Moles and Molar Mass
How chemists count atoms by weighing them — and why the mole is the single most important unit in quantitative chemistry.
Primary sources: NIST CODATA 2018 · IUPAC 2021 Atomic Weights
01 · The mole concept
Count atoms by weighing them.
Atoms are far too small to count individually. Chemists solve this by using the mole — a fixed number of particles (Avogadro's constant) chosen so that one mole of any element has a mass in grams equal to its relative atomic mass.
This means 1 mol of carbon atoms (Ar = 12.011) has a mass of 12.011 g; 1 mol of water molecules (Mr = 18.015) has a mass of 18.015 g. The connection between the atomic scale and the laboratory scale is:
where n is amount in mol, m is mass in g, and M is molar mass in g mol⁻¹. Use our molar mass calculator to compute M for any formula instantly.
02 · Calculating molar mass
Add up the atomic masses.
The molar mass M of a compound is found by summing the relative atomic masses (Ar) of each atom, multiplied by how many of that atom appear in one formula unit.
- H₂O: 2(1.008) + 15.999 = 18.015 g mol⁻¹
- NaCl: 22.990 + 35.45 = 58.44 g mol⁻¹
- H₂SO₄: 2(1.008) + 32.06 + 4(15.999) = 98.07 g mol⁻¹
- C₆H₁₂O₆ (glucose): 6(12.011) + 12(1.008) + 6(15.999) = 180.16 g mol⁻¹
Atomic masses are from the IUPAC 2021 standard atomic weights. See our periodic table guide for how atomic masses relate to isotopes.
03 · Worked examples
Three standard calculations.
How many moles in 22.0 g of CO₂?
M(CO₂) = 12.011 + 2(15.999) = 44.009 g mol⁻¹
n = 22.0 / 44.009 = 0.500 mol
What mass is 0.25 mol of NaCl?
M(NaCl) = 22.990 + 35.45 = 58.44 g mol⁻¹
m = 0.25 × 58.44 = 14.6 g
How many molecules in 1.00 mol of H₂O?
n = 1.00 mol; Nₐ = 6.022 × 10²³ mol⁻¹
N = 1.00 × 6.022 × 10²³ = 6.022 × 10²³ molecules
04 · Stoichiometry
Moles let you balance equations in mass.
A balanced equation gives the mole ratio of reactants and products. For the combustion of methane:
1 mol CH₄ reacts with 2 mol O₂ to give 1 mol CO₂ and 2 mol H₂O. Converting to masses: 16.04 g of methane produces 44.01 g of CO₂. This is how chemists calculate how much reagent to use and what yield to expect.
For solutions, concentration (molarity) links volume to moles: c = n / V. See our molarity and dilutions guide for the full treatment, and our acids and bases guide for how moles relate to pH calculations.
Questions about moles and molar mass
- A mole (symbol: mol) is the SI unit of amount of substance, defined as exactly 6.022 140 76 × 10²³ elementary entities (CODATA 2018). This number is Avogadro's constant (Nₐ). One mole of carbon-12 atoms has a mass of exactly 12 g — which is why the mole links the atomic mass scale to the macroscopic world. See the NIST CODATA constants and our Mole Day page.
- Molar mass (M) in g mol⁻¹ = sum of (relative atomic mass × number of atoms) for each element. Example for H₂SO₄: 2(1.008) + 32.06 + 4(15.999) = 98.07 g mol⁻¹. Use our molar mass calculator to check any formula instantly. Atomic masses follow IUPAC 2021 standard atomic weights.
- The fundamental equation is: n = m / M. If you have 36.03 g of water (M = 18.015 g mol⁻¹), then n = 36.03 / 18.015 = 2.00 mol. Rearrangements: m = n × M (to find mass) and M = m / n (to find molar mass from measured mass and known moles). This is the starting point for stoichiometry calculations.
- A single carbon atom has a mass of about 2 × 10⁻²³ g. At that scale, counting is impossible. The mole solves this: 1 mol of carbon = 12.011 g, which you can weigh. Multiplying moles by Avogadro's constant gives the number of atoms. This is how stoichiometry works — balancing equations in moles tells you the mass ratios of reactants and products.
Try the molar mass calculator
Enter any chemical formula and get the molar mass instantly, with an element-by-element breakdown.