Acidified manganate(VII) ions, $$\(\mathrm{MnO}_{4}^{-}\)$$, can be used to analyse solutions containing nitrite ions, $$\(\mathrm{NO}_{2}^{-}\)$$, by titration. X is a solution of $$\(\mathrm{NaNO}_{2}\)$$. $$\(250.0 \mathrm{~cm}^{3}\)$$ of $$\(\mathbf{X}\)$$ is added to $$\(50.0 \mathrm{~cm}^{3}\)$$ of $$\(0.125 \mathrm{moldm}^{-3}\)$$ acidified $$\(\mathrm{MnO}_{4}^{-}(\mathrm{aq})\)$$. The $$\(\mathrm{MnO}_{4}^{-}(\mathrm{aq})\)$$ ions are in excess; all the $$\(\mathrm{NO}_{2}^{-}\)$$- ions are oxidised in the reaction. The unreacted $$\(\mathrm{MnO}_{4}^{-}(\mathrm{aq})\)$$ required $$\(22.50 \mathrm{~cm}^{3}\)$$ of $$\(0.0400 \mathrm{moldm}^{-3} \mathrm{Fe}^{2+}(\mathrm{aq})\)$$ to reach the end-point. The relevant half-equations are shown. $$\[ \begin{aligned} \mathrm{NO}_{2}^{-}+\mathrm{H}_{2} \mathrm{O} & \rightleftharpoons \mathrm{NO}_{3}^{-}+2 \mathrm{H}^{+}+2 \mathrm{e}^{-} \\ \mathrm{MnO}_{4}^{-}+8 \mathrm{H}^{+}+5 \mathrm{e}^{-} & \rightleftharpoons \mathrm{Mn}^{2+}+4 \mathrm{H}_{2} \mathrm{O} \\ \mathrm{Fe}^{2+} & \rightleftharpoons \mathrm{Fe}^{3+}+\mathrm{e}^{-} \end{aligned} \]$$ Calculate the concentration, in moldm $$\({ }^{-3}\)$$, of $$\(\mathrm{NaNO}_{2}\)$$ in $$\(\mathbf{X}\)$$. concentration of $$\(\mathrm{NaNO}_{2}\)$$ in $$\(\mathrm{X}=\)$$ .......................... moldm $$\({ }^{-3}\)$$

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