What volume (in ml) at STP of ${\mathrm{SO}}_2$ gas is oxidized by 100 ml of  $0.1 \left(\mathrm{M}\right) {\mathrm{H}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7$ in acid solution?

$$\begin{gathered} {\mathrm{SO}}_2\to {{\mathrm{SO}}_4}^{2-}\mathrm{x}-\mathrm{factor}=2 \\ {\mathrm{Cr}}_2{{\mathrm{O}}_7}^{2-}\to {\mathrm{Cr}}^{3+}\mathrm{x}-\mathrm{factor}=6 \\ \mathrm{Now} \\ \mathrm{V}\times 2=100\times 0.1\times 6\times {10}^{-3}\times 22400\mathrm{V} \\ =\frac{100\times 0.1\times 6\times {10}^{-3}\times 22400}{2}=\frac{224\times 6}{2}=672 \mathrm{ml} \end{gathered}$$