Question

Ethylene glycol (molar mass$=62\mathrm{g}{\mathrm{mol}}^{-1}$) is a common automobile antifreeze. calculate the freezing point of a solution containing $12.4\mathrm{g}$ of this substance in $100\mathrm{g}$of water. would it be advisable to keep this substance in the car radiator during summer?

Given: ${\mathrm{k}}_{\mathrm{f}}$ for water $=1.86\mathrm{K}\mathrm{kg}{\mathrm{mol}}^{-1}$, ${\mathrm{k}}_{\mathrm{b}}$ for water $=0.512\mathrm{K}\mathrm{kg}{\mathrm{mol}}^{-1}$

Answer 1

Step 1: Analyze the formula

The formula for depression in freezing point is
${\mathrm{\Delta T}}_{\mathrm{f}}={\mathrm{K}}_{\mathrm{f}}\times \mathrm{b}\times \mathrm{i}$

Where, $\mathrm{i}=1$ for ethylene glycol

$\mathrm{b}=\mathrm{molality}=\frac{\mathrm{moles}\mathrm{of}\mathrm{solute}}{\mathrm{kg}\mathrm{of}\mathrm{solvent}}$

${\mathrm{K}}_{\mathrm{f}}$ is called the molal freezing point depression constant

Step 2: Find the value of Molality

One mole of Ethylene glycol $=62\mathrm{g}$

Therefore, $12.4\mathrm{g}$ constitutes $\frac{12.4}{62}=0.2$mole

Solvent $=100\mathrm{g}=0.1\mathrm{kg}$

Hence, $\mathrm{b}=\frac{0.2}{0.1}=2\mathrm{mol}{\mathrm{kg}}^{-1}$

Step 3: Find freezing point of solution

By the formula for depression in freezing point:

$$\begin{gathered} {\mathrm{\Delta T}}_{\mathrm{f}}=1.86\times 2\mathrm{Kelvin} \\ =3.72\mathrm{K} \end{gathered}$$

The difference in freezing point $=3.72\mathrm{K}$ (depression)

We know the freezing point of pure water is zero deg $\mathrm{C}=273\mathrm{K}$

Therefore freezing point of solution: $=273–3.6=269.4\mathrm{K}=-3.72°\mathrm{C}$ (since temp in $\mathrm{K}=273+$temp in $°\mathrm{C}$)

Step 4: Find boiling point of solution.

Boiling point elevation

$$\begin{gathered} {\mathrm{\Delta T}}_{\mathrm{b}}={\mathrm{K}}_{\mathrm{b}}\times \mathrm{b}\times \mathrm{i} \\ =0.512\times 2=1.024\mathrm{K} \end{gathered}$$

The boiling point of pure water $=100°\mathrm{C}=373\mathrm{K}$

Therefore, the boiling point of the solution $=373+1.024=374.024\mathrm{K}=101.024°\mathrm{C}$

The boiling point of aqueous ethylene glycol, on the other hand, rises as the amount of ethylene glycol increases.

Thus, the inclusion of ethylene glycol not only lowers the freezing point but also raises the boiling point, making it ideal for keeping in a radiator throughout the summer.