Spectroscopy (College Board AP® Chemistry): Exam Questions

A student wants to determine the concentration of permanganate, MnO₄⁻ (aq), in a solution. The student plans to use colorimetric analysis because solutions containing MnO₄⁻ (aq) have a purple color.

To determine the optimum wavelength for an experiment that measures the concentration of MnO₄⁻ (aq), the student takes a sample of the solution and measures the amount of light absorbed by the sample over a range of wavelengths. The data are plotted in the graph shown. Identify the optimum wavelength that the student should use for the experimental procedure.

The student uses a stock solution of 2.40 × 10⁻³ M  KMnO₄ (aq) to prepare the standard solutions of MnO₄⁻ (aq) that are needed to construct a calibration curve.

i) The student uses a 100.0 mL graduated cylinder to measure a certain volume of KMnO₄ (aq) stock solution, as shown in the diagram given. What volume should the student record?

ii) Calculate the volume, in mL, of 2.40 × 10⁻³ M  KMnO₄ (aq) that is required to produce 100.0 mL of a standard 1.68 × 10⁻³ M  MnO₄⁻ (aq) solution.

The student designs the following procedure to produce a calibration curve.

Step 1: Prepare several standard solutions that have known MnO₄⁻ (aq) concentrations by dilution of the stock solution.

Step 2: Rinse the cuvette with distilled water.

Step 3: Rinse the cuvette with the standard solution and fill the cuvette with the standard solution.

Step 4: Measure the absorbance of the standard solution with the colorimeter.

Step 5: Repeat steps 2-4 for each of the standard solutions.

The data are plotted in the calibration curve shown. One of the data points (indicated with an arrow) on the calibration curve is below the line of best fit.

Assuming that all lab equipment is functioning properly, identify which one of the procedural steps the student could have executed incorrectly that would explain why the marked data point is below the line of best fit. Justify your answer.

A solution is analyzed using spectrophotometry, and its absorbance is measured at a specific wavelength. The absorbance of the solution is found to be 0.40 when measured using a cuvette with a path length of 1.0 cm. The molar absorptivity of the solution is 250 L mol^-1 cm^-1.

Calculate the concentration of the solution

The same concentration solution is used, but the absorbance is now tripled. Suggest what this implies about the path length of the cuvette used. Justify your answer.

The same solution is used, and the path length remains unchanged, but the absorbance is now half of the original value. Suggest a possible reason for this and justify your answer.

The absorbance is measured again using the same setup, but the sample was contaminated with another absorbing species. Explain how this would affect the measured absorbance and the calculated concentration?

The hydrogen atom absorbs and emits light as its electron transitions between energy levels.

Explain why a hydrogen atom only absorbs specific wavelengths of light.

i) A hydrogen atom absorbs a photon with an energy of 2.55 × 10⁻¹⁸ J, promoting its electron to a higher energy level. Calculate the wavelength of this photon, in nm.

ii) Describe what happens to the electron after absorption.

When the electron returns to a lower energy level, a photon of the same energy is expected to be emitted. However, when measured outside the atom, the wavelength of the emitted photon is slightly longer than the calculated value. Suggest a possible reason for this discrepancy. Justify your answer.

A calibration curve is constructed to determine the concentration of an unknown solution using spectrophotometry.

Explain the purpose of a calibration curve in spectrophotometry.

The equation of the calibration curve is given as A = 450c + 0.015. If the absorbance of an unknown sample is 0.540, determine its concentration.

A student measures the absorbance of the unknown sample using a different spectrophotometer with a cuvette of twice the path length as those used for the calibration curve. Predict how this error would affect the calculated concentration and justify your answer.

A chemist analyzes two different organic molecules, X and Y, using ultraviolet-visible (UV-Vis) spectroscopy. The maximum absorbance of molecule X occurs at a wavelength of 280 nm, while molecule Y absorbs most strongly at 500 nm.

Explain why molecule X and molecule Y absorb light at different wavelengths.

A student prepares a solution of molecule X and records an absorbance of 0.85 in a spectrophotometer. The solution is then diluted by a factor of 2, and the absorbance is measured again. Predict the new absorbance value and justify your answer.

The student prepares another diluted solution, but the measured absorbance is lower than expected. The spectrophotometer was properly calibrated before the measurement. Suggest two possible reasons for this discrepancy and justify each one.

A student is given the task of determining the molar concentration of a CuSO₄ solution using two different procedures, precipitation and spectrophotometry.

For the precipitation experiment, the student adds 20.0 mL of 0.200 M Ba(NO₃)₂ to 50.0 mL of the CuSO₄ (aq).

The reaction goes to completion, and a white precipitate forms. The student filters the precipitate and dries it overnight. The data are given in the following table.

Write a balanced net ionic equation for the precipitation reaction.

Calculate the number of moles of precipitate formed.

Calculate the molarity of the original CuSO₄  solution.

For the spectrophotometry experiment, the student first makes a standard curve. The student uses a 0.1000 M solution of CuSO₄ (aq) to make three more solutions of known concentration (0.0500 M, 0.0300 M, and 0.0100 M ) in 50.00 mL volumetric flasks.

Calculate the volume of 0.1000 M CuSO₄ (aq) needed to make 50.00 mL of 0.0500 M CuSO₄ (aq).

Briefly describe the procedure the student should follow to make 50.00 mL of 0.0500 M CuSO₄ (aq) using 0.1000 M CuSO₄ (aq),a 50.00 mL volumetric flask, and other standard laboratory equipment. Assume that all appropriate safety precautions will be taken.

The standard curve is given below.

The absorbance of the CuSO₄ solution of unknown concentration is 0.219. Determine the molarity of the solution.

A second student performs the same experiment. There are a few drops of water in the cuvette before the second student adds the CuSO₄ (aq) solution of unknown concentration. Will this result in a CuSO₄ (aq) concentration for the unknown that is greater than, less than, or equal to the concentration determined in part (f) ? Justify your answer.