Answer
a. 2.0 moles of ethylene glycol will have a lower freezing point, since it has a greater quantity of particles in solution.
b. 0.50 moles $MgCl_2$ will have a lower freezing point, since it has a greater quantity of particles in solution.
Work Step by Step
The number of particles of solute is proportional to the decrease in the freezing point.
a. 2.0 moles of ethylene glycol has a greater number of particles than 1.0 mole of glycerol. Thus, the ethylene glycol solution is going to have a lower freezing point.
b. Since $KCl$ is a strong electrolyte, each mole will produce 2 particles: $K^+$ and $Cl^-$. 0.50 mole $\times$ 2 = 1.0 mole
Since $MgCl_2$ is a strong electrolyte, each mole will produce 3 particles: 1 $Mg^{2+}$ and 2 $Cl^-$. 0.50 mole $\times$ 3 = 1.5 mole
1.5 mole is greater than 1.0 mole. Thus, the $MgCl_2$ solution is going to have a lower freezing point.
