Freezing point depression is a phenomenon that occurs when a solute is added to a solvent, resulting in a decrease in the freezing point of the solution as compared to the pure solvent. This process plays a crucial role in various applications, such as antifreeze solutions for automobile engines and maintaining desired physical properties in food and pharmaceutical products. In this article, we will delve into the process of calculating freezing point depression using simple equations and relevant examples.

The Cryoscopic Constant and Molality:

To calculate the freezing point depression, it is essential to understand two key concepts:

1. Cryoscopic constant (Kf): specific to each solvent, this constant represents the freezing point depression of a one molal (1m) solution of a non-volatile solute. It is expressed in °C m⁻¹ and can be found in reference books or tables.

2. Molality (m): a concentration unit defined as the number of moles of solute per kilogram of solvent. It is expressed in mol kg⁻¹.

The Freezing Point Depression Equation:

The equation for freezing point depression is simple and easy to use:

ΔTf = Kf × m

Where,

ΔTf = Freezing Point Depression (°C)

Kf = Cryoscopic Constant (°C m⁻¹)

m = Molality (mol kg⁻¹)

Step-by-Step Guide to Calculate Freezing Point Depression:

Follow these steps to calculate freezing point depression for a given solution:

1. Identify the cryoscopic constant (Kf) for your particular solvent. This information can be found in reference books or tables.

2. Determine the molality (m) of your solution by calculating the moles of solute dissolved per kilogram solvent.

3. Apply the freezing point depression equation (ΔTf = Kf × m) using the values obtained in steps 1 and 2 to calculate the freezing point depression (ΔTf).

Example:

Let’s take a look at an example using a solution of 0.85 moles NaCl (solute) dissolved in 1 kg of water (solvent). The cryoscopic constant for water is 1.86 °C m⁻¹.

1. Kf for water is 1.86 °C m⁻¹.

2. Molality (m) is given as 0.85 mol kg⁻¹.

3. Apply the freezing point depression equation: ΔTf = Kf × m = 1.86 °C m⁻¹ × 0.85 mol kg⁻¹ = 1.581 °C.

So, the freezing point depression of this solution is 1.581 °C.

Conclusion:

Calculating freezing point depression is a straightforward process that involves using the cryoscopic constant and molality of a solution containing a non-volatile solute. By mastering this calculation, you can better understand how adding solutes to solvents affects the physical properties of solutions for various applications, from de-icing to preserving food and pharmaceutical products.