25 ml of the given HCl solution requires 30 mL of 0.1 M sodium carbonate solution. What is the volume of this HCl solution required to titrate 30 mL of 0.2 M aqueous NaOH solution?

Given, 25 ml of the given HCl solution requires 30 mL of 0.1 M sodium carbonate

$$\begin{gathered} \underset{\left(\mathrm{A}\right)}{2\mathrm{HCl}}+\underset{\left(\mathrm{B}\right)}{{\mathrm{Na}}_2{\mathrm{CO}}_3}\to 2\mathrm{NaCl}+{\mathrm{H}}_2\mathrm{O}+{\mathrm{CO}}_2 \\ {\mathrm{V}}_{\mathrm{A}}=25\mathrm{ml} , {\mathrm{V}}_{\mathrm{B}}=30\mathrm{ml} \\ {\mathrm{M}}_{\mathrm{A}}=?, {\mathrm{M}}_{\mathrm{B}}=0.1\mathrm{M} \\ {\mathrm{n}}_{\mathrm{A}}=2, {\mathrm{n}}_{\mathrm{B}}=1 \\ \frac{{\mathrm{V}}_{\mathrm{A}}{\mathrm{M}}_{\mathrm{A}}}{{\mathrm{n}}_{\mathrm{A}}}=\frac{{\mathrm{V}}_{\mathrm{B}}{\mathrm{M}}_{\mathrm{B}}}{{\mathrm{n}}_{\mathrm{B}}} \\ \frac{25\times {\mathrm{M}}_{\mathrm{A}}}{2}=\frac{30\times 0.1}{1} \\ {\mathrm{M}}_{\mathrm{A}}=0.24\mathrm{M} \end{gathered}$$

 The volume of this HCl solution required to titrate 30 mL of 0.2 M aqueous NaOH solution

$$\begin{gathered} \mathrm{HCl}+\mathrm{NaOH}\to \mathrm{NaCl}+{\mathrm{H}}_2\mathrm{O} \\ {\left(\frac{\mathrm{VM}}{\mathrm{n}}\right)}_{\mathrm{HCl}}={\left(\frac{\mathrm{VM}}{\mathrm{n}}\right)}_{\mathrm{NaOH}} \\ \frac{{\mathrm{V}}_{\mathrm{HCl}}\times 0.24}{1}=\frac{30\times 0.2}{1} \\ {\mathrm{V}}_{\mathrm{HCl}}=\frac{30\times 0.2}{0.24}=25\mathrm{ml} \end{gathered}$$