Topic 3.13: Beer-Lambert Law Quiz

These revision notes cover everything you need for AP Chemistry Topic 3.13: Beer-Lambert Law. Read through the key ideas below, then test yourself with the 18-question quiz.

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Beer-Lambert Law Quiz

18 MCQs

Master the Beer-Lambert law with these 18 MCQs on AP Chemistry Topic 3.13: Beer-Lambert Law.

Covered Subtopics: Transmittance and absorbance, Beer-Lambert law, Calibration curves, Deviations from linearity

1 / 18

1. A calibration curve of absorbance vs. concentration has a small positive y-intercept instead of passing through the origin. The most likely cause is

the use of too short a path length

measuring at λ_max instead of another wavelength

proof that the Beer-Lambert law is quadratic, not linear

a systematic error, such as an improperly blanked instrument or a contaminated blank

The correct answer is "a systematic error, such as an improperly blanked instrument or a contaminated blank". The law predicts zero absorbance at zero concentration, so a nonzero intercept signals a background offset.

The correct answer is "a systematic error, such as an improperly blanked instrument or a contaminated blank". The law predicts zero absorbance at zero concentration, so a nonzero intercept signals a background offset.

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2. A solution has a transmittance of 32% (T = 0.32). Its concentration is doubled at constant path length. What is the approximate transmittance of the more concentrated solution?

0.32%, because transmittance is unaffected by concentration

10%

16%

64%

The correct answer is "10%". A = −log(0.32) ≈ 0.50; doubling concentration doubles A to 1.00, so T = 10⁻¹ = 0.10, or 10%.

The correct answer is "10%". A = −log(0.32) ≈ 0.50; doubling concentration doubles A to 1.00, so T = 10⁻¹ = 0.10, or 10%.

3 / 18

3. The absorbance of a solution is 0.70. Which statement about its transmittance is correct?

The transmittance is 0.70%.

The transmittance is 70%.

The transmittance cannot be determined from the absorbance.

The transmittance is 10^(−0.70), which is about 20%.

The correct answer is "The transmittance is 10^(−0.70), which is about 20%". From A = −log T, T = 10^(−0.70) ≈ 0.20.

The correct answer is "The transmittance is 10^(−0.70), which is about 20%". From A = −log T, T = 10^(−0.70) ≈ 0.20.

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4. Which statement best explains why absorbance, rather than transmittance, is plotted against concentration in a calibration curve?

Absorbance is directly proportional to concentration (A = εlc), while transmittance decreases exponentially with concentration.

Transmittance is directly proportional to concentration, but the instruments can only measure absorbance.

Transmittance values are always greater than 1, which cannot be plotted.

Absorbance and transmittance are identical quantities, so either one gives a straight line.

The correct answer is "Absorbance is directly proportional to concentration (A = εlc), while transmittance decreases exponentially with concentration". Only the linear quantity gives a straight-line calibration curve.

The correct answer is "Absorbance is directly proportional to concentration (A = εlc), while transmittance decreases exponentially with concentration". Only the linear quantity gives a straight-line calibration curve.

5 / 18

5. For the most accurate Beer-Lambert law measurements, absorbance is typically measured at the wavelength where the substance absorbs most strongly (λ_max) because

the path length is longest at λ_max

transmittance equals absorbance at λ_max

the molar absorptivity is largest there, giving the greatest sensitivity to concentration changes

the Beer-Lambert law only holds at λ_max

The correct answer is "the molar absorptivity is largest there, giving the greatest sensitivity to concentration changes". At λ_max, ε peaks, so small concentration changes produce the largest absorbance changes.

The correct answer is "the molar absorptivity is largest there, giving the greatest sensitivity to concentration changes". At λ_max, ε peaks, so small concentration changes produce the largest absorbance changes.

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6. Transmittance (T) is defined as

the logarithm of the concentration of the solution

the fraction of incident light that passes through the sample

the amount of light absorbed per centimeter of path length

the constant ε in the Beer-Lambert law

The correct answer is "the fraction of incident light that passes through the sample". Transmittance T = I/I₀ is the transmitted intensity over the incident intensity.

