Problem 82 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

For each of the following dilute solutions, Van't Hoff's factor is equal of 3 , except (a) \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) (b) \(\mathrm{CaF}_{2}\) (c) \(\mathrm{K}_{3} \mathrm{PO}_{4}\) (d) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3}\)

Step-by-Step Solution

Answer

The compound with a Van't Hoff factor not equal to 3 is (c) K3PO4.

Step 1 - Understanding Van't Hoff's Factor

The Van't Hoff factor, denoted by 'i', is the number of particles a compound dissociates into when it is dissolved in solution. For a compound that completely dissociates into three ions in solution (one cation and two anions, or one anion and two cations), the Van't Hoff factor is 3.

Step 2 - Analyzing each compound

Examine each compound and predict the number of ions each will produce when dissolved in water. (a) Na2SO4 will dissociate into 2 Na+ cations and 1 SO4^2- anion, for a total of 3 ions. (b) CaF2 will dissociate into 1 Ca^2+ cation and 2 F- anions, for a total of 3 ions. (c) K3PO4 will dissociate into 3 K+ cations and 1 PO4^3- anion, for a total of 4 ions. (d) (NH4)2CO3 will dissociate into 2 NH4+ cations and 1 CO3^2- anion, for a total of 3 ions.

Step 3 - Identifying the Exception

From the analysis in Step 2, it's clear that all compounds except for K3PO4 will produce 3 ions in solution. K3PO4 will produce 4 ions in solution, making it the exception with a Van't Hoff factor different from 3.

Key Concepts

Physical Chemistry and the Van't Hoff Factor

Physical chemistry is the branch that deals with the study of how matter behaves on a molecular and atomic level and how chemical reactions occur. Understanding the Van't Hoff factor is integral to several concepts in physical chemistry, particularly those involving solutions. The Van’t Hoff factor (i) is significant because it provides insight into the number of particles formed when a substance is dissolved in a solution.

This factor affects the physical properties of solutions, such as freezing point depression, boiling point elevation, and osmotic pressure, all of which are fundamental when studying colligative properties. The step-by-step textbook solution explicitly illustrates the Van't Hoff factor by breaking down ionic compounds into their constituent ions. Evidently, physical chemistry requires a grasp of both theoretical and practical applications, where exercises like these highlight the practical aspects of these chemical principles in a straightforward manner.

Ionic Dissociation in Solutions

Ionic dissociation is a process where an ionic compound separates into its ions when dissolved in a solvent, typically water. This process is essential for understanding the behavior of salts and other ionic compounds in solution.

In the educational example provided, comprehension of ionic dissociation helps students identify the Van't Hoff factor for various compounds. For instance, Na₂SO₄ dissociates into three ions (2 Na⁺ and 1 SO₄^2-), which correlates to the Van’t Hoff factor of 3. Conversely, compounds that produce a different number of ions, such as K₃PO₄, which dissociates into four ions, have a different factor. Highlighting the dissociation process emphasizes the predictive power of these concepts in determining the properties of a solution.

Colligative Properties and Their Reliance on the Van't Hoff Factor

Colligative properties are properties of solutions that depend on the number of dissolved particles in the solution, regardless of their nature. These include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure. The Van't Hoff factor plays a crucial role in calculating these properties.

For a given solute, the higher the Van’t Hoff factor, the more significant the effect on the colligative properties. For example, K₃PO₄ having a Van’t Hoff factor of 4 means it would have a greater impact on the solution's colligative properties compared to a substance with a lower factor of 3, such as CaF₂.

It is imperative for students to recognize that colligative properties are influenced by the amount of the solute rather than its identity, and exercises elucidating the Van't Hoff factor offer a practical approach to understanding these solution characteristics.