Beer-Lambert law worksheet with answers for AP Chemistry (free PDF download)

Quick answer: Molarity is moles of solute per litre of solution, and dilution follows M₁V₁ = M₂V₂. This AP Chemistry worksheet on Beer-Lambert law gives 20 problems from easy to hard: molarity of salt solution, mass for a solution and simple dilution. The worked answers are on a separate page, and the worksheet is a free printable PDF.

These problems train molarity and dilution calculations, interpretation of chromatograms and calibration graphs, and use of the Beer-Lambert law. They follow AP Chemistry unit 3 and the quantitative and experimental skills of the free-response section.

The first problems use one step. Later problems combine dilution with spectrophotometry or ask you to design a method. In the last five, explain each choice in sentences and give units throughout.

Level: AP Chemistry · Curriculum: AP Chem Unit 3

Contents

Problem 1 Molarity of salt solution ★★★

Kofi in Accra dissolves 11.7 g of NaCl (58.44 g/mol) and makes the solution up to 500.0 mL. Calculate the molarity.

Problem 2 Mass for a solution ★★★

Calculate the mass of KCl (74.55 g/mol) needed to make 250.0 mL of 0.100 M solution.

Problem 3 Simple dilution ★★★

A 25.0 mL sample of 1.00 M stock is diluted to a total of 250.0 mL. Calculate the new concentration.

Problem 4 Calculate R_f values ★★★

Chromatogram of a food-colouring mixture.

A chromatogram shows three spots X, Y and Z.
1. Read the distance moved by each spot and by the solvent front.
2. Calculate R_f for each spot.
3. State which spot is most strongly held by the stationary phase.

Problem 5 Transmittance and absorbance ★★★

1. Calculate the absorbance of a solution that transmits 50 percent of the light.
2. Calculate the percentage transmittance when A = 1.000.

Problem 6 Choose a separation method ★★★

Name the best method to separate each: (1) sand from salt water, (2) pure water from salt water, (3) the dyes in a black pen ink, (4) ethanol from a water-ethanol mixture.

Problem 7 Ion concentrations ★★★

Calculate the concentration of each ion in (1) 0.30 M CaCl₂ and (2) 0.20 M Al₂(SO₄)₃.

Problem 8 Lead in drinking water ★★★

A 1.50 L sample of tap water in a Nairobi school contains 0.0210 mg of lead.
1. Calculate the concentration in mg/L (ppm).
2. Convert this to µg/L (ppb).

Problem 9 Make a copper sulfate solution ★★★

Describe how you would make 100.0 mL of 0.250 M CuSO₄ from the hydrated solid CuSO₄·5H₂O (249.70 g/mol), and calculate the mass needed.

Problem 10 A dilution series ★★★

Mei in Singapore needs 50.0 mL each of 0.100 M, 0.0500 M, 0.0250 M and 0.0100 M solutions from a 0.500 M stock. Calculate the volume of stock for each.

Problem 11 Find a concentration with Beer-Lambert ★★★

A solution has A = 0.450 at λ_max in a 1.00 cm cuvette. Its molar absorptivity is ε = 9.0 × 10³ L/(mol·cm). Calculate the concentration.

Problem 12 Change the path length ★★★

A solution has A = 0.300 in a 1.00 cm cuvette.
1. Predict A in a 2.00 cm and in a 0.50 cm cuvette.
2. Calculate the percentage transmittance for the 1.00 cm cuvette.

Problem 13 Use a calibration graph ★★★

Calibration line for a blue dye, measured in a 1.00 cm cuvette.

1. A sample of the dye gives A = 0.360. Read its concentration.
2. Calculate the gradient of the line and the molar absorptivity ε.
3. Explain why the line passes through the origin.

Problem 14 Why chromatography separates ★★★

Wanjiru in Nairobi runs a mixture of a polar dye and a nonpolar dye on a silica TLC plate with a nonpolar solvent. Predict which dye has the larger R_f and explain.

Problem 15 Mixing two solutions ★★★

Mix 50.0 mL of 0.200 M NaCl with 150.0 mL of 0.100 M NaCl. Assume the volumes add. Calculate the final concentration.

Problem 16 Volume for a titration-style reaction ★★★

Silver nitrate reacts with chloride: Ag⁺ + Cl⁻ → AgCl. Calculate the volume of 0.150 M AgNO₃ needed to precipitate all the chloride in 25.0 mL of 0.100 M NaCl.

Problem 17 When Beer’s law fails ★★★

Chiamaka in Lagos measures a dye series (1.00 cm cuvette):

c (10⁻⁵ mol/L)	1	2	4	8	16	32
A	0.12	0.24	0.48	0.95	1.80	2.60

1. Calculate A/c for each standard.
2. Identify the range where Beer’s law holds.
3. A sample reads A = 2.30. Explain what to do.

Problem 18 Absorbance from percent transmittance ★★★

A solution transmits 18.0 percent of the light in a 1.00 cm cuvette. Its ε is 1.5 × 10⁴ L/(mol·cm). Calculate its absorbance and concentration.

Problem 19 Diluted sample ★★★

Parts of a spectrophotometer.

A sample of dye is diluted by transferring 10.00 mL to a 100.0 mL flask. The diluted solution gives A = 0.480 in a 1.00 cm cuvette (ε = 1.20 × 10⁴ L/(mol·cm)).
1. Calculate the concentration of the diluted solution.
2. Calculate the concentration of the original sample.
3. Explain the role of the monochromator.

Problem 20 Design a colorimetric analysis ★★★

Diego in Texas wants to find the concentration of copper(II) ions in a blue solution using a spectrophotometer. Design the procedure, state how to choose the wavelength and what graph to plot, and state one source of error.