Which one of these tripositive ions is the most stable in aqueous sol…

The correct answer is Option (1) → \(Cr^{3+}\)

An ion is stable in aqueous solution when it shows no tendency to be oxidised or reduced by water or dissolved air. In the 3d series this depends largely on the d-electron configuration: a half-filled \( t_{2g} \) level (d³) in an octahedral aqua complex is particularly stable. First derive the configuration of each ion:

• Ti (Z = 22) is \( \mathrm{[Ar]\,3d^{2}\,4s^{2}} \). Losing the two 4s electrons and one 3d electron gives \( \ce{Ti^3+} \): \( \mathrm{3d^{1}} \).

• V (Z = 23) is \( \mathrm{[Ar]\,3d^{3}\,4s^{2}} \); \( \ce{V^3+} \) is \( \mathrm{3d^{2}} \).

• Cr (Z = 24) is \( \mathrm{[Ar]\,3d^{5}\,4s^{1}} \). Losing the 4s electron and two 3d electrons gives \( \ce{Cr^3+} \): \( \mathrm{3d^{3}} \).

• Mn (Z = 25) is \( \mathrm{[Ar]\,3d^{5}\,4s^{2}} \); \( \ce{Mn^3+} \) is \( \mathrm{3d^{4}} \).

\( \ce{Cr^3+} \) (d³) has the three \( t_{2g} \) orbitals singly filled. That is why \( \ce{Cr^2+} \) (d⁴) is a reducing agent that readily becomes \( \ce{Cr^3+} \), while \( \ce{Cr^3+} \) itself neither gains nor loses an electron easily. So the most stable tripositive ion in water is \( \ce{Cr^3+} \), chromium(III).

Why the other options are incorrect

• Option (2) \(Ti^{3+}\) — Incorrect. With a single 3d electron, \( \ce{Ti^3+} \) is a reducing agent; air oxidises it to the d⁰ state of titanium(IV).

• Option (3) \(V^{3+}\) — Incorrect. \( \ce{V^3+} \) (d²) is also slowly oxidised in air to vanadium(IV), \( \ce{VO^2+} \).

• Option (4) \(Mn^{3+}\) — Incorrect. \( \ce{Mn^3+} \) (d⁴) is a strong oxidising agent: gaining one electron gives the extra-stable half-filled d⁵ configuration of \( \ce{Mn^2+} \), so it oxidises water and disproportionates.

NCERT (2026-27 edition):
Trends in the M²⁺/M Standard Electrode Potentials – “… Cr²⁺ is reducing as its configuration changes from d⁴ to d³, the latter having a half-filled t_2g level (see Unit 5). On the other hand, the change from Mn³⁺ to Mn²⁺ results in the half-filled (d⁵) configuration which has extra stability.”