Problem 80 - Chemistry: The Central Science

Question

Solutions of \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+},\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) (both octahedral), and \(\left[\mathrm{CoCl}_{4}\right]^{2-}\) (tetrahedral) are colored. One is pink, one is blue, and one is yellow. Based on the spectrochemical series and remembering that the energy splitting in tetrahedral complexes is normally much less than that in ectahedral ones, assign a color to each complex.

Step-by-Step Solution

Answer

Based on the spectrochemical series and energy splitting in different geometries, the colors of the complexes are as follows: - \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\) (octahedral): Yellow - \(\left[\mathrm{Co}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{2+}\) (octahedral): Pink - \(\left[\mathrm{CoCl}_{4}\right]^{2-}\) (tetrahedral): Blue

Step 1: Understand the Spectrochemical Series

The spectrochemical series is an empirical ordering of ligands based on their ability to split the d-orbitals of the metal center in a complex. Ligands at the beginning of the series cause smaller energy splitting, while those at the end cause larger splitting. The series can be represented as: I- < Br- < Cl- < F- < OH- < H2O < NCS- < CH3CN < NH3 < en < bipy < phen < NO2- < CN- < bpy < CO In this exercise, we are concerned with three ligands: NH3, H2O, and Cl-. According to the series, NH3 causes more significant energy splitting than H2O, which, in turn, causes more significant splitting than Cl-.

Step 2: Relate Energy Splitting to Absorbed Color

The energy gap between the split d-orbitals (∆) corresponds to the energy of the light (color) absorbed by the complex. The larger the energy gap, the higher the energy (shorter wavelength) of the color absorbed. The visible light spectrum follows the order: Red < Orange < Yellow < Green < Blue < Indigo < Violet Since the color we observe is the complementary color to the one absorbed by the complex, we can establish the following relationships: - The complex with the smallest energy gap will absorb lower energy light (towards the red end of the spectrum) and appear with a complementary color on the opposite end of the spectrum (towards blue). - The complex with the highest energy gap will absorb higher energy light (towards the blue end of the spectrum) and appear with a complementary color on the opposite end of the spectrum (towards red).

Step 3: Assign Colors to the Complexes

We are now ready to assign colors to the three complexes based on the energy splitting caused by their ligands: 1. \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\) (octahedral): Since NH3 is a strong-field ligand and causes the most significant energy splitting of the three complexes, this complex will absorb higher energy light (towards the blue end of the spectrum) and appear with a color on the opposite end of the spectrum. The complementary color to blue is yellow. Therefore, this complex is yellow. 2. \(\left[\mathrm{Co}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{2+}\) (octahedral): H2O is a weaker field ligand than NH3, causing an intermediate energy splitting. Following the logic above, this complex will absorb light in the intermediate region of the spectrum and appear with a color on the opposite end. The complementary color to green in the approximated spectrum is pink. Therefore, this complex is pink. 3. \(\left[\mathrm{CoCl}_{4}\right]^{2-}\) (tetrahedral): Cl- is the weakest field ligand among the three. Additionally, the tetrahedral geometry causes smaller energy splitting than octahedral complexes. Hence, this complex has the smallest energy gap and will absorb lower energy light (towards the red end of the spectrum) and appear with a color on the opposite end of the spectrum. The complementary color to red is blue. Therefore, this complex is blue. In conclusion, the colors of the complexes are: - \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\): Yellow - \(\left[\mathrm{Co}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{2+}\): Pink - \(\left[\mathrm{CoCl}_{4}\right]^{2-}\): Blue

Key Concepts

Ligand Field Theory

Ligand field theory is a model that helps chemists understand how ligands interact with the d-orbitals of a transition metal atom in a complex. The theory extends from crystal field theory and focuses on the effects of different ligands when they bind to the metal center.
When a ligand approaches the metal, it can either increase or decrease the energy levels of the d-orbitals depending on its electron-donating or accepting ability. This interaction alters the electron density around the metal ion, which directly impacts the splitting of d-orbitals—leading us to the idea of spectrochemical series.

• Strong field ligands: These cause significant splitting in d-orbitals and include NH3 and CO.
• Weak field ligands: These result in smaller splitting and include ligands like Cl- and F-.

The spectrochemical series helps determine the strength of a ligand as either strong or weak based on its position within the series, thus influencing the resultant color of a compound.

d-orbital Splitting

d-orbital splitting is fundamental to understanding why transition metal complexes have distinct colors. The d-orbitals, which are composed of five different orbitals, split into different energy levels when ligands approach the transition metal.
This splitting pattern depends on both the geometry of the complex and the type of ligands attached to the metal. For instance, in octahedral complexes like r> egin{align*}[ ext{Co(NH}_3 ext{)}_6]^{2+} ext{ and }[ ext{Co(H}_2 ext{O)}_6]^{2+},ewlinethe d-orbitals split into two levels: t2g (lower energy) and eg (higher energy).ewlinetetrahedral complexes, such as [ ext{CoCl}_4]^{2-}, display a reversed splitting pattern.ewline ext{No inversion center causes smaller splitting.}ewlinedifference in energy, denoted as \( \Delta \), decides which light wavelength is absorbed and, thus, the color of the complex.

Color of Complexes

The vibrant colors exhibited by transition metal complexes are a direct result of d-orbital splitting. When light shines on a complex, certain wavelengths are absorbed to promote electrons across the split orbitals.
The color we observe is the complementary color of the absorbed light.
A complex with a large splitting energy \( \Delta \) absorbs high-energy light (like violet or blue), appearing in hues of yellow or red—complementary on the color wheel. Conversely, a small \( \Delta \) means absorption of lower energy light (like red), resulting in the complex appearing blue or green.

• Yellow: Indicates high energy, short-wavelength light is absorbed (observed in strong field ligands like NH3).
• Blue: Suggests low-energy, long-wavelength light is absorbed (as seen in weak field tetrahedral complexes like [CoCl4]^{2-}).
• Pink: Intermediate absorption aligns with ligands a step down from the strongest, fitting the behavior of H2O.

This interplay between absorption and observed color demonstrates how ligand type and geometry connect to visual properties.