freezing point depression formula

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18-03-2025

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Freezing point depression is a colligative property, meaning it depends on the number of solute particles in a solution, not their identity. This phenomenon describes the decrease in the freezing point of a solvent when a solute is added. Understanding the freezing point depression formula is crucial in various scientific and practical applications.

Understanding the Formula

The freezing point depression formula is expressed as:

ΔTf = Kf * m * i

Where:

• ΔTf: Represents the change in freezing point (in °C or K). This is the difference between the freezing point of the pure solvent and the freezing point of the solution.
• Kf: Is the cryoscopic constant (in °C·kg/mol or K·kg/mol). This constant is specific to the solvent and represents the extent to which the freezing point is lowered for a 1 molal solution. You can find cryoscopic constants for common solvents in chemistry handbooks or online resources.
• m: Represents the molality of the solution (in mol/kg). Molality is defined as the number of moles of solute per kilogram of solvent. It's crucial to use molality, not molarity, in this calculation because molality is independent of temperature.
• i: Represents the van't Hoff factor. This factor accounts for the number of particles a solute dissociates into when dissolved in the solvent. For non-electrolytes (substances that don't dissociate into ions), i = 1. For strong electrolytes (like NaCl, which dissociates into Na+ and Cl-), i is approximately equal to the number of ions formed per formula unit. For weak electrolytes, 'i' is between 1 and the theoretical number of ions, depending on the degree of dissociation.

Calculating Freezing Point Depression: A Step-by-Step Example

Let's calculate the freezing point depression of a solution containing 10 grams of ethylene glycol (C₂H₆O₂) in 100 grams of water. The molar mass of ethylene glycol is 62.07 g/mol, and the cryoscopic constant (Kf) for water is 1.86 °C·kg/mol. Ethylene glycol is a non-electrolyte, so i = 1.

Step 1: Calculate the molality (m)

1. Moles of ethylene glycol: (10 g) / (62.07 g/mol) = 0.161 moles
2. Kilograms of water: (100 g) / (1000 g/kg) = 0.1 kg
3. Molality: (0.161 moles) / (0.1 kg) = 1.61 mol/kg

Step 2: Apply the formula

ΔTf = Kf * m * i = (1.86 °C·kg/mol) * (1.61 mol/kg) * (1) = 2.99 °C

Step 3: Determine the new freezing point

The freezing point of pure water is 0 °C. Therefore, the new freezing point of the solution is 0 °C - 2.99 °C = -2.99 °C.

Applications of Freezing Point Depression

Freezing point depression has numerous practical applications:

• De-icing: Salts like sodium chloride (NaCl) are spread on roads and sidewalks to lower the freezing point of water, preventing ice formation. The van't Hoff factor plays a significant role here; NaCl dissociates into two ions, resulting in a greater freezing point depression than a non-electrolyte of the same molality.
• Antifreeze: Ethylene glycol is commonly used as an antifreeze in car radiators. It lowers the freezing point of the coolant, preventing it from freezing in cold weather.
• Food preservation: Freezing food at lower temperatures helps preserve it for longer periods. Adding salt or sugar to food lowers the freezing point, allowing for faster and more efficient freezing.
• Determination of molar mass: The freezing point depression can be used to determine the molar mass of an unknown solute. By measuring the change in freezing point and knowing the cryoscopic constant of the solvent, the molality and subsequently the molar mass can be calculated.

Limitations of the Formula

The formula for freezing point depression provides a good approximation, but several factors can influence its accuracy:

• Ideal solutions: The formula assumes an ideal solution, meaning there are no significant interactions between solute and solvent molecules. In real-world solutions, these interactions can affect the accuracy of the calculation.
• Concentrated solutions: The formula is most accurate for dilute solutions. At higher concentrations, deviations from ideality become more significant.
• Ion pairing: In electrolyte solutions, ion pairing can reduce the effective number of particles, leading to a lower than expected freezing point depression.

Understanding the freezing point depression formula and its applications is essential in various fields of science and engineering. While the formula provides a good approximation, it's crucial to be aware of its limitations and the factors that can affect its accuracy.