What is the electron configuration for the transition metal ion in each of the following compounds? a. \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) b. \(\left[\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right] \mathrm{Cl}\) c. \(\left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{Br}_{2}\) d. \(\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\left(\mathrm{NO}_{2}\right)_{2}\right] \mathrm{I}\)

: In the given compounds, the transition metal ions are as follows: a. Fe in \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) b. Ag in \(\left[\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right] \mathrm{Cl}\) c. Ni in $\left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{Br}_{2}$ d. Cr in $\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\left(\mathrm{NO}_{2}\right)_{2}\right] \mathrm{I}$

: By analyzing the charges of the ligands and counter-ions, we can determine the oxidation states of the transition metal ions: a. \(\mathrm{Fe^{III+}}\): \(3 \times (\mathrm{K^{I+}}) = \mathrm{Fe^{III+}} + 6 \times (\mathrm{CN^{-}})\) b. \(\mathrm{Ag^{I+}}\): \(\mathrm{Ag^{I+}} + 2 \times (\mathrm{NH_3}) = [\mathrm{Ag}(\mathrm{NH}_{3})_{2}]^{+} + \mathrm{Cl^{-}}\) c. \(\mathrm{Ni^{II+}}\): \(\mathrm{Ni^{II+}} + 6 \times (\mathrm{H_{2}O}) = [\mathrm{Ni}(\mathrm{H_2O})_{6}]^{2+} + 2 \times (\mathrm{Br^{-}})\) d. \(\mathrm{Cr^{III+}}\): \(\mathrm{Cr^{III+}} + 4 \times (\mathrm{H_2O}) + 2 \times (\mathrm{NO_2^{-}}) = [\mathrm{Cr}(\mathrm{H_2O})_{4}(\mathrm{NO_2})_{2}]^{3+} + \mathrm{I^{-}}\)

: Now we will write the ground-state electron configuration for the transition metal ions: a. \(\mathrm{Fe^{III+}}\): \(\mathrm{1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^0, 3d^5}\) b. \(\mathrm{Ag^{I+}}\): \(\mathrm{1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^2, 3d^{10}, 4p^6, 5s^0, 4d^{10}}\) c. \(\mathrm{Ni^{II+}}\): \(\mathrm{1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^0, 3d^{8}}\) d. \(\mathrm{Cr^{III+}}\): \(\mathrm{1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^0, 3d^{3}}\)

: Finally, we will write the electron configuration for the transition metal ions: a. \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\): \(\mathrm{Fe}^{3+}\) has an electron configuration of \(\mathrm{3d^5}\). b. \(\left[\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right] \mathrm{Cl}\): \(\mathrm{Ag}^{+}\) has an electron configuration of \(\mathrm{4d^{10}}\). c. $\left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{Br}_{2}\(: \)\mathrm{Ni}^{2+}\( has an electron configuration of \)\mathrm{3d^{8}}$. d. $\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\left(\mathrm{NO}_{2}\right)_{2}\right] \mathrm{I}\(: \)\mathrm{Cr}^{3+}\( has an electron configuration of \)\mathrm{3d^{3}}$.