For the reaction,
\(3 \mathrm{I}^{-}+\mathrm{S}_2 \mathrm{O}_8^{2-} \rightarrow \mathrm{I}_3^{-}+2 \mathrm{SO}_4^{2-}\), at a particular time \(\mathrm{t}\), \(\frac{\mathrm{d}\left[\mathrm{SO}_4^{2-}\right]}{\mathrm{dt}}\) is \(2.2 \times 10^{-2} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}\). What is the value of \(-\frac{\mathrm{d}\left[\mathrm{I}^{-}\right]}{\mathrm{dt}}\) ?

\(3 \mathrm{I}^{-}+\mathrm{S}_2 \mathrm{O}_8^{2-} \rightarrow \mathrm{I}_3^{-}+2 \mathrm{SO}_4^{2-} \)
\( \text {Rate of reaction}=-\frac{1}{3} \frac{\mathrm{d}\left[\mathrm{I}^{-}\right]}{\mathrm{dt}}=+\frac{1}{2} \frac{\mathrm{d}\left[\mathrm{SO}_4^{2-}\right]}{\mathrm{dt}} \)
\( -\frac{\mathrm{d}\left[\mathrm{I}^{-}\right]}{\mathrm{dt}} =\frac{3}{2} \frac{\mathrm{d}\left[\mathrm{SO}_4^{2-}\right]}{\mathrm{dt}}=\frac{3}{2} \times 2.2 \times 10^{-2} \)
\( =3.3 \times 10^{-2} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}\)
[Note: In the question, \(\frac{\mathrm{d}\left[\mathrm{I}^{-}\right]}{\mathrm{dt}}\) is changed to \(-\frac{\mathrm{d}\left[\mathrm{I}^{-}\right]}{\mathrm{dt}}\) to apply appropriate textual concepts.]