Solution ‘x’ contains $N{a}_{2}C{O}_3$  and $NaHC{O}_3,$  20 ml of ‘x’ when titrated using Methyl orange indicator consumed 60 ml of 0.1M HCl solution. In another experiment 20ml of ‘x’ solution when titrated using phenolphthalein consumed 20 ml of 0.1 M HCl solution. The concentrations (in mole ${\text{litre}}^{-1}$ ) of $N{a}_{2}C{O}_3$  and $N{a}_{2}HC{O}_3$  in ‘X’ are respectively 

When phenolphthalein indicator is used, sodium carbonate is titrated to sodium bicarbonate.

Hence, 20 ml 0.1 M HCl corresponds to sodium carbonate

Number of milli-moles of sodium carbonate present =20×0.1=2mmol

Equivalents of Na₂CO₃= Equivalents of HCl

20 a = 2 (with Ph indicator)

a = 0.1M (concentration of Na₂CO₃)

When methyl orange indicator is used, sodium carbonate is titrated to sodium bicarbonate and sodium bicarbonate is titrated to carbonic acid.

60 ml of 0.1 M HCl used for titration with methyl orange indicator corresponds to mixture of sodium carbonate and sodium bicarbonate out of which complete titration of sodium carbonate to carbonic acid will require 40 mL of 0.1 M HCl and the remaining 20 mL of 0.1 M HCl will correspond to the titration of sodium bicarbonate present in the original mixture.

40a+20b =6 (with Methyl orange)

b = 0.1M(concentration of NaHCO₃)