What is not zeroing on a matrix-matched blank?

If your sample is in acid, your blank should be the same acid. Water-only blanks under-correct.

A calibration curve gives the equation A = 0.180 × c where c is in mg L^-1. A sample reads 0.072 absorbance. Calculate the concentration.

§-Syllabus dot point

NSWChemistrySyllabus dot point

Inquiry Question 1: How are the ions present in the environment identified and measured?

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

A focused answer to the HSC Chemistry Module 8 dot point on instrumental concentration measurement. The Beer-Lambert law, building and using a calibration curve, when to choose colourimetry vs UV-vis vs AAS, how AAS uses a hollow-cathode lamp to reach part-per-billion detection of metals, and worked HSC past exam questions.

Generated by Claude Opus 4.811 min answerUpdated 2026-06-22

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking
The answer
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In plain English

Think of measuring a coloured or metal-laced solution like judging how strong a cup of tea is just by how much light gets through it. A weak, pale cup lets most of the light straight through; a strong, dark cup blocks a lot of it. Beer-Lambert's law is just the maths version of that everyday observation: the darker (more concentrated) the solution, the more light it absorbs, and that relationship is a straight line as long as the tea is not so strong that the cup looks almost black (that is where the linear rule breaks down). Colourimetry is the simplest version of this idea, using a coloured filter like squinting through a coloured pair of sunglasses. UV-vis is a more precise version that can also see into the invisible ultraviolet, like a camera with an extra colour channel your eyes cannot detect. AAS is a completely different trick for finding tiny traces of a single metal: it uses a lamp built from that exact metal, so it only "sees" that metal's own colour, the way a key only turns its own matching lock, letting it spot amounts a billion times smaller than a cup of tea.

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:

A = \varepsilon \, c \, l

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

Prepare standards by serial dilution of a stock solution of the target species. Use at least five standards bracketing the expected concentration range.
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).
Zero the instrument on a blank (distilled water or solvent) to subtract the cell and solvent contribution.
Measure absorbance of each standard.
Plot $A$ vs $c$ and fit a line. Slope is $\varepsilon \cdot l$ .
Measure the unknown and read its concentration from the line, or solve $c = A / (\varepsilon l)$ .

The Beer-Lambert equation and calibration checkpoints

Beer-Lambert law: $A = \varepsilon \, c \, l$ , where $A$ = absorbance (no unit), $\varepsilon$ = molar absorptivity (L mol $^{-1}$ cm $^{-1}$ ), $c$ = concentration (mol L $^{-1}$ ), $l$ = path length (cm, usually 1.00 cm).
Absorbance definition: $A = \log_{10}(I_0 / I)$ , comparing incident intensity $I_0$ to transmitted intensity $I$ .
Linear range: the law holds only while $A$ is below about 2; a calibration line is a straight line through (or very near) the origin over this range.
Slope of the calibration line equals $\varepsilon \cdot l$ ; you can read an unknown's concentration straight off the graph, or solve $c = A / (\varepsilon l)$ .
Always zero on a matrix-matched blank (same solvent, acid strength and reagents as the samples, minus the analyte) before measuring any standard.

An owned illustrative calibration curve, built exactly the way the six-step procedure above describes, shows how the unknown's concentration is read off a straight Beer-Lambert line:

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:

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.
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.
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.

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

Question	Use
Solution is already coloured, ppm-level, need a quick number	Colourimetry
Need to use UV, or higher accuracy on a coloured complex	UV-vis
Target is a metal in the ppb range	AAS
Need to distinguish many metals at once at ppb	ICP-MS (beyond HSC scope)

Common reagents to colour the colourless

Target	Reagent	Coloured product	Wavelength
$PO_4^{3-}$	Molybdate, ascorbic acid	Molybdenum blue	880 nm
$Fe^{3+}$	KSCN	$[FeSCN]^{2+}$ red	480 nm
$NO_3^-$	Diazotising reagent	Pink azo dye	540 nm
$NH_4^+$	Nessler's reagent	Yellow $HgI_2 \cdot NH_3$ complex	425 nm

Calibration and detection-limit worked examples

Worked example 1: reading an unknown off a calibration line.

Standards of aqueous $Cu^{2+}$ at 600 nm give the line $A = 15.0 \, c$ (from Step 1 of the six-step method above).
An unknown reads $A = 0.78$ .
Rearranging: $c = A / 15.0 = 0.78 / 15.0 = 0.052\ \text{mol L}^{-1}$ .

Marker's note: always state the equation of the line (or show the graphical read-off) before quoting the final concentration; a bare numeric answer with no working loses the method mark even if correct.

