Question

The limiting value of Van't Hoff's factor for \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) is (a) 2 (b) 3 (c) 4 (d) 5

Short answer

The limiting value of Van't Hoff's factor for \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) is 3.

Step-by-step solution

Understand Van't Hoff's Factor

Van't Hoff's factor (\(i\)) is a measure of the degree of dissociation of a compound into ions in a solution. For an electrolyte that dissociates completely, the Van't Hoff's factor is equal to the number of particles the compound dissociates into.

Write the Dissociation Reaction

Write down the balanced chemical equation for the dissociation of \(\mathrm{Na}_2\mathrm{SO}_4\) in water. \(\mathrm{Na}_2\mathrm{SO}_4 \rightarrow 2\mathrm{Na}^+ + \mathrm{SO}_4^{2-}\).

Count the Ions

Count the total number of ions produced from the dissociation of one formula unit of \(\mathrm{Na}_2\mathrm{SO}_4\). The reaction produces 2 sodium ions \(\mathrm{Na}^+\) and 1 sulfate ion \(\mathrm{SO}_4^{2-}\), totaling 3 ions.

Determine Van't Hoff's Factor

The Van't Hoff's factor for \(\mathrm{Na}_2\mathrm{SO}_4\) is the sum of the ions, which is 3. Therefore, the limiting value of Van't Hoff's factor for \(\mathrm{Na}_2\mathrm{SO}_4\) is 3.

Key concepts

Degree of Dissociation

The degree of dissociation, often represented by the symbol \( \alpha \), is a quantitative measure of the extent to which a compound separates into its individual ions in a solution. It's expressed as a fraction or percentage reflecting the ratio of dissociated molecules to the initial number of molecules before dissolution. In a solution where a compound fully dissociates, like most strong electrolytes, the degree of dissociation is 1 or 100%.

For example, an ionic compound such as \( \mathrm{NaCl} \) would have a degree of dissociation close to 1 in water because it dissociates completely into \( \mathrm{Na}^+ \) and \( \mathrm{Cl}^- \) ions. On the other hand, a weak electrolyte like acetic acid has a degree of dissociation much less than 1, as a significant portion remains non-dissociated in the form of \( \mathrm{CH}_3\mathrm{COOH} \). Understanding the degree of dissociation is crucial in predicting the behavior of substances in solution and has practical applications in fields like pharmacology and environmental science.

Chemical Dissociation in Solutions

Chemical dissociation in solutions occurs when molecules or ionic compounds separate into smaller particles, usually ions, when they dissolve in a solvent. The process is vital for understanding how substances interact in a solution, particularly in water, which is a common solvent.

When an ionic compound undergoes dissociation, the ions are surrounded by solvent molecules, a process known as solvation. The extent of dissociation is influenced by several factors, including the temperature, the nature of the solvent, and the presence of other ions in the solution. Additionally, the electrical charge and size of the ions can affect the strength of the solvation and, consequently, the degree of dissociation. These factors combined dictate solubility, electrical conductivity of the solution, and its chemical reactivity.

Ionic Compounds in Aqueous Solutions

Ionic compounds in aqueous solutions are salts that disintegrate into their constituent ions when dissolved in water. This behavior is crucial for numerous biological and chemical processes, as the ions become available for reactions and transport within the solution.

Solute-solvent interactions are the central reason why ionic compounds dissociate in water. Due to water's polar nature, its molecules are attracted to the positive and negative charges of the ions, effectively pulling them apart. Following this logic, the solubility of an ionic compound in water depends on the strength of these interactions relative to the forces holding the ions together in the solid state.

It's also worth noting that the presence of ionic compounds in a solution can affect the boiling point, freezing point, and vapor pressure of the solvent, phenomena which are collectively known as colligative properties. These properties all depend, in part, on the number of dissolved particles in the solution, which brings us back to the significance of Van't Hoff's factor in determining the behavior of solutions in various conditions.