Mole Fraction Calculator
Mole fraction tells you what share of all the molecules in a mixture belongs to each component. Choose your input mode: enter moles directly, let the calculator convert masses using molar masses, or use partial pressures for a gas mixture. Results include each mole fraction, mole percent, molality (for solution mode), and an optional Raoult's law vapour pressure.
Formula
Worked example
A solution contains 36 g of water (molar mass 18.015 g/mol, so 2.00 mol) and 46 g of ethanol (molar mass 46.068 g/mol, so 1.00 mol). Total moles = 3.00. chi_water = 2.00 / 3.00 = 0.667, chi_ethanol = 1.00 / 3.00 = 0.333. They sum to 1.00. If pure water has a vapour pressure of 23.8 mmHg at 25 C, Raoult's law gives the partial vapour pressure of water as 0.667 x 23.8 = 15.9 mmHg.
What mole fraction measures
Mole fraction is a way of expressing concentration based on counting molecules rather than weighing them or measuring volume. The mole fraction of a component, written with the Greek letter chi (chi), is the number of moles of that component divided by the total number of moles of every substance in the mixture. Because both the numerator and denominator are in moles, the units cancel and the result is a pure number between 0 and 1. A value of 0 means the component is absent; a value approaching 1 means the mixture is almost entirely that substance. Mole fraction is valued in thermodynamics because, unlike molarity, it does not change with temperature: moles do not expand or contract when a solution is warmed.
Three calculation modes explained
This calculator offers three input modes to match however your data arrives. In moles mode you type the amount of each substance directly; this is the fastest path when you have already done the moles conversion. In mass mode you enter the mass and molar mass of each component and the calculator divides them for you: n = mass / molar mass. This mode also returns molality (moles of solute per kilogram of solvent), which is useful for boiling-point elevation and osmotic-pressure problems. In gas mode the calculator applies Dalton's law: the mole fraction of a gas equals its partial pressure divided by the total pressure of the mixture, so you only need partial pressures, not moles at all. All three modes support two or three components, and the fractions always sum to 1 as a built-in check.
Raoult's law and vapour pressure
In moles mode you can enable Raoult's law to estimate the partial vapour pressure of component A above the solution. Raoult's law states that the partial vapour pressure of a component equals its mole fraction multiplied by the vapour pressure of the pure component at the same temperature: P_A = chi_A x P*_A. For example, water at 25 C has a pure vapour pressure of 23.8 mmHg. If water's mole fraction in a solution is 0.667, its partial vapour pressure is 0.667 x 23.8 = 15.9 mmHg. The law holds well for ideal solutions such as benzene-toluene mixtures, and is a starting approximation for dilute non-ideal solutions. It underpins vapour-liquid equilibrium calculations in distillation and is the theoretical basis for colligative-property predictions.
Why the fractions always add to one
Every component in a mixture is divided by the same denominator: the total moles present. When you add the individual numerators together you recover that total, so the sum of all mole fractions must equal one by construction. This makes mole fraction self-checking: if your values do not add to 1.00, there is an arithmetic error somewhere. The same property holds in gas mode, where each partial pressure is a fraction of the total pressure. The calculator shows a verification step in the "show your work" panel so you can confirm the sum without doing any extra arithmetic.
Mole fraction reference: common mixtures
| Mixture | chi_A | chi_B | Mole % A | Mole % B |
|---|---|---|---|---|
| 2 mol A + 3 mol B | 0.4000 | 0.6000 | 40.00 | 60.00 |
| 1 mol A + 1 mol B | 0.5000 | 0.5000 | 50.00 | 50.00 |
| 1 mol A + 9 mol B | 0.1000 | 0.9000 | 10.00 | 90.00 |
| 4 mol A + 1 mol B | 0.8000 | 0.2000 | 80.00 | 20.00 |
| Air: O2 (0.21 atm) + N2 (0.78 atm) + Ar (0.01 atm) | 0.2100 | 0.7800 | 21.00 | 78.00 |
Calculated values; all fractions within a row sum to 1. Mass-mode examples use water (18.015 g/mol) and ethanol (46.068 g/mol).
Frequently asked questions
What is the difference between mole fraction and molarity?
Molarity is moles of solute per litre of solution, so it depends on volume and therefore on temperature. Mole fraction is moles of a component divided by the total moles, a pure ratio with no volume term, so it stays constant when the temperature changes. Use molarity for lab-preparation calculations and mole fraction for thermodynamic and vapour-pressure work.
Can a mole fraction be greater than 1?
No. Each component's moles are part of the total, so any single mole fraction lies between 0 and 1. The fractions of all components in a mixture must add up to exactly 1, which is a quick arithmetic check you can use to catch calculation errors.
How do I find moles from a mass to use this calculator?
Divide the mass of each substance by its molar mass: n = mass (g) / molar mass (g/mol). For example, 18 g of water has a molar mass of 18.015 g/mol, giving about 1.00 mol. Alternatively, switch to mass mode and enter the mass and molar mass directly: the calculator does the division for you and also returns molality.
How do I use mole fraction for gas mixtures?
Switch to gas mode and enter the partial pressure of each gas in any consistent unit (atm, kPa, mmHg). The calculator applies Dalton's law: chi_i = P_i / P_total. For example, the mole fraction of oxygen in dry air is roughly 0.21 because its partial pressure is about 0.21 atm out of 1.00 atm total.
What is Raoult's law and how does this calculator use it?
Raoult's law states that the partial vapour pressure of a component above an ideal solution equals its mole fraction times the vapour pressure of the pure component at the same temperature: P_A = chi_A x P*_A. Enable the Raoult's law toggle in moles mode, enter the pure vapour pressure of component A, and the calculator returns the partial vapour pressure above the solution. This is useful for distillation design and colligative-property predictions.
What is the difference between mole fraction and mole percent?
Mole percent (also called molar percentage or n/n%) is simply the mole fraction multiplied by 100. A mole fraction of 0.40 equals 40 mole percent. Both express the same information; mole fraction is the dimensionless ratio used in equations, while mole percent is more intuitive for reporting composition.