The mole is the unit used to measure amounts of substance. It links mass, numbers of particles, gas volumes and solution concentrations.
No atoms are lost or made in a reaction, so the total mass of the products equals the total mass of the reactants. Every symbol equation must therefore balance.
Balance by putting whole numbers in front of formulae. Never change a subscript inside a formula, because that changes the substance.
A reaction in an open container can appear to gain or lose mass, and in the examples studied here the explanation is a gas.
Magnesium burning gains mass because it combines with oxygen from the air. A metal carbonate heated in an open crucible loses mass because carbon dioxide escapes. Seal the container and the mass does not change.
The relative formula mass (Mr) of a compound is the sum of the relative atomic masses of all the atoms in its formula.
For H2SO4: (2×1) + 32 + (4×16) = 98. In a balanced equation, multiplying each relative formula mass by its balancing coefficient gives the same total on both sides, which is a useful check.
One mole contains \(6.02\times10^{23}\) specified entities, whether atoms, molecules, ions or formula units. That number is the Avogadro constant. The mass of one mole in grams is numerically equal to the relative atomic mass for an element, or the relative formula mass for a compound.
The relationship to memorise is \(\text{moles} = \frac{\text{mass}}{M_r}\). Many calculations in this topic start by converting a mass into moles, though others begin from a concentration or a gas volume.
The coefficients in a balanced equation give ratios of moles, not ratios of masses. In 2H2 + O2 → 2H2O, two moles of hydrogen react with one of oxygen.
So the method is to convert the known mass to moles, use the equation's ratio to find the moles of the substance you want, then convert back to a mass. Working the other way, dividing masses by relative formula masses and simplifying the ratio gives the balancing numbers.
When reactants are not present in the ratio required by the equation, one reactant is completely used up first. This is the limiting reactant, and it determines how much product forms. Any other reactant supplied beyond the amount needed is in excess.
To find it, convert the masses to moles and compare against the equation’s ratio. Base the rest of the calculation on the limiting reactant only.
Concentration can be given as mass per unit volume, in g/dm3, or as moles per unit volume, in mol/dm3.
\(\text{concentration} = \frac{\text{amount}}{\text{volume}}\), and the volume must be in cubic decimetres, so divide a volume in cm3 by 1000. Converting between the two forms uses the relative formula mass.
The theoretical yield is the mass predicted by the balanced equation. The actual yield is usually lower; an apparent yield above 100% points to measurement error or a wet or impure product.
\(\text{percentage yield} = \frac{\text{actual}}{\text{theoretical}} \times 100\). Yield is lost because the reaction is incomplete or reversible, because some product is lost in handling, or because side reactions produce something else.
Atom economy measures how much of the mass of the reactants ends up in the useful product. Both totals come from the balanced equation, each relative formula mass multiplied by its coefficient: \(\frac{\text{total } M_r \text{ of desired product}}{\text{total } M_r \text{ of all reactants}} \times 100\).
It is different from yield: a reaction can have a high yield and a poor atom economy if most of the reactant mass ends up as by-products. High atom economy means less waste, so industry prefers it, alongside cost, rate and how useful the by-products are.
Equal numbers of moles of gases occupy equal volumes at the same temperature and pressure. At room temperature and pressure, one mole of gas occupies approximately 24 dm3.
So \(\text{volume} = \text{moles} \times 24\), and for gases measured at the same temperature and pressure the mole ratio in an equation is also the volume ratio.
Every measurement has uncertainty. Repeating measurements helps identify random variation, and calculating a mean from repeat measurements can reduce the effect of random error. A result lying well away from the others is anomalous and should be investigated. It may be excluded from the mean if there is good reason to think it unreliable.
The range of repeated measurements gives an indication of their spread and therefore of the random uncertainty.
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