Depression inzing Point of a Solution: Can you make your own ice cream in a baggie without a refrigerator? Yes, we can. Just add salt to the ice; the mixture becomes so cold that it can give frostbite if held for long. Why does it happen so? Is it similar to adding salt to the water? Let’s find out more about it in this article.

The salt and ice mixture is quite cold because it follows a basic scientific principle. This principle is one of the colligative properties of a solution that depends on the number of solute particles present in the solution. The depression in thezing point of a solution is a consequence of adding a non-volatile solute to the solvent.

What is Depression in thezing Point of a Solution?

At normal atmospheric pressure, the temperature at which a liquid becomes a solid is known as thezing point of a liquid. In simple words, it is the temperature at which liquid and solid phases of a substance coexist in equilibrium. A solution willze when its vapour pressure equals the vapour pressure of the pure solid solvent.

When a non-volatile solute is added to a volatile liquid solvent, the vapour pressure of the resulting solution becomes lower than that of the pure solvent. Hence, the temperature required by the liquid solvent to reach its solid state is lowered. This results in the Depression of thezing point of the solution compared to the solvent.

The difference in temperature between thezing point of the pure solvent and that of the solution is called the freezing point depression of a solution. On the graph below, thezing point depression is represented by \(\Delta {{\rm{T}}_{\rm{f}}}\).

The blue line indicates the vapour pressure of a solution which is lower than the vapour pressure of a pure solvent indicated by the purple line. As a result, thezing point of a solvent decreases when any solute is dissolved into it.

Learn All About Colligative Properties

Why Depression in thezing point of the solvent occurs on adding a non-volatile solute?

When a substance starts toze, the molecules slow down. This is due to the decrease in temperature, and the intermolecular forces start to dominate. The molecules undergo rearrangement in a particular pattern and thus turn into a solid. For example, the water molecules when cooled to thezing point, become slower. This results in hydrogen bonds dominating over, creating a solid network of ice. On adding salt to the water, the Na⁺ and Cl^– ions interfere with the rearrangement of molecules. To achieve a solid, the solution must be cooled to an even lower temperature.

Formula ofzing Point Depression

The difference in temperature between thezing point of the pure solvent and that of the solution is called the freezing point depression of a solution.

\(\Delta {{\rm{T}}_{\rm{f}}} = {\rm{T}}_{\rm{f}}^0 – {{\rm{T}}_{\rm{f}}}\)

Where, \({\rm{T}}_{\rm{f}}^0 = \)zing point of pure solvent

\({{\rm{T}}_{\rm{f}}} = \)zing point of the solution (non-volatile solute \(+\) solvent)

In a dilute solution, the Depression of thezing point \(\Delta {{\rm{T}}_{\rm{f}}}\) is directly proportional to the molality of the solution. Mathematically,

\(\Delta {{\rm{T}}_{\rm{f}}} \propto {\rm{m}}\)

\(\Delta {{\rm{T}}_{\rm{f}}} = {{\rm{K}}_{\rm{f}}}{\rm{m}} \ldots  \ldots {\rm{Eqn}}\left( 1 \right)\)

Here, \({{\rm{K}}_{\rm{f}}}\) is the proportionality constant that depends upon the nature of the solvent. It is also known aszing Point Depression Constant or Molal Depression Constant or Cryoscopic Constant. The unit of \({{\rm{K}}_{\rm{f}}}\) is \({\rm{K}}\,{\rm{kg}}\,{\rm{mo}}{{\rm{l}}^{ – 1}}\).

Let \({{\rm{w}}_2}\) gram of the solute having a molar mass of \({{\rm{M}}_2}\) is present in \({{\rm{w}}_1}\) gram of solvent. If the resulting solution produces a depression in thezing point \(\Delta {{\rm{T}}_{\rm{f}}}\) of the solvent, then molality of the solute is given by-

Molality of the solute \(({\rm{m}}) = \frac{{{{\rm{w}}_2}/{{\rm{M}}_2}}}{{{{\rm{w}}_1}/1000}}\)

Substituting this value of molality in Eqn(1), we get-

\(\Delta {{\rm{T}}_{\rm{f}}} = \frac{{{{\rm{K}}_{\rm{f}}} \times {{\rm{w}}_2}/{{\rm{M}}_2}}}{{{{\rm{w}}_1}/1000}}\)

\(\Delta {{\rm{T}}_{\rm{f}}} = \frac{{{{\rm{K}}_{\rm{f}}} \times {{\rm{w}}_2} \times 1000}}{{{{\rm{w}}_1} \times {{\rm{M}}_2}}}\)

\({{\rm{M}}_2} = \frac{{{{\rm{K}}_{\rm{f}}} \times {{\rm{w}}_2} \times 1000}}{{{{\rm{w}}_1} \times \Delta {{\rm{T}}_{\rm{f}}}}}\)

The value of \({{{\rm{K}}_{\rm{f}}}}\) can be determined from the following relations-

\({{\rm{K}}_{\rm{f}}} = \frac{{{\rm{R}} \times {{\rm{M}}_1} \times {\rm{T}}_{\rm{f}}^2}}{{1000 \times {\Delta _{{\rm{fus}}}}{\rm{H}}}}\)

Where \({\rm{R}} = \) gas constant
\({{\rm{M}}_1} = \) molar mass of the solvent
\({\Delta _{{\rm{fus}}}}{\rm{H}} = \) enthalpies for the fusion of the solvent.

