Chemistry
Moles calculator
Convert between grams, moles, number of particles and litres of gas. You can type the molar mass or let it be worked out from the chemical formula.
The mole as a counting unit
The mole measures neither a mass nor a volume: it counts particles, exactly as a dozen counts objects. One mole contains 6.02214076·10²³ entities, a number chosen so that the mass in grams of one mole matches the atomic or molecular mass in atomic mass units. This is the bridge between the formula written in a notebook and the substance on the balance.
Every conversion turns on two relations. The first, n = m/M, links moles to mass through the molar mass: dividing grams by grams per mole leaves moles. The second, N = n·Nₐ, takes you from moles to the number of particles. For gases a third is added, V = n·22.414 L at 0 °C and 1 atm, which holds for any gas because the molar volume does not depend on the kind of molecule.
In a chemical reaction the stoichiometric coefficients are ratios between moles, not between grams. That is why calculating moles is always the first step of a stoichiometry problem: convert grams to moles, apply the ratios of the balanced equation, and only at the end go back to grams of product.
Common mistakes
- Applying the 22.4-litre molar volume to solids and liquids: it holds only for gases, and only at the reference conditions. A litre of water is not a fraction of a mole computed that way.
- Using the atomic rather than the molecular molar mass: oxygen gas is O₂ and has a molar mass of 32 g/mol, not 16.
- Confusing the reference conditions: the classic textbook STP is 0 °C and 1 atm, with a molar volume of 22.414 L/mol. Under the current IUPAC definition, 0 °C and 1 bar, the molar volume is 22.711 L/mol.
Frequently asked questions
How do you calculate moles from grams?
Divide the mass by the molar mass: n = m/M. Twenty-five grams of sodium chloride, with a molar mass of 58.44 g/mol, is 0.428 moles.
How many particles are there in a mole?
6.02214076·10²³, Avogadro's number. Since 2019 it has been an exact value by definition rather than a measured quantity.
How many litres does one mole of gas occupy?
22.414 litres at 0 °C and 1 atmosphere, whatever the gas. The value applies to an ideal gas: real gases depart from it slightly at these conditions, considerably at high pressures.
Do I have to know the molar mass?
No: you can type the chemical formula and the calculator works it out by summing the atomic weights of the elements in it.
How this calculation works
Moles from mass: n = m/M, with m in grams and M in g/mol. Mass from moles: m = n·M. Number of particles: N = n·Nₐ, with Nₐ = 6.02214076·10²³ mol⁻¹ (an exact value by definition). Moles from particles: n = N/Nₐ. Volume of an ideal gas at STP (0 °C, 1 atm): V = n·22.414 L; under the current IUPAC definition, which uses 1 bar, the molar volume is 22.711 L/mol. The molar mass of a compound is the sum of the atomic masses of its elements multiplied by their subscripts.
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