AP Chemistry Beer-Lambert Law
Finding concentration from absorbance, three full worked examples.
The Beer-Lambert law connects how much light a solution absorbs to its concentration. The formula itself is short; the actual tested skill is using it correctly whether a problem hands you molar absorptivity directly, or expects you to find it first from a calibration curve.
The Beer-Lambert Formula
A = εbc, where A is absorbance (unitless), ε is molar absorptivity (L/(mol·cm)), b is path length (cm, usually 1.00 cm for a standard cuvette), and c is concentration (mol/L). Solved for concentration: c = A / (εb).
Worked Example 1: Finding Concentration From Absorbance
A solution has absorbance A = 0.450 in a 1.00 cm cuvette, at a wavelength where ε = 1500 L/(mol·cm). Find the concentration.
c = A / (εb) = 0.450 / [(1500)(1.00)] = 3.00 × 10−4 M
Worked Example 2: Using a Calibration Curve
Several standard solutions of known concentration were measured, and a plot of absorbance vs. concentration gave a straight line with slope = 850 L/(mol·cm). An unknown sample measured under the same conditions gives A = 0.680. Find its concentration.
Since the calibration curve's slope equals εb directly, c = A / slope = 0.680 / 850 = 8.00 × 10−4 M
Worked Example 3: Finding ε From a Standard
A standard solution with a known concentration of 2.00 × 10−4 M gives A = 0.300 in a 1.00 cm cuvette. Find ε, then use it to find the concentration of an unknown sample that gives A = 0.500 under the same conditions.
ε = A / (bc) = 0.300 / [(1.00)(2.00 × 10−4)] =
1500 L/(mol·cm)
Unknown: c = A / (εb) = 0.500 / [(1500)(1.00)] = 3.33 × 10−4 M
Common Beer-Lambert Mistakes
- Assuming higher absorbance always means higher concentration between different substances. The direct comparison only holds when ε and b are the same; different species absorb light differently even at identical concentrations.
- Forgetting path length isn't always 1.00 cm. A standard cuvette usually is, but always check what the problem actually states, b is part of the formula, not a constant you can skip.
- Mixing up the slope of a calibration curve with ε alone. The slope equals εb combined, not ε by itself, unless b is also known separately and divided out.
- Trusting an absorbance reading outside the linear range. A sample that's too concentrated needs to be diluted first, then the result scaled back up by the dilution factor.
This same absorbance-to-concentration method applies across the rest of AP Chemistry too -- for every other free tool and guide on this site, start from the AP Chem Score Calculator.
Related Resources
- AP Chem Score Calculator
- Unit 3 Review: Properties of Substances and Mixtures
- AP Chemistry Dilution Calculations
- AP Chemistry Ideal Gas Law
- AP Chemistry Study Guide
Frequently Asked Questions
What is the Beer-Lambert law?
A = εbc, relating a solution's absorbance (A) to its molar absorptivity (ε), the path length light travels through it (b), and its concentration (c). When ε and b are held constant, absorbance is directly proportional to concentration.
How do you find an unknown concentration from absorbance?
Rearrange the law to c = A / (εb). If ε and b are both known, plug in the measured absorbance directly. If ε isn't given, it's usually found first from a calibration curve or a standard solution of known concentration.
What is a calibration curve, and how does it relate to Beer-Lambert?
A plot of absorbance versus concentration for several standard solutions of known concentration. Because A = εbc is linear, the plot's slope equals εb. Once you have that slope, measuring an unknown sample's absorbance and solving for its concentration is a single division.
Does AP Chemistry require memorizing molar absorptivity values?
No. Any ε value needed is given in the problem, or has to be calculated first from a standard solution's known concentration and measured absorbance. The tested skill is applying the relationship correctly, not recalling a specific substance's ε.
What happens if an absorbance reading is too high to trust?
The Beer-Lambert law is only reliably linear over a limited absorbance range; a reading that's too high (the solution is too concentrated) falls outside that range. The standard fix is diluting the sample by a known factor, measuring again, then multiplying the result back up by that same dilution factor.
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