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A 40 mL sample of 0.05 M sodium sesquicarbonate dihydrate [Na2CO3*NaHCO3*2H2O] is titrated against 0.05 M HCl. The volume of acid required to reach the phenolphthalein end point is x mL, and in a separate titration using methyl orange indicator, the volume required is y mL. Which of the following statements are correct?

1. y - x = 80 mL
2. y + x = 160 mL
3. If the titration is started with phenolphthalein and methyl orange is added at the end point, an additional 2x mL of HCl would be needed to reach the methyl orange end point.
4. y + x = 120 mL

Correct answer: y + x = 120 mL

Solution

The sesquicarbonate gives equal moles of Na2CO3 and NaHCO3. At phenolphthalein end point, CO3²- -> HCO3⁻. At methyl orange end point, all carbonate species -> H2CO3. Computing moles and volumes of HCl for each end point and checking the given relationships identifies the correct statement.

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