a
\(CaCO _{3(s)}+2 HCl _{(\text {aq) })} \rightarrow CaCl _{2(a q)}+ CO _{2(q)}+ H _{2} O _{(q)}\)

no. of moles of \(CaCO _{3}\) (pure) \(=\frac{1}{2} \times\) mole of \(HCl\)

\(\quad \text { [Mole }=\text { molarity } \times \text { volume(in Itr. }) \text { ] }\)

\(=\frac{1}{2} \times 0.5 \times \frac{50}{1000}=0.0125\)

weight of \(CaCO _{3}\) (pure) \(=\) mole \(\times\) mol. wt

\(=0.0125 \times 100=1.25 \,g\)

\(\%\) purity \(=\frac{\text { wt. of pure substance }}{\text { wt. of impure sample }} \times 100\)

\(95=\frac{1.25}{\text { wt. of impure sample }} \times 100\)

wt. of impure sample \(=\frac{1.25 \times 100}{95}=1.32 \,g\)