# Freezing Point Depression Calculator

Created by Krishna Nelaturu
Last updated: Jul 04, 2022

This freezing point depression calculator will help you determine the drop in the solution's freezing point compared to the pure solvent's freezing point when you add a non-volatile solute. We use this phenomenon everywhere, from de-icing roads to keeping ice cream soft in subzero temperatures. Are you curious to learn more about freezing point depression? Grab some ice cream🍧 to set the mood and scroll through this article as we discuss some fundamentals, including:

• What is freezing point depression?
• Freezing point depression formula
• Molal freezing point depression constant and van't Hoff factor
• Calculating the freezing point of a solution

Adding a solute changes the boiling point of the solution too! Learn how through our boiling point elevation calculator.

## What is freezing point depression?

When we add a non-volatile solute to a pure solvent, we notice a drop in the freezing point of the resulting solution, which means that the solution will freeze at a lower temperature than the pure solvent. We call this phenomenon the freezing point depression of a solution.

Pure water freezes at $0 \degree \text{C}$ or $32 \degree \text{F}$. Let's say you add some salt to form a saltwater solution. Due to freezing point depression, we know that the saltwater freezing point is lower than $0 \degree \text{C}$. In the following sections, we shall learn how to calculate the freezing point depression for our saltwater solution.

To avoid cumbersome temperature conversions, use our temperature converter.

## Freezing point depression equation

The freezing point depression is directly proportional to the solute concentration. Let us first define the freezing point depression $\Delta T_f$ as:

$\Delta T_f = T_{f(solvent)} - T_{f(solution)}$

where:

• $\Delta T_f$ - The freezing point depression of the solution;
• $T_{f(solvent)}$ - The freezing point of the pure solvent; and
• $T_{f(solution)}$ - The freezing point of the solution.

The formula for the freezing point depression is given by:

$\Delta T_f = K_f \cdot m$

where:

• $K_f$ - The molal freezing point depression constant, also called the cryoscopic constant;
• $m$ - The molality of the solution.

## Molal freezing point depression constant and van't Hoff factor

In our saltwater example, suppose the salt concentration is $1 \text{ mol/kg}$ (or 1 molal), then the freezing point depression equals the cryoscopic constant. In other words, the molal freezing point depression constant is the freezing point depression observed in a 1-molal solution.

Its units are $\text{K}\cdot\text{kg/mol}$, $\text{C}\cdot\text{kg/mol}$ and $\text{F}\cdot\text{kg/mol}$. The value of this constant depends on the solvent's properties, not the solute. The following table lists some values for selected solvents:

Freezing point depression constant for some solvents.

Solvent

Freezing point $(\degree \text{C})$

$K_f (\text{C}\cdot\text{kg/mol})$

Water

0

1.86

Benzene

5.5

5.12

Chloroform

-63.5

4.68

Ethanol

-114.6

1.99

Phenol

41

7.27

This table shows that our 1-molal saltwater solution would result in a $1.86\degree \text{C}$ freezing point decrease. But this is not the complete story, especially for electrolytic solutes like salt.

While the freezing point depression formula we have seen is enough for non-electrolytes, there is more to consider for electrolytes because they will dissociate into ions in a solution. Dissociation will result in a greater concentration of particles than what is reflected by their total mass. In water, table salt $(\text{NaCl}$) will dissolve into its ions $\text{Na}^+$ and $\text{Cl}^-$, so there are twice the number of particles in the solution than what morality indicates.

We introduce the van't Hoff factor as the ratio of the concentration of particles and the number of moles of formula units dissolved. For most electrolytes, this is equal to the number of ions in one formula unit of the solute. However, the actual concentration might be slightly less due to ionic pairing. For $\text{NaCl}$, although there are two ions in the formula unit, the measured van't Hoff factor is $1.9$.

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

Here $i$ is the van't Hoff factor. For non-electrolytes, its value is $1$.

Let's test our understanding of how to calculate the freezing point depression on our 1-molal saltwater:

\begin{align*} \Delta T_f &= i \cdot K_f \cdot m\\ &= 1.9 \cdot 1.8 \cdot 1\\ \Delta T_f &= 3.42 \degree \text{C}\\ \end{align*}

Let's calculate the freezing point of this solution:

\begin{align*} \Delta T_f &= 3.42 \degree \text{C}\\ T_{f(water)} -& T_{f(saltwater)} = 3.42\\ T_{f(saltwater)} &=T_{f(water)} - 3.42\\ &= 0 - 3.42\\ T_{f(saltwater)} &= 3.42 \degree \text{ C} \end{align*}

Now you know how to find the freezing point depression of a solution.

## How to use this freezing point depression calculator

This freezing point depression calculator is simple to use:

1. Enter the molality of the solution.
2. Select any solvent from the drop-down list to generate its freezing point depression constant. Alternatively, you can manually enter a custom value for the constant.
3. If the solute is an electrolyte, click on the Advanced mode button to provide the van't Hoff factor. Otherwise, leave its value at $1$.
4. Provide the freezing point of the pure solvent to calculate the solution's freezing point.

Our tool is versatile enough for you to enter any two known parameters to calculate the third unknown parameter. Try it!

Krishna Nelaturu
Molality
mol
/kg
Solvent (optional)
Water
Freezing point depression constant
°F
kg/mol
Freezing point of pure solvent
°F
Freezing point of solution
°F
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