Moles, Stoichiometry & Limiting Reactants

The Mole

Avogadro's number — the chemist's counting unit

One mole = 6.02 × 10²³ particles

602,000,000,000,000,000,000,000

A mole (mol) is simply a count — like "a dozen" means 12, "a mole" means 6.02 × 10²³. That count is called Avogadro's number (N_A). Particles can be atoms, molecules, or formula units — you must always say which.

How big is a mole, really?

Reference—

One mole6.02 × 10²³

A mole is bigger by—

A mole of seconds

If you counted one particle every second, without ever stopping, counting out a single mole would take about 1.9 × 10¹⁶ years — roughly 1.4 million times the current age of the universe. This is why chemists never count particles directly: they weigh them instead.

Atomic Mass & Molar Mass

Weighing one mole of something

Atomic mass

The mass of one mole of atoms of an element, in g/mol. Read it straight off the periodic table.

Fe = 55.8 g/mol · O = 16.0 g/mol · Cl = 35.5 g/mol

Molar mass

The mass of one mole of molecules (or formula units) of a compound, in g/mol. Found by adding up the atomic masses of every atom in the formula.

H₂ = 2(1.01) = 2.02 g/mol

Molar mass calculator

Periodic table lookup

Click an element to add it to the formula box

The Mole Road Map

Three equations — every route passes through moles

Volume ↔ moles

n = V / MV

MV = 22.4 L/mol at STP

Mass ↔ moles

n = m / mm

mm = molar mass (g/mol)

Particles ↔ moles

n = #p / N_A

N_A = 6.02 × 10²³ /mol

STP = Standard Temperature and Pressure, 0 °C and 1 atmosphere. The molar volume 22.4 L/mol applies to any gas at STP — it does not apply to solids or liquids.

Interactive road map

Substance mm = 32.00 g/mol

Volume (L at STP)

Mass (g)

Moles (mol)

Particles

Try these (from the slides)

Road map · moles → particles → atoms

Atoms from molecules

Type any formula in the box below — the tool works out moles → molecules → atoms of whichever element you choose, for whatever you enter.

Compound Moles Element

Mole Ratios

The coefficients of a balanced equation

A mole ratio comes straight from the coefficients of a balanced chemical equation. It only works if the equation is balanced — so balance first, always.

How to use it: divide by the coefficient of what you HAVE, multiply by the coefficient of what you WANT.

Mole ratio explorer

Mole ratio:

If I have mol of how much ?

Stoichiometry Solver

Mole-mole · mole-mass · mass-mass · mixed

Every stoichiometry problem is the same journey: convert what you HAVE into moles → use the mole ratio → convert moles into what you WANT. The quantity must be in moles before you use the mole ratio.

Solver

Equation

I HAVE of

I WANT of

Energy Stoichiometry

Treating heat as another species in the equation

Endothermic

Heat ENTERS — it appears on the reactant side, because it is consumed.

A + B + 40.0 kJ → C + D

Exothermic

Heat EXITS — it appears on the product side, because it is released.

E + F → G + H + 120. kJ

Energy calculator

Amount of

Reaction typeExothermic

Energy— kJ

DirectionReleased

Limiting Reactants

Whatever runs out first decides how much you can make

The limiting reactant (LR) is the one that gets used up first. It caps how much product can form. Everything else is in excess and some of it will be left over when the reaction stops.

⚠ Careful — a very common trap. The limiting reactant is not simply "the one with the fewest moles". You must divide each reactant's moles by its coefficient first, then take the smallest result.

In CH₄ + 2O₂ → CO₂ + 2H₂O with 2.50 mol CH₄ and 4.80 mol O₂: fewest moles would wrongly say CH₄ — but 2.50 ÷ 1 = 2.50 while 4.80 ÷ 2 = 2.40, so O₂ is actually limiting. Always divide by the coefficient.

🍔 Build a double cheeseburger

Recipe: 1 bun · 1 tomato slice · 1 lettuce leaf · 2 cheese slices · 2 patties

Burgers made0

Limiting ingredient—

Left over—

🚲 Quick check — bicycles

1 frame + 2 wheels → 1 bicycle

Frames2

Wheels6

Limiting reactant calculator

Equation

Reactant A

Reactant B

Find product

Limiting reactant—

In excess—

Product formed—

Excess left over—

Visualising it — 10 H₂ + 7 O₂

	2 H₂(g)	+ O₂(g)	→ 2 H₂O(g)
Initial	10 mol	7 mol	0 mol
Change	−10 mol	−5 mol	+10 mol
Final	0 mol	2 mol	10 mol

H₂ runs out completely — it is the limiting reactant. Two moles of O₂ are left over as excess.

Theoretical, Actual & Percent Yield

Comparing experimental and calculated yields

Theoretical yield — what stoichiometry says you should get. Always calculated.

Actual yield — what you really scraped out of the flask. Always measured.

% yield = actual yield theoretical yield × 100

Actual yield is almost always lower than theoretical — product is lost on filter paper and glassware, reactions run incompletely, and side reactions steal material. A % yield above 100 % usually means the product is still wet or contaminated.

Percent yield calculator

Theoretical yield g

Actual yield (lab) g

Percent yield—

Product lost—

Verdict—

Stoichiometry in the Real World

Why chemists count in moles

🏭 The Haber process — industrial stoichiometry

Ammonia for fertiliser is made by N₂ + 3H₂ → 2NH₃. The plant feeds nitrogen and hydrogen in a precise 1 : 3 mole ratio over an iron catalyst. Only about 15 % converts on each pass, so the unreacted gas is separated and recycled — that is how the overall percent yield is pushed close to 100 %.

Where mole ratios, limiting reactants and percent yield show up

Periodic Table

Class-standard table · based on mass of carbon-12 = 12.00

Read atomic masses straight off this table when finding molar masses for the mole road map and the stoichiometry solver.

Ion Chart

Class-standard chart · common cations, anions & polyatomic ions with their charges

Names, formulae, and charges of common ions — positive ions (cations) and negative ions (anions)

Use these charges to write correct formulas before you balance an equation or run a stoichiometry calculation — the subscripts come from making the positive and negative charges cancel.

Quantities Practice Quiz

30 questions · 20 s conceptual / 40 s numerical · Speed bonus scoring

🐹

Ready to test your knowledge?

Covers moles, molar mass, the three mole equations, mole ratios, stoichiometry, energy, limiting reactants & percent yield

30

Questions

20–40s

Per question

1000

Max points

Summary

Quick reference

Concept	Equation	Notes
Avogadro's number	N_A = 6.02 × 10²³ /mol	Particles = atoms, molecules or formula units
Volume ↔ moles	n = V / MV	MV = 22.4 L/mol — gases at STP only
Mass ↔ moles	n = m / mm	Rearranged: m = n × mm
Particles ↔ moles	n = #p / N_A	Rearranged: #p = n × N_A
Mole ratio	÷ coefficient of HAVE, × coefficient of WANT	Requires a balanced equation
Limiting reactant	smallest of (moles ÷ coefficient)	Not simply the fewest moles
Excess left over	moles at start − moles used	Moles used comes from the LR via stoichiometry
Percent yield	(actual ÷ theoretical) × 100	Theoretical = calculated, actual = measured

Energy: endothermic → heat on the reactant side (absorbed) · exothermic → heat on the product side (released)
Golden rule: the quantity must be in moles before you use the mole ratio.

Moles, Stoichiometry & Limiting Reactants — Interactive Study Tool