IB Chemistry HLTopic 1 — Counting Particles by MassPaper 1 & 2Core idea~10 min read
The Mole
You can never count atoms one at a time — they are far too small and there are far too many of them. So chemists do what a hardware shop does with screws: they count by weighing. The mole is the counting word that makes it work.
📘 What you need to know
The mole is just a counting word, like “dozen” or “pair”. It means 6.02 × 1023 particles.
The Avogadro constant, NA (sometimes written L), is 6.02 × 1023 mol−1.
One mole of anything contains the same number of particles. The mass is different every time.
n = N ÷ NA — to go from moles to particles you multiply, to come back you divide.
“Particles” means whatever the formula says: atoms, molecules, ions or formula units. Always say which one.
Relative atomic massAr compares an atom with one twelfth of a carbon-12 atom. It is a ratio, so it has no units.
Why chemists invented the mole
Imagine you had to sell 50 000 identical screws. Nobody counts them out. You weigh one screw, weigh the whole box, and divide. You have counted without counting.
Atoms are the same problem, but a million times worse. A single carbon atom has a mass of about 2 × 10−23 g. Even the tiniest speck of soot you can see contains more atoms than there are grains of sand on a beach. So we need a bulk unit — a “box” of atoms big enough to weigh on a normal balance.
That box is the mole. It holds 6.02 × 1023 particles, and it was chosen for one very deliberate reason: one mole of an element has a mass in grams equal to its relative atomic mass. That single design choice is what turns a balance reading into a particle count.
Do not be scared of the mole. It is not a chemical, it is not a thing you can hold — it is a number, exactly like “dozen”. A dozen eggs and a dozen elephants are both twelve. A mole of hydrogen and a mole of uranium are both 6.02 × 1023 particles.
The Avogadro constant
The number itself has a name and a symbol, and you will see both in exam papers.
The Avogadro constantNA = 6.02 × 1023 mol−1
Notice the units: per mole. That is your clue about how to use it — it is a conversion factor between an amount in moles and a raw count of particles.
The red and blue circles in the third panel are ions held in a lattice, so NaCl has no molecules at all — we count formula units instead.
One mole of what? The mix-up that costs marks
This is where most marks are lost, and it is not a maths problem. A question asks for the number of atoms, you give the number of molecules, and you lose the mark even though your arithmetic was perfect.
The fix is a habit: read the formula, then decide what one mole of it contains.
Substance
1 mol is made of
Particles in 1 mol
Atoms or ions in total
Helium, He
atoms
6.02 × 1023 atoms
6.02 × 1023 atoms
Oxygen, O2
molecules
6.02 × 1023 molecules
1.20 × 1024 atoms
Water, H2O
molecules
6.02 × 1023 molecules
1.81 × 1024 atoms
Sodium chloride, NaCl
formula units
6.02 × 1023 units
1.20 × 1024 ions
Magnesium chloride, MgCl2
formula units
6.02 × 1023 units
1.81 × 1024 ions
Where those totals come from: water has 3 atoms in every molecule, so 3 × 6.02 × 1023 = 1.81 × 1024. MgCl2 splits into one Mg2+ and two Cl−, which is 3 ions per formula unit — the same multiplier.
Converting between moles and particles
There is only one equation here, and you can rearrange it in your head if you remember which quantity is the big one.
Amount and number of particlesn = N ÷ NA and N = n × NA
Use the size of the answer as a sanity check — a laboratory-sized amount is usually a small number of moles and a colossal number of particles.
🧩 Counting particles: the method
Read the formula and decide what one particle of it is: an atom, a molecule or a formula unit.
Find the number of those particles: multiply the amount in moles by 6.02 × 1023.
Check what the question actually asked for. If it wants atoms or ions, multiply again by how many are in one particle.
Give the answer in standard form to 3 significant figures unless told otherwise.
Relative atomic mass and relative formula mass
Before you can weigh out a mole you need to know what one mole weighs, and that comes from relative masses.
Relative atomic massAr = weighted average mass of one atom ÷ (1/12 × mass of one 12C atom)
Three things are worth pulling out of that definition:
It is a comparison, not a mass. Top and bottom are both masses, so the units cancel and Ar has none. Writing “12.01 g” for the Ar of carbon is wrong.
