Cr²⁺ has the highest enthalpy of hydration among Ti²⁺, V²⁺, Cr²⁺, and Mn²⁺ due to its optimal balance of small ionic size and high crystal field stabilization energy (CFSE). This makes it the correct choice for competitive exams like CSIR NET Life Sciences.

Understanding Hydration Enthalpy

Enthalpy of hydration measures the energy released when gaseous ions form hydrated complexes with water, primarily driven by ion charge density (charge/size) and crystal field effects in transition metals. For divalent first-row ions like Ti²⁺ (d²), V²⁺ (d³), Cr²⁺ (d⁴), and Mn²⁺ (d⁵), smaller radii increase attraction to water dipoles, while CFSE in octahedral [M(H₂O)₆]²⁺ adds extra stability. Across the series, ionic radii decrease (Ti²⁺ > V²⁺ > Cr²⁺ > Mn²⁺), favoring higher hydration enthalpy from left to right, but CFSE modulates this.

Option Analysis

• Ti²⁺ (Z=22, d²): Largest radius (~0.90 Å), low CFSE (-0.8 Δ₀). Lowest hydration enthalpy at -1862 kJ/mol due to poor charge density.
• V²⁺ (Z=23, d³): Smaller radius, higher CFSE (-1.2 Δ₀). Hydration enthalpy increases but remains below Cr²⁺.
• Cr²⁺ (Z=24, d⁴ high spin): Smallest effective radius among options, high CFSE (-0.6 Δ₀ with pairing energy consideration). Highest value at -1908 kJ/mol, confirmed experimentally.
• Mn²⁺ (Z=25, d⁵): Small radius but zero CFSE (half-filled t₂g), resulting in -1851 kJ/mol—lower than Cr²⁺ despite size.

Hydration Enthalpy Comparison Table

Ion	Approx. Radius (Å)	d Electrons	CFSE (Δ₀)	ΔHhyd (kJ/mol)
Ti²⁺	0.90	d²	-0.8	-1862
V²⁺	0.88	d³	-1.2	~ -1890
Cr²⁺	0.84	d⁴	-0.6	-1908
Mn²⁺	0.80	d⁵	0	-1851

Key Trend Insights

Hydration enthalpy peaks near Cr²⁺/Fe²⁺ due to CFSE maxima (d³/d⁶ configurations), deviating from a smooth charge density line—Ca²⁺, Mn²⁺, Zn²⁺ lie on it (zero CFSE). Ti²⁺ is unstable in water, but values confirm Cr²⁺ dominance here.