The Mole

Chapter 6 ended with a limit: a coefficient in a balanced equation counts molecules, not grams. Yet in a laboratory you cannot count molecules; you can only weigh things. This chapter builds the bridge. It introduces the mole, the Avogadro constant and molar mass, then uses them in two worked examples: converting between grams and moles, and finding the mass of a product from a balanced equation. Each fact is attributed to the Wikipedia page that states it, and my own arithmetic or general knowledge is marked "(check)".

Why Count in Moles?

Chapter 2 gave atoms masses of a few dalton each, far too small to see or weigh one at a time (the scale is from Chapter 2's proton and neutron figures). Any sample you can pick up holds a vast number of them. So chemists use a counting unit big enough to match that scale, in the way a shop counts eggs by the dozen. The Mole (unit) article says the mole measures "the amount of substance", and defines the ratio n = N/N_A, the number of entities N divided by the Avogadro constant N_A, as "a measure of the amount of substance (with the unit mole)". The article says the "elementary entity" counted may be "an atom, a molecule, an ion, an ion pair, or a subatomic particle", so a mole of oxygen could mean a mole of atoms or a mole of O₂ molecules, and you must say which (that last warning is my own advice (check)).

The Avogadro Constant

After the 2019 changes, the Mole (unit) article says, one mole contains "exactly 6.02214076×10²³ elementary entities". The same page says the constant's numerical value "has units of mol^-1", so the Avogadro constant is 6.02214076 × 10²³ mol^-1. In this course I round it to 6.02 × 10²³ when the arithmetic allows (my rounding (check)). The same article says the name "mole" was "coined by the chemist Wilhelm Ostwald in 1894 from the German word Molekül". I did not fetch the Amedeo Avogadro article, so I make no claims here about the man himself.

The Molar mass article says that "the coherent unit of molar mass is kg/mol" but that "molar masses are almost always expressed with the unit g/mol". Use g/mol, as the worked examples below do.

Molar Mass and Relative Atomic Mass

This is where Chapter 2's relative atomic mass pays off. The Molar mass article says that for an element the molar mass "is given by the relative atomic mass A_r(X) of the element multiplied by the molar mass constant", and that this constant is about 1 g/mol. In practice: the number is the same, only the unit differs. Chlorine's relative atomic mass is about 35.5 (Chapter 2), so a mole of chlorine atoms has a mass of about 35.5 g (my reading of the page's rule (check)).

For a compound, the page says the molar mass is "given by the sum of the relative atomic masses" of its elements, each multiplied by its atom count, then multiplied by the molar mass constant. Chapter 4 and Chapter 5 gave you the formulae to sum over. The page's own sodium chloride example is:

M(NaCl) = [22.98976928 + 35.453] x M_u
M(NaCl) = 58.443 g/mol      (Molar mass article: 58.443(2) g/mol; my Python sum: 58.44277)

The same article gives water's molar mass as 18.0153(3) g/mol. It shows no working for water, so I do not claim to reproduce its figures.

Worked Example: Grams to Moles and Back

The two conversions are one formula, n = m / M, rearranged. This example uses the Molar mass article's value for sodium chloride, 58.443 g/mol. All results were calculated in Python.

The units cancel as a check: g ÷ (g/mol) leaves mol. If your units do not cancel to the unit you wanted, you have the formula upside down (my advice (check)). Sodium chloride is ionic (Chapter 4), so the particles counted in the last row are formula units, not molecules; the choice of word is mine (check).

Worked Example: Mass of Product from a Balanced Equation

Chapter 6 balanced 2H₂ + O₂ → 2H₂O. Its coefficients now give mole ratios: the Stoichiometry article says "The molar ratio allows for conversion between moles of one substance and moles of another", with the coefficients supplying the ratio. The article's own example is copper and silver nitrate, which I follow in pattern but not in substance: it converts grams to moles, applies the ratio, then converts moles to grams. Question: how much water forms from 4.00 g of hydrogen, with oxygen in plenty?

Molar masses: for H₂ I use 1.00794 for hydrogen, the figure the Molar mass article uses in its sucrose example, so M(H₂) = 2.01588 g/mol (my Python sum). For water I use that article's 18.0153 g/mol.

So 4.00 g of hydrogen yields about 35.7 g of water, provided there is enough oxygen (Python gave 35.7468 g before rounding to three figures). The product is much heavier than the hydrogen because oxygen atoms join in, which is Chapter 6's conservation of mass at work (my reading (check)). The mole ratio here happens to be 1 : 1; in the Stoichiometry article's copper example it is 1 : 2 and the middle step matters more.

Where to Read More

• Encyclopaedias. The Wikipedia articles Mole (unit), Molar mass and Stoichiometry are the sources used here.
• A school textbook. Look for graded mole calculations and the idea of limiting reactants, which this chapter does not cover (the Stoichiometry example only says silver nitrate was in excess).
• Practical. Weigh a teaspoon of table salt on a kitchen scale and turn the mass into moles with the method above (the weighing is my suggestion (check)).

Exercises