Worked example 2: choosing between colourimetry, UV-vis and AAS by detection limit.

A stormwater sample must be checked for lead at a limit of 5 $\mu$ g L $^{-1}$ (5 ppb).
Colourimetry's detection limit (about 500 ppb) and UV-vis's (about 10 to 100 ppb) both sit above the 5 ppb target, so neither can reliably resolve compliance.
Flame AAS (1 to 10 ppb) is borderline; graphite furnace AAS (about 0.1 ppb) comfortably resolves the target with margin to spare.
Conclusion: graphite furnace AAS is the appropriate technique.

Marker's note: a full-mark comparison names at least approximate detection limits for all three techniques and explicitly checks each against the stated regulatory limit, rather than just ranking them qualitatively as "AAS is more sensitive".

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.

Exam-style practice questions

Practice questions written in the style of NESA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

2021 HSC5 marksA series of standard

Cu^{2+}

solutions gave the following absorbances at 600 nm in a 1.00 cm cell: 0.020 mol/L gave 0.30; 0.040 mol/L gave 0.61; 0.060 mol/L gave 0.92; 0.080 mol/L gave 1.21; 0.100 mol/L gave 1.50. An unknown gave an absorbance of 0.78. Determine the unknown concentration and the molar absorptivity of

Cu^{2+}

at 600 nm. State one assumption inherent in the calculation.

Show worked answer →

A 5 mark answer needs a calibration line, the unknown read off (or interpolated), the molar absorptivity from Beer-Lambert and one explicit assumption.

Step 1: Show linearity: The standards give a near-straight line. Slope from end points: $(1.50 - 0.30)/(0.100 - 0.020) = 1.20/0.080 = 15.0$ L/mol per cm. Intercept is essentially zero, so $A = 15.0 c$ .
Step 2: Find the unknown concentration: $c = A / \text{slope} = 0.78 / 15.0 = 0.052$ mol/L.
Step 3: Molar absorptivity: Beer-Lambert: $A = \varepsilon c l$ . With $l = 1.00$ cm and slope $\varepsilon \cdot l = 15.0$ , we have $\varepsilon = 15.0$ L mol $^{-1}$ cm $^{-1}$ .
Assumption: The Beer-Lambert relationship is linear only at sufficiently low concentrations. Beyond about $A = 2$ the linearity breaks because stray light and refractive-index effects matter. The unknown's absorbance of 0.78 falls comfortably in the linear range, so the assumption holds. Other valid assumptions: monochromatic light, no chemical equilibrium shift with concentration, no scattering from particulates, matrix-matched standards.

Markers reward (1) the calibration line or equation, (2) correct interpolated concentration, (3) correct $\varepsilon$ with units, (4) a stated assumption justified.

2019 HSC4 marksCompare colourimetry, UV-visible spectrophotometry and atomic absorption spectroscopy in terms of the species each is best suited to measure and the typical detection limits achievable.

Show worked answer →

A 4 mark answer needs a clear comparison across at least two of the named dimensions for all three techniques.

Colourimetry uses a coloured filter to select a band of visible light. It is the cheapest and simplest technique and works on any solution with a visible colour (or one made coloured by a complexation reagent, for example $Fe^{3+}$ with thiocyanate, or phosphate with molybdate). Typical detection limits are around 0.5 ppm. Suited to field testing and education.

UV-visible spectrophotometry uses a monochromator to select a narrow wavelength in the 200 to 800 nm range and a more sensitive detector. It covers UV (proteins, DNA, conjugated organics absorbing below 400 nm) as well as visible (coloured complexes). Detection limits are around 0.01 to 0.1 ppm. Suited to laboratory analysis of inorganic complexes and organic chromophores.

Atomic absorption spectroscopy (AAS) atomises the sample in a flame or graphite furnace and uses a hollow-cathode lamp emitting the line spectrum of the target element. Only that element absorbs the lamp's specific wavelengths. Detection limits are 1 to 10 ppb for most metals (flame), and 0.1 ppb (furnace). Suited to trace metal analysis in environmental and biological samples.

Markers reward (1) at least one named target per technique, (2) the order-of-magnitude detection limit per technique, (3) a clear hierarchy from colourimetry to AAS in sensitivity.

Practice questions

Original practice questions graded from foundation to exam level, each with a full worked solution. Try them before revealing the solution.

foundation2 marksState the Beer-Lambert law in symbols and name each variable, including its unit.

Show worked solution →

A = \varepsilon \, c \, l

$A$ = absorbance (no unit), $\varepsilon$ = molar absorptivity (L mol $^{-1}$ cm $^{-1}$ ), $c$ = concentration (mol L $^{-1}$ ), $l$ = path length (cm).

