One molecule of hydrogen chloride can give one hydrogen ion, sulfuric acid can give two and phosphoric acid can give three. Such acids are called monoprotic, diprotic and triprotic.
In these acids, the hydrogen atoms that leave are the ones bonded to oxygen, or to chlorine in hydrogen chloride. Ethanoic acid, \mathrm{CH_3COOH}, has four hydrogen atoms, but only the one in the \mathrm{O{-}H} group can leave, so it is monoprotic.
In the same way, one formula unit of sodium hydroxide gives one hydroxide ion and calcium hydroxide gives two. The number of ions an acid or base can give is not a measure of its strength.
Concentration is given here in mol/L: the number of moles of a substance dissolved in each litre of solution, where a mole is a fixed, very large number of particles.
The degree of ionization is the fraction of the dissolved acid or base that has ionized. At 0.1 mol/L and 25 °C it is about 1 for hydrochloric acid and for sodium hydroxide, but only 0.013 for ethanoic acid and for ammonia.
So in 0.1 mol/L ethanoic acid only about 13 of every 1000 molecules have given up a hydrogen ion at any moment, and the rest stay as molecules.
Acids and bases that ionize almost completely in water are called strong, and those that ionize only partly are called weak. Hydrochloric acid, nitric acid and sulfuric acid are strong acids, while ethanoic acid, carbonic acid and phosphoric acid are weak.
Sodium hydroxide, potassium hydroxide, calcium hydroxide and barium hydroxide are strong bases, while ammonia is a weak base.
Strength and the number of hydrogen ions are separate properties: sulfuric acid is a strong diprotic acid, but phosphoric acid is a weak triprotic acid, and hydrogen fluoride, unlike the other hydrogen halides, is a weak monoprotic acid.
When equal pieces of magnesium ribbon are added to hydrochloric acid and to ethanoic acid of the same concentration and volume, hydrogen bubbles off quickly from the hydrochloric acid but slowly from the ethanoic acid.
The rate depends on the concentration of hydrogen ions, which is much higher in the strong acid. In the weak acid, most of the acid is still in molecules, so far fewer hydrogen ions are free to react at any moment.
As the hydrogen ions react, more ethanoic acid molecules ionize. With magnesium left over, both acids in the end give the same volume of hydrogen, because they contain the same amount of acid.
Diluting a weak acid raises its degree of ionization. For ethanoic acid at 25 °C it is 0.013 at 0.1 mol/L, 0.041 at 0.01 mol/L and 0.12 at 0.001 mol/L.
In a more dilute solution, the ions are further apart and meet less often to join back into molecules, so a larger fraction of the acid stays ionized.
Even so, the concentration of hydrogen ions still falls on dilution, because the total amount of acid in each litre falls faster than the fraction ionized rises.