Chemistry: AP Chemistry: Spectroscopy and Beer-Lambert Law
Using absorbance, concentration, path length, and spectra
Chemistry: AP Chemistry: Spectroscopy and Beer-Lambert Law
Using absorbance, concentration, path length, and spectra
Chemistry - Grade 9-12
- 1
State the Beer-Lambert law and identify what each variable represents.
Absorbance has no units, but the other quantities must combine so the units cancel.
The Beer-Lambert law is A = εbc. A is absorbance, ε is molar absorptivity in L mol^-1 cm^-1, b is path length in cm, and c is concentration in mol/L. - 2
A solution has a molar absorptivity of 1.50 x 10^4 L mol^-1 cm^-1 at 520 nm. If the path length is 1.00 cm and the concentration is 2.00 x 10^-5 M, calculate the absorbance.
Using A = εbc, A = (1.50 x 10^4 L mol^-1 cm^-1)(1.00 cm)(2.00 x 10^-5 mol/L) = 0.300. The absorbance is 0.300. - 3
A sample in a 1.00 cm cuvette has an absorbance of 0.742 at its wavelength of maximum absorbance. The molar absorptivity is 3.71 x 10^3 L mol^-1 cm^-1. Calculate the concentration of the sample.
Solve the Beer-Lambert law for concentration before substituting values.
Rearranging A = εbc gives c = A/(εb). The concentration is c = 0.742/[(3.71 x 10^3 L mol^-1 cm^-1)(1.00 cm)] = 2.00 x 10^-4 M. - 4
A calibration curve for a colored ion gives the equation A = 2450c + 0.012, where c is in mol/L. An unknown solution has an absorbance of 0.502. Calculate the concentration of the unknown.
Substitute the absorbance into the calibration equation: 0.502 = 2450c + 0.012. Then c = (0.502 - 0.012)/2450 = 2.00 x 10^-4 M, so the unknown concentration is 2.00 x 10^-4 M. - 5
Explain why the wavelength of maximum absorbance, λmax, is usually chosen for quantitative spectrophotometric analysis.
Think about the slope of absorbance versus concentration at different wavelengths.
The wavelength of maximum absorbance is chosen because the analyte absorbs most strongly there, giving better sensitivity. Small concentration changes produce larger absorbance changes at λmax. - 6
A solution transmits 25.0 percent of the incident light at a certain wavelength. Calculate its absorbance.
Percent transmittance must be converted to transmittance, so T = 0.250. Absorbance is A = -log(T) = -log(0.250) = 0.602. - 7
Two solutions of the same absorbing species are measured in the same 1.00 cm cuvette at the same wavelength. Solution 1 has concentration 1.20 x 10^-4 M and absorbance 0.360. Solution 2 has concentration 2.40 x 10^-4 M. Predict the absorbance of solution 2.
Compare the concentration ratio of solution 2 to solution 1.
Because absorbance is directly proportional to concentration when ε and b are constant, doubling the concentration doubles the absorbance. The predicted absorbance is 0.720. - 8
A student measures the absorbance of a solution and obtains A = 1.95. Explain why the student might dilute the solution before making a final concentration determination.
An absorbance of 1.95 is relatively high and may be outside the most reliable linear range of the instrument. Diluting the solution can bring the absorbance into a range where the Beer-Lambert law and the calibration curve are more dependable. - 9
A 10.00 mL sample of an unknown solution is diluted to 50.00 mL. The diluted solution has a concentration of 3.60 x 10^-5 M based on spectrophotometric data. Calculate the concentration of the original unknown solution.
The original solution was diluted by a factor of 5.00.
Using M1V1 = M2V2, M1 = (M2V2)/V1 = (3.60 x 10^-5 M)(50.00 mL)/(10.00 mL) = 1.80 x 10^-4 M. The original concentration was 1.80 x 10^-4 M. - 10
An absorption spectrum shows a strong peak at 620 nm. What color of visible light is most strongly absorbed, and what color might the solution appear to the eye?
Light near 620 nm is orange-red light, so the solution most strongly absorbs orange-red wavelengths. The solution may appear blue-green because transmitted and reflected light is often close to the complementary color of the absorbed light. - 11
A blank cuvette is not used to zero a spectrophotometer before measuring samples. Describe one likely effect on the measured absorbance values and explain why this matters.
The blank corrects for anything that absorbs or scatters light other than the analyte.
The measured absorbance values may be too high because absorbance from the solvent, cuvette, or background light loss is included with the analyte signal. This matters because the calculated concentration would likely be overestimated. - 12
The following calibration data are collected for an absorbing species in a 1.00 cm cuvette: 0.00 x 10^-5 M gives A = 0.000, 1.00 x 10^-5 M gives A = 0.115, 2.00 x 10^-5 M gives A = 0.230, and 3.00 x 10^-5 M gives A = 0.345. Determine the molar absorptivity ε.
The slope of A versus concentration equals εb. Using the data, slope = 0.115/(1.00 x 10^-5 M) = 1.15 x 10^4 L mol^-1. Since b = 1.00 cm, ε = 1.15 x 10^4 L mol^-1 cm^-1.