the principles and use of colorimetry and UV-visible spectroscopy (including the Beer-Lambert relationship) and atomic absorption spectroscopy (AAS), and the use of calibration curves to determine the concentration of an analyte in water

What this dot point is asking

VCAA wants you to describe the principles of colorimetry, UV-visible spectroscopy and atomic absorption spectroscopy, to apply the Beer-Lambert relationship (A = ecl), to use a calibration curve to determine the concentration of an analyte, and to compare the techniques for suitability.

The answer

Why use instrumental analysis

Volumetric methods are accurate but limited to analytes that react in a known stoichiometry and at concentrations high enough to titrate. Instrumental methods extend the toolkit to:

• Coloured solutions (where the colour itself is the analyte).
• Trace metals at ppm or ppb levels (well below titration's reliable range).
• Mixtures where one component absorbs at a wavelength others do not.

Common principle: pass light through the sample, measure how much is absorbed at a chosen wavelength, and convert absorbance to concentration using a calibration curve.

Colorimetry and UV-visible spectroscopy

Coloured solutions absorb visible light because their electrons are promoted between energy levels separated by a visible-light photon. The colour of a solution is the complement of the colour it absorbs (a blue solution absorbs orange/red; a red solution absorbs green).

A colorimeter passes a narrow band of visible light (often filtered) through the sample. A UV-visible spectrophotometer scans across a range of wavelengths (often 200 to 800 nm) and produces an absorbance spectrum.

The Beer-Lambert relationship quantifies the absorbance:

A = e x c x l

• A is absorbance (dimensionless; log10 of I0/I).
• e is the molar absorptivity (or extinction coefficient), characteristic of the analyte at that wavelength, in L mol^-1 cm^-1.
• c is the concentration of the absorbing species, in mol L^-1.
• l is the path length of the cuvette, in cm (usually 1.00 cm).

For a given analyte and cuvette, A is proportional to c at low concentration: A = constant x c. This is exactly what a calibration curve relies on.

Calibration curves

The standard workflow:

1. Prepare a series of standards of known concentration spanning the expected range of the unknown.
2. Measure absorbance for each at a chosen wavelength (usually the wavelength of maximum absorbance, lambda_max).
3. Plot absorbance (y) against concentration (x). At low concentration the plot is linear and passes through (or near) the origin.
4. Measure the absorbance of the unknown.
5. Read the concentration of the unknown directly from the line (do not extrapolate beyond the calibrated range).

Why use the wavelength of maximum absorbance? Two reasons:

• Sensitivity: the calibration curve has its steepest slope, so a small change in c produces the largest change in A.
• Robustness: small wavelength drifts in the instrument do not change A much (the peak is locally flat).

Atomic absorption spectroscopy (AAS)

AAS is used for metal ions in water at trace concentrations (ppm or ppb). The principle: free, gaseous, ground-state metal atoms absorb light at the same wavelengths their atoms emit. Each element has a unique line spectrum, so a specific lamp gives a specific element's lines.

The instrument:

1. Hollow-cathode lamp: a tube containing the same element being analysed. A current through it excites atoms of that element, which emit only the wavelengths characteristic of that element. (A Pb lamp emits Pb wavelengths only.)
2. Atomiser (a flame, typically air/acetylene): aspirates the sample, evaporates the solvent, breaks compounds into atoms, and reduces ions to ground-state atoms.
3. Monochromator: selects one specific wavelength (usually the strongest line).
4. Detector: measures the intensity of light that passes through the flame.

The absorbance is proportional to the number density of ground-state atoms of that element in the flame, which is proportional to the concentration in the original sample.

Calibration is identical to UV-visible: a series of standards of known concentration of the same element, measured under the same conditions, gives a linear calibration curve.

Strengths of AAS:

• Element-specific (the lamp ensures only the target element is measured).
• Sensitive to ppm/ppb.
• Many elements can be analysed (Cu, Fe, Pb, Cd, Zn, Hg, etc., one at a time per lamp).

Limitations:

• One element at a time (multiple elements require multiple lamps).
• Not suitable for non-metals or for total organic content.
• Sample matrix (other species in the water) can interfere; matrix-matched standards help.

Comparison of techniques

Examples in context

Example 1. Lead in Mount Isa kindergarten dust by AAS. Public health chemists at the National Measurement Institute test settled dust from kindergartens within $2 \, \text{km}$ of the Mount Isa lead smelter using flame AAS. A wipe sample is digested in concentrated $\text{HNO}_3$ and made up to $25.0 \, \text{mL}$. A lead hollow-cathode lamp emits at $217.0 \, \text{nm}$; the sample absorbance is $0.412$ against calibration standards of $1, 2, 5$ and $10 \, \text{ppm}$ giving slope $0.0825 \, \text{ppm}^{-1}$. Concentration in solution $= 0.412 / 0.0825 = 5.00 \, \text{ppm}$. Mass of lead $= 5.00 \, \text{mg/L} \times 0.0250 \, \text{L} = 0.125 \, \text{mg}$. Against the $25 \, \mu\text{g}$ per $100 \, \text{cm}^2$ NHMRC reference, the wipe (from $0.5 \, \text{m}^2$) is six times the threshold.

Example 2. Iron in Yarra Valley winery storage tanks by UV-vis. Winemakers monitor dissolved iron because levels above $5 \, \text{ppm}$ catalyse oxidation that browns chardonnay. A wine sample is buffered to pH $3.5$ and reacted with $1,10$-phenanthroline to form a red $\text{Fe(phen)}_3^{2+}$ complex with maximum absorbance at $510 \, \text{nm}$. With path length $b = 1.00 \, \text{cm}$ and molar absorptivity $\epsilon = 11{,}100 \, \text{L} \cdot \text{mol}^{-1} \cdot \text{cm}^{-1}$, an absorbance of $0.498$ gives $c = A / (\epsilon b) = 0.498 / 11{,}100 = 4.49 \times 10^{-5} \, \text{mol/L}$. Multiplying by $M(\text{Fe}) = 55.8$ converts to $2.50 \, \text{mg/L} = 2.50 \, \text{ppm}$, well within specification.

Try this

Q1. State the wavelength chosen for analysis in UV-vis spectroscopy and explain why this choice gives the most accurate result. [2 marks]

• Cue. The wavelength of maximum absorbance ($\lambda_{max}$). Small wavelength errors give smallest change in absorbance, so the calibration is most sensitive there.

Q2. Four copper standards of $1.00, 2.00, 4.00$ and $6.00 \, \text{ppm}$ give absorbances of $0.085, 0.170, 0.340$ and $0.510$. A sample reads $0.255$. Calculate the copper concentration in the sample. [3 marks]

• Cue. Slope of calibration $\approx 0.0850 \, \text{ppm}^{-1}$; $c = 0.255 / 0.0850 = 3.00 \, \text{ppm}$ of Cu.

Q3. A water sample is analysed by AAS for zinc. The dilution factor is $\times 10$; the cuvette absorbance is $0.220$ on a calibration with slope $0.044 \, \text{ppm}^{-1}$. (a) Calculate cuvette $[\text{Zn}]$. (b) Calculate the original $[\text{Zn}]$. (c) Compare AAS and UV-vis for this analysis. [2+2+2 marks]

• Cue. (a) $5.00 \, \text{ppm}$. (b) $50.0 \, \text{ppm}$. (c) AAS uses element-specific hollow-cathode lamp on atomised sample; very low detection limit for metals; UV-vis needs coloured complex. Zinc is colourless, so AAS preferred.