# How to calculate freezing point

Understanding how to calculate the freezing point of a substance is essential in various scientific and industrial applications. This article will walk you through the process of calculating freezing point, explain the concepts behind it, and offer examples to clarify the procedure.

**1. Basic concepts of freezing point:**

Freezing point is the temperature at which a liquid turns into a solid. Pure substances like water have a fixed freezing point (0°C or 32°F) under stable atmospheric pressure. However, when impurities or solutes are introduced, the freezing point of the solution will usually decrease. This phenomenon is known as freezing-point depression.

**2. Freezing-point depression:**

The change in the freezing point of a solution compared to a pure solvent’s freezing that occurs upon adding a solute, such as salt or sugar, is called freezing-point depression (ΔTf).

**3. Calculating freezing-point depression:**

To calculate the change in freezing point (ΔTf), use this formula:

ΔTf = Kf * molality * i

Where:

– ΔTf is the freezing-point depression (°C or K)

– Kf is the cryoscopic constant or molal freezing point depression constant for specific solvent (°C/m or K/m)

– molality is the molality of solution (mol/kg), defined as moles of solute per kilogram of solvent

– i is the van ‘t Hoff factor, accounting for electrolyte dissociation in solutions

**4. Cryoscopic constant (Kf):**

The cryoscopic constant differs for each solvent and represents its sensitivity to impurities concerning lowering its freezing point. For example, water has a Kf value of 1.86 °C/m.

**5. Van ‘t Hoff factor (i):**

The van ‘t Hoff factor accounts for dissociation in solutions containing ions, such as electrolytes. For non-electrolytes (e.g., sugar), the factor is 1. For a strong electrolyte (e.g., NaCl), the factor is equal to the number of ions produced from the dissociation, in this case, 2.

**6. Example:**

To illustrate how to calculate freezing point, let’s use a saltwater solution containing 20 g of NaCl and 1 kg of water.

**Step 1: Calculate molality**

Number of moles (NaCl) = mass (g) / molar mass (g/mol) = 20 g / (58.44 g/mol) ≈ 0.342 mol

molality = moles of solute/weight of solvent in kg = 0.342 mol / 1 kg of water ≈ 0.342 mol/kg

**Step 2: Find ΔTf**

ΔTf = Kf * molality * i = (1.86 °C/m) * (0.342 mol/kg) * (2) ≈ 1.27°C

**Step 3: Determine the new freezing point**

New freezing Point = pure solvent freezing point – ΔTf

New freezing point (saltwater solution) = 0°C – 1.27°C ≈ -1.27°C

**Conclusion:**

The calculations above illustrate that adding salt to water creates a solution with a lower freezing point than pure water, resulting in a freezing point of approximately -1.27°C for our example saltwater solution. Understanding how to calculate freezing points is fundamental for numerous applications, including using antifreeze agents in engines and optimizing temperature-controlled environments for perishable goods during transportation or storage.