The mole

A number nobody can picture

• Spread $6.02 \times 10^{23}$ grains of sand over the United Kingdom and the country would be buried ten metres deep. That is the number of water molecules in a tablespoon.
• Chemistry and physics both need to count particles, and no experiment can count them one at a time. So we count them in packets, and the packet holds that number.
• The packet is called the mole 摩尔, and it is an SI base unit alongside the metre, the kilogram and the second.
• This lesson is what the mole is, how to convert between moles, particles and mass, and the wording the examiner accepts.

Amount of substance and the mole

• Amount of substance 物质的量 is an SI base quantity, and its base unit is the mole (mol), one of the seven alongside the kilogram, metre, second, ampere and kelvin 开尔文.
• One mole of any substance contains a number of particles equal to the Avogadro constant 阿伏伽德罗常量:

• The examiner's one-mark definition: the Avogadro constant is the number of atoms or molecules in one mole of a substance. Adding "in 0.012 kg of carbon-12" is accepted but not required.

A fixed count, whatever the substance

Say what you are counting

• A "particle" means whatever the substance is made of: atoms 原子 for a monatomic 单原子 element such as helium, molecules 分子 for $\text{O}_2$ or $\text{H}_2\text{O}$.
• One mole of oxygen gas contains $6.02 \times 10^{23}$ molecules, and therefore twice as many atoms. A question that says "molecules" and an answer that gives atoms is out by a factor of two.
• For $n$ moles the number of particles is:

A laboratory quantity on one side, an atomic count on the other

Molar mass

• The molar mass 摩尔质量 $M_{\text{m}}$ is the mass of one mole of the substance, in $\text{kg/mol}$ or $\text{g/mol}$.
• The mass of $n$ moles is $M = n M_{\text{m}}$, so the number of moles in a sample of mass $M$ is $n = M / M_{\text{m}}$.
• The mass of a single particle follows by dividing the mass of a mole by the number in a mole:

Worked example: oxygen, both ways

The three conversions

• Moles to particles: multiply by $N_{\text{A}}$. Particles to moles: divide by $N_{\text{A}}$.
• Moles to mass: multiply by $M_{\text{m}}$. Mass to moles: divide by $M_{\text{m}}$.
• Mass to particles: go through moles. There is no single step, and inventing one is where errors come from.
• Every question in this subtopic is one or two of these six conversions in a row. Write down which one you need before reaching for the calculator.

How the mole links to the gas constants

• The mole is what connects the per mole and per molecule versions of the gas equations you meet next.
• The Boltzmann constant is the gas constant per molecule: $k = R / N_{\text{A}}$, equivalently $R = N_{\text{A}} k$.
• When a question asks for "the relationship between $N_{\text{A}}$, $R$ and $k$", that one line is the whole answer.

Marks that slip away

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