A carbonate ion can take two hydrogen ions. When hydrochloric acid is added to sodium carbonate solution, the carbonate ions first take one hydrogen ion each and become hydrogencarbonate ions: \mathrm{Na_2CO_3 + HCl \longrightarrow NaHCO_3 + NaCl}.
Only when almost all the carbonate ions have changed does the second step begin. The hydrogencarbonate ions take a second hydrogen ion and become carbonic acid, which breaks down into water and carbon dioxide: \mathrm{NaHCO_3 + HCl \longrightarrow NaCl + H_2O + CO_2}.
A 10.00 mL sample of 0.100 mol/L sodium carbonate solution holds 1.00 mmol of carbonate ions. With 0.100 mol/L hydrochloric acid, each step uses 10.00 mL, so the whole titration takes 20.00 mL.
The titration curve has two jumps, one at each equivalence point. The pH starts at about 11.6, because carbonate ions take hydrogen ions from water and leave hydroxide ions, and falls to about 8.3 at 10.00 mL.
The first jump is small. The pH falls only from about 8.5 at 9.90 mL to about 8.1 at 10.10 mL, because hydrogencarbonate ions can both take and give hydrogen ions and so resist a change in pH.
The second jump comes at 20.00 mL, where the hydrogencarbonate ions have become carbonic acid and the pH is about 3.9. The curve is flattest halfway through each step, at 5.00 mL and 15.00 mL. All the values are for 25 °C.
Each jump needs its own indicator. Phenolphthalein is added first, and the pink solution turns colourless as the pH falls through about 8, close to the first equivalence point at 10.00 mL.
Methyl orange is then added, and the titration continues. The solution is yellow at first and turns red as the pH falls from about 4.5 to 3, which happens close to the second equivalence point at 20.00 mL.
Each indicator is used for one jump only. Methyl orange does not change at the first jump, and phenolphthalein is already colourless long before the second, so the two volumes are read one after the other in a single titration.
A solution of sodium hydrogencarbonate starts where the second step of the carbonate titration begins. For 10.00 mL of 0.100 mol/L solution, the pH starts at about 8.3, the same as at the first equivalence point of sodium carbonate.
Each hydrogencarbonate ion takes only one hydrogen ion, so the curve has a single jump at 10.00 mL, where the pH is about 3.8. It looks much like the second half of the sodium carbonate curve.
Phenolphthalein is almost colourless from the start, so it shows no change. Methyl orange alone is used, and it turns from yellow to red at the end point.
Sodium hydroxide absorbs carbon dioxide from the air, \mathrm{2NaOH + CO_2 \longrightarrow Na_2CO_3 + H_2O}, so a solution left open to the air comes to contain sodium carbonate. The amount of each can be found in one titration with both indicators.
Up to the first end point, the acid neutralizes the hydroxide ions and also turns the carbonate ions into hydrogencarbonate ions. Between the two end points, it only turns hydrogencarbonate ions into carbonic acid, so that volume matches the carbonate alone.
For 10.00 mL of a mixture, the end points come at 10.00 mL and 15.00 mL of 0.100 mol/L hydrochloric acid. The carbonate takes 5.00 mL in each step and the hydroxide the other 5.00 mL, so the mixture holds 0.0500 mol/L of each.