Introduction: The World of Colour and Chemistry
Have you ever wondered why a solution of copper(II) sulfate is a vivid sky blue, while table salt dissolved in water is completely clear? Or why the natural dyes in flowers or synthetic dyes in your clothes appear so brightly coloured? The answer lies at the intersection of energy, electron transitions, and visible light.
In this chapter, we explore how matter interacts with electromagnetic radiation to produce colour, examine why transition metal complexes and conjugated organic molecules absorb visible light, and master the practical analytical technique of colorimetry. Colorimetry allows chemists to determine unknown concentrations of coloured solutions accurately by measuring the amount of light they absorb.
Note: For a broader study of the entire electromagnetic spectrum and molecular rotations or vibrations, see the chapter "Radiation, the electromagnetic spectrum and molecules". Here, our focus is squarely on the visible region and light absorption.
1. Light, Energy, and the Origin of Perceived Colour
The Visible Spectrum and Energy
Visible light forms a very narrow sliver of the electromagnetic spectrum, with wavelengths roughly ranging from \(400\text{ nm}\) (violet light, highest energy) to \(700\text{ nm}\) (red light, lowest energy). Light can be thought of as streams of energy packets called photons.
The energy change \(\Delta E\) associated with absorbing a photon of light is given by the fundamental Planck relationship:
\(\Delta E = h\nu = \frac{hc}{\lambda}\)
Where:
• \(\Delta E\) is the energy difference between two electronic energy levels in joules (\(\text{J}\))
• \(h\) is Planck's constant (\(6.63 \times 10^{-34}\text{ J Hz}^{-1}\) or \(\text{J s}\), provided on your Data Sheet)
• \(\nu\) is the frequency of the light in hertz (\(\text{Hz}\) or \(\text{s}^{-1}\))
• \(c\) is the speed of light in a vacuum (\(3.00 \times 10^8\text{ m s}^{-1}\), provided on your Data Sheet)
• \(\lambda\) is the wavelength of light in metres (\(\text{m}\))
Notice the inverse relationship: A larger energy gap \(\Delta E\) corresponds to higher frequency \(\nu\) and shorter wavelength \(\lambda\). A smaller energy gap corresponds to lower frequency and longer wavelength.
Complementary Colours: What We See vs. What Is Absorbed
White light contains an equal mixture of all the wavelengths of the visible spectrum. When white light passes through a solution or reflects off a substance, three things can happen to different wavelengths: they can be reflected, transmitted (let through), or absorbed.
If a substance absorbs no visible light, all wavelengths are transmitted or reflected, and the substance appears white or colourless. If a substance absorbs all visible wavelengths completely, it appears black.
However, if a substance absorbs only specific wavelengths of visible light, the light that emerges is no longer white. What our eyes perceive is the complementary colour—the colour formed by the mixture of the transmitted (unabsorbed) wavelengths.
The Colour Wheel
A simple and reliable way to predict what colour a substance will appear is to use a colour wheel. Colours directly opposite each other on the wheel are complementary pairs:
• Red is opposite Cyan / Green-Blue
• Blue is opposite Orange
• Yellow is opposite Violet / Purple
• Green is opposite Magenta / Red-Violet
Example: A solution of hydrated copper(II) ions, \([\text{Cu}(\text{H}_2\text{O})_6]^{2+}\), strongly absorbs light in the red-orange region of the spectrum (around \(600\text{ to }700\text{ nm}\)). Because red and orange photons are removed from the white light, the transmitted light consists mainly of blue and green wavelengths, so the solution appears pale blue!
Key Takeaway: The colour you see is never the colour of light that was absorbed. You see the light that was transmitted, which is the complementary colour to the absorbed light.
