\(2.5 \mathrm{~cm}^{3}\) of \(0.2 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) solution is diluted to \(0.5\) \(\mathrm{dm}^{3}\). Find normality of the diluted solution.

Given, volume of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) before dilution, \(V_{1}=2.5 \mathrm{~cm}^{3}\)
\(
=2.5 \times 10^{-3} \mathrm{dm}^{3}
\)
volume of \(\mathrm{II}_{2} \mathrm{SO}_{4}\) after dilution, \(V_{2}-0.5 \mathrm{dm}^{3}\)
Concentration of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) before dilution \(=0.2 \mathrm{M}\)
\(
=0.4 \mathrm{~N} \quad[\because 1 \mathrm{~N}=2 \mathrm{M}]
\)
Concentration (normality) of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) after dilution, \(N_{2}=\) ? Normality equation is
\(
N_{1} V_{1} = N_{2} V_{2}
\)
(before dilution) \(\quad\) (after dilution)
\(2.5 \times 10^{-3} \times 0.4 =N_{2} \times 0.5 \)
\( N_{2} =\frac{2.5 \times 10^{-3} \times 0.4}{0.5} \)
\( =2 \times 10^{-3}=0.002 \mathrm{~N}\)