colligative properties of the solution are dependent on the number and type of ions present. In the context of the exercise, \(\mathrm{K}_{3}\left[\mathrm{F}e(\mathrm{CN})_{6}\right]\) is considered a strong electrolyte because it dissociates completely into potassium ions and the complex iron cyanide ion. As such, the electrolyte solution made from this compound would exhibit significant changes in colligative properties, due to the high Van't Hoff's factor associated with its full dissociation into ions.