2. The Chemical Origins of Colour
Why do certain molecules and ions absorb visible light, while most simple molecules only absorb in the ultraviolet region? To absorb visible light, a chemical species must have an electronic energy gap \(\Delta E\) that exactly matches the energy of a visible photon (\(400\text{ to }700\text{ nm}\)). In chemistry, this happens in two main families of compounds:
A. Transition Metal Complexes (d-to-d Transitions)
In an isolated, gaseous transition metal atom or ion, all five \(\text{d}\)-orbitals have identical energy—they are termed degenerate.
However, in a transition metal complex, ligands attach to or surround the central metal cation by forming dative covalent (coordinate) bonds. The lone pairs of electrons on the approaching ligands repel the electrons in the metal's \(\text{d}\)-orbitals. Because of the spatial shapes and orientations of the five \(\text{d}\)-orbitals relative to the ligands, some \(\text{d}\)-orbitals experience greater electrostatic repulsion than others. This causes the \(\text{d}\)-orbitals to split into two sets of unequal energy levels separated by an energy difference, \(\Delta E\).
When visible light shines on the complex:
1. An electron in a lower-energy \(\text{d}\)-orbital absorbs a photon of light whose energy matches the splitting gap: \(\Delta E = h\nu\).
2. The electron is promoted from the lower \(\text{d}\)-orbital to a higher-energy vacant or partially filled \(\text{d}\)-orbital. This process is called a \(\text{d-d}\) transition.
3. The remaining unabsorbed wavelengths pass through to our eyes, producing the complementary colour.
Why are some ions colourless?
For a \(\text{d-d}\) transition to occur, there must be both an electron in a lower \(\text{d}\)-orbital to promote and space in an upper \(\text{d}\)-orbital to receive it.
• \(\text{Sc}^{3+}\) has an electron configuration of \([\text{Ar}]\,3\text{d}^0\). With no \(\text{d}\)-electrons, no transition is possible, so \(\text{Sc}^{3+}\) compounds are colourless.
• \(\text{Zn}^{2+}\) has an electron configuration of \([\text{Ar}]\,3\text{d}^{10}\). All \(\text{d}\)-orbitals are completely full, so an electron cannot be promoted to another \(\text{d}\)-orbital. Thus, \(\text{Zn}^{2+}\) compounds are also colourless.
Factors Affecting the Colour of Transition Metal Complexes:
Any factor that alters the size of the energy gap \(\Delta E\) will change the frequency of light absorbed, and therefore change the observed colour:
• The nature of the ligand: Different ligands produce different electrostatic field strengths. For example, replacing water ligands in pale blue \([\text{Cu}(\text{H}_2\text{O})_6]^{2+}\) with ammonia gives deep royal blue \([\text{Cu}(\text{NH}_3)_4(\text{H}_2\text{O})_2]^{2+}\) because \(\text{NH}_3\) causes a larger splitting gap \(\Delta E\).
• The oxidation state of the metal: A higher oxidation state exerts a stronger pull on ligand electron pairs, generally increasing \(\Delta E\). For instance, \(\text{Fe}^{2+}(\text{aq})\) is pale green, whereas \(\text{Fe}^{3+}(\text{aq})\) is yellow/brown.
• The coordination number and geometry: Octahedral and tetrahedral complexes have different splitting patterns and magnitudes of \(\Delta E\).
B. Organic Molecules and Delocalised Systems
Most simple organic compounds (like ethanol, hexane, or glucose) are completely colourless. Why? Because the energy gap between their occupied bonding orbitals (\(\sigma\) or \(\pi\)) and unoccupied anti-bonding orbitals (\(\sigma^*\) or \(\pi^*\)) is very large. Absorbing light across this gap requires high-energy ultraviolet radiation, so no visible light is absorbed.
To produce colour in an organic compound, the energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) must be reduced until it falls into the visible light range.
This is achieved through extended conjugation (delocalisation):
• Conjugation occurs when molecules contain alternating double (or triple) bonds and single bonds, or alternating double bonds and atoms with available lone pairs.
• As the system of overlapping \(\text{p}\)-orbitals becomes longer and more extended, the \(\pi\) electrons become delocalised across a larger number of carbon atoms.
