Question

Arrange the following complexes in order of increasing wavelength of the light absorbed by them: \(\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\) \(\left[\mathrm{CrCl}_{6}\right]^{3-},\left[\mathrm{Cr}(\mathrm{en})_{3}\right]^{3+},\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{3-},\left[\mathrm{Cr}\left(\mathrm{NO}_{2}\right)_{6}\right]^{3-},\) \(\left[\mathrm{CrF}_{6}\right]^{3-},\) and \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}.\)

Short answer

[Cr(H2O)6]3+ < [CrCl6]3- < [CrF6]3- < [Cr(NH3)6]3+ < [Cr(en)3]3+ < [Cr(NO2)6]3- < [Cr(CN)6]3-

Step-by-step solution

- Understand the Concept of Crystal Field Theory

Crystal Field Theory (CFT) explains the different colors produced by transition metal complexes based on the splitting of the d-orbitals when ligands approach the central metal ion. The energy gap between the split d-orbitals (Δ) dictates the wavelength of the light absorbed. A larger Δ results in the absorption of light with a shorter wavelength.

- Identify the Spectrochemical Series

The ligands can cause different splits in the d-orbital energy levels according to the spectrochemical series. The series in order of increasing field strength (and therefore increasing Δ) is: I- < Br- < Cl- < F- < OH- < H2O < NH3 < en < NO2- < CN-. Stronger field ligands produce a larger Δ and hence absorb light of shorter wavelengths.

- Arrange Complexes According to Ligand Field Strength

Based on the ligands' positions in the spectrochemical series, arrange the complexes in order of increasing Δ: [Cr(H2O)6]3+ (H2O is a weak field ligand) < [CrCl6]3- (Cl- is stronger than H2O, but still in the weaker half) < [CrF6]3- (F- is stronger than Cl-) < [Cr(NH3)6]3+ (NH3 is a moderately strong field ligand) < [Cr(en)3]3+ (en is stronger than NH3) < [Cr(NO2)6]3- (NO2- is stronger than en) < [Cr(CN)6]3- (CN- is the strongest field ligand in this list).

- Determine the Order of Increasing Wavelength of Absorption

Remembering that a larger ∆ corresponds to a shorter wavelength of light absorbed, the order from smallest to largest Δ is also the order of increasing wavelength of absorbed light. The list from Step 3 is the order of increasing Δ, therefore, the reverse of this list gives the order of increasing wavelength: [Cr(CN)6]3- < [Cr(NO2)6]3- < [Cr(en)3]3+ < [Cr(NH3)6]3+ < [CrF6]3- < [CrCl6]3- < [Cr(H2O)6]3+.

Key concepts

Spectrochemical Series

The spectrochemical series is a vital concept in understanding the behavior of transition metal complexes. It essentially ranks ligands based on their ability to split the d-orbitals of transition metals. This splitting is crucial because it affects the color of the light absorbed by the complex.

Ligands and Color
Each ligand has a distinct 'field strength', which influences the energy gap between the d-orbitals, known as the crystal field splitting energy (Δ). The spectrochemical series lists common ligands from weakest field strength to strongest: I- < Br- < Cl- < F- < OH- < H2O < NH3 < en < NO2- < CN-.

When a ligand with a higher field strength (like CN-) binds to a metal, it generates a larger Δ than a ligand with lower field strength (like H2O). The larger the gap, the shorter the wavelength of light that's absorbed, and vice versa. For students, remembering the order of ligands in the spectrochemical series assists in predicting the colors of various complexes.

Transition Metal Complexes

Transition metal complexes are formed when central metal ions (usually from transition metals) bind with surrounding ligands. Any ion or molecule that can donate a pair of electrons to the metal ion can act as a ligand.

Structural Diversity
These complexes exhibit a vast array of geometries and properties, owing to the versatile electronic configurations of transition metals. This diversity is reflected in the way ligands arrange themselves around the central metal, influencing properties like color, magnetism, and reactivity.

For clarity, students should imagine these complexes as central metal ions surrounded by various 'clouds' of electron density provided by the ligands. This image helps in visualizing how these arrangements can affect the metal's electronic structure and, therefore, its physical characteristics.

Ligand Field Strength

Ligand field strength is essentially a measure of a ligand's ability to split the d-orbitals of a transition metal ion within a complex. It's intertwined with the concept of crystal field theory and plays a massive role in predicting the colors observed in metal complexes.

Impact on Electronic Transitions
Ligand field strength impacts the electronic transitions that are possible within a complex. Strong field ligands cause a large splitting in d-orbital energy levels, leading to the absorption of photons in the visible light range, resulting in the complex displaying vivid colors. Conversely, weak field ligands cause a smaller splitting, which could either result in colors in a different part of the spectrum or no noticeable color at all.

For educational purposes, a helpful analogy can be to compare the ligands to different strengths of magnets, affecting the metal's 'd-orbital dance' to varying degrees, hence changing the 'color of the dance'. Understanding ligand field strength enables students to rationally infer the color of a complex based on the type of ligands present.