Which one of the following ions is the most stable in aqueous solution? (At no. Ti=22, V=23, Cr=24, Mn=25)

The stability of transition metal ions in aqueous solution is influenced by their electronic configuration and the Crystal Field Stabilization Energy (CFSE). In an aqueous medium, water molecules act as ligands, creating an octahedral field that splits the $d$-orbitals into lower energy $t_{2g}$ and higher energy $e_g$ sets.

1. Analyze Electronic Configurations:

• Cr³⁺ (Z=24): $[Ar] 3d^3$. In an octahedral field, the 3 electrons occupy the $t_{2g}$ orbitals singly ($t_{2g}^3$). This corresponds to a half-filled $t_{2g}$ level, which provides significant stability due to high CFSE.
• V³⁺ (Z=23): $[Ar] 3d^2$ ($t_{2g}^2$).
• Ti³⁺ (Z=22): $[Ar] 3d^1$ ($t_{2g}^1$).
• Mn³⁺ (Z=25): $[Ar] 3d^4$ ($t_{2g}^3 e_g^1$). Mn³⁺ is less stable and acts as a strong oxidising agent because it readily accepts an electron to achieve the stable half-filled $d^5$ configuration ($Mn^{2+}$).

Therefore, Cr³⁺ is the most stable ion among the options due to its stable $t_{2g}^3$ configuration.