1. why is it necessary to use boiled and cooled water in the dilution of the carbonate sample?

Question

2. an aliquot of the diluted sample is titrated with some standard HCl until near the equivalence point, then it is boiled for 2-3 minutes. why should we boil it?
3. any method to test the completeness of the precipitation of the sample with BaCl2?

Answer 1

1. Water is boiled to assure CO2 is not dissolved in it, then cooled to room temperature.
2. The water near the equivalence point is saturated with CO2 and this causes the end point to be somewhat obscured (at least it isn't very sharp.) By boiling, the CO2 is expelled the pH rises, the indicator returns to the basic color of the indicator, and the final few drops of HCl titrant gives a sharp end point.
3. I don't understand what you want with this part.