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Beer-Lambert Law

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The Beer-Lambert law, A = εbc, says a solution's absorbance is proportional to its concentration (c), its path length (b), and a constant (ε). Because absorbance rises linearly with concentration, a calibration curve — absorbance measured for known concentrations — lets you find the concentration of an unknown from its absorbance.

UNIT 3 TOPIC 3.13 • BEER-LAMBERT LAW CUVETTE LAB Light passes through a solution in a cuvette — more absorbance means less light gets through. LIGHT THROUGH A CUVETTE DILUTE SOLUTION (LOW CONCENTRATION) MORE LIGHT TRANSMITTED DETECTOR SHORT PATH b = 1.00 cm LOW ABSORBANCE (HIGH TRANSMITTANCE) CONCENTRATED SOLUTION (HIGH CONCENTRATION) LESS LIGHT TRANSMITTED DETECTOR SHORT PATH b = 1.00 cm HIGH ABSORBANCE (LOW TRANSMITTANCE) BEER–LAMBERT LAW A = εbc A = absorbance (unitless) ε = molar absorptivity (L·mol⁻¹·cm⁻¹) b = path length (cm) c = concentration (mol·L⁻¹) INCREASING CONCENTRATION OR PATH LENGTH INCREASE CONCENTRATION (c) DECREASES TRANSMITTED LIGHT (I) INCREASES ABSORBANCE (A) low A high A OR INCREASE PATH LENGTH (b) DECREASES TRANSMITTED LIGHT (I) INCREASES ABSORBANCE (A) low A high A CALIBRATION: A vs c A 0 c (mol·L⁻¹) A c calibration standards unknown sample Read A → get c off the line. KEY TAKEAWAY A is directly proportional to c and b · more c or longer b → more absorbance CED SAP-8.C AP Chemistry · Unit 3 · Properties of Substances & Mixtures
The Beer-Lambert law: A = εbc. Absorbance rises in direct proportion to concentration (and path length), so a more concentrated solution transmits less light. A calibration curve of absorbance versus known concentrations lets you read off an unknown's concentration.
Cuvette Lab · Open the sandbox →

The errors are about the linearity and the calibration: assuming transmitted light (rather than absorbance) is linear in concentration, or misusing the calibration curve. Absorbance, not transmittance, is the quantity that scales directly with concentration.

The work

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Lesson
Beer-Lambert Law ›

A = εbc makes absorbance linear in concentration, the basis of calibration curves. The lesson reads a calibration line to find an unknown, then closes with a ten-scenario check.

Skill check · 10 scenarios
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Diagnostic
10-item topic check ›

Ten items spanning the Topic 3.13 misconceptions: absorbance linearity misread (transmittance vs absorbance), and calibration-curve practice errors.

Not started · 10 items · ~15 min
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Targeted Practice
Drill a single misconception ›

Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears the misconception and moves you to the next.

Take the diagnostic to identify your misconceptions
Diagnostic first