2.5 g of a mixture containing `CaCO_(3), Ca(HCO_(3))_(2)` and NaCl was dissolved in 100 mL water and its 10 mL portion required 10 mL 0.05 M `H_(2)SO_(4)` solution to reach the phenolphthalein end point. An another 10 mL portion of the same stock solution required 32.35 mL of the same acid solution to reach the methyl orange end point. Determine mass percentage of `CaCO_(3)` and `Ca(HCO_(3))_(2)` in the original mixture.

Explanation

To solve the problem, we need to determine the mass percentage of calcium carbonate (CaCO₃) and calcium bicarbonate (Ca(HCO₃)₂) in a mixture that also contains sodium chloride (NaCl). We will use the information provided about the acid titrations to calculate the milliequivalents of each compound and then find their respective masses.

### Step 1: Calculate the milliequivalents of H₂SO₄ used for phenolphthalein endpoint

The first titration with phenolphthalein only reacts with CaCO₃. The formula for calculating milliequivalents (meq) is:

\[
\text{meq} = \text{Volume (L)} \times \text{Molarity (mol/L)} \times \text{n-factor}
...