For complexes of the same metal ion with no change in...

For complexes of the same metal ion with no change in oxidation number, the stability increases as the number of electrons in the $t_{2 g}$ orbitals increases. Which complex in each of the following pairs of complexes is more stable? (a) $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$ or $\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}$ (b) $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}$ or $\left[\mathrm{CoF}_{6}\right]^{3-}$ (c) $\left[\mathrm{Mn}(\mathrm{CN})_{6}\right]^{4-}$ or $\left[\mathrm{MnCl}_{6}\right]^{4-}$

For complexes of the same metal ion with no change in oxidation number, the stability increases as the number of electrons in the $t_{2 g}$ orbitals increases. Which complex in each of the following pairs of complexes is more stable?
(a) $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$ or $\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}$
(b) $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}$ or $\left[\mathrm{CoF}_{6}\right]^{3-}$
(c) $\left[\mathrm{Mn}(\mathrm{CN})_{6}\right]^{4-}$ or $\left[\mathrm{MnCl}_{6}\right]^{4-}$

Key Concepts

Spectrochemical Series

The spectrochemical series is an ordered list of ligands arranged according to the strength of the crystal field splitting they produce. Strong field ligands, such as cyanide, cause a larger splitting of the d-orbitals, leading to a greater LFSE and increased stability of the complex. Conversely, weak field ligands like water or chloride produce a smaller splitting, resulting in lower LFSE and less stable complexes.

Ligand Field Stabilization Energy (LFSE)

LFSE is the energy reduction achieved when electrons occupy the lower-energy t?g orbitals instead of the higher-energy e_g orbitals in a split d-orbital system. A complex with more electrons in the t?g orbitals will have a higher LFSE and, therefore, be more stable. This concept helps explain why certain complexes, with the same metal ion and oxidation state, can exhibit different stabilities based on their ligand environments.

Crystal Field Theory

Crystal Field Theory explains how the degenerate d-orbitals of a metal ion split into different energy levels in the presence of surrounding ligands. In an octahedral complex, the d-orbitals split into two sets: the lower-energy t?g orbitals and the higher-energy e_g orbitals. This splitting is crucial for understanding the distribution of electrons in these orbitals, which directly influences the stability of the complex.

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