The mole and Avogadro's constant
Introduced| English | Meaning |
|---|---|
| mole/məʊl/ | The SI unit of amount of substance, containing exactly 6.02214076 times ten to the power 23 specified entities. |
| Avogadro constant/ˌævəˈɡædrəʊ ˈkɒnstənt/ | The number of specified elementary entities in one mole, exactly 6.02214076 times ten to the power 23 per mole. |
| molar mass/ˈməʊlə mæs/ | The mass of one mole of a substance. |
Counting atoms by the trillion
- Chemists count particles in groups called moles 摩尔 — like counting eggs in dozens.
- One mole always holds the same huge number of particles.
- The mole connects mass to number of particles.
Mole mass lab
n = m / M
Change mass and see moles scale through molar mass.
One mole of any substance contains 6.02 × 10²³ ______.
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This number is the Avogadro constant.
The mole and Avogadro's constant
- One mole (mol) is the amount with as many particles as there are atoms in exactly 12 g of carbon-12.
- That number is the Avogadro constant 阿伏伽德罗常量: $N_A = 6.02 \times 10^{23}$ particles per mole.
- Always say what the particles are — atoms, molecules or ions.
Equal volumes of gases at the same temperature and pressure hold equal numbers of molecules
One mole of any substance contains:
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A mole always contains the Avogadro number of particles, 6.02 × 10²³.
Molar mass 摩尔质量 and $n = m/M$
- The molar mass $M$ is the mass of one mole, in grams — numerically equal to $A_r$ or $M_r$ (units $\text{g}/\text{mol}$).
- The key equation:
where $n$ = moles, $m$ = mass (g), $M$ = molar mass.
How many moles are in 36 g of water (M = 18 g/mol)?
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n = m / M = 36 / 18 = 2 mol.
The molar mass of a substance (in g/mol) is:
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The molar mass in grams equals the relative atomic or molecular mass.
Match each quantity or formula to its meaning.
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Use n = m/M to find moles, and rearrange to m = n×M to find a mass; molar mass is just the Mr in grams.
The molar mass of a substance in g/mol is numerically equal to its relative formula mass.
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e.g. water has Mr 18, so its molar mass is 18 g/mol — that is why one mole of water is 18 g.
Worked example
- How many moles in 36 g of water ($M = 18\ \text{g}/\text{mol}$)?
$$n = \frac{m}{M} = \frac{36}{18} = 2\ \text{mol}$$
What is the mass of 0.5 mol of NaCl (M = 58.5 g/mol)?
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m = n × M = 0.5 × 58.5 = 29.25 g.
You've got it
- one mole = $6.02 \times 10^{23}$ particles ($N_A$)
- molar mass $M$ = relative mass in grams ($\text{g}/\text{mol}$)
- $n = \dfrac{m}{M}$ (moles = mass ÷ molar mass)
- always state the particle type (atoms / molecules / ions)