Marking criteria: 1 mark for the correct equation, 1 mark for correctly naming all three variables with units.

foundation3 marksA colourimetric calibration curve for

Fe^{3+}

(as the red

[FeSCN]^{2+}

complex) gives the line

A = 42.0 \times c

, where

c

is in mol L

^{-1}

. An unknown reads an absorbance of 0.294 in a 1.00 cm cell. Calculate the unknown concentration to 3 significant figures.

Show worked solution →

Step 1: rearrange for $c$ .

c = \frac{A}{42.0}

Step 2: substitute.

c = \frac{0.294}{42.0} = 0.0070000\ \text{mol L}^{-1}

Step 3: round to 3 significant figures (matching the 3 s.f. of the absorbance data).

c = 7.00 \times 10^{-3}\ \text{mol L}^{-1}

Marking criteria: 1 mark for correct rearrangement, 1 mark for correct substitution and arithmetic, 1 mark for the answer to 3 significant figures with correct units.

core6 marksA calibration series for

Cu^{2+}

was measured at 600 nm in a 1.00 cm cell: 0.0200 mol L

^{-1}

gave

A = 0.302

; 0.0400 mol L

^{-1}

gave

A = 0.610

; 0.0600 mol L

^{-1}

gave

A = 0.905

; 0.0800 mol L

^{-1}

gave

A = 1.203

. (a) Calculate the mean molar absorptivity

\varepsilon

from the four standards, to 3 significant figures. (b) An unknown gives

A = 0.750

. Calculate its concentration to 3 significant figures. (c) State one reason the four calculated

\varepsilon

values might not be identical.

Show worked solution →

(a) Molar absorptivity from each standard, using $\varepsilon = A / (c \, l)$ with $l = 1.00$ cm:

\varepsilon_1 = \frac{0.302}{0.0200} = 15.10\ \text{L mol}^{-1}\text{cm}^{-1}

\varepsilon_2 = \frac{0.610}{0.0400} = 15.25\ \text{L mol}^{-1}\text{cm}^{-1}

\varepsilon_3 = \frac{0.905}{0.0600} = 15.083\ \text{L mol}^{-1}\text{cm}^{-1}

\varepsilon_4 = \frac{1.203}{0.0800} = 15.0375\ \text{L mol}^{-1}\text{cm}^{-1}

Mean:

\varepsilon_{\text{mean}} = \frac{15.10 + 15.25 + 15.083 + 15.0375}{4} = \frac{60.47}{4} = 15.1175\ \text{L mol}^{-1}\text{cm}^{-1}

Rounded to 3 significant figures: $\varepsilon = 15.1\ \text{L mol}^{-1}\text{cm}^{-1}$ .

(b) Unknown concentration.

c = \frac{A}{\varepsilon \, l} = \frac{0.750}{15.1 \times 1.00} = 0.049669...\ \text{mol L}^{-1}

Rounded to 3 significant figures: $c = 0.0497\ \text{mol L}^{-1}$ .

(c) Reason for slight variation. Small random measurement/pipetting errors in preparing each standard, or minor instrument noise in each absorbance reading, mean the four individual $\varepsilon$ values scatter slightly around the true value rather than being identical; averaging (or using the line of best fit slope) reduces this random error.

Marking criteria: (a) 1 mark per correctly calculated $\varepsilon_i$ (max 3), 1 mark for the correctly averaged and rounded mean. (b) 1 mark for correct rearrangement and substitution, 1 mark for the correct answer to 3 significant figures with units. (c) 1 mark for a valid source of random error correctly linked to the scatter in $\varepsilon$ .

core5 marksThe calibration graph below is an owned illustrative Beer-Lambert plot of absorbance versus concentration for a series of

Cu^{2+}

standards measured at 600 nm, with an unknown sample marked on the axis. (a) Describe the shape of the graph and state what it confirms about the Beer-Lambert law over this concentration range. (b) Use the graph to estimate the unknown's concentration and justify your reading.

Show worked solution →

(a) Shape. The plotted points lie on a straight line passing through (or very close to) the origin, rising with a constant positive slope across the standard concentrations shown. This confirms the Beer-Lambert law holds linearly over this concentration range (all points fall below $A \approx 1.5$ , well inside the linear regime), i.e. absorbance is directly proportional to concentration at this wavelength and path length.

(b) Reading the unknown. The unknown's absorbance is marked as a horizontal dashed line meeting the calibration line at approximately $c \approx 0.052$ mol L $^{-1}$ on the concentration axis (found by drawing across from the unknown's absorbance to the line, then down to the c-axis). This is valid only because the unknown's absorbance falls within the linear range spanned by the standards; extrapolating far beyond the highest standard would not be justified.

