Titration Calculations - 2

Sodium carbonate is a common standard solution because it can be weighed accurately as a pure, stable solid. It is often used to find the concentration of hydrochloric acid, with methyl orange as the indicator.Na₂CO₃(aq) + 2HCl(aq) → 2NaCl(aq) + H₂O(l) + CO₂(g)Here the ratio is Na₂CO₃ : HCl = 1 : 2, so this time you multiply by 2 to go from the carbonate to the acid.Worked example: 25.0 cm³ of 0.0500 mol dm^-3 sodium carbonate solution was titrated with hydrochloric acid. The concordant titres were 20.05, 19.95 and 20.00 cm³. Calculate the concentration of the acid.Mean titre = (20.05 + 19.95 + 20.00) ÷ 3 = 20.00 cm³Step 1: amount of Na₂CO₃ = 0.0500 × (25.0 ÷ 1000) = 1.25 × 10^-3 molStep 2: 1 mol Na₂CO₃ reacts with 2 mol HCl, so amount of HCl = 1.25 × 10^-3 × 2 = 2.50 × 10^-3 molStep 3: concentration of HCl = 2.50 × 10^-3 ÷ (20.00 ÷ 1000) = 0.125 mol dm^-3Compare this with the sulfuric acid example: there the unknown was the diprotic reagent and you divided by 2; here the known is the reagent that needs two moles of acid, so you multiply. Reading the ratio from the equation, rather than remembering a rule, avoids the mistake.