Chemistry (9701) | Colour of complexes

The Beautiful Science: Colour of Transition Metal Complexes (9701 A Level)

Hello future chemists! This is one of the most visually exciting topics in A Level Chemistry. Have you ever wondered why Copper(II) compounds are blue, or why Chromium compounds can be green, violet, or yellow depending on what you mix them with? The answer lies in the unique electron structure of the transition elements.

In this section (Syllabus 28.3), we will unlock the secret to these vibrant colours by looking closely at how light interacts with the central metal ion in a complex. Don't worry if the concepts seem a little quantum mechanical—we will break them down using clear steps and analogies!

1. Understanding d Orbitals: Degenerate vs. Non-Degenerate

Transition metal ions form complex ions where a central metal ion is surrounded by ligands. To understand colour, we first need to look at the d orbitals.

What are Degenerate d Orbitals?

• The transition metals use their five 3d orbitals (e.g., $d_{xy}, d_{yz}, d_{xz}, d_{x^2-y^2}, d_{z^2}$).
• When a transition metal ion (like $\text{Fe}^{3+}$ or $\text{Cu}^{2+}$) is isolated (in the gas phase) or surrounded by a perfectly symmetrical environment, all five of its d orbitals have the exact same energy.
• We call these orbitals degenerate.
  Memory Aid: Degenerate means Equal Energy. They are all 'on the same floor'.

Introducing the Ligands: Breaking the Degeneracy

A ligand is a species (ion or molecule) that forms a dative covalent bond with the central metal ion. Ligands carry lone pairs of electrons.

• When ligands approach the central metal ion to form a complex, their lone pairs repel the electrons already in the metal's d orbitals.
• Because the d orbitals point in different directions in 3D space, this repulsion is not equal.
• The five d orbitals split into groups of non-degenerate orbitals (different energy levels). This process is called Crystal Field Splitting.

2. Splitting Patterns: Octahedral vs. Tetrahedral Complexes

The way the d orbitals split depends entirely on the geometry of the complex formed (which is usually determined by the coordination number). We focus on the two main geometries: Octahedral (coordination number 6) and Tetrahedral (coordination number 4).

Octahedral Complexes (6 Ligands)

In an octahedral complex, the six ligands approach the central ion exactly along the x, y, and z axes.

• The two d orbitals that point directly along the axes ($d_{x^2-y^2}$ and $d_{z^2}$) feel the greatest repulsion. They are pushed up to a higher energy level. (The $e_g$ set: 2 orbitals).
• The remaining three d orbitals that lie between the axes ($d_{xy}, d_{yz}, d_{xz}$) feel the least repulsion. They remain at a lower energy level. (The $t_{2g}$ set: 3 orbitals).
• The energy difference between the lower set ($t_{2g}$) and the higher set ($e_g$) is called the crystal field splitting energy, often symbolised as \(\Delta E\) or \(\Delta_o\) (where 'o' stands for octahedral).

Tetrahedral Complexes (4 Ligands)

In a tetrahedral complex, the four ligands approach the central ion between the axes.

• The splitting pattern is inverted compared to octahedral.
• The five d orbitals split into three orbitals at a higher energy level and two orbitals at a lower energy level.
• The magnitude of the splitting energy \(\Delta E\) in tetrahedral complexes is generally much smaller than in octahedral complexes, usually only about $4/9$ of \(\Delta_o\).

Key Takeaway: The presence of ligands breaks the degeneracy of the d orbitals, creating an energy gap (\(\Delta E\)) crucial for colour. Octahedral complexes have a 2-up, 3-down split, while Tetrahedral complexes have a 3-up, 2-down split.

3. The Origin of Colour: d-d Transitions

The Mechanism of Light Absorption (LO 3)

Transition metal ions are coloured because they absorb specific frequencies of visible light, causing an electron to jump the energy gap, \(\Delta E\).

1. A metal ion in a complex has d electrons filling the lower set of non-degenerate d orbitals.
2. When white light (which contains all colours/frequencies) hits the complex, the electrons can absorb a photon if the photon's energy exactly matches the splitting energy \(\Delta E\).
   $$ \Delta E = hf = \frac{hc}{\lambda} $$
   where \(h\) is Planck's constant, \(f\) is frequency, \(c\) is the speed of light, and \(\lambda\) is the wavelength.
3. Upon absorbing this photon, the electron is promoted from a lower-energy d orbital to a higher-energy d orbital. This is called a d-d transition.
4. The complex removes this specific frequency of light from the white light spectrum.
5. The light that is transmitted or reflected back to our eyes is missing the absorbed colour. We therefore observe the complementary colour.

Analogy: Imagine shining a white light (the full colour spectrum) through a red window. The window absorbs green/blue light, and only the red light (its complementary colour) is transmitted through.

The Complementary Colour Wheel (Memory Aid)

The colour you see is always the opposite of the colour absorbed:

• Absorbed Red $\rightarrow$ Observed Green
• Absorbed Orange $\rightarrow$ Observed Blue
• Absorbed Yellow $\rightarrow$ Observed Violet

If a complex absorbs all frequencies, it appears black. If it absorbs none, it appears white or colourless (e.g., $\text{Zn}^{2+}$ complexes, which have a full d subshell and cannot undergo d-d transitions).

