# Which one of the following solutions will have the lowest freezing point?

$\begin{array}{1 1}(a)\;\text{1% of solution of urea in water}\\(b)\;\text{1% solution of zinc sulphate in water}\\(c)\;\text{1% solution magnesium chloride in water}\\(d)\;\text{1% solution of glucose in water}\end{array}$

Answer: - 1% solution of $MgCl_2$
Depression of Freezing point, $\Delta\; T_f = i\;K_f\; m$, where $i$ is the van't Hoff factor, $K_f$ is the Freezing Point Depression Constant and $m$ is the molality.
Molality $m = \large\frac{w/M}{W(g)/1000}$
For the given problem, the solutions are all 1% solution and hence Molality $m \propto \large\frac{1}{M}$
Therefore $\Delta T_f \propto \large\frac{i}{M}$
Note: Molecular mass of Glucose $= 180\;g\;mol^{-1}$, Urea $= 60\;g\;mol^{-1}$, $MgCl_2 = 95.2\;g\;mol^{-1}$, $ZnSO_4 = 161.5\;g\;mol^{-1}$,
Note: van't Hoff factor for Glucose $= 1$, Urea $= 1$, $ZnSO_4 = 2$ and $MgCl_2 = 3$.
$\Rightarrow$ the solution with the lowest freezing point based on the above data is $MgCl_2$.
edited Jul 16, 2014