2. Atoms, molecules and stoichiometry

The unified atomic mass unit, u, is defined as one twelfth of the mass of one carbon-12 atom. It provides a common reference scale for comparing atomic and isotopic masses, which are too small to weigh conveniently as individual absolute masses.

Use u as the reference in a ratio: a particle with a relative isotopic mass near 12 is being compared with the one-twelfth carbon-12 standard. The reference scale and the absolute mass of a particular atom are different quantities.

Keep the definition exact: one u is one twelfth of carbon-12, not the whole carbon-12 mass. Relative masses such as Aᵣ and Mᵣ are ratios and have no units; do not attach grams or kilograms to them, and do not confuse them with a nuclide’s mass number.

This card establishes the reference scale only. Isotope-abundance weighting and the separate definitions of relative atomic, molecular and formula mass belong to the neighbouring 2.1 objective; mole and stoichiometric calculations belong to later topics.

Relative atomic mass, Aᵣ, is the weighted average mass of the atoms of an element compared with one twelfth of the mass of one carbon-12 atom. It is a ratio and therefore has no units; the isotope abundances of the element determine the weighting.

For percentage abundances, calculate each isotope contribution, add the contributions, then divide by 100: Aᵣ = Σ(isotopic mass × percentage abundance) / 100. If fractional abundances are supplied instead, multiply by those fractions and add. The result need not be an integer.

Keep the objects distinct: relative isotopic mass describes one specified isotope; relative molecular mass is found by adding the relative atomic masses in one molecule; relative formula mass uses the simplest formula unit for an ionic compound and is calculated in the same additive way.

Do not use the mass number of the most abundant isotope as the element’s Aᵣ, attach units to Aᵣ or Mᵣ, or treat an ionic lattice as a collection of discrete molecules. Use the stated isotope abundances and formula, and leave mole/stoichiometric calculations to later topics.

A mole is an amount of substance containing the Avogadro constant, N_A, of the specified entities. Use N_A = 6.02 × 10²³ mol⁻¹ in the supported convention; one mole can count atoms, molecules, ions, electrons or the appropriate formula units of an ionic substance.

Choose the entity before counting: 1 mol of sodium contains N_A sodium atoms, 1 mol of hydrogen molecules contains N_A H₂ molecules, and each formula subscript determines how many atoms are present per entity. Therefore the total number of a particular atom can be a multiple of N_A.

The mole is an amount, not a mass or a volume. Relative atomic, molecular or formula mass provides the numerical molar-mass bridge: one mole of a substance has a mass numerically corresponding to its relative mass in grams per mole, while the particle count remains N_A for one mole.

Do not say that a mole always means molecules, or that all one-mole samples have the same mass. State the particle type and formula, keep particle number separate from mass, and leave reacting-mass, concentration, gas-volume and limiting-reagent calculations to later topics.

An ionic formula represents a neutral ionic compound: the total positive charge from the cations must equal the total negative charge from the anions. Use the ion charges and choose the simplest whole-number ratio of ions that gives overall charge zero.

Use a fixed sequence: (1) write the cation and anion with their charges, (2) choose subscripts so total charge balances, (3) simplify the ratio if a common factor remains, and (4) remove charge labels from the final neutral formula. Do not change a polyatomic ion's internal subscripts.

If more than one polyatomic ion is needed, put the ion in brackets before adding its subscript, for example Ca²⁺ with NO₃⁻ gives Ca(NO₃)₂. Common ions such as NO₃⁻, CO₃²⁻, SO₄²⁻, OH⁻, NH₄⁺ and PO₄³⁻ must be treated as intact charged groups when constructing the formula.

Use a Roman numeral as the oxidation number of a variable-charge metal, not as a formula subscript: iron(III) is Fe³⁺ before balancing. Do not balance an equation by changing these formula subscripts; equation coefficients belong to the neighbouring objective.

A balanced chemical equation conserves each element: the number of atoms of every element is the same on both sides. For an ionic equation, total charge must also be conserved, and state symbols should identify the reacting species and products.

Use a fixed sequence: (1) write the correct formulae and state symbols, (2) count atoms on both sides, (3) change coefficients until every element balances, (4) simplify to the smallest whole-number ratio, and (5) check atoms, charge and states. Never change a formula subscript to balance an equation.

