Q.Identify the following :

Variable Oxidation States – The Intuition

Think of an atom as having a wallet with two compartments. In most elements, one compartment is much easier to open than the other — you can only take money from the shallow one, so the amount you can spend (the oxidation state) is fixed. For transition metals, both compartments are at nearly the same depth. You can reach into either, and you can take different combinations of notes from each. That is variable oxidation states in a nutshell.

Iron, for example, can lose two electrons to become $\text{Fe}^{2+}$ or three to become $\text{Fe}^{3+}$. Manganese can show +2, +3, +4, +6, and +7. This is not random — it follows a clear pattern rooted in energy.

The Precise Statement

The key is similar energies. In main-group elements (like sodium or chlorine), the outermost $ns$ and $np$ electrons are far higher in energy than the inner core — you lose only the valence electrons, and the oxidation state is fixed. In transition metals, the $(n-1)d$ orbital is not much lower than the $ns$ orbital. Both are close enough that losing a few $d$ electrons along with the $s$ electrons costs comparable energy.

Why This Happens – The Energy Picture

For a transition metal like iron ($[\text{Ar}]\,3d^6 4s^2$), the 4s orbital is actually slightly lower in energy than the 3d when the atom is neutral. But once you start removing electrons, the energy ordering shifts. The first two electrons lost are from the 4s orbital (giving $\text{Fe}^{2+}$). The next electron lost comes from the 3d orbital (giving $\text{Fe}^{3+}$). Because the 3d and 4s are so close in energy, removing that third electron does not require a huge jump in energy — it is feasible.

The Pattern Across the Series

For the first transition series (Sc to Zn), the common oxidation states are:

Notice the trend: the maximum oxidation state increases from Sc (+3) to Mn (+7), then decreases. The maximum possible oxidation state equals the total number of electrons in the $(n-1)d$ and $ns$ orbitals (the "group number" for many). Manganese, with $3d^5 4s^2$, can lose all seven — giving $\text{MnO}_4^-$ where Mn is +7. After manganese, the $d$ orbitals become more stable (higher effective nuclear charge), and it becomes harder to remove all of them.

Stability and the Environment

Not all oxidation states are equally stable. The stability depends on:

• The medium: $\text{Cr}^{3+}$ is stable in acidic solution, but $\text{Cr}^{6+}$ (as chromate) is stable in alkaline medium.
• The ligand: Some oxidation states are stabilised by certain ligands (this is where coordination chemistry meets redox). …