Step 1: Understand the van't Hoff factor.
The van't Hoff factor (\( i \)) represents the number of particles a compound dissociates into in solution.
For ionic compounds, \( i \) depends on the degree of dissociation.
Step 2: Analyze the given compounds. 1. KCl:
Dissociates into \( K^+ \) and \(Cl^-\).
Total particles = 2. \( i = 2 \). 2. NaCl:
Dissociates into \( Na^+ \) and \( Cl^-\).
Total particles = 2. \( i = 2 \). 3. \( K_2SO_4 \):
Dissociates into \( 2K^+ \) and \( SO_4^{2} \).
Total particles = 3. \( i = 3 \).
Step 3: Determine the correct answer.
The van't Hoff factors for KCl, NaCl, and \( K_2SO_4 \) are 2, 2, and 3, respectively.