Colorimetry and Beer-Lambert Law

Learning Objectives (OCR Spec 5.3.1)

By the end of this lesson you should be able to:

• Describe the principle of a colorimeter and state the components (light source, filter, cuvette, sensor)
• Explain how wavelength and complementary colour are chosen for a given complex
• State and apply the Beer-Lambert Law A = eps c l
• Use a calibration curve to determine the concentration of an unknown coloured solution
• Explain why a ligand exchange is sometimes used to intensify the colour before measurement
• Describe the practical procedure for a colorimetric determination of Cu2+ or Fe3+

Why Colorimetry?

Many transition metal complexes are coloured, and the intensity of the colour is proportional to the concentration of the metal ion. This means colour can be used as a quantitative tool:

More concentrated solution -> more intense colour -> more light absorbed.

A colorimeter measures the amount of light absorbed by a solution at a specific wavelength. It is cheaper and easier to use than a full spectrophotometer but relies on the same physical principle: the Beer-Lambert Law.

How a Colorimeter Works

A simple colorimeter has four main components:

1. Light source (usually a tungsten filament lamp or LED) - emits light covering the visible spectrum.
2. Filter - selects a narrow wavelength range from the source. The filter is chosen to match the complementary colour of the solution (the colour the solution absorbs, not the colour it appears).
3. Cuvette (sample holder) - a rectangular plastic or glass vessel of known path length (usually 1 cm) containing the solution.
4. Photodetector - measures the intensity of the transmitted light.

The colorimeter displays the absorbance A, which is calculated from the ratio of incident to transmitted intensities:

A = log10(I0 / I)

where I0 is the incident light intensity and I is the transmitted intensity. A = 0 means no absorption (I = I0); A = 1 means 90% absorbed (I = I0/10); A = 2 means 99% absorbed.

graph LR
  A[Light source<br/>white light] --> B[Filter<br/>selects complementary colour]
  B --> C[Cuvette<br/>sample]
  C --> D[Photodetector<br/>measures intensity]
  D --> E[Display<br/>absorbance A]

Choosing the Right Filter

The filter must match the colour of light that is absorbed by the solution, not the colour the solution appears. The absorbed and transmitted colours are complementary (opposite on the colour wheel):

Solution colour (transmitted)	Absorbed colour (use this filter)	Approx. wavelength
Red	Green	500-570 nm
Orange	Blue	430-490 nm
Yellow	Violet	400-440 nm
Green	Red	620-700 nm
Blue	Orange	580-620 nm
Violet	Yellow	560-590 nm

So to measure [Cu(NH3)4(H2O)2]2+ (royal blue), you use an orange filter (around 600 nm), because the solution absorbs orange light.

To measure [Fe(SCN)(H2O)5]2+ (red / orange), you use a green or blue-green filter.

The wavelength of maximum absorbance (lambda_max) can be determined experimentally by scanning a range of filters and plotting A vs. wavelength. The peak is lambda_max, and this wavelength is then used for all subsequent measurements to maximise sensitivity.

The Beer-Lambert Law

The Beer-Lambert Law relates absorbance to concentration:

A = eps c l

where:

• A = absorbance (dimensionless)
• eps = molar absorptivity (or extinction coefficient), units of mol-1 dm3 cm-1
• c = concentration of absorbing species (mol dm-3)
• l = path length of cuvette (cm)

For a given solution, eps and l are constant, so A is directly proportional to c. A graph of absorbance vs. concentration is therefore a straight line through the origin.

Assumptions of Beer-Lambert Law

1. The solution is dilute (no interactions between absorbing species).
2. Monochromatic light (single wavelength).
3. The absorbing species does not associate or dissociate.
4. The cuvette has a constant path length and is consistently oriented.

At high concentrations, the graph starts to curve (deviation from linearity) - stick to dilute solutions.

The Calibration Curve Method

The standard procedure for determining an unknown concentration:

Step 1: Prepare Standards

Make up a series of standard solutions of known concentration of the metal ion (e.g. 0.000, 0.020, 0.040, 0.060, 0.080, 0.100 mol dm-3). Use a volumetric flask and an accurate stock solution.

If the ion is weakly coloured, convert it to a more intensely coloured complex first by adding an excess of a strong-field ligand. For example:

• Cu2+ -> [Cu(NH3)4(H2O)2]2+ by adding excess NH3
• Fe3+ -> [Fe(SCN)(H2O)5]2+ by adding excess KSCN solution
• Cr3+ -> Cr2O7^2- by oxidising with an excess of acidified peroxide

Step 2: Measure Absorbance of Each Standard

Place each standard solution in a cuvette and measure its absorbance in the colorimeter. Use the filter with wavelength closest to lambda_max. Remember to "zero" the colorimeter with a blank cuvette containing distilled water (or the solvent without analyte).

Step 3: Plot Calibration Curve

Plot A on the y-axis and c on the x-axis. Draw a line of best fit through the points (it should pass through the origin if Beer-Lambert is obeyed).