4. The Influence of Ligands on Colour (LO 4)

Since colour depends directly on the magnitude of the energy gap \(\Delta E\), anything that changes \(\Delta E\) will change the colour observed. The type of ligand is the most significant factor affecting \(\Delta E\).

The Spectrochemical Series (Qualitative Terms)

Ligands are ranked according to their ability to cause d-orbital splitting. This ranking is called the spectrochemical series. We only need to understand this qualitatively (i.e., strong vs. weak).

• Weak Field Ligands (e.g., $\text{I}^-, \text{Cl}^-, \text{H}_2\text{O}$): These cause a small repulsion, resulting in a small \(\Delta E\).
• Strong Field Ligands (e.g., $\text{NH}_3, \text{CN}^-$): These cause a large repulsion, resulting in a large \(\Delta E\).

Relating Ligand Strength to Observed Colour

The relationship is: Stronger Ligand $\rightarrow$ Larger $\Delta E \rightarrow$ Higher Frequency (\(f\)) Absorbed $\rightarrow$ Shorter Wavelength (\(\lambda\)) Absorbed.

For example, if you swap a weak ligand for a strong ligand in a complex:

1. The energy gap \(\Delta E\) increases.
2. The complex must absorb a higher energy photon (e.g., shift from absorbing red light to absorbing green light).
3. The observed complementary colour will change (e.g., shift from seeing green to seeing purple/red).

Key Takeaway: Ligand exchange changes \(\Delta E\). A stronger ligand means a larger \(\Delta E\) and thus the complex absorbs higher energy light (shorter wavelength).

5. Colour Changes via Ligand Exchange (LO 5)

One of the most observable characteristic properties of transition elements is the drastic colour change that occurs when one ligand is exchanged for another. This usually occurs when different ligands are added to aqueous solutions of metal ions.

A. Copper(II) Ions ($\text{Cu}^{2+}$)

In water, $\text{Cu}^{2+}$ forms the light blue octahedral complex: $[\text{Cu}(\text{H}_2\text{O})_6]^{2+}$ (Light Blue).

i) Reaction with Aqueous Ammonia ($\text{NH}_3$)

• Ammonia molecules are stronger ligands than water molecules.
• When excess concentrated aqueous ammonia is added, ligand exchange occurs, replacing four $\text{H}_2\text{O}$ ligands with four $\text{NH}_3$ ligands, resulting in a deep blue solution:
  $$ [\text{Cu}(\text{H}_2\text{O})_6]^{2+} + 4\text{NH}_3 \rightleftharpoons [\text{Cu}(\text{NH}_3)_4(\text{H}_2\text{O})_2]^{2+} + 4\text{H}_2\text{O} $$
• The $\text{NH}_3$ ligand creates a larger \(\Delta E\) than $\text{H}_2\text{O}$, causing the complex to absorb higher frequency light, leading to the formation of a characteristic Deep Blue solution.

ii) Reaction with Chloride Ions ($\text{Cl}^-$)

• When concentrated hydrochloric acid (source of $\text{Cl}^-$) is added, the large $\text{Cl}^-$ ion replaces the water ligands.
• Due to steric hindrance (clash of large $\text{Cl}^-$ ions), the geometry changes from octahedral (CN 6) to tetrahedral (CN 4).
  $$ [\text{Cu}(\text{H}_2\text{O})_6]^{2+} + 4\text{Cl}^- \rightleftharpoons [\text{CuCl}_4]^{2-} + 6\text{H}_2\text{O} $$
• The change in geometry (Tetrahedral splitting is much smaller than Octahedral splitting) and ligand strength (Cl- is weaker than H2O) leads to a substantial change in \(\Delta E\), and the observed colour becomes Yellow/Green.

B. Cobalt(II) Ions ($\text{Co}^{2+}$)

In water, $\text{Co}^{2+}$ forms the pink/red octahedral complex: $[\text{Co}(\text{H}_2\text{O})_6]^{2+}$ (Pink/Red).

i) Reaction with Chloride Ions ($\text{Cl}^-$)

• Adding concentrated hydrochloric acid drives the ligand exchange reaction, changing the coordination number from 6 to 4 (tetrahedral geometry).
  $$ [\text{Co}(\text{H}_2\text{O})_6]^{2+} + 4\text{Cl}^- \rightleftharpoons [\text{CoCl}_4]^{2-} + 6\text{H}_2\text{O} $$
• This drastic change in geometry and ligand nature leads to a new \(\Delta E\) and a clear colour change to Deep Blue. This reaction is often used to demonstrate Le Chatelier's principle (it is reversible and highly sensitive to concentration changes).

ii) Reaction with Hydroxide Ions ($\text{OH}^-$)

While this involves precipitation rather than simple ligand exchange to form a soluble complex, the colour change is important:

• Adding small amounts of $\text{OH}^-$ causes precipitation:
  $$ [\text{Co}(\text{H}_2\text{O})_6]^{2+} + 2\text{OH}^- \rightarrow \text{Co}(\text{OH})_2(\text{H}_2\text{O})_4 + 2\text{H}_2\text{O} $$
• The precipitate, $\text{Co}(\text{OH})_2(\text{H}_2\text{O})_4$, is initially blue or pink.

Key Takeaway: The geometry change from CN 6 (Octahedral, typically $H_2O$ or $NH_3$ complexes) to CN 4 (Tetrahedral, typically $Cl^-$ complexes) causes a significant shift in \(\Delta E\), leading to dramatic colour differences.