IB Chemistry: Colour Chemistry and Spectroscopy

Colour is more than just an aesthetic property; it is a powerful analytical tool that reveals the electronic structure of molecules. In IB Chemistry, understanding the origin of colour in both transition metal complexes and organic dyes is essential, as it bridges foundational atomic theory with advanced applications in analytical spectroscopy, material science, and biochemistry. This knowledge allows you to deduce the identity and structure of unknown substances by interpreting the light they interact with.

The Origin of Colour in Transition Metal Complexes

Colour arises from the absorption of specific wavelengths of visible light. When white light passes through or reflects off a substance, certain colours are removed (absorbed), and we perceive the remaining combination as the substance's colour. This is directly observable with transition metal complexes, ions of d-block elements surrounded by ligands.

The key to their colour is d-orbital splitting. In an isolated ion, all five d-orbitals are degenerate, meaning they have the same energy. However, when ligands approach to form a complex, the electrostatic interactions differ depending on the orbital's orientation. Ligands along the axes (x, y, z) repel electrons more strongly than those between the axes. This causes the d-orbitals to split into two sets with different energies: the higher-energy $e_g$ set ($d_{x^2-y^2}$ and $d_{z^2}$) and the lower-energy $t_{2g}$ set ($d_{xy}$, $d_{xz}$, $d_{yz}$). The energy difference between these sets is called the crystal field splitting energy, denoted by ${\Delta }_{oct}$ for an octahedral complex.

Crystal field theory provides a model for this splitting. The magnitude of $\Delta$ depends on two main factors: the identity of the metal ion (its charge and identity) and the nature of the ligands. Ligands can be arranged in a spectrochemical series according to their ability to split the d-orbitals. A weak-field ligand like $I^{-}$ causes a small $\Delta$, while a strong-field ligand like $C{N}^{-}$ causes a large $\Delta$.

The Absorption of Light and Complementary Colours

The splitting of d-orbitals creates an opportunity for electrons to absorb energy. Electrons in the lower-energy $t_{2g}$ orbitals can be promoted to the $e_g$ orbitals. The energy required for this transition corresponds to the crystal field splitting energy $\Delta$.

This energy is supplied by photons of visible light. The relationship is given by the Planck-Einstein equation: $\Delta E=h\nu$, where $h$ is Planck's constant and $\nu$ is the frequency of light. Since $\Delta E$ is fixed for a given complex under specific conditions, the complex absorbs light of a specific frequency (and thus wavelength). We perceive the complementary colour to the colour absorbed.

For example, a complex that absorbs photons in the yellow region of the spectrum will appear violet. You can use a colour wheel to predict this relationship: the colour absorbed and the colour observed are directly opposite each other. If a complex absorbs high-energy light (violet/blue), $\Delta$ is large, and it appears yellow/orange. If it absorbs low-energy light (red), $\Delta$ is small, and it appears blue/green.

Colour in Organic Molecules: The Role of Conjugation

While transition metals produce colour via d-d transitions, most coloured organic molecules, like dyes and pigments, rely on a different principle: conjugation. Conjugation refers to the alternation of single and double bonds in a molecule, which allows the p-orbitals on adjacent atoms to overlap, creating a system of delocalised $\pi$-electrons.

The length of this conjugated system directly affects the colour. In a simple conjugated molecule like ethene, the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) is large. This corresponds to absorbing high-energy ultraviolet light, so the compound is colourless. As the conjugated system lengthens, this energy gap decreases. The molecule then absorbs lower-energy light, moving from violet into the blue, green, and eventually red parts of the spectrum.

A classic example is the carotenoid beta-carotene, found in carrots. Its long conjugated chain of 11 double bonds absorbs blue and green light, resulting in its characteristic orange colour. This concept is often modeled using the "particle in a box" quantum model, where a longer "box" (the conjugated system) leads to a smaller energy difference between electronic levels.

Applying Spectroscopic Principles for Identification

Spectroscopy is the practical application of light-matter interactions to identify compounds. For coloured substances, two key techniques are ultraviolet-visible (UV-Vis) spectroscopy and colorimetry.

A UV-Vis spectrophotometer measures how much light a sample absorbs across a range of wavelengths. The output is a graph of absorbance versus wavelength, called an absorption spectrum. For a transition metal complex, the spectrum will show one or more absorption peaks. The wavelength of maximum absorption (${\lambda }_{max}$) is directly related to the crystal field splitting energy: $\Delta E=hc/{\lambda }_{max}$, where $c$ is the speed of light.

You can use this data quantitatively via the Beer-Lambert Law: $A=ϵcl$, where $A$ is absorbance, $ϵ$ is the molar absorptivity (a constant for the compound at a specific wavelength), $c$ is concentration, and $l$ is the path length. This allows you to determine the concentration of a coloured species in solution, a fundamental technique in analytical chemistry.

For organic molecules, the ${\lambda }_{max}$ of its UV-Vis spectrum indicates the extent of its conjugation. A dye that absorbs at 500 nm has a more extended conjugated system than one absorbing at 400 nm. By comparing measured spectra to known databases, you can begin to identify or characterize unknown coloured compounds.

Common Pitfalls

1. Confusing absorption with emission. A complex that absorbs blue light does not emit blue light. It removes blue from white light, so we see the complementary colour, orange. Emission occurs when an excited electron falls back down and releases a photon, which is the principle behind fluorescence, not standard colour perception.
2. Assuming all transition metal complexes are coloured. Complexes with empty d-orbitals (e.g., $S{c}^{3+}$) or full d-orbitals (e.g., $Z{n}^{2+}$) have no possibility of d-d electron transitions. The d-orbitals are either all empty or all full, so no electron can be promoted within the d-subshell by absorbing visible light, rendering these complexes colourless.
3. Overlooking the effect of oxidation state and coordination. The same metal can form complexes of different colours. For instance, aqueous $[Cu(H_{2}O{)}_6{]}^{2+}$ is pale blue, while $[CuC{l}_4{]}^{2-}$ is yellow. This is due to the different ligands ($H_{2}O$ vs. $C{l}^{-}$) and different geometries (octahedral vs. tetrahedral) changing the value of $\Delta$.
4. Misapplying the conjugation rule. Not every molecule with double bonds is conjugated. Isolated double bonds separated by more than one single bond do not create a delocalised system. The alternation is key. But-1,3-diene is conjugated and absorbs at a longer wavelength than but-1-ene, which has an isolated double bond.

Summary

• The colour of transition metal complexes results from d-orbital splitting caused by ligand fields. Electrons absorb specific wavelengths of light to jump from lower to higher energy d-orbitals.
• The observed colour is the complementary colour to the wavelength absorbed. The size of the energy gap ($\Delta$) depends on the metal ion and the ligand's position in the spectrochemical series.
• In organic molecules, colour arises from conjugation. Longer conjugated systems have smaller energy gaps between molecular orbitals, leading to absorption of longer wavelengths (lower energy) of light.
• UV-Vis spectroscopy measures absorption spectra. The wavelength of maximum absorption (${\lambda }_{max}$) identifies the compound or system, while the absorbance, governed by the Beer-Lambert Law, can determine its concentration.
• Colour chemistry provides a direct link between the microscopic structure of a compound and its macroscopic properties, forming a cornerstone of analytical chemistry.