It is a weighted average. Chlorine’s Ar of 35.45 is not the mass of any real chlorine atom — it sits between the 35Cl and 37Cl isotopes, closer to 35 because that isotope is more common.
Carbon-12 is the reference. Everything is measured against one twelfth of it, which is why Ar values come out close to whole numbers.
Add up the Ar values of everything in a formula and you get the relative formula mass, Mr. For a molecule you may see it called relative molecular mass; for an ionic compound, relative formula mass. The arithmetic is identical.
Why “relative formula mass” for ionic compounds? Because there is no such thing as an NaCl molecule — the lattice goes on for billions of ions. NaCl is just the simplest ratio, so we say formula mass, not molecular mass. Examiners do notice.
Worked examples
WORKED EXAMPLE
Moles to particles, then to atoms
A flask contains 0.150 mol of carbon dioxide, CO2. Calculate the number of CO2 molecules and the total number of atoms present.
Step 1: what is one particle of CO₂?It is a molecule, made of 3 atoms (1 C + 2 O).Step 2: moles → molecules, so multiplyN = 0.150 × 6.02 × 10²³ = 9.03 × 10²²9.03 × 10²² moleculesStep 3: atoms — multiply by 33 × 9.03 × 10²² = 2.709 × 10²³2.71 × 10²³ atomsthe two answers differ by a factor of 3 — that is the whole trap
WORKED EXAMPLE
Particles back to moles, and counting ions
A sample of magnesium chloride contains 1.505 × 1023 formula units of MgCl2. Calculate the amount in moles, and the total number of ions in the sample.
Step 1: particles → moles, so dividen = (1.505 × 10²³) ÷ (6.02 × 10²³)n = 0.2500.250 molStep 2: how many ions per formula unit?MgCl₂ gives one Mg²⁺ and two Cl⁻ — that is 3 ions.Step 3: multiply the count of units by 33 × 1.505 × 10²³ = 4.515 × 10²³4.52 × 10²³ ionsnotice the powers of ten only change when the digits cross 10
WORKED EXAMPLE
Which sample contains more atoms?
Which contains more atoms: 0.20 mol of ammonia, NH3, or 0.15 mol of ethane, C2H6? Justify your answer.
Step 1: atoms in one molecule of eachNH₃ has 4 atoms. C₂H₆ has 8 atoms.Step 2: work in moles of atoms — no need for big numbers yetNH₃: 0.20 × 4 = 0.80 mol of atomsC₂H₆: 0.15 × 8 = 1.20 mol of atomsStep 3: compare, then convert only if asked1.20 × 6.02 × 10²³ = 7.22 × 10²³ atomsEthane, by 0.40 mol of atomsfewer molecules can still mean more atoms — always check the formula
💡 Exam tip
Underline the particle word in the question — “atoms”, “molecules”, “ions”, “formula units”. It tells you whether you need one multiplication or two.
Use 6.02 × 1023 from the data booklet rather than a rounded 6 × 1023; the extra digits matter at 3 significant figures.
Keep everything in standard form on the calculator using the EXP or ×10x key. Typing “6.02 × 10 ^ 23” by hand is where sign errors creep in.
Sanity check the size. Amounts in moles for school-sized samples are usually between 0.001 and 10. Particle counts are always astronomically large.
For “which has more” questions, compare in moles of atoms first. It is faster and less error-prone than converting both to raw counts.
Round only at the very end, and quote 3 significant figures unless the question says otherwise.
⚠ Common mix-up
Giving molecules when atoms were asked for. The most common lost mark on this whole topic. One mole of O2 is 6.02 × 1023 molecules but 1.20 × 1024 atoms.
Multiplying when you should divide. If you are given a huge number of particles, you are going towards moles, so divide.
Saying “molecules of NaCl”. Ionic compounds have formula units, not molecules. Same for MgO, CaCO3 and every other ionic solid.
Putting units on Ar or Mr. They are ratios. Molar mass has units (g mol−1); relative masses do not.
Thinking a mole is a mass. A mole is a count. One mole of lead and one mole of lithium contain the same number of atoms and have wildly different masses.
Forgetting that Ar is an average. No chlorine atom has a mass of 35.45; that value reflects the isotope mixture.
Up next: Molar Mass — how a number on a balance turns into a number of moles, and why the periodic table is really a table of molar masses in disguise.
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