Freezing Point Depression: Videos & Practice Problems

Freezing point depression occurs when a solute is added to a pure solvent, lowering its freezing point. The change in freezing point (ΔT_f) can be calculated using the formula ΔT_f = I × K_f × m, where I is the van’t Hoff factor, K_f is the freezing point constant, and m is the molality (moles of solute per kilogram of solvent). The freezing point of the solution is the normal freezing point of the solvent minus ΔT_f. More solute results in a greater decrease in freezing point.

Freezing Point Depression Concept 1

The phenomenon of freezing point depression occurs when a solute is added to a pure solvent, resulting in a decrease in the solvent's freezing point. The normal freezing point (fp) refers to the freezing point of the pure solvent before any solute is introduced, while the freezing point of the solution (fp solution) is the freezing point after the solute has been added. This change in freezing point can be quantified using the freezing point depression formula:

$$\Delta T_f = i \cdot K_f \cdot m$$

In this equation, ΔT_f represents the change in freezing point, i is the van't Hoff factor (which accounts for the number of particles the solute dissociates into), K_f is the freezing point constant of the solvent (expressed in degrees Celsius per molality), and m is the molality of the solution, defined as the number of moles of solute per kilogram of solvent.

To determine the freezing point of a solution, the relationship can be expressed as:

$$\text{Freezing Point of Solution} = \text{Freezing Point of Pure Solvent} - \Delta T_f$$

Common solvents such as water, benzene, chloroform, and ethanol each have distinct normal freezing points and unique freezing point constants. While it is not necessary to memorize these values, understanding that the freezing point decreases with the addition of solute is crucial. The more solute added, the greater the depression of the freezing point, illustrating the significant impact of solute concentration on the physical properties of solutions.

Freezing Point Depression Example 1

To calculate the freezing point of a solution containing glucose (C₆H₁₂O₆) dissolved in water, we start with the formula for the freezing point depression:

Freezing Point of Solution = Freezing Point of Solvent - ΔT_f

In this case, the solvent is water, which has a freezing point of 0 degrees Celsius. To find ΔT_f, we use the equation:

ΔT_f = I × K_f × m

Here, I is the van 't Hoff factor, which is 1 for glucose since it is a covalent compound and does not dissociate into ions. The freezing point constant (K_f) for water is 1.86 °C/m.

Next, we need to calculate the molality (m) of the solution. First, we convert the mass of water from grams to kilograms:

302.6 g of water = 0.3026 kg of water

Now, we calculate the number of moles of glucose using its molar mass (180.156 g/mol):

Moles of glucose = 110.7 g × (1 mol / 180.156 g) = 0.6145 mol

Now we can find the molality:

m = moles of solute / kg of solvent = 0.6145 mol / 0.3026 kg ≈ 2.03 mol/kg

Now we can substitute the values into the ΔT_f equation:

ΔT_f = 1 × 1.86 °C/m × 2.03 mol/kg ≈ 3.78 °C

Finally, we can find the new freezing point of the solution:

Freezing Point of Solution = 0 °C - 3.78 °C = -3.78 °C

Thus, the freezing point of the glucose solution is approximately -3.78 degrees Celsius.

How many moles of ethylene glycol, C₂H₆O₂, must be added to 1,000 g of water to form a solution that has a freezing point of – 10ºC?

• A. 334 moles
• B. 5.4 moles
• C. 3.2 moles
• D. 200 moles

Answer: (B)

An ethylene glycol solution contains 28.3 g of ethylene glycol, C₂H₆O₂ in 97.2 mL of water. Calculate the freezing point of the solution. The density of water 1.00 g/mL.

• A. –8.72°C
• B. –0.848°C
• C. –0.541°C
• D. –17.4°C

Answer: (A)

When 825 g of an unknown is dissolved in 3.45 L of water, the freezing point of the solution is decreased by 2.89ºC. Assuming that the unknown compound is a non-electrolyte, calculate its molar mass.

• A. 154 g/mol
• B. 42.4 g/mol
• C. 44.5 g/mol
• D. 159 g/mol

Answer: (A)

Here’s what students ask on this topic:

What is freezing point depression and how is it calculated?

Freezing point depression occurs when a solute is added to a pure solvent, causing the freezing point of the solvent to decrease. The change in freezing point (ΔT_f) can be calculated using the formula:

$\mathrm{\Delta T_f}=I\times \mathrm{K_f}\times m$

where I is the van’t Hoff factor (number of particles the solute dissociates into), K_f is the freezing point depression constant of the solvent, and m is the molality (moles of solute per kilogram of solvent). The freezing point of the solution is then the normal freezing point of the pure solvent minus ΔT_f.

How does the van’t Hoff factor affect freezing point depression?

The van’t Hoff factor (I) represents the number of particles into which a solute dissociates in solution. It directly affects the magnitude of freezing point depression. For example, if a solute dissociates into more particles, the van’t Hoff factor increases, leading to a greater decrease in the freezing point. The formula for freezing point depression is:

$\mathrm{\Delta T_f}=I\times \mathrm{K_f}\times m$

Thus, a higher I value results in a larger ΔT_f, meaning the solution's freezing point is lower.

What is the difference between the normal freezing point and the freezing point of a solution?

The normal freezing point is the temperature at which a pure solvent freezes. It is denoted as f.p. The freezing point of a solution, on the other hand, is the temperature at which a solvent containing a dissolved solute freezes. This temperature is lower than the normal freezing point due to freezing point depression. The relationship can be expressed as:

$\mathrm{f.p.\; solution}=\mathrm{f.p.\; pure\; solvent}-\mathrm{\Delta T_f}$

where ΔT_f is the change in freezing point caused by the addition of the solute.

Why does adding a solute to a solvent lower its freezing point?

Adding a solute to a solvent lowers its freezing point because the solute particles disrupt the formation of the solid structure of the solvent. This disruption requires a lower temperature to achieve the same solid structure, thus lowering the freezing point. The phenomenon is quantified by the freezing point depression formula:

$\mathrm{\Delta T_f}=I\times \mathrm{K_f}\times m$

where I is the van’t Hoff factor, K_f is the freezing point depression constant, and m is the molality of the solution.

What are some common solvents and their freezing point constants?

Some common solvents and their freezing point constants (K_f) are:

• Water: K_f = 1.86 °C·kg/mol
• Benzene: K_f = 5.12 °C·kg/mol
• Chloroform: K_f = 4.68 °C·kg/mol
• Ethanol: K_f = 1.99 °C·kg/mol

These constants are used in the freezing point depression formula to calculate the change in freezing point when a solute is added to these solvents.