Question

Which of the following solutes has highest $\frac{\Delta T}{m}$ value in its 0.05 molal aqueous solution?

• A. Potassium sulphate
• B. Glucose
• C. Ammonium chloride
• D. Aluminium chloride

Answer 1

Answer: (D)

Aluminium chloride

Answer 2

The freezing point depression (or boiling point elevation) is given by:

$\Delta T = i \cdot K \cdot m$

where $i$ is the van’t Hoff factor. For the same molality $m$:

• Potassium sulphate ($K_2SO_4$) dissociates into 2 $K^+$ + 1 $SO_4^{2-}$ $\Rightarrow i = 3$.
• Glucose does not dissociate $\Rightarrow i = 1$.
• Ammonium chloride ($NH_4Cl$) dissociates into $NH_4^+$ and $Cl^-$ $\Rightarrow i = 2$.
• Aluminium chloride ($AlCl_3$) dissociates into $Al^{3+}$ + 3 $Cl^-$ $\Rightarrow i = 4$.

Since $\Delta T \propto i$, the solution with the highest $i$ value will have the highest $\frac{\Delta T}{m}$ value. Therefore, Aluminium chloride is the correct solute.