Short on time? This page is the recap. For explanations and worked examples, use the full study guide.
Recap
- You cannot count particles directly in the lab, so chemists count them by weighing.
- The mole is a counting unit: 1 mol of anything contains 6.022 × 10²³ of its particles (atoms, molecules or formula units).
- Molar mass, M, is the mass of one mole, in g mol⁻¹. Find it by adding average atomic masses from the periodic table.
- The average mass of one particle in amu has the same number as the molar mass in grams per mole.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| n = m / M | n in mol, m in g, M in g mol⁻¹ | turn a mass into moles (or rearrange: m = n × M) |
| N = n × N_A | N particles, N_A = 6.022 × 10²³ mol⁻¹ | turn moles into a particle count (or n = N / N_A) |
| Atoms of X = N × (subscript of X) | from the formula | count atoms of one element inside a compound |
Assumptions behind the numbers
- The sample is pure: all of the mass belongs to the substance in the formula.
- Average atomic masses assume the natural mix of isotopes.
- Masses are measured accurately; the answer can be no more precise than the least precise measurement (significant figures).
Mistakes to avoid
- Ignoring brackets. Ca(NO₃)₂ has 2 N and 6 O.
- Equal mass ≠ equal particles. Compare moles, not grams.
- Molecules vs atoms. 1 mol O₂ = 2 mol O atoms.
- Wrong direction with N_A. Particles → moles: divide. Moles → particles: multiply.
- Rounding early. Keep full calculator values; round once at the end.
- Dropping units. Units that do not cancel to the answer’s unit mean the setup is wrong.
Quick self-check
- What is the molar mass of CO₂? (44.01 g mol⁻¹)
- How many moles are in 9.01 g of water? (0.500 mol)
- How many atoms are in 0.100 mol of Fe? (6.02 × 10²² atoms)
Next: practice questions.