# Freezing Point Depression Calculator

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:

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:

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:

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 $1.9$.

Adjusting the formula for freezing point depression to include the van't Hoff factor:

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:

Let's calculate the freezing point of this solution:

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:

- Enter the
**molality**of the solution. - 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. - If the solute is an electrolyte, click on the
`Advanced mode`

button to provide the**van't Hoff factor**. Otherwise, leave its value at $1$. - 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!