Question

What is the expected value of $\Delta T_f$ for 1.25mCaCl₂ solution if 1.25 m sucrose solution has $\Delta T_f$ value x K?

Answer 1

$\Delta T_f = 3x \text{ K}$

Answer 2

For any solution, the freezing point depression is given by:

$$\Delta T_f = i \cdot K_f \cdot m$$

For sucrose (a non-electrolyte), the van't Hoff factor, $i = 1$. Thus:

$$\Delta T_f (\text{sucrose}) = 1 \cdot K_f \cdot 1.25 = x \quad \Rightarrow \quad 1.25K_f = x$$

For $\text{CaCl}_2$ (an electrolyte), it dissociates into 3 ions: one $\text{Ca}^{2+}$ and two $\text{Cl}^-$ ions, so $i = 3$. Hence:

$$\Delta T_f (\text{CaCl}_2) = 3 \cdot K_f \cdot 1.25 = 3\left(1.25K_f\right) = 3x$$