SPI Chemistry · Mole Concept and Stoichiometry

The Mole and Avogadro's Number

A mole is 6.022 × 10²³ particles, the number in one gram molecular mass of a substance, and it lets you count atoms, molecules and even electrons by weighing.

All Mole Concept and Stoichiometry notes

Why this matters

Three questions in the bank, one EASY, one MODERATE and one HARD: how many molecules are in one gram molecular mass, which flask holds more oxygen atoms, and which metals need the same charge to deposit one mole. Each is a count of particles, so the skill is multiplying by the right number per molecule or per ion.

Concept 1 of 2: Moles, Avogadro's number and counting atoms

A dozen means 12 of anything; a mole means 6.022 × 10²³ of anything. Chemists use it because one mole of a substance weighs, in grams, the same number as its molecular mass. So you can count particles on a balance.

Definition

1 mole of any substance contains 6.022 × 10²³ particles. This is Avogadro's number, $N_A$ .
The gram molecular mass (molecular mass written in grams) of a substance is one mole of it, so it holds $N_A$ molecules. Likewise one gram atomic mass holds $N_A$ atoms.
Moles $=$ mass in grams $\div$ molar mass. Particles $=$ moles $\times N_A$ .
To count atoms, multiply the moles of molecules by the number of atoms in each molecule: 1 mole of $\text{O}_2$ has 2 moles of oxygen atoms, 1 mole of $\text{O}_3$ has 3.
Atomic masses used here: H 1, C 12, N 14, O 16.

Moles and particles

n = \frac{m}{M} \qquad N = n \times N_A \qquad N_A = 6.022 \times 10^{23}

nnumber of moles
mmass in grams
Mmolar mass in grams per mole
Nnumber of particles

Worked example

How many molecules are there in 36 g of water? (H = 1, O = 16)

Practice this conceptself-check · 4 quick reps

The same idea in a practice question:

Practice questionEasy

Example 1 · Mole Concept and Stoichiometry · The Mole and Avogadro's Number

How many molecules are present in one gram molecular mass of a substance?

Counting molecules when atoms are asked

Moles of molecules and moles of atoms differ for any element that is not monoatomic. Multiply by the atoms in each molecule before comparing.

Dividing by Avogadro's number

Particles

=

moles

\times N_A

. One mole holds

N_A

particles itself,

6.022 \times 10^{23}

, not

\frac{1}{N_A}

. Dividing by

N_A

gives a tiny fraction that cannot be a count.

Drill 1 more on moles, avogadro's number and counting atoms

Concept 2 of 2: Charge needed to deposit one mole of a metal

To turn a metal ion back into a metal atom in electrolysis, you must hand it back the electrons it lost. An ion with a charge of 2+ needs two electrons per atom, so a mole of such ions needs two moles of electrons.

Definition

One mole of electrons carries a charge of about 96,500 coulombs. This amount of charge is called one faraday (1 F).
To deposit one mole of a metal from ions of charge $n+$ , you need $n$ moles of electrons, so n faradays.
So metals need the same charge per mole only if their ions carry the same charge.

Charge to deposit one mole of metal

Q = n \times 96500\ \text{C} \quad \text{for ions of charge } n+

Worked example

How much charge is needed to deposit one mole of aluminium from

\text{Al}^{3+}

ions?

Practice this conceptself-check · 3 quick reps

The same idea in a practice question:

Practice questionHard

Example 2 · Mole Concept and Stoichiometry · The Mole and Avogadro's Number

Which of the following set of metals require the same amount of charge of deposition of one mole of metal?

Thinking every metal needs one faraday per mole

One faraday deposits one mole only for a 1+ ion such as

\text{Ag}^{+}

. A 3+ ion such as

\text{Al}^{3+}

needs 3 F per mole.

Grouping metals by their mass instead of their charge

The charge needed per mole depends only on the charge of the ion, not on how heavy the metal is. Group the metals by ion charge.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Moles, Avogadro's number and counting atoms
Moles and particles
$n = \frac{m}{M} \qquad N = n \times N_A \qquad N_A = 6.022 \times 10^{23}$
Charge needed to deposit one mole of a metal
Charge to deposit one mole of metal
$Q = n \times 96500\ \text{C} \quad \text{for ions of charge } n+$

Watch out for (4)

Counting molecules when atoms are asked
→ Moles, Avogadro's number and counting atoms
Dividing by Avogadro's number
→ Moles, Avogadro's number and counting atoms
Thinking every metal needs one faraday per mole
→ Charge needed to deposit one mole of a metal
Grouping metals by their mass instead of their charge
→ Charge needed to deposit one mole of a metal

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