The Racah parameter B for [Cr(H₂O)₆]³⁺ is 725 cm⁻¹, while the free-ion value for Cr³⁺ is 918 cm⁻¹. What is the nephelauxetic ratio, and what does it indicate?
Aβ = 1.27, indicating the complex has stronger electron repulsion than the free ion
Bβ = 0.79, indicating that the d-electron cloud has expanded due to covalent metal-ligand interaction, reducing interelectronic repulsion to 79% of the free-ion value
Cβ = 0.79, indicating that 79% of the crystal field splitting comes from electrostatic interactions
Dβ = 193, representing the absolute reduction in repulsion energy
β = B_complex/B_free ion = 725/918 = 0.79. A value less than 1 means the interelectronic repulsion in the complex is less than in the free ion. This reduction occurs because the d-electron cloud is no longer confined to the metal — it delocalizes partially onto the ligands through covalent bonding, effectively expanding the cloud and reducing electron-electron repulsion. The 21% reduction for [Cr(H₂O)₆]³⁺ indicates modest covalent character. More covalent complexes (like [Cr(CN)₆]³⁻) have even smaller β values.
Question 2 True / False
The nephelauxetic series ranks ligands by their ability to reduce the Racah parameter: F⁻ > H₂O > NH₃ > en > ox > NCS⁻ > Cl⁻ > CN⁻ > Br⁻ > I⁻ (from least to most cloud-expanding).
TTrue
FFalse
Answer: True
This series ranks ligands from most ionic (F⁻, smallest nephelauxetic effect, β closest to 1) to most covalent (I⁻, largest nephelauxetic effect, smallest β). The ordering correlates with ligand polarizability and the extent of orbital overlap with the metal: small, hard, electronegative ligands like F⁻ interact primarily electrostatically and do not expand the d-cloud much. Large, soft, polarizable ligands like I⁻ and CN⁻ engage in significant covalent bonding, delocalizing d-electron density onto the ligand and strongly reducing B. Note that this series is NOT the same as the spectrochemical series — it measures covalency, not field strength.
Question 3 True / False
A complex with β = 0.5 has more ionic character in its metal-ligand bonds than one with β = 0.9.
TTrue
FFalse
Answer: False
β = 0.5 means the Racah parameter is reduced to half the free-ion value — a large reduction indicating substantial d-electron delocalization onto the ligands, which means high covalent character. β = 0.9 means only 10% reduction — the d-electrons remain largely metal-centered, indicating predominantly ionic character. Lower β = more covalent, higher β = more ionic. A perfectly ionic complex (point-charge ligands with zero orbital overlap) would have β = 1.0.
Question 4 Short Answer
Explain why the nephelauxetic effect and the spectrochemical series are related but distinct, using a specific example where a ligand ranks differently in each series.
Think about your answer, then reveal below.
Model answer: The spectrochemical series ranks ligands by crystal field splitting Δ (which includes both sigma and pi bonding effects), while the nephelauxetic series ranks them by covalency (the degree of d-electron delocalization). These are related — more covalent bonding generally affects Δ — but they measure different things. F⁻ illustrates the difference: it is a moderate-field ligand in the spectrochemical series (above I⁻ and Cl⁻ but below H₂O and NH₃) but has the smallest nephelauxetic effect (most ionic). Its small size and high electronegativity create a strong electrostatic interaction (contributing to Δ) but poor orbital overlap (low covalency). CN⁻ ranks high in both series because it is both a strong-field ligand (pi-acceptor, large Δ) and highly covalent (strong orbital overlap, small β).
This distinction matters because models that treat all metal-ligand bonding as either purely electrostatic (CFT) or purely covalent (naive MO theory) miss the spectrum of bonding character that real complexes display. The nephelauxetic ratio provides the experimental evidence for where each specific metal-ligand combination falls on this spectrum.