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

Step 1: Understanding the Question:
We need to determine the Van't Hoff factor (\(i\)), which accounts for the dissociation of a solute in a solvent.
Step 2: Key Formula or Approach:
For a strong electrolyte that dissociates completely, the Van't Hoff factor \(i\) is equal to the total number of ions produced per formula unit of the solute.
Step 3: Detailed Explanation:
Potassium sulfate (\(\text{K}_2\text{SO}_4\)) is a strong electrolyte. In aqueous solution, it dissociates as follows:
\[ \text{K}_2\text{SO}_4(s) \xrightarrow{H_2O} 2\text{K}^+(aq) + \text{SO}_4^{2-}(aq) \]
Counting the ions:
- Number of \(\text{K}^+\) ions = 2
- Number of \(\text{SO}_4^{2-}\) ions = 1
Total number of particles (\(i\)) = \(2 + 1 = 3\).
Step 4: Final Answer:
The Van't Hoff factor for \(\text{K}_2\text{SO}_4\) is 3.