Mole Formula and Mole Calculator
The Mole Formula and Mole Calculator
Convert between mass and moles, number of particles and gas volume at STP, with worked examples.
What is a mole?
The mole is the unit for amount of substance. One mole contains 6.022 × 1023 particles (atoms, molecules or ions), the Avogadro constant (NA). The mass of one mole in grams equals the molar mass, so one mole of water (18.02 g/mol) weighs 18.02 g.
Mole formula
| Known | Formula |
|---|---|
| Mass | n = mass ÷ molar mass |
| Number of particles | n = particles ÷ 6.022 × 1023 |
| Gas volume at STP (0 °C, 1 atm) | n = V ÷ 22.4 L |
| Gas volume at RTP (25 °C, 1 atm) | n = V ÷ 24.5 L |
| Gas at other conditions | n = PV ÷ RT, R = 0.08206 L·atm/(mol·K) |
| Molarity and solution volume | n = M × V (V in litres) |
Work out the molar mass from a chemical formula with the molar mass calculator.
Worked examples
Example 1: moles from mass
How many moles are in 9 g of water (18.02 g/mol)?
- n = mass ÷ molar mass
- n = 9 g ÷ 18.02 g/mol = 0.4994 mol
Answer: about 0.5 mol.
Example 2: mass from moles
What is the mass of 0.25 mol of NaOH (40.00 g/mol)?
- mass = n × molar mass
- mass = 0.25 mol × 40.00 g/mol = 10.00 g
Answer: 10 g of NaOH.
Example 3: moles from gas volume
How many moles and grams are in 11.2 L of O2 at STP (32.00 g/mol)?
- n = 11.2 L ÷ 22.4 L/mol = 0.5 mol
- mass = 0.5 mol × 32.00 g/mol = 16.00 g
Answer: 0.5 mol, or 16 g.
Example 4: number of particles
How many molecules are in 0.5 mol of CO2?
- particles = n × NA
- = 0.5 × 6.022 × 1023 = 3.011 × 1023
Answer: 3.011 × 1023 molecules.
Frequently asked questions
What is the difference between moles and molarity?
Moles measure amount of substance. Molarity is concentration: moles per litre of solution. See the molarity formula.
What is the difference between atomic mass and molar mass?
Relative atomic mass applies to one element, e.g. C = 12.01. Molar mass is the sum for all atoms in a formula, e.g. CO2 = 12.01 + 2 × 16.00 = 44.01 g/mol.
How do I find the moles in a solution?
Multiply molarity by volume in litres. 250 mL of 0.1 M HCl contains 0.1 × 0.25 = 0.025 mol HCl.
Why is the Avogadro constant 6.022 × 10<sup>23</sup>?
The mole is defined by exactly 6.02214076 × 1023 particles, chosen so that one mole in grams equals the molar mass.
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