Consequences ofzing Point Depression

1. In areas with lower temperatures, salting is done to prevent ice deposition on roads. This is done to lower thezing point of water and prevent ice build-up. The salt interferes with the water’s ability to form solid ice crystals. The salt must be in a solution with liquid water.
2. \({\rm{CaC}}{{\rm{l}}_2}\) is used instead of \({\rm{NaCl}}\) in places with extremely low temperatures to melt the ice on the roads. This is because \({\rm{CaC}}{{\rm{l}}_2}\) dissociates into three ions, whereas \({\rm{NaCl}}\) dissociates into two ions. The more the number of solute particles, the greater is the Depression in thezing point of water.
3. Water and ethylene glycol are generally used to make radiator fluids in automobiles. This is useful in preventing thezing of the radiator during the winter season.
4. Seawater remains liquid at temperatures lower than that of thezing point of pure water. This is due to the salts that are dissolved in the seawater.

Solved Examples

Q.1. Calculate the mass of ascorbic acid (Vitamin \({\rm{C}},\,{{\rm{C}}_6}{{\rm{H}}_8}{{\rm{O}}_6}\)) to be dissolved in \(75\;{\rm{g}}\) of acetic acid to lower its melting point by \(1.5\,^\circ {\rm{C}}\). \({{\rm{K}}_{\rm{f}}} = 3.9\;{\rm{K}}\;{\rm{kg}}\;{\rm{mo}}{{\rm{l}}^{ – 1}}\).
Ans: Mass of acetic acid, \({{\rm{w}}_1} = 75\;{\rm{g}}\) Molar mass of ascorbic acid \(\left( {{{\rm{C}}_6}{{\rm{H}}_8}{{\rm{O}}_6}} \right)\),
\({{\rm{M}}_2} = 6 \times 12 + 8 \times 1 + 6 \times 16 = 176\;{\rm{g}}\;{\rm{mo}}{{\rm{l}}^{ – 1}}\)
Lowering of melting point, \(\Delta {{\rm{T}}_{\rm{f}}} = 1.5\;{\rm{K}}\)

\(\Delta {{\rm{T}}_{\rm{f}}} = \frac{{{{\rm{K}}_{\rm{f}}} \times {{\rm{w}}_2} \times 1000}}{{{{\rm{w}}_1} \times {{\rm{M}}_2}}}\)

\({{\rm{w}}_2} = \frac{{\Delta {{\rm{T}}_{\rm{f}}} \times {{\rm{M}}_2} \times {{\rm{w}}_1}}}{{1000 \times {{\rm{K}}_{\rm{f}}}}} = \frac{{1.5 \times 176 \times 75}}{{1000 \times 3.9}} = 5.08\;{\rm{g}}\)

Hence, \(5.08{\rm{ g}}\) of ascorbic acid is needed to be dissolved.

Summary

We now know the answer to how adding salt to water can be used to make ice cream without azer. On adding salt to the water, the boiling point of the solution increases, whereas itszing point decreases. All these are consequences of vapour pressure lowering due to the addition of a non-volatile solute to a volatile solvent. Next time when you boil an egg, remember to add salt to it. The egg will boil faster.

Frequently Asked Questions

Q.1. Why is there a depression inzing point?
Ans: According to Raoult’s law, when a non-volatile solute is added to a volatile liquid solvent, the vapour pressure of the resulting solution becomes lower than that of the pure solvent. Hence, the temperature required by the liquid solvent to reach its solid state is lowered, resulting in the Depression of thezing point of the solution compared to the solvent. The difference in temperature between thezing point of the pure solvent and that of the solution is called the freezing point depression of a solution.

Q.2. What is the difference between thezing point andzing point depression?
Ans: At normal atmospheric pressure, the temperature at which a liquid becomes a solid is known as thezing point of a liquid. In simple words, it is the temperature at which liquid and solid phases of a substance coexist in equilibrium. A solution willze when its vapour pressure equals the vapour pressure of the pure solid solvent. The difference in temperature between thezing point of the pure solvent and that of the solution is called the freezing point depression of a solution.

Q.3. How iszing point depression used in real life?
Ans: A very common example of this phenomenon in everyday life is the salting of the roads in cold countries. Pure waterzes at \(0\,^\circ {\rm{C}}\). On adding salt to the water, thezing point of water falls below \(0\,^\circ {\rm{C}}\). Hence, water changes to the ice at a relatively lower temperature than that of pure water. The salt interferes with the water’s ability to form solid ice crystals. The salt must be in a solution with liquid water.

Q.4. Iszing point depression a colligative property?
Ans:zing point depression is a colligative property because it depends on the number of solutes added to the solution. This property is observed in solutions that result from introducing solute molecules to a solvent. Thezing points of solutions are directly proportional to the molality of the solute.

Q.5. Why is molality used forzing point depression?
Ans:zing point depression is a colligative property of a solution that depends on the number of solute particles present in the solution. On adding solute to the solvent, the temperature of the solution is changed, which means that the volume of the solution is also changing.

Since molarity is moles solute per litre of solution and depends on the temperature of the solution, we cannot use it as our concentration unit. Therefore we use molality (moles solute per \({\rm{kg}}\) of solvent) since \({\rm{kg}}\) of solvent doesn’t change with temperature.

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