The mole

\(\require{mhchem}\)

In English we have lots of names for a number of items: a pair is 2, a dozen is 12, a score is 20, and a gross is 144. In chemistry the mole is also a number of items, but a much larger number.

The mole is a convenient way for chemists to count particles (atoms, molecules, ions, or electrons) so that we can think about them in manageable numbers. If I say that 4 g of He gas contains 602 214 07 000 000 000 000 000 atoms of helium, that becomes painful to think about and is hard to write down. If I write the number in standard form, as \(6.022 \times 10^{23}\), it becomes easier to write but is still tricky to imagine. If instead I give that amount of substance a short and friendly name (“mole”), chemical reactions become easier to talk about. One mole of oxygen reacts with two moles of hydrogen to make two moles of water. Mole really just means “a standard number of particles”.

$$\ce{hydrogen + oxygen -> water}$$ $$\begin{equation} \ce{2H2(g) + O2(g) -> 2H2O(g)} \end{equation}\label{water}$$

Balanced chemical equations tell us the number of moles of each reactant we need, and the number of moles of product we will get under ideal conditions. In this reaction, the combustion of methane, $$\ce{methane + oxygen -> carbon~dioxide + water}$$ $$\begin{equation} \ce{CH4(g) + 2O2(g) -> CO2(g) + 2H2O(g)} \end{equation}$$ one mole of methane reacts with two moles of oxygen, to produce one mole of carbon dioxide and two moles of water.

The mole can refer to atoms, molecules, ions, and even electrons (which we need to use in our electrochemical reactions). For instance, one mole of \(\ce{Cu^{2+}}\) ions reacts with 2 moles of electrons to produce one mole of Cu atoms.

$$\begin{equation} \ce{Cu^{2+}(aq) + 2e^{-}(aq) -> Cu(s)} \end{equation} $$

We know from the Periodic Table that atoms of different elements have different masses. The mole was originally cunningly defined so that a mole of a pure substance has the same mass in grams as its relative atomic or molecular weight. So a mole of radon atoms has a mass of 222 g, while a mole of neon has mass 20 g. A mole of carbon dioxide has a mass of 12 (from C) + 16 (from O) + 16 (from the other O) = 44 g.

We have to consider the nature of the particles when thinking about moles: a mole of chlorine molecules (\(\ce{Cl2}\)) would have the same number of molecules as there are ions in a mole of chloride ions (\(\ce{Cl^-}\)) but would have twice the mass (35.5 x 2 versus 35.5).

Test yourself

    1. How many atoms in a mole of argon?
    2. How many molecules in a mole of phosphorus (\(\ce{P4}\))?
    3. How many atoms in a mole of ozone molecules (\(\ce{O3}\))?
The enormous number of particles found in a mole is called the Avogadro constant, after a scientist called Amedeo Avogadro (\(1776-1856\)). The constant is usually represented by the symbol \(N_A\).

Mole is Italian (pronounced molay) for size, dimension, or mass.

Answers to Test Yourself questions

    1. \(6.022 \times 10^{23}\)
    2. \(6.022 \times 10^{23}\)
    3. \(18.066 \times 10^{23}\) or \(1.8066 \times 10^{24}\) - there are three oxygen atoms in each molecule of ozone, so three times as many atoms as molecules.

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