Lesson 3 of 4

Grams, moles and particles.

About 25 minutes · 5 practice questions

Two formulas link what you weigh to what you count: n = m ÷ M and N = n × Nₐ. Working both ways, molecules against atoms, and checking with units.

Step 1 of 5 · From grams to moles

Step 1 of 5

From grams to moles

Three quantities link the balance to the particles: the mass $m$ ⁠ in grams, the molar mass $M$ ⁠ in grams per mole, and the amount of substance $n$ ⁠ in moles. If a mole weighs $M$ ⁠ grams, then $m$ ⁠ grams hold

$n = \frac{m}{M}$ ⁠

The units check themselves: g ÷ g/mol = mol. If you multiplied instead of dividing, you would get g²/mol, which is not an amount.

The Scene shows 9 g of water, with the readings showing the molar mass but hiding the amount.

To the question

Step 2 of 5

From moles to grams

The same formula works the other way: $m = n \times M$ ⁠. To weigh out a given number of moles, multiply by the molar mass. The Scene shows table salt, NaCl, with the readings hiding the amount again.

To the question

Step 3 of 5

From moles to particles

Each mole is $6.022 \times 10^{23}$ ⁠ particles, so the number of particles is

$N = n \times N_A$ ⁠

A “particle” is what the formula describes: an atom in an element such as iron, a molecule in a substance such as water, and a formula unit, one sodium ion and one chloride ion, in salt. Each water molecule holds three atoms, so a mole of water is one mole of molecules and three moles of atoms. The Scene shows 4.5 g of water, with Look inside open at Particles.

To the question

Step 4 of 5

Mass from moles

Sometimes you know how many moles you need, and want to know how much to weigh. The Scene shows chalk, calcium carbonate. Work it out yourself, then check on the balance with Mass and the readings.

To the question

Step 5 of 5

Which holds the most

At a fixed mass, $n = m / M$ ⁠ shrinks as $M$ ⁠ grows: a substance with a large molar mass gives fewer particles per gram. The Scene shows exactly one gram, with Mass locked. Change Substance and compare.