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 that that in octahedral ones, assign a color to each complex.

Short answer

The colors of the complexes are: - $[Co(N{H}_3{)}_6{]}^{2+}$: Yellow (largest energy splitting, absorbs lower wavelength, complementary color) - $[Co(H_{2}O{)}_6{]}^{2+}$: Pink (intermediate energy splitting, absorbs mid-wavelength, complementary color) - $[CoC{l}_4{]}^{2-}$: Blue (smallest energy splitting, absorbs higher wavelength, complementary color)

Step-by-step solution

Spectrochemical Series

The spectrochemical series ranks the ligands in order of their ability to cause the energy splitting in the metal orbitals. The series can be given as: I^− < Br^− < Cl^− < F^− < OH^− < H_2O < NH_3 < en < NO_2^− < CN^− Ammonia (NH_3) and water (H_2O) are stronger ligands than chloride (Cl^−) in this series. Stronger ligands produce higher energy splitting.

Energy Splitting in Octahedral and Tetrahedral Complexes

Typically, the energy splitting in octahedral complexes (Δ_oct) is much larger than the energy splitting in tetrahedral complexes (Δ_tet). The tetrahedral complexes usually have 4/9 Δ_oct.

Assigning Colors Based on Absorbed Energy

The color of a complex is determined by the color of light it absorbs. The complementary color of the absorbed light is the color we see. The energy and wavelength of absorbed light are inversely related, which means that a higher energy transition requires a shorter wavelength. As we know, the energy of light increases in the order: red < orange < yellow < green < blue < violet. Based on the spectrochemical series, the complex with NH_3 ligands should experience the largest energy splitting, followed by the one with H_2O ligands. The complex with Cl^− ligands will have the lowest energy splitting as it is a tetrahedral complex. 1. $[Co(N{H}_3{)}_6{]}^{2+}$: The largest energy splitting - absorbs lower wavelength (blue/violet) - appears yellow/pale orange (complementary color). 2. $[Co(H_{2}O{)}_6{]}^{2+}$: The intermediate energy splitting - absorbs mid-wavelength (green/blue) - appears pink/red (complementary color). 3. $[CoC{l}_4{]}^{2-}$: The smallest energy splitting - absorbs higher wavelength (red/orange) - appears blue/green (complementary color). So, the colors of the complexes are: - $[Co(N{H}_3{)}_6{]}^{2+}$: Yellow - $[Co(H_{2}O{)}_6{]}^{2+}$: Pink - $[CoC{l}_4{]}^{2-}$: Blue

Key concepts

Spectrochemical Series

In the world of coordination chemistry, the spectrochemical series is a list that ranks ligands based on their ability to split the d-orbitals of a central metal ion. This ranking plays a crucial role in determining the color of metal complexes. Let's break it down.

Ligands like ammonia ( H_3 gen) and water ( H_2 O) are considered moderate to strong ligands, whereas chloride (Cl^−) is a weaker ligand. The stronger the ligand, the more it can influence a central metal ion's electron cloud, causing greater energy splitting in its d-orbitals. This series, stretching from weaker to stronger ligands, reads as:

• I^−
• Br^−
• Cl^−
• F^−
• OH^−
• H_2O
• NH_3
• en (ethylene diamine)
• NO_2^−
• CN^−

Understanding this series helps chemists predict not just the colors, but also the stability and reactivity of metal complexes. It is a vital tool when assigning colors to complexes, such as determining why one complex appears pink while another appears yellow.

Energy Splitting in Complexes

When ligands surround a metal ion, they interact with its d-orbitals, splitting their energy levels into two groups. This phenomenon is known as crystal field splitting and is different in octahedral and tetrahedral complexes.

In octahedral complexes, six ligands create an environment with high energy splitting, denoted as ${\mathrm{\Delta }}_{\text{oct}}$. This results in dramatic d-orbital interaction—take [Co(NH_3)_6]^{2+}, which has a very notable energy split. On the other hand, the tetrahedral arrangement, like in [CoCl_4]^{2-}, involves only four ligands. The energy difference here is much less, about $\frac{4}{9}\text{ of }{\mathrm{\Delta }}_{\text{oct}}$. This smaller splitting results in more visible light being absorbed at longer wavelengths.

These concepts lead to different electronic transitions in these metal complexes, which in turn influence the color they exhibit. Strong ligands, such as ammonia, lead to greater splitting and higher energy absorptions compared to weaker ligands, like chloride.

Color and Light Absorption in Complexes

The beautiful colors we observe in metal complexes arise from their absorption of certain light wavelengths, a direct consequence of energy splitting. Here's where it gets fascinating. The color we see is actually the complement of the light absorbed.

For instance, if a complex absorbs high-energy, blue light, as with [Co(NH_3)_6]^{2+} absorbing in that range, it appears yellow. This is because yellow is the complementary color to blue. Similarly, a complex like [Co(H_2O)_6]^{2+} may absorb the intermediate mid-wavelength of green or blue light, thus appearing pink or red.

In cases with low energy splitting, such as [CoCl_4]^{2-} , red or even orange light is absorbed. This means the complex itself will generally look blue or green.

Understanding these light absorption properties not only reveals why complexes appear in certain colors, but it also uncovers details about the molecular interactions within the complexes themselves. This principle is fundamental when studying or designing new complexes in various fields of chemistry.