# Mole Fraction Calculator

Created by Łucja Zaborowska, MD, PhD candidate
Reviewed by Bogna Szyk and Jack Bowater
Last updated: Jun 14, 2023

Our mole fraction calculator is a handy tool that computes the mole fraction of your solutions using two different methods. It doesn't matter if you only know the total number of moles in a solution, or your task requires you to work with solvents and solutes - we're here for you to help!

In the text below, we will explore the details of the mole fraction formula, calculate the mole fraction of gas, and transform mole fraction to molality.

Hey! You may also find our molality calculator and molarity calculator useful. 😉

## What is mole fraction?

Mole fraction is a concentration unit that relates the moles of a particular solute to the total moles of a solution. It provides a measure of the proportion of a specific substance in a mixture.

## How to use the mole fraction calculator?

Our tool can be used in two ways - it all depends on your initial data. Firstly, a few essential definitions:

1. Solute - a minor part of the solution, dissolved in a solvent. The mixture may contain several different solutes;
2. Solvent - the greater part of the solution which dissolves the solute; and
3. Solution - a homogenous mixture of at least two substances (homogenous means you cannot distinguish the parts of the mixture).

Method #1

This is the method you'll use if you've been given the following data:

• Number of moles of a solute; and
• Number of moles of the solvent.

This method works best if there's only one solute in the mixture. You can still use this method for multiple solutes, however, you just need to add the moles of other solutes to the moles of the solvent.

Method #2

If you already know the number of moles of your entire solution, then this is what you need! This method is also handier when you have multiple solutes dissolved in one solution.

• Number of moles of a solute; and
• Number of moles of a solution.

🔔 You can use the calculator several times to find out the mole fraction of multiple substances dissolved in the same solution!

Remember ! The sum of all the mole fractions is always equal to 1.

## How to calculate the mole fraction of a solution?

This is the part of the text where we tell you how to use the mole fraction formula all by yourself. It might look scary, but it's not as difficult as you may think:

$\scriptsize \begin{split} &\text{Mole fraction} (X_{\text{solute}}) = \frac{\text{moles of solute}} {\text{total moles of solution}} \\ &\text{or} \\ &\text{Mole fraction} (X_{\text{solute}}) = \frac{\text{moles of solute}} {\text{(moles of solute + moles of solvent)}} \end{split}$

How to calculate the mole fraction of a solution with multiple solutes?

The proper, expanded version of the formula looks as follows:

$\scriptsize \begin{split} &\text{Mole fraction} (X_{\text{solute}}) = \\ &\frac{\text{moles of solute}} {\mathrm{(moles\ of\ solute_1 + ...+ moles\ of\ solute_\mathit{n} + moles\ of\ solvent)}} \end{split}$

Where n is the number of solutes in the solution. You need to add exactly as many solutes as you have in your mixture.

Do you already know how to calculate the molar mass and titrate your solution and its substances? 👩🏽‍🔬 👨🏻‍🔬 If not, our titration calculator can be of help.

## How to calculate the mole fraction of a gas?

The mole fraction of gas can be calculated in a very similar way to method #2: the fundamental principle stays the same - we just change the variables.

$\text{Mole fraction} (X_a) = P_a/P_t$

Where:

• $X$ is the molar fraction of a gas A;
• $P_a$ is the partial pressure of gas A; and
• $P_t$ is the partial pressure of every gases present = $P_a + P_b + P_c...$ etc.

You may need to calculate the molar mass of the gas.

## How to find a mole percent?

Molar percentage (n/n%) is the mole fraction multiplied by 100!

n/n% = mole fraction * 100

## How to convert mole fraction to molality?

You'll need to use both of the methods presented in our mole fraction calculator.

1. Calculate the mole fraction using the mole fraction formula.

2. You need to assume that the total amount of moles in the solution is equal to 1 (method #2).

3. Calculate the number of moles of the solvent (method #1).

4. Find the mass of calculated moles of the solvent:
mass = moles * molar mass.

5. Take the number of moles of solute calculated in point 2 and divide them by the estimated mass of the solvent:
moles of solute / mass of solvent = molality.

Mole fraction plays an important role in calculating the vapor pressure of a solution using Raoult's law. To learn more, visit the Raoult's law calculator.

## FAQ

### What's the mole fraction of oxygen in air?

The mole fraction of oxygen in the air is 0.21053. To calculate the mole fraction of oxygen in the air, follow these steps:

1. Use the mole fraction formula for gases, which involves taking the ratio of the partial pressure of gas A Pa to the partial pressure of all the gases present in the mixture Pt:

Xa = Pa / Pt

2. Substitute the partial pressure values. For air at sea level, its partial pressure is 760 mmHg, and for oxygen, it's 160 mmHg:

Xa = 160 mmHg / 760 mmHg
Xa = 0.21053.

### What's the mole fraction of a 17.5% nitric acid solution?

The mole fraction of the nitric acid solution HNO3 is 0.05721. Follow these steps to calculate this value:

1. Assume a 100 g solution, where 17.5 g are HNO3.

2. Calculate or look up the molar mass of HNO3, which is 63.01 g/mol.

3. Determine the moles of HNO3:

moles = mass / molar_mass = 17.5 g / 63.01 g/mol = 0.2778 mol

4. Similarly, calculate the moles of water:

moles = mass / molar_mass = (100 g - 17.5 g) / 18.02 g/mol = 4.5782 mol

5. Use the mole fraction formula:

Xsolute = moles_solute / moles_solution

Xsolute = 0.2778 mol / (0.2778 mol + 4.5782)

Xsolute = 0.05721.

### Why is the total mole fraction equal to 1?

The total mole fraction of a mixture equals 1 because it represents all the components in the solution. The mole fractions of the solutes and solvent are parts of the total moles of the solution. When we add up these fractions, they equal the whole.

### How do I find the mole fraction of a solution?

To find the mole fraction of a solution, follow these steps:

1. Determine the number of moles of the solute and the total moles of the solution.

2. Apply the mole fraction formula:

X(solute) = moles_solute / moles_solution.

3. Substitute the values for the moles of the solute and moles of the solution.

4. Calculate.

Łucja Zaborowska, MD, PhD candidate Solute
mol
Solvent
mol
Solution
mol
Mole fraction
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