# Raoult's Law Calculator

Created by Komal Rafay
Reviewed by Dominik Czernia, PhD candidate and Jack Bowater
Last updated: Mar 14, 2022

Our Raoult's law calculator is a convenient tool to calculate the vapor pressure of an ideal solution. It not only provides calculation options for the vapor pressure of a solution 🧪 but also for the solvent and mole fraction of the solute as well.

Here you will learn the definition of Raoult's law, what Raoult's law is used for and what its applications are. You will also find answers to your questions of how to find the vapor pressure of a solution and how to calculate mole fraction using Raoult's law.

## Raoult's law equation - calculate the total pressure with Raoult's law

Are you one of those curious people who have wondered what is Raoult's law in chemistry? Well, Raoult's law bears similarities to the ideal gas law - except that it applies to solutions. Raoult's law states that:

The relative lowering of the vapor pressure of a solution containing a non-volatile solute is equal to the mole fraction of the solute in the solution.

Mathematically, we express it using the following formula:

$p_{solution} = x_{solvent} × p\degree_{solvent}$

where:

• $p_{solution}$ - Vapor pressure of an ideal solution;
• $x_{solvent}$ - Mole fraction of the solvent; and
• $p\degree_{solvent}$ -Partial pressure of the pure solvent.

This Raoult's law formula forms the basis of the calculation performed by this Raoult's law calculator.

🔎 In case you are interested, you might find it useful to take a look at our alligation, molarity and molality calculators.

## How to use our Raoult's law calculator - a Raoult's law example

Our Raoult's law calculator primarily determines the vapor pressure of a solution, but you can also use it to calculate the partial pressure or mole fraction of the solvent.

You can choose from two different formulas: one uses the number of moles while the other uses the mole fractions of the solvent.

Start by selecting how you want to determine the vapor pressure. The first option uses moles. To calculate vapor pressure, follow these steps:

1. Input the partial pressure of the solvent. It has a list of units to choose from as well.
2. Input the moles of the solute.
3. Input moles of the solvent.
4. As a result, the calculator will compute the vapor pressure of the solution. It will also plot a graph of vapor pressure vs. mole fraction for you, based on the moles of the solute and solvent provided.

The second option finds vapor pressure using the mole fraction:

1. Input the partial pressure of the solvent.
2. Input the mole fraction of the solvent.
3. As a result, the calculator will work out the** vapor pressure of the solution**. A graph of vapor pressure of the solution vs. the mole fraction of the solvent will be plotted for you.

Let us consider an example of a Raoult's law calculation.

Let's say you have a solution where chemical x is the solvent. It has a partial pressure of 12 mmHg and a mole fraction of 0.25. Multiply 0.25 by 12 to get a vapor pressure of 3 mmHg.

## What is Raoult's law used for?

Raoult's law applies to solutions containing non-volatile solutes ⚗️, which make ideal solutions.

In certain situations, you may want to do the calculations by hand and not use Raoult's law calculator. For that, the following points may come in handy:

• Calculate the total pressure with Raoult's law

To calculate the total pressure with Raoult's law, we will use the formula for Raoult's law mentioned earlier:

$p_{solution} = x_{solvent} × p\degree_{solvent}$

All you need to do is find the vapor pressure of the solvent and multiply it by the mole fraction of the solvent As a result, you get the vapor pressure of the solution. This method applies to non-volatile solutes, and you may need to use other methods to calculate the total pressure for volatile solutes.

• How to find the vapor pressure of a solvent

Vapor pressure is a characteristic of solids and liquid that depends on the type of liquid and its temperature.

The formula for Raoult's law can be modified to calculate the vapor pressure of the solvent:

$p\degree_{solvent} = p_{solution} / x_{solvent}$

In this case, you divide the vapor pressure of the solution by the mole fraction of the solvent, and as a result, you will get the vapor pressure of the pure solvent.

• How to calculate mole fraction using Raoult's law

The Raoult's law calculator can also calculate the mole fraction of a solvent in a solution.
The modified form of the Roault's law formula becomes:

$x_{solvent} = p_{solution} / p\degree_{solvent}$

To calculate the mole fraction using Raoult's law, you divide the solution's vapor pressure by the solvent's vapor pressure.

There are other methods used to calculate the mole fraction of a solution without using Raoult's law. If you want to know more, check out our mole fraction calculator.

## Raoult's law graph

Our tool also allows you to plot a graph showing the vapor pressure and its mole fraction of the solution.
The mole fraction is on the x-axis, and vapor pressure is on the y-axis.

The Raoult's law graph is a straight line, which means that the partial vapor pressure of a substance is proportional to its mole fraction under the condition that the temperature remains the same.

## Applications of Raoult's law

One of the most widely used laws to study non-aqueous mixtures is Raoult's law. It applies to ideal solutions, which means solutions where the solute is non-volatile.

You can find some applications of Raoult's law below:

1. It helps determine the molecular mass of an unknown solute.

2. It can also be applied to non-ideal solutions by accounting for certain other factors, such as the intermolecular interactions.

3. Raoults's law is significant in the calculation of the contributions of each component in a mixture to the total pressure exerted by the system. This is particularly true for mixtures where we know the quantity of each component.

## FAQ

### What does Raoult's law state?

Raoult's law states that:

The relative lowering of the vapor pressure of a solution containing a non-volatile solute is equal to the mole fraction of the solute in the solution.

It gives the value of vapor pressure at which the solvent evaporates from liquid to gas.

### What is the equation of Raoult's law?

The equation of Raoul's law is:

p = x × p°

where:

• x - Mole fraction of solvent;
• p - Vapor pressure of an ideal solution; and
• p° - Partial pressure of the pure solvent.

To calculate the vapor pressure of an ideal solution, you have to multiply the mole fraction of the solvent by the partial pressure of the solvent.

For instance, if the mole fraction is 0.3 and partial pressure is 9 mmHg, the vapor pressure would be 2.7 mmHg.

### How do I calculate mole fraction using Raoult's law ?

To calculate the mole fraction using Raoult's law:

1. Find the vapor pressure of an ideal solution.
2. Determine the partial pressure of the pure solvent.
3. Divide the first value by the second to obtain the mole fraction.

For instance, 3 mmHg and 5 mmHg are the vapor and partial pressure values, respectively. To calculate the mole fraction, divide 3 by 5 to get 0.6.

### What is the vapor pressure of a solution with a mole fraction of 0.86?

Let's assume the partial pressure of the solution is 24.7 mmHg, in which case its vapor pressure is 21.24 mmHg.

This value indicates the pressure at which the solvent molecules in the solution will evaporate. The value is determined by simply multiplying the partial pressure by the mole fraction. So, multiplying 0.86 by 24.7, you get 21.24 mmHg.

Komal Rafay
Partial pressure of solvent (pº)
mmHg
Moles of solute (n₁)
mol
Moles of solvent (n₂)
mol
Mole fraction of solvent (x)
Vapor pressure of solution (p)
mmHg
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