Question

A motor radiator vehicle was filled with 8 L of water to which 2 L of methyl alcohol (density $0.8{\text{gm}}{{\text{L}}^{{\text{ - 1}}}}$) was added. What is the lowest temperature at which the vehicle can be parked outdoors without the danger that the water in the radiator will freeze? Given that ${K_f}$ ​for water is $1.86^\circ {\text{C kg mo}}{{\text{l}}^{{\text{ - 1}}}}$. Write the answer as the modulus of the nearest integer of the obtained temperature.

Answer 1

In order to solve this numerical the formula for the freezing temperature will be used which is as follows: $\Delta {T_f} = {K_f}m\;$,here Tf is the absolute freezing temperature, m is the molality of solute and Kf is molal freezing temperature of the solute.

Complete step by step answer:
According to the question:
Mass of 8 L water = 8 kg or 8000 g because density is 1.

Mass of density alcohol added = Density$\times$ Volume
= $0.8 \times 2000 = 1600{\text{ g}}$

$$\Delta {T_f} = {K_f}m\; = 1.86 \times \dfrac{{1600}}{{32}} \times \dfrac{1}{{8000}} \times 1000 \\\ \Rightarrow \Delta {T_f} = 11.625^\circ {\text{C}} \\\$$

Therefore, the lowest temperature at which the vehicle can be parked outdoors without the danger that the radiator will freeze is $11.625^\circ {\text{C}}$.
So, the nearest integer is 12.

Additional note: Freezing point depression is the phenomena where the freezing of solute occurs at lower temperature than for the pure solvent. It is a colligative which is directly proportional to the number of dissolved solute particles. Freezing point will be maximum when the concentration of solute is high and will be lower when the concentration will be low.

Note:
Freezing-point depression’s phenomenon has many applications:
-The radiator fluid in an automobile is a mixture of water and ethylene glycol issued in radiator fluid preventing it from freezing.
-To remove ice from the roads road salting is done which follows the same process.
Factors affecting freezing point:
-Types of Molecules determine the freezing point of solvent: If the intermolecular force of attraction between molecules is strong then the freezing point will be high or solvent if forces are weak then freezing point will be lower.