6.2.4 Formation of Coloured Ions

The Formation of Coloured Ions

The colour observed in transition metal ions is due to the absorption of certain wavelengths of visible light. When light is absorbed by the ion, specific wavelengths are taken in, while others are transmitted or reflected, giving rise to the observed colour. This colour change depends on several factors within the metal ion's structure and environment.

Energy Levels and Electron Transitions

d-Orbital Splitting:

Normally, the five $3d$ orbitals in a transition metal ion have equal energy. However, when ligands bond to the metal ion, they influence the $3d$ orbitals, splitting them into two groups with different energy levels.

Electron Excitation:

Electrons generally occupy the lower energy orbitals (ground state). When light hits the metal ion, electrons absorb energy and transition to higher energy $3d$ orbitals (excited state).

Energy Absorption and Colour:

The energy absorbed by the electrons is exactly equal to the difference in energy ($\Delta E$) between the ground and excited states:

$$\Delta E = h f = \frac{hc}{\lambda}$$

Where:

• $h$ is Planck's constant ($6.63 \times 10^{-34} \text{ J s}$)
• $f$ is the frequency of the light absorbed (Hz)
• $c$ is the speed of light ($3.00 \times 10^8 \text{ m/s}$)
• $\lambda$ is the wavelength of the absorbed light (m)

Factors Affecting Colour

The colour observed in a transition metal complex depends on:

• The Metal Ion: Different metals have unique arrangements of d-orbitals, affecting the energy gap ($\Delta E$)
• Oxidation State: Higher oxidation states usually increase the energy difference between $d$-orbitals.
• Coordination Number: The number of ligands around the metal ion can influence the extent of $d$-orbital splitting.
• Ligand Type: Different ligands cause varying degrees of d-orbital splitting. Strong-field ligands (like $CN⁻$) cause larger energy gaps than weak-field ligands (like $\text{H}_2\text{O}$).

Observing Colour

When visible light interacts with a transition metal ion:

• Certain wavelengths are absorbed, exciting electrons to higher energy levels. The wavelengths absorbed depend on the $\Delta E$ value.
• The remaining wavelengths are reflected, combining to form the colour we see.

If a transition metal ion has no $3d$ electrons or a completely filled $3d$ sub-level, electron transitions cannot occur.

In this case, no light is absorbed, and the compound appears colourless because all wavelengths are reflected.

Spectroscopy and Colourimetry

Spectroscopy can be used to analyze the concentration of a solution by measuring how much visible light it absorbs.

1. Light and Filter: White light passes through a filter that transmits only the colour most strongly absorbed by the sample.
2. colourimeter: The filtered light then passes through the sample and into a colourimeter, which detects the amount of light absorbed. More concentrated solutions absorb more light.
3. Calibration Graph: To find an unknown concentration, plot a calibration graph using solutions of known concentrations. The unknown concentration can then be determined by comparing its absorbance to the graph.

Practical Applications in Colourimetry

Determining the Concentration of Copper(II) Ions Using Colourimetry

In this example, you will determine the concentration of a $\text{Cu}^{2+}$ solution by measuring its absorbance with a colourimeter.

By comparing this absorbance to a calibration graph, prepared from standard solutions of known concentrations, you can accurately find the unknown concentration of $\text{Cu}^{2+}$ ions.

Materials Needed

• Copper(II) sulfate ($\text{CuSO}_4$) solutions of known concentrations (e.g., 0.1 M, 0.2 M, 0.3 M, etc.)
• Copper(II) sulfate solution of unknown concentration
• colourimeter
• Distilled water
• Cuvettes (containers for holding liquid samples in the colourimeter)
• Filter (blue, or any filter complementary to the colour of the solution)
• Pipettes

Method

1. Prepare Calibration Standards: Prepare a set of standard $\text{CuSO}_4$ solutions with known concentrations.

These will serve as the reference solutions for creating a calibration graph.

2. Zero the colourimeter: Turn on the colourimeter and set it to the correct wavelength (use a blue filter to let through the complementary colour of the copper(II) ion solution, which appears blue-green).

Fill a cuvette with distilled water and place it in the colourimeter to calibrate (zero) the instrument.

This ensures that only the absorbance of the $\text{Cu}^{2+}$ solution is measured.

3. Measure Absorbance of Standard Solutions: Fill a clean cuvette with the first standard solution (e.g., 0.1 M $\text{CuSO}_4$) and measure its absorbance.

Repeat this process with each standard solution, recording each absorbance.

4. Plot a Calibration Graph: Plot a graph of absorbance (y-axis) against concentration (x-axis) for the standard solutions.

This should yield a straight line if Beer's Law is obeyed, meaning absorbance is directly proportional to concentration.

5. Measure Absorbance of Unknown Solution: Rinse a cuvette and fill it with the $\text{Cu}^{2+}$ solution of unknown concentration.

Measure and record its absorbance.

6. Determine the Concentration: Use the calibration graph to find the concentration corresponding to the absorbance of the unknown solution.

Locate the absorbance on the y-axis and read across to the calibration line, then down to the x-axis to find the concentration.

Explanation

This colourimetric method relies on the fact that $\text{Cu}^{2+}$ ions in solution absorb specific wavelengths of light. The higher the concentration of $\text{Cu}^{2+}$ ions, the more light is absorbed, leading to a higher absorbance reading. By comparing the absorbance of the unknown sample to the known standards, you can accurately determine its concentration.