Question

The Van't Hoff factor for a solution of \( \text{K}_2\text{SO}_4 \) in water is:

• A. \(1 \)
• B. \(2 \)
• C. \(3 \)
• D. \(4 \)

Hint:

For ionic compounds in water, the Van't Hoff factor equals the total number of ions produced after dissociation. Example: \( \text{NaCl} \rightarrow \text{Na}^+ + \text{Cl}^- \Rightarrow i = 2 \) \( \text{K}_2\text{SO}_4 \rightarrow 2\text{K}^+ + \text{SO}_4^{2-} \Rightarrow i = 3 \)

Answer 1

The Correct Option is C

Concept: The Van't Hoff factor (\(i\)) represents the number of particles formed when one formula unit of a solute dissociates in solution. \[ i = \text{Number of ions produced after dissociation} \] For strong electrolytes that dissociate completely in water, the Van't Hoff factor equals the total number of ions produced.

Step 1: Write the dissociation of potassium sulfate in water. \[ \text{K}_2\text{SO}_4 \rightarrow 2\text{K}^+ + \text{SO}_4^{2-} \]

Step 2: Count the total number of ions formed. From one formula unit of \( \text{K}_2\text{SO}_4 \):
• \(2\) potassium ions \( (\text{K}^+) \)
• \(1\) sulfate ion \( (\text{SO}_4^{2-}) \) Total ions formed: \[ 2 + 1 = 3 \]

Step 3: Determine the Van't Hoff factor. \[ i = 3 \] Thus, the Van't Hoff factor for \( \text{K}_2\text{SO}_4 \) in water is \[ \boxed{3} \]