Question

Which of the following solutes has the ratio of theoretical molar mass to the experimentally observed molar mass is \(3\)?

• A. \(\text{KCl}\)
• B. \(\text{K}_2\text{SO}_4\)
• C. \(\text{MgSO}_4\)
• D. \(\text{Al}_2(\text{SO}_4)_3\)

Hint:

Ratio of theoretical to observed molar mass equals i. Count ions.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The van't Hoff factor is \(i = \dfrac{\text{normal (theoretical) molar mass}}{\text{observed molar mass}}\). So the question asks for a solute with \(i = 3\).

Step 2: Complete dissociation:
For complete dissociation, \(i\) equals the number of ions per formula unit.

Step 3: Count ions:
KCl gives 2 ions (\(K^+\), \(Cl^-\)), so \(i = 2\).
\(K_2SO_4\) gives \(2K^+ + SO_4^{2-}\), which is 3 ions, so \(i = 3\).
\(MgSO_4\) gives 2 ions, so \(i=2\).
\(Al_2(SO_4)_3\) gives \(2Al^{3+} + 3SO_4^{2-}\), which is 5 ions, so \(i=5\).

Step 4: Select:
Only \(K_2SO_4\) has \(i=3\), option (B).

Final Answer:
K2SO4 gives three ions, so the ratio is 3. \[ \boxed{B:\ \text{K}_2\text{SO}_4} \]