The correct answer is "the fraction of incident light that passes through the sample". Transmittance T = I/I₀ is the transmitted intensity over the incident intensity.

7 / 18

7. In the equation A = εlc, the symbol ε (molar absorptivity) represents

the path length of the sample container in centimeters

the concentration of the solution in mol/L

a constant that indicates how strongly a substance absorbs light at a given wavelength

the percentage of light transmitted through the sample

The correct answer is "a constant that indicates how strongly a substance absorbs light at a given wavelength". Molar absorptivity is characteristic of each substance at each wavelength, with units M⁻¹cm⁻¹.

The correct answer is "a constant that indicates how strongly a substance absorbs light at a given wavelength". Molar absorptivity is characteristic of each substance at each wavelength, with units M⁻¹cm⁻¹.

8 / 18

8. When preparing a calibration curve, why is the absorbance of a blank (solvent with no absorbing substance) measured and set to zero?

To convert transmittance readings into concentration units

To correct for light absorbed or scattered by the solvent and cuvette, so the absorbance reflects only the analyte

To double the path length of the measurement

To determine the molar absorptivity of the solvent

The correct answer is "To correct for light absorbed or scattered by the solvent and cuvette, so the absorbance reflects only the analyte". Zeroing on the blank subtracts background absorption from every reading.

The correct answer is "To correct for light absorbed or scattered by the solvent and cuvette, so the absorbance reflects only the analyte". Zeroing on the blank subtracts background absorption from every reading.

9 / 18

9. Which of the following best explains, at the particle level, why absorbance increases with concentration?

The photons slow down as concentration increases, giving them more time to be absorbed.

Each dissolved absorbing particle independently intercepts a fraction of the photons, so more particles per unit volume absorb more light.

Higher concentration increases the speed of light through the solution, raising the energy absorbed.

The molar absorptivity of each particle increases as particles get closer together.

The correct answer is "Each dissolved absorbing particle independently intercepts a fraction of the photons, so more particles per unit volume absorb more light". This independent interception is the physical basis of the linear Beer-Lambert law.

The correct answer is "Each dissolved absorbing particle independently intercepts a fraction of the photons, so more particles per unit volume absorb more light". This independent interception is the physical basis of the linear Beer-Lambert law.

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10. A student plots measured data and finds that absorbance vs. concentration curves upward (deviates from linearity) at high concentrations. Which is the most likely explanation?

At high concentrations, solute particles interact or the detector receives too little light, so the linear relationship breaks down.

The path length increased during the measurement.

The molar absorptivity becomes exactly zero at high concentration.

The Beer-Lambert law has been disproven by this experiment.

The correct answer is "At high concentrations, solute particles interact or the detector receives too little light, so the linear relationship breaks down". These effects violate the law's assumptions, so samples must be diluted into the linear range.

The correct answer is "At high concentrations, solute particles interact or the detector receives too little light, so the linear relationship breaks down". These effects violate the law's assumptions, so samples must be diluted into the linear range.

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11. Two solutions of the same substance are measured in different cuvettes at the same wavelength. Solution X in a 1.00 cm cuvette has A = 0.60. Solution Y in a 0.50 cm cuvette has A = 0.60. What can be concluded?

Solution Y is twice as concentrated as solution X.

Solution X is twice as concentrated as solution Y.

No conclusion is possible without knowing the molar absorptivity.

The two solutions have the same concentration.

The correct answer is "Solution Y is twice as concentrated as solution X". With equal A and ε, (1.00)c_X = (0.50)c_Y, so c_Y = 2c_X.

The correct answer is "Solution Y is twice as concentrated as solution X". With equal A and ε, (1.00)c_X = (0.50)c_Y, so c_Y = 2c_X.

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12. Three standard solutions give: Concentration (M): 0.10, 0.20, 0.30; Absorbance: 0.25, 0.50, 0.75. An unknown has absorbance 0.40 under identical conditions. What is its concentration?

