Conduct investigations to use colourimetry, UV-visible spectrophotometry and atomic absorption spectroscopy (AAS) to measure the concentration of species in aqueous solution

What this dot point is asking

NESA wants you to explain how a coloured or absorbing species can be quantified by measuring how much light it absorbs, apply the Beer-Lambert law, use a calibration curve to determine an unknown concentration, and choose between colourimetry, UV-vis and AAS based on the species and the concentration range.

The answer

Beer-Lambert law: the common foundation

For a solution that absorbs light, the absorbance $A$ is related to the path length $l$ and concentration $c$ by:

where $\varepsilon$ (molar absorptivity, L mol$^{-1}$ cm$^{-1}$) is a constant for a given species at a given wavelength. Absorbance is defined as $A = \log_{10}(I_0 / I)$, where $I_0$ is the incident light intensity and $I$ is what passes through.

The law is linear in the dilute regime (typically $A < 2$). The calibration curve is therefore a straight line through the origin, and you can read off any unknown by measuring its absorbance and using the line.

Building a calibration curve

1. Prepare standards by serial dilution of a stock solution of the target species. Use at least five standards bracketing the expected concentration range.
2. Choose the wavelength at which the species absorbs most strongly ($\lambda_{\max}$). For $Cu^{2+}$ this is around 600 nm (a copper sulfate solution is blue, so it absorbs orange).
3. Zero the instrument on a blank (distilled water or solvent) to subtract the cell and solvent contribution.
4. Measure absorbance of each standard.
5. Plot $A$ vs $c$ and fit a line. Slope is $\varepsilon \cdot l$.
6. Measure the unknown and read its concentration from the line, or solve $c = A / (\varepsilon l)$.

Colourimetry

The simplest version. A coloured filter (a piece of coloured glass or plastic) selects a band of visible light a few tens of nanometres wide. A photocell measures the light passing through the cuvette. Suitable for any solution with a visible colour.

For colourless ions, a reagent is added that forms a coloured complex:

• Phosphate: react with molybdate and reductant to give a deep blue complex (molybdenum blue), absorbance at 880 nm.
• Iron(III): react with thiocyanate to give the blood-red $[FeSCN]^{2+}$ complex.
• Nitrate: reduce to nitrite, react with sulfanilamide and N-(1-naphthyl)ethylenediamine to give a pink azo dye.

Detection limits are about 0.5 ppm. Colourimetry is the standard field method for swimming-pool chemistry, aquarium testing, and basic water quality work.

UV-visible spectrophotometry

A more capable instrument. A diffraction grating (monochromator) selects a narrow (about 1 nm) band anywhere from 200 to 800 nm. A photomultiplier or photodiode detector measures the transmitted intensity.

Extends colourimetry into:

• The UV region, 200 to 400 nm, where many organic molecules with conjugated $\pi$ systems absorb. Aromatic rings absorb around 260 to 280 nm; conjugated carbonyls around 220 to 260 nm.
• Higher accuracy, because the bandwidth is narrower and the wavelength can be tuned to $\lambda_{\max}$.
• Multi-wavelength scans that produce a full absorption spectrum, useful for identification as well as quantitation.

Detection limits are 0.01 to 0.1 ppm. UV-vis is the workhorse of biochemistry (DNA at 260 nm, protein at 280 nm) and inorganic complex analysis.

Atomic absorption spectroscopy (AAS)

The technique of choice for trace metal analysis. Three components are unique:

1. Hollow-cathode lamp, with a cathode made of the target element. The lamp emits the line spectrum of that element only. To analyse lead, use a lead lamp; to analyse copper, use a copper lamp.
2. Atomiser (flame or graphite furnace). The sample is aspirated into an air-acetylene flame (about 2300 degrees C), which evaporates the solvent and breaks the metal salts into free gaseous atoms.
3. Monochromator and detector, tuned to a single line of the target element.

The free atoms absorb the lamp's light at exactly the wavelength they would emit. Other elements present do not absorb because they have different atomic energy levels. The selectivity is intrinsic.

Calibration is by Beer-Lambert against standards. Detection limits are 1 to 10 ppb for most metals in flame AAS, and around 0.1 ppb in graphite furnace AAS.

AAS is used for:

• Lead, mercury, cadmium in drinking water.
• Iron, calcium, magnesium in plant nutrition studies.
• Trace metals in blood and urine for forensic and clinical work.
• Metallurgical assays of ores and alloys.

Choosing the right tool

Common reagents to colour the colourless

Examples in context

Example 1. Lead testing in Sydney water mains by AAS. Sydney Water's central laboratory at Potts Hill uses atomic absorption spectroscopy with a lead hollow-cathode lamp at 217.0 nm to test for lead at the regulatory threshold of 10 $\mu$g L$^{-1}$. A calibration curve from five lead standards (0, 5, 10, 20, 50 $\mu$g L$^{-1}$) gives a linear plot of absorbance vs concentration with $R^2 > 0.998$. An unknown reading 0.052 absorbance units back-converts to 14 $\mu$g L$^{-1}$, flagging an exceedance. AAS is preferred over colourimetry here because lead in tap water is at parts-per-billion levels, two orders of magnitude below colourimetry's detection limit, and the hollow-cathode lamp gives element-specific selectivity.

Example 2. Phosphate in NSW catchment monitoring by colourimetry. WaterNSW field officers test phosphate in rural streams using the molybdenum-blue colourimetric method: $PO_4^{3-}$ reacts with molybdate and ascorbic acid to give a blue complex with maximum absorbance at 880 nm. A calibration curve from standards at 0.1, 0.5, 1.0, 2.0 mg L$^{-1}$ enables field instruments to report concentration directly. Readings above 0.10 mg L$^{-1}$ flag potential eutrophication risk and trigger algal bloom monitoring. The HSC Beer-Lambert framework $A = \varepsilon c l$ explains the linear range and the limit of detection set by blank noise.

Try this

Q1. State the Beer-Lambert law in symbols and words, and define each variable. [3 marks]

• Cue. $A = \varepsilon c l$: absorbance is proportional to molar absorptivity $\varepsilon$, concentration $c$ and path length $l$.

Q2. A calibration curve gives the equation $A = 0.180 \times c$ where $c$ is in mg L$^{-1}$. A sample reads 0.072 absorbance. Calculate the concentration. [2 marks]

• Cue. $c = 0.072 / 0.180 = 0.40$ mg L$^{-1}$.

Q3. A NSW HSC depth study uses AAS to measure iron in a tablet. (a) Explain why an iron hollow-cathode lamp is used. (b) Outline how a calibration curve is constructed. (c) State two assumptions of the Beer-Lambert law that must hold for the measurement to be accurate. [2+2+2 marks]

• Cue. (a) Lamp emits iron-specific wavelengths matching the absorption transitions of gaseous iron atoms. (b) Prepare standards of known $[Fe]$, measure absorbance, plot $A$ vs $c$. (c) Monochromatic light, dilute solution (no aggregation), constant path length.