Coloured Ions and Colorimetry

Coloured Ions and Colorimetry

One of the most distinctive properties of transition metal compounds is their colour. Understanding why transition metal complexes are coloured links electronic structure to spectroscopy and analytical chemistry.

Why Are Transition Metal Complexes Coloured?

In an isolated transition metal ion, the five 3d orbitals are all at the same energy (degenerate). When ligands coordinate to the metal ion, they create an electrostatic field that causes the d orbitals to split into two groups at different energy levels.

This is explained by crystal field theory:

In an octahedral complex:

• The 3d orbitals split into a lower set of three (t₂g) and an upper set of two (eg)
• The energy gap between these sets is called ΔE (or Δoct)

In a tetrahedral complex:

• The splitting is reversed (upper set of three, lower set of two) and the gap is smaller

When visible light passes through the complex, photons with energy equal to ΔE are absorbed. An electron is promoted from the lower d orbitals to the upper d orbitals. The frequencies of light that are not absorbed are transmitted or reflected — these give the complex its observed colour.

The colour observed is the complementary colour of the light absorbed.

The Colour Wheel

Light absorbed	Colour observed (complementary)
Violet (~400 nm)	Yellow
Blue (~470 nm)	Orange
Blue-green (~500 nm)	Red
Green (~530 nm)	Purple/magenta
Yellow (~580 nm)	Violet/blue
Orange (~600 nm)	Blue
Red (~700 nm)	Green/cyan

Example: [Cu(H₂O)₆]²⁺ absorbs red/orange light → appears blue

Factors That Affect the Colour of a Complex

The energy gap ΔE (and hence the colour) depends on:

1. The metal ion — different metals have different nuclear charges and d electron configurations.

2. The oxidation state — a higher oxidation state means a higher charge density on the metal, which increases the splitting (stronger ligand interaction).

• [Fe(H₂O)₆]²⁺ is pale green
• [Fe(H₂O)₆]³⁺ is pale yellow/brown
• Same metal, same ligands, but different oxidation state → different colour

3. The ligand — different ligands cause different amounts of d-orbital splitting. The spectrochemical series orders ligands by their splitting ability:

I⁻ < Br⁻ < Cl⁻ < F⁻ < OH⁻ < H₂O < NH₃ < en < CN⁻ < CO

Weak-field ligands (left) cause small splitting → absorb low-energy (red) light

Strong-field ligands (right) cause large splitting → absorb high-energy (blue/violet) light

Example:

• [Cr(H₂O)₆]³⁺ is violet (H₂O is mid-range)
• [Cr(NH₃)₆]³⁺ is yellow (NH₃ causes larger splitting → absorbs violet)
• [CrCl₆]³⁻ is green (Cl⁻ causes smaller splitting → absorbs red)

4. Coordination number / geometry:

• [CuCl₄]²⁻ is yellow (tetrahedral, small ΔE)
• [Cu(H₂O)₆]²⁺ is blue (octahedral, larger ΔE with different ligand)

When Are d-Block Compounds Colourless?

A compound is colourless when d-d transitions are not possible:

• d⁰ configuration: No d electrons to promote. E.g. Sc³⁺ (d⁰), Ti⁴⁺ (d⁰), MnO₄⁻ (though MnO₄⁻ IS purple — its colour comes from a charge transfer transition, not d-d)
• d¹⁰ configuration: d orbitals are completely full — no empty orbital to promote into. E.g. Cu⁺ (d¹⁰), Zn²⁺ (d¹⁰)

This is why zinc compounds are typically white/colourless — Zn²⁺ has a full d¹⁰ configuration.

Charge Transfer Transitions

Some intensely coloured species (MnO₄⁻ purple, CrO₄²⁻ yellow, Fe³⁺/SCN⁻ blood red) get their colour from charge transfer rather than d-d transitions. An electron is transferred from a ligand orbital to a metal orbital (ligand-to-metal charge transfer, LMCT) or vice versa. These transitions are allowed (not Laporte-forbidden like d-d), so they produce very intense colours.

Colorimetry

Colorimetry uses the absorption of light by coloured solutions to determine concentration. It is an application of the Beer-Lambert law.

The Beer-Lambert Law

A = ε × c × l

Where:

• A = absorbance (no units)
• ε = molar absorption coefficient (dm³ mol⁻¹ cm⁻¹) — characteristic of the substance at a given wavelength
• c = concentration (mol dm⁻³)
• l = path length (cm) — usually 1.00 cm in a standard cuvette

Absorbance is proportional to concentration (at a fixed wavelength and path length).

Using a Colorimeter

1. Select a filter (or wavelength) that corresponds to the complementary colour of the solution — the wavelength the solution absorbs most strongly

2. Prepare a series of standard solutions of known concentration

3. Measure the absorbance of each standard

4. Plot a calibration curve (absorbance vs concentration — should be a straight line through the origin)

5. Measure the absorbance of the unknown solution

6. Read the concentration from the calibration curve

Example: To measure Cu²⁺ concentration, use an orange/red filter (around 600–650 nm) because [Cu(H₂O)₆]²⁺ absorbs in this region (it appears blue because it absorbs the complementary red/orange).

Applications of Colorimetry

• Determining the concentration of transition metal ions in solution
• Measuring the concentration of coloured organic compounds (e.g. food dyes)
• Monitoring the progress of reactions that involve colour changes
• Environmental analysis (e.g. determining phosphate or nitrate levels in water by reacting with a reagent to form a coloured complex)

Exam Tips

• When explaining colour, follow this sequence: ligands cause d-orbital splitting → visible light absorbed → electron promoted from lower to upper d orbitals → complementary colour is observed
• If asked why a compound is colourless, state whether it is d⁰ (no electrons to promote) or d¹⁰ (no empty d orbital)
• In colorimetry, the filter must match the colour absorbed, not the colour observed
• Draw calibration curves with concentration on the x-axis and absorbance on the y-axis; read off the unknown on this graph