MHTCET 23 Apr 2025 Shift 1 Paper

Concept:The depression in freezing point is directly proportional to the van't Hoff factor:$$\Delta T_f = i \cdot K_f \cdot m$$Explanation:Step 1: Find the freezing point depression.The pure solvent freezes at $0^\circ C$ and the solution freezes at $-0.54^\circ C$.So, $\Delta T_f = 0 - (-0.54) = 0.54 \, K$.Step 2: Write the formula and substitute the given values.$\Delta T_f = i \cdot K_f \cdot m$Here, $K_f = 1.86 \, K \, kg \, mol^{-1}$ and $m = 0.18 \, mol \, kg^{-1}$.Step 3: Solve for the van't Hoff factor $i$.$i = \frac{\Delta T_f}{K_f \cdot m}$Substitute the values:$i = \frac{0.54}{1.86 \times 0.18}$First, calculate the denominator:$1.86 \times 0.18 = 0.3348$Now, compute $i$:$i = \frac{0.54}{0.3348} = 1.612$Answer:The van't Hoff factor is $1.612$.Therefore, the correct option is C.