A harder balance
The reaction: aluminium metal and dilute hydrochloric acid react to form aluminium chloride and hydrogen gas.
The start — write correct formulae on both sides of the arrow
Al + HCl → AlCl3 + H2
Step 1 — the lowest common multiple
The products hold three chlorine (Cl) atoms and two hydrogen (H) atoms.
The lowest common multiple of 2 and 3 is 6, so write the coefficient of the acid HCl as 6.
Al + 6HCl → AlCl3 + H2
Step 2 — evening up the right-hand side
There are now six hydrogen atoms in the reactants, so write the coefficient of H2 as 3.
There are six chlorine atoms in the reactants, so write the coefficient of AlCl3 as 2.
Al + 6HCl → 2AlCl3 + 3H2
Step 3 — evening up the aluminium
There are two aluminium atoms in the products, so write the coefficient of aluminium as 2.
2Al + 6HCl → 2AlCl3 + 3H2
This is the balanced equation for the reaction.
The inspection method
Balancing a chemical equation in the way shown above is called the inspection method.
The main trick is to take the more complicated side first and use the lowest common multiple. Leave lone elements (Al here) until last — they are the easiest to even up.