Problem 82 - Chemistry The Central Science In Si Units

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 octahedral ones, assign a color to each complex.

Step-by-Step Solution

Answer

[Co(NH3)6]2+ is pink, [Co(H2O)6]2+ is blue, and [CoCl4]2- is yellow.

Step 1: Understand Color and Light Absorption

Complexes appear colored because they absorb certain wavelengths of light. The color we see is the complementary color of the light absorbed. For example, if a complex absorbs green light, it will appear red (the complementary color of green).

Step 2: Review the Spectrochemical Series

The spectrochemical series ranks ligands by the strength of the field they produce. Strong field ligands, like ammonia (NH3), cause a large splitting of d-orbitals, leading to absorption of shorter wavelengths (higher energy), typically in the violet to blue range. Weak field ligands, like chloride (Cl-), cause smaller splitting, leading to absorption of longer wavelengths (lower energy), typically in the red to yellow range.

Step 3: Analyze the Complexes

For \([\mathrm{Co(NH_3)_6}]^{2+}\), NH3 is a strong field ligand, causing large splitting. \([\mathrm{Co(H_2O)_6}]^{2+}\) with water is a moderate field ligand, causing moderate splitting. \([\mathrm{CoCl_4}]^{2-}\) has Cl-, a weak field ligand, and being tetrahedral, it inherently has less splitting than octahedral ones.

Step 4: Assign Colors Based on Energy and Complementary Colors

1. \([\mathrm{Co(NH_3)_6}]^{2+}\): Absorbs high energy (blue light) due to strong field ligand, appears pink (complementary to blue).2. \([\mathrm{Co(H_2O)_6}]^{2+}\): Absorbs moderate energy (red light) due to moderate field ligand, appears blue (complementary to red).3. \([\mathrm{CoCl_4}]^{2-}\): Absorbs low energy (yellow light) due to weak field ligand and tetrahedral, appears yellow (absorbs violet, opposite of yellow).

Key Concepts

Color and Light Absorption

When you see a colored solution, what you're actually witnessing is the interaction between chemical compounds and light. Complexes absorb light in specific wavelengths, leading to the emergence of certain colors. The intriguing part is that these colors are not the absorbed ones. Instead, we observe the complementary colors. For instance, if a complex like \([Co(NH_3)_6]^{2+}\) absorbs predominantly blue light, the color it presents is pink, which complements blue in the visible spectrum.

• The absorbed light excites electrons within d-orbitals of transition metals, like cobalt, to higher energy states.
• Each ligand around a metal affects how much energy is needed to promote these electrons.
• This interaction is the foundation of observed colors in coordination compounds.

By studying the wavelengths absorbed and not absorbed by these complexes, we can infer quite a bit about their chemical nature and composition. Light absorption isn't just about color; it tells us a lot about the internal electronic transitions at play.

Ligand Field Strength

Ligands play a crucial role in determining the properties of a coordination complex. The ligand field strength is assessed by the degree to which a ligand can split the d-orbitals of the central metal ion. This splitting is quantified by what we call "crystal field splitting energy," \(\Delta\).

• Strong field ligands, such as ammonia (NH₃), result in a larger value of \(\Delta\). This means that these ligands cause higher energy separation between d-orbitals, leading to shorter wavelength absorption (higher energy).
• Weak field ligands like chloride (Cl⁻) result in a smaller \(\Delta\), absorbing longer wavelengths of light (lower energy).

The ranking of ligands based on their field strength is known as the spectrochemical series. Understanding this series helps predict the color and magnetic properties of metal complexes through their ligand interactions. Strong field ligands often make complexes that absorb in the ultraviolet or blue part of the spectrum, while weak field ligands cause absorption in the visible yellow or red range.

Octahedral and Tetrahedral Complexes

In coordination chemistry, the shape or geometry of a complex also impacts its electronic properties and colors. Two common geometries are octahedral and tetrahedral.

• Octahedral complexes, like \([Co(H_2O)_6]^{2+}\) and \([Co(NH_3)_6]^{2+}\), consist of six ligands symmetrically around the central metal. This arrangement leads to a typical crystal field splitting scheme with higher energy separation.
• Tetrahedral complexes, like \([CoCl_4]^{2-}\), are shaped such that their ligands form a triangular pyramid around the metal. This geometry results in less splitting of the metal's d-orbitals, often making these complexes absorb less energetic light.

In summary, the smaller splitting in tetrahedral complexes versus octahedral counterparts means they often absorb at higher wavelengths (lower energy), and thus, they exhibit different colors under the same ligand conditions. This fundamental difference in geometry, alongside ligand field strength, is central to understanding why different metal complexes display such a variety of colors.