Marking criteria: (a) 1 mark for describing the straight line through/near the origin, 1 mark for correctly linking this to Beer-Lambert linearity over the range shown. (b) 1 mark for correctly reading the concentration from the graph (allow +/- 0.002 mol L $^{-1}$ tolerance), 1 mark for correctly describing the graphical method (across then down), 1 mark for noting the reading is only valid within the calibrated range.

core4 marksExplain, with reference to instrument design, why AAS achieves lower detection limits for metals than UV-visible spectrophotometry.

Show worked solution →

AAS uses a hollow-cathode lamp that emits an extremely narrow, element-specific line spectrum matched exactly to the target atom's electronic transitions, so essentially all of the measured absorption is due to that one analyte with very little background or spectral overlap from other species. UV-vis measures absorbance of molecular species (or complexes) using a monochromator that selects a wider band from a broadband white-light source, which is inherently less selective and less sensitive than a matched atomic line. In addition, AAS's flame or graphite-furnace atomiser converts the metal into free gaseous ground-state atoms with a sharply defined absorption wavelength, giving a much larger effective molar absorptivity for that specific transition than the broader molecular absorption bands measured in UV-vis.

Marking criteria: 1 mark for identifying the hollow-cathode lamp's element-specific line spectrum, 1 mark for linking this to reduced background/interference, 1 mark for contrasting with UV-vis's broader, less selective molecular absorption, 1 mark for a correct link to sensitivity/detection limit.

exam7 marksA water authority must decide whether to monitor trace cadmium in a stormwater catchment using colourimetry, UV-vis spectrophotometry, or AAS, given a regulatory action limit of 5 microgram per litre (ppb). Evaluate which technique is most appropriate, and justify a complete monitoring plan including calibration.

Show worked solution →

This is a 7-mark EVALUATE: markers reward a clear recommendation backed by quantitative reasoning about detection limits, plus a workable calibration plan.

Band 6 PLAN.

State the three techniques' typical detection limits: colourimetry about 0.5 ppm (500 ppb), UV-vis about 0.01 to 0.1 ppm (10 to 100 ppb), flame AAS about 1 to 10 ppb, graphite furnace AAS about 0.1 ppb.
Compare each against the 5 ppb action limit: colourimetry and UV-vis cannot reliably resolve concentrations this low (their detection limits sit at or above the target itself); flame AAS is borderline (1 to 10 ppb straddles 5 ppb); graphite furnace AAS comfortably resolves 5 ppb with a wide safety margin.
Recommend graphite furnace AAS, justified by its lower detection limit and by cadmium's selectivity requirement (a cadmium-specific hollow-cathode lamp avoids interference from other trace metals in stormwater).
Outline the calibration plan: prepare at least five cadmium standards bracketing 5 ppb (e.g. 0, 2, 5, 10, 20 ppb) in a matrix-matched blank (same acid/ionic background as the stormwater samples), zero the instrument on the blank, measure absorbance of each standard at cadmium's characteristic wavelength (228.8 nm) using the cadmium hollow-cathode lamp, plot the Beer-Lambert calibration line, then measure the unknown stormwater sample and read its concentration from the line (or solve $c = A/(\varepsilon l)$ ), checking the reading falls within the linear range spanned by the standards.
Judgement: graphite furnace AAS is the only one of the three techniques capable of reliably distinguishing concentrations at and below the 5 ppb action limit, so it should be adopted despite its higher cost and slower throughput than flame AAS or colourimetry.

Model paragraph (excerpt). Because the regulatory action limit of 5 ppb sits at or above the detection limits of colourimetry (about 500 ppb) and UV-vis (about 10 to 100 ppb), neither technique can distinguish a compliant sample from a non-compliant one at this concentration, making both unsuitable regardless of cost. Flame AAS, with a detection limit of 1 to 10 ppb, is marginal: a true concentration near 5 ppb could fall below the instrument's reliable quantitation threshold. Graphite furnace AAS, with a detection limit around 0.1 ppb, gives roughly a fifty-fold safety margin below the action limit, so is the only technique that should be used for compliance monitoring; the higher cost is justified by the legal and public-health consequences of a false negative.

Marker's note: top-band answers (1) quote at least approximate detection limits for all three techniques, (2) explicitly compare each to the 5 ppb limit rather than just ranking them qualitatively, (3) describe a complete, workable calibration procedure (standards, matrix-matched blank, correct wavelength/lamp, linear range check), and (4) end with an explicit, justified recommendation rather than a neutral summary.