0.16 M

0.40 M

0.10 M

0.25 M

The correct answer is "0.16 M". The standards show A = 2.5c, so c = 0.40 / 2.5 = 0.16 M.

The correct answer is "0.16 M". The standards show A = 2.5c, so c = 0.40 / 2.5 = 0.16 M.

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13. A student measures a calibration curve and finds it is a straight line that passes through (or very near) the origin. The best interpretation is that

the molar absorptivity changes with concentration

transmittance was plotted instead of absorbance

the instrument is broken, because real data never pass through the origin

the measurements obey the Beer-Lambert law, with zero absorbance at zero concentration as expected

The correct answer is "the measurements obey the Beer-Lambert law, with zero absorbance at zero concentration as expected". A = εlc predicts A = 0 at c = 0, so this straight line confirms the law holds.

The correct answer is "the measurements obey the Beer-Lambert law, with zero absorbance at zero concentration as expected". A = εlc predicts A = 0 at c = 0, so this straight line confirms the law holds.

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14. A solution's concentration is tripled while the path length and wavelength are kept constant. What happens to the absorbance?

It increases by a factor of 9.

It triples.

It stays the same because molar absorptivity adjusts.

It is reduced to one third.

The correct answer is "It triples". With ε and l fixed, A = εlc is directly proportional to c, so tripling concentration triples absorbance.

The correct answer is "It triples". With ε and l fixed, A = εlc is directly proportional to c, so tripling concentration triples absorbance.

15 / 18

15. The Beer-Lambert law, A = εlc, states that absorbance is

inversely proportional to concentration and path length

independent of the identity of the absorbing substance

directly proportional to concentration and path length

directly proportional to transmittance

The correct answer is "directly proportional to concentration and path length". In A = εlc, with ε fixed for the substance and wavelength, absorbance scales linearly with both c and l.

The correct answer is "directly proportional to concentration and path length". In A = εlc, with ε fixed for the substance and wavelength, absorbance scales linearly with both c and l.

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16. A calibration curve for Beer-Lambert law analysis is a plot of

transmittance vs. concentration, which gives a straight line through the origin

absorbance vs. concentration, which gives a straight line

absorbance vs. path length, which gives a curved line

concentration vs. molar absorptivity, which gives a straight line

The correct answer is "absorbance vs. concentration, which gives a straight line". Since A = εlc is linear in c, plotting standards this way yields a straight calibration line.

The correct answer is "absorbance vs. concentration, which gives a straight line". Since A = εlc is linear in c, plotting standards this way yields a straight calibration line.

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17. A solution has an absorbance of 0.40 in a 1.00 cm cuvette. If the same solution is transferred to a 2.00 cm cuvette, what is the new absorbance?

0.40

0.80

1.60

0.20

The correct answer is "0.80". Absorbance is directly proportional to path length, so doubling the cuvette from 1.00 cm to 2.00 cm doubles the absorbance: 2 × 0.40 = 0.80.

The correct answer is "0.80". Absorbance is directly proportional to path length, so doubling the cuvette from 1.00 cm to 2.00 cm doubles the absorbance: 2 × 0.40 = 0.80.

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18. If the concentration of an absorbing solution is doubled and the path length is halved, what happens to the absorbance?

It doubles.

It is halved.

It increases fourfold.

It stays the same.

The correct answer is "It stays the same". Absorbance depends on the product l × c, and (2c)(l/2) = cl, so the two changes cancel exactly.

The correct answer is "It stays the same". Absorbance depends on the product l × c, and (2c)(l/2) = cl, so the two changes cancel exactly.

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Transmittance and Absorbance

A spectrophotometer shines light of one selected wavelength through a sample and compares the intensity reaching the detector with the intensity that entered. Transmittance is the fraction that gets through: T = I/I₀, a number between 0 and 1, often reported as percent transmittance, %T = 100 × I/I₀.

