Mole Fraction Calculator (2 to 4 Components)
Find the mole fraction and mole percent of each component in a mixture of 2 to 4 substances from moles or from grams and molar mass, with mass percent, molality, partial pressures (Dalton’s law) and the worked steps.
How it works
xᵢ = nᵢ ÷ (n_A + n_B + …) · nᵢ = mᵢ ÷ Mᵢ (from grams) · Σx = 1 · mole % = x × 100 · mass % = mᵢ ÷ Σm × 100 · molality = nᵢ ÷ kg of solvent · pᵢ = xᵢ × P (Dalton)
The mole fraction (IUPAC: amount fraction) of a component is its share of all the moles in the mixture, which is the same as its share of all the molecules. It has no units and the fractions of every component add up to exactly 1, so mole percent is simply the fraction × 100. Choose whether you know the moles or the grams of each component and how many components there are (2 to 4). From grams the calculator first divides each mass by its molar mass to get moles. With moles and every molar mass filled in it also converts back to grams and gives the mass percent (w/w), which differs from the mole percent whenever the molar masses differ, and the molality of each solute with B taken as the solvent. Enter a total pressure under More options to get each gas’s partial pressure from Dalton’s law, p = x × P, which holds for ideal gases. For salts and acids that dissociate, the molecular mole fraction ignores the ions; count the ions yourself if you need particle fractions for vapor pressure, freezing point or boiling point work.
Worked example
A mixture of 1 mol of ethanol (A, 46.07 g/mol) and 3 mol of water (B, 18.015 g/mol) has 4 mol in total. xA = 1 ÷ 4 = 0.2500 and xB = 3 ÷ 4 = 0.7500, so the mixture is 25% ethanol by moles. In grams it is 46.07 g of ethanol and 54.045 g of water, 100.115 g in all, so ethanol is 46.02% by mass. The molality of ethanol in the water is 1 mol ÷ 0.054045 kg = 18.5031 mol/kg.
Sources: IUPAC Gold Book — amount fraction (mole fraction) · Mole fraction — Wikipedia
Frequently asked questions
What do all the mole fractions add up to?
Exactly 1. Each fraction is one component’s share of the total moles, so together they make up the whole mixture. If your fractions add up to 0.98 or 1.02 the difference is rounding, or a component was left out.
Can I use grams instead of moles?
Yes. Pick a “Grams + molar mass” option and enter the mass and molar mass of each component; the calculator divides each mass by its molar mass first. Using the grams directly would give the mass fraction, which is a different number whenever the molar masses differ.
What is the difference between mole fraction and mole percent?
Only a factor of 100. A mole fraction of 0.25 is 25 mol %. Gas compositions such as air (about 78% nitrogen, 21% oxygen) are usually quoted in mole or volume percent, which are the same for ideal gases.
How does mole fraction relate to partial pressure?
For an ideal gas mixture, each gas’s partial pressure is its mole fraction times the total pressure (Dalton’s law). Oxygen at a mole fraction of 0.21 in air at 1 atm has a partial pressure of about 0.21 atm, or 21.3 kPa.
How do I convert mole fraction to molality?
Assume 1 mol of mixture: the solute has x moles and the solvent 1 − x moles. Convert the solvent moles to kilograms with its molar mass, then divide the solute moles by that mass. This calculator does it for you when you enter the molar mass of B, the solvent.
Do I count ions separately for a salt solution?
For the molecular composition, no: 1 mol of NaCl counts as 1 mol. For colligative properties such as vapor-pressure lowering, the particles matter, so 1 mol of NaCl gives about 2 mol of ions; enter that amount instead.
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