To find the number of moles from a number of particles, divide by the Avogadro constant: n = N / NA, where NA is 6.02 x 1023 per mole. Particles may be atoms, molecules or ions, so read the question carefully.
Counting in moles instead of individual particles is the whole point of the mole, and SPM Chemistry tests it directly with “how many atoms / molecules / ions” questions. Our online one-to-one teachers make sure you can move both ways, particles to moles and moles to particles, without losing track of what kind of particle the question means.
When you use it
Use this whenever a question gives, or asks for, a number of particles: atoms, molecules, ions, or electrons. It is very often combined with n = m / M, so that you go from a mass, to moles, to a number of particles in a single chain.
The formula
n = N / NA
- n = number of moles, in mol
- N = number of particles (no unit)
- NA = the Avogadro constant = 6.02 x 1023 mol−1
To go the other way, N = n x NA.
Units
n is in mol. N is a pure count with no unit. The Avogadro constant tells you that one mole of any particle contains 6.02 x 1023 mol−1 of those particles.
Working in standard form
Almost every particle-count answer is written in standard form, so a little care with powers of ten saves easy marks. Keep the two significant figures of the Avogadro constant, divide the front numbers first, then handle the powers separately. A quick check is that a sensible number of moles for a school-level question usually lands between about 0.01 and a few mol; an answer of, say, 5 x 1022 mol should make you stop and re-read, because it is far too large to be moles and is almost certainly a number of particles instead.
Worked example 1 (easy), sodium atoms
How many moles are there in 3.01 x 1023 atoms of sodium?
- Step 1, write the formula: n = N / NA.
- Step 2, substitute: n = (3.01 x 1023) / (6.02 x 1023) = 0.5 mol.
Worked example 2 (medium), water molecules
How many moles are there in 1.204 x 1024 molecules of water?
- Step 1, n = N / NA = (1.204 x 1024) / (6.02 x 1023).
- Step 2, divide the numbers and subtract the powers: 1.204 x 1024 is 12.04 x 1023, so n = 12.04 / 6.02 = 2 mol.
Worked example 3 (SPM level), counting ions
How many chloride ions are there in 0.2 mol of magnesium chloride, MgCl2?
- Step 1, read the formula: one MgCl2 gives one Mg²⁺ ion and two Cl⁻ ions.
- Step 2, moles of Cl⁻: 0.2 mol MgCl2 x 2 = 0.4 mol of Cl⁻.
- Step 3, number of ions: N = n x NA = 0.4 x (6.02 x 1023) = 2.408 x 1023 chloride ions.
The trap here is stopping at 0.2 mol; the formula MgCl2 doubles the chloride ions.
Common traps
- Turning the formula over and multiplying by NA when you should divide (or vice versa).
- Ignoring the type of particle. “Atoms of oxygen” in O2 is twice the number of O2 molecules.
- Forgetting that one formula unit can release several ions, as MgCl2 does with chloride.
- Slips in standard form: line up the powers of ten before dividing.
- Dropping the unit mol, or wrongly attaching a unit to N.
How we help
Our teachers set questions that chain n = m / M with n = N / NA, and that deliberately switch between atoms, molecules and ions, so you build the habit of asking “which particle?” every time, the single discipline that secures these marks in SPM Chemistry. Lessons are one-to-one, taught in English, from RM50 per hour, with a paid one-hour trial so you can judge the method first. Get this relationship secure and standard-form arithmetic stops being a source of careless errors.
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