Colorimetry and the standard curve

When to use colorimetry instead of titration

• Use it when the species is coloured and present at low concentration — too low to titrate accurately.

• It is fast once set up, and analysing many samples is much quicker than many titrations, which suits a trend investigation with several data points.

• Typical school contexts: Cu²⁺ in solution, Fe³⁺ as its thiocyanate complex, MnO₄⁻, food dyes, nitrate or phosphate after colour development.

The principle

• A colorimeter passes light of a chosen wavelength through the solution and measures how much is absorbed.
• The more concentrated the coloured species, the more light is absorbed.

The relationship is the Beer–Lambert law:

$$A = \varepsilon c l$$

• $A$ — absorbance, a dimensionless number

• $\varepsilon$ — the molar absorptivity, a constant for that species at that wavelength, in L mol⁻¹ cm⁻¹

• $c$ — concentration, in mol L⁻¹

• $l$ — the path length through the solution, in cm

• Since $\varepsilon$ and $l$ are constant for a given setup, absorbance is directly proportional to concentration — a straight line through the origin.

Choosing the wavelength

• Use the wavelength of maximum absorbance for the species being measured, usually written $\lambda_{max}$.

• This maximises the sensitivity: a given change in concentration produces the largest change in absorbance, so small differences between samples are detectable.

• It also makes the reading least sensitive to small errors in the wavelength setting, because the absorbance curve is flat at its peak.

• A coloured solution absorbs the complementary colour to the one it appears. A blue copper solution absorbs strongly in the orange-red, around 600–700 nm.

Building the standard curve

• Prepare a series of standards of accurately known concentration, by diluting a stock solution with volumetric glassware.
• Zero the colorimeter with a blank — the solvent and all reagents except the analyte.
• Measure the absorbance of each standard at $\lambda_{max}$.
• Plot absorbance (y) against concentration (x), and draw the line of best fit.
• Measure each unknown and read its concentration off the line.

Making the curve valid

Explanatory Note 6 requires the range of the standard curve to be appropriate, and this is where colorimetry investigations most often fail.

• Your samples' absorbances must fall inside the range covered by your standards.

  • A sample reading above the highest standard is being extrapolated, not interpolated — and extrapolation beyond the measured range is not supported by the data.
  • A sample reading near zero is in the region where the percentage uncertainty is largest.

• Use at least five standards, spread evenly across the range.

• Include the origin as a point only if a blank of zero concentration genuinely reads zero absorbance — which it should, if the blank was prepared correctly.

• If a sample reads off the top of the curve, dilute it by a known factor and re-measure, then multiply back. This is a modification you can justify.

Where the Beer–Lambert law breaks down

• The linear relationship fails at high concentrations, typically above about $A = 1$. The curve bends towards the concentration axis, so a sample in that region reads lower than its true concentration.

• Causes include interactions between the absorbing particles at high concentration, and stray light in the instrument.

• This is why the range matters. A calibration built entirely within the linear region, with samples inside it, is valid; one extending into the curved region is not.

• Other things to control: the same cuvette, the same orientation, clean and dry outer faces, no bubbles, and consistent temperature.

Colour development reactions

• Some analytes are colourless and must be converted to a coloured species first.
  • Fe³⁺ with thiocyanate gives a deep red complex.
  • Phosphate with molybdate and a reducing agent gives molybdenum blue.
• If you use a colour development reaction, the same amount of reagent must be added to every standard and every sample, and the same development time allowed — otherwise the colour intensity varies for reasons unrelated to the analyte.