• Crucially, as delocalisation increases, the energy gap \(\Delta E\) between the HOMO and LUMO decreases.
• Eventually, with enough conjugated double bonds (often around eight or more, or via extended aromatic and azo networks), \(\Delta E\) becomes small enough to absorb light in the visible region rather than the UV region.
Chromophores and Dyes:
A chromophore is the specific functional group or structural unit within a molecule responsible for absorbing radiation. Examples include the azo group (\(-\text{N}=\text{N}-\)), carbonyl groups (\(\text{C}=\text{O}\)), nitro groups (\(-\text{NO}_2\)), and extended alternating \(\text{C}=\text{C}\) polyene chains. When linked into delocalised aromatic rings (as in azo dyes), they produce intense, vibrant colours.
Key Takeaway: Whether in transition metal complexes (\(\text{d-d}\) splitting) or organic dyes (extended delocalisation reducing the \(\text{HOMO-LUMO}\) gap), colour occurs because \(\Delta E\) is tuned to match the energy of visible light photons.
3. Principles of Colorimetry
What is a Colorimeter?
A colorimeter is an instrument used to measure the intensity of light absorbed by a coloured solution. Because the amount of light absorbed depends directly on the concentration of the absorbing solute, colorimetry is an ideal, rapid, and non-destructive technique for finding the concentration of an unknown solution.
Key Components of a Colorimeter
A typical laboratory colorimeter operates through a simple optical pathway:
1. Light source: Emits white light containing all visible wavelengths.
2. Coloured filter: Selects a specific narrow band of wavelengths to pass through the sample.
3. Cuvette holder: Holds the transparent plastic or glass sample container (the cuvette).
4. Detector: A light-sensitive photocell that measures the intensity of light emerging from the cuvette.
5. Meter / Digital display: Converts the detected light into an electrical signal and displays it as either Absorbance (\(A\)) or Transmission (\(\%\)).
Choosing the Right Filter: The Golden Rule
To obtain maximum sensitivity and the most reliable readings, you must choose a filter that transmits the wavelength of light that the solution absorbs most strongly.
This means the filter must be the complementary colour to the solution being tested:
• If testing a blue solution (such as copper(II) sulfate), you must use a red / orange filter.
• If testing a yellow / brown solution (such as iodine), you must use a blue filter.
• If testing a purple solution (such as manganate(VII)), you must use a green filter.
Why is this critical? If you used a blue filter for a blue solution, the blue light would pass straight through without being absorbed, giving almost zero absorbance regardless of whether the solution was concentrated or dilute!
The Absorbance-Concentration Relationship
For dilute solutions, absorbance (\(A\)) is directly proportional to two factors:
• The concentration (\(c\)) of the coloured species in \(\text{mol dm}^{-3}\).
• The path length (\(l\)) of light through the solution (standard cuvettes have a fixed path length of \(1.0\text{ cm}\)).
Because the path length is held constant by using identical cuvettes, Absorbance is directly proportional to concentration:
\(A \propto c\)
Key Takeaway: Always select a filter complementary in colour to the sample solution to ensure maximum light absorption and highest experimental sensitivity.
4. Quantitative Analysis: Using Calibration Curves
To determine the concentration of a substance in an unknown solution, chemists construct and use a calibration curve (which is typically a straight line for dilute solutions).
Step-by-Step Procedure
Step 1: Prepare standard solutions of known concentration
Start with a concentrated standard solution of known concentration. Use accurate glassware—such as a burette or volumetric pipette—to dilute this stock solution into volumetric flasks, creating a series of standard solutions (for example, \(0.02\), \(0.04\), \(0.06\), \(0.08\), and \(0.10\text{ mol dm}^{-3}\)).
