# Double Titration

The purpose of double titration is to determine the percentage composition of an alkali mixture or an acid mixture. In the present case, we will find the percentage composition of an alkali mixture. Let us consider a solid mixture of NaOH, Na2CO3, and some inert impurities, weighing w gram. We are required to find the percentage composition of this alkali mixture. We are also given an acid reagent (HCl) of known concentration M1 that can react with the alkali sample.

We first dissolve this mixture in water to make an alkaline solution, and then we add two indicators (indicators are substances that indicate color change of solution when a reaction gets completed), namely phenolphthalein and methyl orange to the solution. Now, we titrate this alkaline solution with standard HCl.

NaOH is a strong base, while Na2CO3 is a weak base. So it is obvious that NaOH reacts first with HCl completely and Na2CO3 reacts only after complete NaOH is neutralized.

NaOH + HCl â†’ NaCl + H2Oâ€¦(i)

Once NaOH has reacted completely, then Na2CO3 starts reacting with HCl in two steps as follows:

Na2CO3 + HCl â†’ NaHCO3 + NaClâ€¦(ii)

NaHCO3 + HCl â†’ NaCl + CO2 + H2Oâ€¦(iii)

It is clear that when we add HCl to the alkaline solution, alkali is neutralized and the pH of the solution decreases. Initially, the pH decrease would be rapid as strong base (NaOH) is neutralized completely. When Na2CO3 is converted into NaHCO3 completely, the solution is still weakly basic due to the presence of NaHCO3 (which is weaker as compared to Na2CO3). At this point, phenolphthalein changes color since it requires this weakly basic solution to show its color change. When HCl is further added, the pH again decreases and when all the NaHCO3 reacts to form NaCl, CO2, and H2O, the solution becomes weakly acidic due to the presence of the weak acid (H2CO3). At this point, methyl orange changes color as it requires this weakly acidic solution to show its color change.

Thus, in general, phenolphthalein shows color change when the solution contains weakly basic NaHCO3 along with other neutral substances, while methyl orange shows color change when solution contains weakly acidic H2CO3 along with other neutral substances.

Let the volume of HCl used up for the first and the second reactions be V1 liter (this is the volume of HCl used from the beginning of the titration up to the point when phenolphthalein shows color change), and the volume of HCl required for the third reaction be V2 liter (this is the volume of HCl used from the point where phenolphthalein had changed color upto the point when methyl orange shows color change). Then,

Moles of HCl consumed by NaHCO3 = Moles of NaHCO3 reacted = M1V2

Moles of NaHCO3 formed from Na2CO3 = M1V2

Moles of Na2CO3 in the mixture = M1V2

Mass of Na2CO3 in the mixture = M1V2 Ã— 106

% Na2CO3 in the mixture =

Moles of HCl used in the reactions (i) and (ii) = M1V1

Moles of HCl used in reaction (ii) = M1V2

Moles of HCl used in reaction (i) = (M1V1 â€“ M1V2)

âˆ´ Moles of NaOH = (M1V1 â€“ M1V2) Ã— 40

% NaOH in the mixture =