A student analyzes a \(1.060\text{ g}\) sample of an impure powdered mixture containing soluble \(\text{Na}_2\text{CO}_3\) and water-insoluble chalk filler. The student extracts the sample with deionized water and filters the mixture into a \(100.0\text{ mL}\) volumetric flask. The residue and filter paper are washed with several small portions of deionized water, and the washings are added to the flask. The solution is then diluted to the mark. The solid residue is subsequently dried and weighed as a gravimetric check.

A \(25.00\text{ mL}\) aliquot of the solution is combined with \(60.00\text{ mL}\) of \(0.1000\text{ M}\) \(\text{HCl}\).

\[ \text{Na}_2\text{CO}_3\text{(aq)}+2\text{HCl(aq)}\rightarrow 2\text{NaCl(aq)}+\text{H}_2\text{O(l)}+\text{CO}_2\text{(g)} \]

After the mixture is heated gently to remove the \(\text{CO}_2\), the excess \(\text{HCl}\) is back-titrated with \(20.00\text{ mL}\) of \(0.1000\text{ M}\) \(\text{NaOH}\). Which choice gives the estimated mass percentage of \(\text{Na}_2\text{CO}_3\) and correctly explains why the residue and filter paper must be washed?