Carbonic acid is a weak diprotic acid (H₂CO₃) with K_a1 = 4.43 x 10^-7 and K_a2 = 4.73 x 10^-11. The equivalence points for the titration come at approximately pH 4 and 9. Suitable indicators for use in titrating carbonic acid or carbonate solutions are methyl orange and phenolphthalein.

(a) Sketch the titration curve that would be obtained in titrating a 10.0 mL sample of 1.00 M NaHCO₃(aq) with 1.00 M HCl.

(b) Sketch the titration curve for the titration of a 10.0 mL sample of 1.00 M Na₂CO₃(aq) with 1.00 M HCl.

(c) What volume of 0.100 M HCl is required for the complete neutralization of 1.00 g NaHCO₃(s)?

(d) What volume of 0.100 M HCl is required for the complete neutralization of 1.00 g Na₂CO₃(s)?

(e) A sample of NaOH contains a small amount of Na₂CO₃. For titration to the phenolphthalein end point, 0.1000 g of this sample requires 23.98 mL of 0.1000 M HCl. An additional 0.78 mL is required to reach the methyl orange end point. What is the percent Na₂CO₃, by mass, in the sample?