Beer-Lambert Law Practice Problems

Solve for A: ε = 5,000 L·mol⁻¹·cm⁻¹, l = 1 cm, c = 3.0 × 10⁻⁴ M.

Solve for c: A = 0.42, ε = 8,400 L·mol⁻¹·cm⁻¹, l = 1 cm.

Solve for ε: A = 0.75, l = 1 cm, c = 2.5 × 10⁻⁴ M.

Solve for l: A = 0.96, ε = 12,000 L·mol⁻¹·cm⁻¹, c = 4.0 × 10⁻⁵ M.

Transmittance conversion: If transmittance T = 25%, what is the absorbance?

If A = 1.5, what percentage of light is transmitted?

A stock solution with c = 0.01 M is diluted 1:100. If ε = 25,000 L·mol⁻¹·cm⁻¹ and l = 1 cm, what absorbance do you expect?

A solution of unknown concentration gives A = 0.68 at 540 nm in a 1 cm cell. The molar absorptivity at 540 nm is 34,000 L·mol⁻¹·cm⁻¹. (a) What is the concentration? (b) If you need to dilute to get A = 0.20, what dilution factor is needed?

A solution has T = 45%. Calculate its absorbance, then find the concentration if ε = 6,300 L·mol⁻¹·cm⁻¹ and l = 1 cm.

Two cuvettes are available: 0.5 cm and 2.0 cm. A dye has ε = 22,000 L·mol⁻¹·cm⁻¹ at 490 nm. For a 1.5 × 10⁻⁵ M solution, which cuvette gives an absorbance closest to 0.5?

A calibration curve for compound X in a 1 cm cell gives a linear fit with slope = 12,500 AU·L·mol⁻¹. An unknown reads A = 0.38. (a) What is the concentration? (b) What is ε?

You need a solution that gives A = 0.60 at 280 nm for BSA protein (ε = 43,824 L·mol⁻¹·cm⁻¹, MW = 66,463 g/mol) in a 1 cm cuvette. What molar concentration and mass concentration (mg/mL) do you need?

A forensic lab measures A = 1.20 at 550 nm for a sample in a 1 cm cell. After a 1:5 dilution, A = 0.24. Does this sample obey Beer's law? Explain your reasoning.

An environmental lab needs to detect lead at 10 ppb (μg/L) using a reagent that forms a 1:1 complex with ε = 85,000 L·mol⁻¹·cm⁻¹ at 520 nm (MW of Pb = 207.2 g/mol). What absorbance would a 10 cm cell give?

A solution shows %T = 63.1% at 520 nm in a 1 cm cell. If ε = 4,200 L·mol⁻¹·cm⁻¹, what is the concentration?

You mix 25 mL of a 4.0 × 10⁻⁴ M dye solution with 75 mL of water. If ε = 8,500 L·mol⁻¹·cm⁻¹ at 490 nm, what absorbance do you expect in a 1 cm cuvette?

A protein solution gives A₂₈₀ = 0.45 in a 1 cm cuvette. The protein has ε₂₈₀ = 29,400 L·mol⁻¹·cm⁻¹ and MW = 25,000 g/mol. Find (a) the molar concentration and (b) the mass concentration in mg/mL.

A solution contains two dyes, P and Q, in a 1 cm cell. At 420 nm: ε_P = 12,000, ε_Q = 3,000. At 560 nm: ε_P = 1,500, ε_Q = 10,000. Measured: A₄₂₀ = 0.570, A₅₆₀ = 0.360. Find c_P and c_Q.