Correct Option: (D) 3

Step 1 (Governing Principle & Dissociation Equation): [0.5 Mark]

The Van't Hoff factor ($i$) for a solute undergoing complete dissociation is equal to the total number of ions produced per formula unit of the solute in an aqueous solution. The dissociation reaction for the given compound is:

$$ \text{CaCl}_2 \cdot 6\text{H}_2\text{O} (s) \xrightarrow{\text{H}_2\text{O}} \text{Ca}^{2+} (aq) + 2\text{Cl}^- (aq) + 6\text{H}_2\text{O} (l) $$

Note: The water of crystallization ($6\text{H}_2\text{O}$) does not dissociate into ions; it simply becomes part of the solvent.

Step 2 (Step-by-Step Mathematical Working): [0.25 Mark]

From the balanced dissociation equation, we identify the number of ions produced:

• Number of $\text{Ca}^{2+}$ ions = $1$
• Number of $\text{Cl}^-$ ions = $2$

The total number of particles ($n$) after dissociation is:

$$ i = \text{Total number of ions} = 1 + 2 = 3 $$

Step 3 (Final Concluded Answer): [0.25 Mark]

Since the compound undergoes complete dissociation, the Van't Hoff factor ($i$) is 3. Therefore, the correct option is (D).

💡 EL10 Concept Insight:

Think of the compound like a Lego set: when you drop it in water, the "bricks" (ions) break apart. Since one $\text{CaCl}_2$ unit splits into one calcium piece and two chlorine pieces, you end up with 3 separate pieces floating in the water, which is why $i = 3$.