To obtain a net ionic equation, write the complete ionic equation, split only appropriate aqueous strong electrolytes into ions, then cancel ions that are unchanged on both sides. The remaining species are the particles that undergo the chemical change; recheck charge as well as atom counts.

Coefficients change the amounts of substances while subscripts define the substances themselves. Do not cancel a reacting ion as a spectator, assume every dissolved species should be split, or omit state symbols when they are needed to distinguish the ionic form.

An empirical formula shows the simplest whole-number ratio of atoms or ions in a substance. A molecular formula shows the actual number of each atom in one molecule and is a whole-number multiple of the empirical formula when the substance is molecular.

Use the question being asked to choose the representation: empirical formula answers 'what is the simplest composition ratio?', whereas molecular formula answers 'how many atoms are present in one molecule?'. For an ionic compound, the formula unit gives the simplest ratio rather than a discrete molecule.

To relate the two, divide the molecular formula by the empirical formula to obtain a whole-number multiple. The molecular formula may equal the empirical formula when the simplest ratio is already the actual molecular composition; otherwise every empirical subscript is multiplied by the same integer.

Do not call an empirical formula an incomplete molecular formula, and do not change individual subscripts independently. Calculating the ratio from mass or percentage data belongs to the neighbouring calculation objective; this card establishes the meanings and relationship of the two terms.

An anhydrous salt contains no water of crystallisation in its crystal structure. A hydrated salt contains a fixed number of water molecules associated with each formula unit; the water is part of the crystal composition and is written after a dot in the hydrate formula.

Water of crystallisation is not simply liquid solvent or surface moisture. It is held in a definite stoichiometric ratio, so a hydrate can be represented as salt · nH₂O, where n is the number of water molecules per formula unit in that crystal.

Heating a hydrated salt can remove its water of crystallisation and form the anhydrous salt. The salt formula and its recorded mass therefore change together; use the stated hydrate ratio rather than treating the water content as arbitrary.

Do not interpret hydrated as dissolved, wet or chemically bonded into a new molecular compound, and do not assume every salt has water of crystallisation. The quantitative mass-loss calculation belongs to the neighbouring formula-calculation objective.

To calculate an empirical formula from composition data, first record the mass or percentage of each element. Convert each value to amount using its relative atomic mass, divide every amount by the smallest amount, and scale the ratios to the smallest whole numbers that fit the data.

Keep the element order and units consistent, then check that the final integer ratio reproduces the supplied composition within the stated precision. Do not round each raw ratio independently before comparing the ratios; use a common multiplier when a simple fraction is present.

If a relative molecular mass is supplied, calculate the empirical-formula mass and find the whole-number multiple: multiplier = relative molecular mass ÷ empirical-formula mass. Multiply every empirical subscript by that same integer to obtain the molecular formula.

An empirical formula is the simplest ratio, whereas a molecular formula gives the actual atom numbers in one molecule. Do not use the molecular-multiple step for an ionic lattice, alter individual subscripts, or extend the calculation into reacting-mass or percentage-yield problems.

Start every stoichiometric calculation with the correct balanced equation and identify the quantity requested. Convert the supplied data to moles, apply the mole ratio from the coefficients, then convert the calculated amount into the required mass, gas volume or solution quantity.

Use the appropriate relationship and units: amount from mass uses n = m/M; solution concentration uses c = n/V with a consistent volume unit; gas volume uses the stated molar-volume conditions. Coefficients give mole ratios, not direct mass ratios, so do not apply them before the mole conversion.

For percentage yield, compare actual product with the theoretical amount: percentage yield = actual yield ÷ theoretical yield × 100. When more than one reactant is supplied, calculate the product possible from each reactant and identify the smaller amount as the limiting-reagent result; the other reactant is in excess and can be treated only after the limiting amount is established.

Finish by checking units, significant figures, the balanced atom/charge relationship, and whether the result is chemically sensible. Keep gas conditions, solution volume units, percentage-yield direction and limiting/excess labels explicit; a calculated stoichiometric relationship is a conclusion supported by these checks, not a replacement for them.