Step 2: Zero the colorimeter using a reference blank
Fill a clean cuvette with pure solvent (typically distilled water) and place it in the colorimeter. Adjust the instrument so that the absorbance reads zero (\(A = 0.00\)). This is called zeroing with a blank. It accounts for any light reflection or absorption caused by the cuvette walls and the solvent itself.
Step 3: Measure the absorbance of each standard solution
Rinse and fill the cuvette with each standard solution in turn. Record the absorbance value for each known concentration, making sure to insert the cuvette with the same orientation each time.
Step 4: Plot the calibration curve
Plot a graph of Absorbance on the vertical (\(y\)) axis against Concentration on the horizontal (\(x\)) axis. Draw a line of best fit. For dilute solutions, this will be a straight line passing directly through the origin \((0,0)\), because a concentration of zero absorbs zero light.
Step 5: Measure the unknown sample and read the concentration
Place the unknown solution into the colorimeter and record its absorbance. Locate this absorbance value on the \(y\)-axis of your calibration graph, move horizontally to intersect your line of best fit, and then move vertically down to the \(x\)-axis to read off the unknown concentration.
Worked Example: Finding the Concentration of Copper(II) Ions
Problem: A student uses a colorimeter with a red filter to determine the concentration of \(\text{Cu}^{2+}(\text{aq})\) in an industrial wastewater sample. The calibration line obtained has the equation:
\(\text{Absorbance} = 12.5 \times c\)
where \(c\) is the concentration in \(\text{mol dm}^{-3}\).
The wastewater sample gives an absorbance reading of \(0.45\). Calculate the concentration of \(\text{Cu}^{2+}\) in the wastewater.
Solution:
Rearranging the relationship:
\(c = \frac{\text{Absorbance}}{12.5}\)
\(c = \frac{0.45}{12.5} = 0.036\text{ mol dm}^{-3}\)
5. Practical Skills and Minimising Experimental Errors
In written exam components (Components 01, 02, and 03), you are frequently asked to identify sources of error or explain how to ensure high accuracy when using a colorimeter.
• Cuvette handling: Always hold cuvettes by their frosted or ribbed edges. Never touch the clear optical faces, because grease and fingerprints on the glass/plastic scatter light and cause falsely high absorbance readings.
• Cleaning and wiping: Wipe the clear outside faces of the cuvette with a soft lint-free tissue before placing it into the colorimeter.
• Eliminating air bubbles: Gently tap the cuvette to dislodge any bubbles clinging to the inner surfaces, as bubbles scatter light and lead to inaccurate measurements.
• Rinsing between samples: When switching from one standard to another, rinse the cuvette with a small portion of the new solution first. Rinsing with water would dilute the solution, causing a falsely low reading.
• Orientation: Ensure the cuvette is always placed into the holder in the exact same orientation, as tiny manufacturing variations in wall thickness can alter light transmission.
• High concentrations (Deviations from linearity): If a solution is too concentrated, the calibration graph curves and flattens out at higher absorbances because too little light reaches the detector. If the unknown absorbance falls off the linear scale, accurately dilute the unknown by a known factor (e.g. tenfold), re-measure, and multiply the resulting concentration by the dilution factor.
Summary of Key Concepts
• Photon absorption: Light absorption promotes electrons between energy levels according to \(\Delta E = h\nu = \frac{hc}{\lambda}\).
• Perceived colour: The colour of a chemical species is the complementary colour of the wavelengths it absorbs.
• Transition metals: Ligands split degenerate \(\text{d}\)-orbitals into two energy levels; absorption of visible light drives \(\text{d-d}\) transitions. Only ions with partially filled \(\text{d}\)-orbitals (\(\text{d}^1\) to \(\text{d}^9\)) are coloured.
• Organic chromophores: Extended systems of alternating single and double bonds (conjugated systems) lower the \(\text{HOMO-LUMO}\) gap into the visible range.
• Colorimetry: Uses a filter complementary to the solution's colour to measure absorbance. A calibration curve of absorbance versus concentration allows the direct determination of unknown concentrations.