Absorbance is defined from transmittance by A = −log T. A sample that transmits 10% of the light has T = 0.10 and A = 1.00. A sample that transmits 1% has A = 2.00. Each absorbance unit corresponds to a tenfold drop in transmitted light, and absorbance has no units.

These two quantities behave differently, and the difference runs the whole topic. Absorbance is directly proportional to concentration and path length. Transmittance is not proportional to anything; it falls exponentially as concentration rises.

The Beer-Lambert Law

A = εlc

Absorbance equals molar absorptivity times path length times concentration. The path length l is the width of the cuvette the light passes through, in centimetres, usually 1.00 cm. The concentration c is in mol/L. The molar absorptivity ε, in L mol⁻¹ cm⁻¹, is a constant for a given substance at a given wavelength: it measures how strongly that substance absorbs at that wavelength.

Because ε and l are fixed in any one experiment, absorbance tracks concentration exactly. Double the concentration and the absorbance doubles. Double the path length and the absorbance also doubles. Triple the concentration and absorbance triples. This proportionality is what makes absorbance a measuring tool rather than just an observation.

Absorbance also explains itself at the particle level. Doubling the concentration doubles the number of absorbing particles in the light path, so twice as many photons are captured in each segment of the journey, and the absorbance rises in step.

Calibration Curves

An unknown concentration is found from a calibration curve: a plot of absorbance against concentration for a series of standard solutions of known concentration, all measured at the same wavelength in the same cuvette. The plot is a straight line through the origin, and its slope equals εl. Measuring the unknown’s absorbance and reading across to the line gives its concentration.

Two features make the measurement trustworthy. First, absorbance is measured at λ_max, the wavelength where the substance absorbs most strongly, because there a given concentration produces the largest signal and small concentration changes produce the largest absorbance changes. Second, the cuvette is first filled with a blank, the solvent with no absorbing substance, and the instrument is zeroed on it, so the absorbance recorded afterward belongs to the solute alone, not to the solvent or the cuvette walls.

A calibration line that misses the origin slightly, with a small positive intercept, points to a blank problem: something in the solvent, cuvette, or instrument offset is absorbing a little light before any solute is added.

Worked Examples

Example 1: absorbance and percent transmittance

A solution of concentration 2.0 × 10⁻⁴ M is measured in a 1.00 cm cuvette at a wavelength where ε = 1.20 × 10³ L mol⁻¹ cm⁻¹. Find the absorbance and the percent transmittance.

A = εlc = (1.20 × 10³)(1.00)(2.0 × 10⁻⁴) = 0.240.

T = 10^(−A) = 10^(−0.240) = 0.575, so %T = 57.5%.

Example 2: unknown from a calibration curve

Standards of a substance give A = 0.30 at 0.050 M and A = 0.60 at 0.100 M, measured at l = 1.00 cm. An unknown of the same substance gives A = 0.45. Find its concentration and the value of ε.

Slope = 0.60 / 0.100 = 6.0 L/mol. Concentration = A / slope = 0.45 / 6.0 = 0.075 M.

Since slope = εl and l = 1.00 cm, ε = 6.0 L mol⁻¹ cm⁻¹.

Traps Specific to This Topic

Transmittance does not halve when concentration doubles. A solution with A = 0.70 has T = 0.20; doubling its concentration gives A = 1.40 and T = 0.040. Absorbance doubled, but transmittance fell to one fifth, not one half. Any answer that scales T linearly is wrong.

If two solutions of the same substance show equal absorbance in different cuvettes, their concentrations are not equal. The solution in the shorter cuvette must be more concentrated to make up for the shorter path.

At high concentrations the calibration curve bends and Beer’s law fails, because absorbing particles are crowded close enough to interact with each other and with neighbours’ charges, changing how each one absorbs. Dilute the sample into the linear range instead of extrapolating the line.

Combining changes multiplies through A = εlc. Doubling concentration while halving path length leaves absorbance unchanged, because the two factors cancel. Work each factor separately rather than guessing the combined effect.