Atoms, Molecules and the Mole Concept: Exam Notes

Chemistry begins with two ideas: matter is made of atoms, and atoms combine in fixed whole number ratios. Everything in this chapter, from the laws of chemical combination to the mole, is a way of counting atoms that are far too small to see. One mark questions come from the laws and the scientists who framed them, and two mark sums come from molecular mass and the mole, so both the names and the arithmetic have to be at your fingertips.

The laws of chemical combination

The law of conservation of mass, stated by Antoine Lavoisier in the late eighteenth century, says that mass is neither created nor destroyed in a chemical reaction, so the total mass of the products equals the total mass of the reactants. The law of constant proportions, also called the law of definite proportions and given by Joseph Proust, says that a pure compound always contains the same elements in the same proportion by mass, whatever its source: water from any river or any laboratory has hydrogen and oxygen in the mass ratio of one to eight. The law of multiple proportions, given by John Dalton, applies when two elements form more than one compound: the masses of one element that combine with a fixed mass of the other are in a simple whole number ratio, as in carbon monoxide and carbon dioxide, where twelve grams of carbon take sixteen and thirty two grams of oxygen, a ratio of one to two. Gay-Lussac's law of gaseous volumes says that gases react in volumes that bear a simple ratio to one another, and Avogadro's law says that equal volumes of all gases at the same temperature and pressure contain an equal number of molecules.

Dalton's atomic theory and its limits

Dalton put the laws together in 1808. Matter is made of indivisible atoms; all atoms of an element are identical in mass and properties; atoms of different elements differ; atoms combine in small whole number ratios; and atoms are neither created nor destroyed in a reaction. Later work showed the first two postulates to be wrong, because the atom has electrons, protons and neutrons inside it, and because isotopes of the same element have different masses. The rest of the theory still stands and explains the first three laws neatly.

Atomic mass, molecular mass and formula unit mass

Atomic masses are measured on a relative scale. One unified atomic mass unit, written u, is one twelfth of the mass of one atom of carbon twelve, so hydrogen is about 1 u, carbon 12 u, nitrogen 14 u, oxygen 16 u, sodium 23 u, sulphur 32 u, chlorine about 35.5 u and calcium 40 u. The molecular mass of a substance made of molecules is the sum of the atomic masses in its formula, so water is 18 u, ammonia is 17 u, carbon dioxide is 44 u and sulphuric acid is 98 u. For an ionic compound, which has no separate molecules, the same sum is called the formula unit mass: sodium chloride is 58.5 u and calcium chloride, that is forty plus two times thirty five and a half, is 111 u.

Valency and writing formulae

To write a formula, put the symbols side by side and cross over the valencies as subscripts, then reduce the numbers if they have a common factor. Aluminium with valency three and oxygen with valency two give aluminium oxide as Al2O3, and calcium with valency two and chlorine with valency one give CaCl2.

The mole concept

A chemist cannot count atoms one by one, so the mole was defined as a fixed number of particles. One mole of any substance contains 6.022 into ten to the power twenty-three particles, a figure called the Avogadro constant and named after Amedeo Avogadro, who never measured it himself. Three relations follow and together they solve almost every sum in this chapter. The number of moles equals the given mass divided by the molar mass. It also equals the number of particles divided by the Avogadro constant. For a gas at standard temperature and pressure it equals the volume divided by 22.4 litres, because one mole of any gas occupies 22.4 litres under those conditions.

The molar mass is simply the atomic or molecular mass expressed in grams, so one mole of water weighs 18 grams, one mole of oxygen gas weighs 32 grams and one mole of carbon weighs 12 grams. Thirty six grams of water is therefore two moles and holds twice the Avogadro number of molecules, while 44 grams of carbon dioxide is one mole and contains one Avogadro number of carbon dioxide molecules but three times that many atoms, since each molecule has one carbon and two oxygen atoms.

Common exam sums

Three types repeat. Find the molecular or formula unit mass of a compound: add the atomic masses, remembering that chlorine is 35.5 and not 35. Convert between mass, moles and number of particles: divide by the molar mass first and then multiply by the Avogadro constant. Find the mass of a given volume of gas at standard temperature and pressure: divide the volume by 22.4 to get moles and multiply by the molar mass. A fourth type, percentage composition, asks what share of the mass of a compound is one element, which is the mass of that element in one mole divided by the molar mass, multiplied by a hundred; in water, hydrogen is two out of eighteen, about 11.1 per cent.