AP Chemistry · Free-response skill

Analyze a spectrophotometry lab

The move. Use a Beer's law calibration to find an unknown concentration and amount, and predict how a named procedural error changes the result.

How to do it

  1. The calibration line goes through the origin, so its slope is any standard's absorbance divided by its concentration. Check it with a second standard, and keep the unit (per μM) with it.
  2. To find an unknown concentration, divide the unknown's absorbance by the slope.
  3. To go from concentration to amount, multiply by the volume in liters. Write each step with units.
  4. For an error, trace it through A = εbc: does the error make the measured absorbance higher or lower? The calculated concentration moves the same way.

Practice prompt Try it

A student measures the concentration of a fictional purple dye in a 100.0 mL sample of sports drink. The student makes four standard solutions of the dye, fills a clean 1.00 cm cuvette with each, and measures the absorbance at 560 nm. The student then puts some of the undiluted sports drink in the cuvette and measures it in the same way.

Absorbance at 560 nm

SolutionDye concentration (μM)Absorbance
Standard 12.000.104
Standard 24.000.208
Standard 36.000.312
Standard 48.000.416
Sports drinkunknown0.260

Use the information above to answer each part.

  1. The absorbances of the standards fall on a straight line through the origin. Find the slope of that line, in absorbance units per μM.
  2. Use the slope to find the concentration of dye in the sports drink, in μM.
  3. Find the number of moles of dye in the 100.0 mL sample.
  4. Suppose that, after the standards were measured, the student left a fingerprint on the clear side of the cuvette before measuring the sports drink. The fingerprint scatters some light away from the detector. Will the absorbance the instrument reads for the sports drink be higher or lower than it should be?
  5. With the fingerprint in place, will the dye concentration the student calculates for the sports drink be too high or too low?

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Checklist

Our own checklist of what a full answer does, one line per point. Tick each one your response earns.

0 of 5 points

Model answer, annotated

(a) Slope = 0.104 ÷ 2.00 μM = 0.0520 per μM. Standard 4 gives the same value: 0.416 ÷ 8.00 μM = 0.0520 per μM.

  • Point 1 Divides an absorbance by its concentration to get 0.0520 per μM, and checks it with a second standard.

(b) The sports drink has A = 0.260, so its concentration is 0.260 ÷ 0.0520 per μM = 5.00 μM.

  • Point 2 Divides the unknown's absorbance by the slope from part (a).

(c) 5.00 μM is 5.00 × 10⁻⁶ mol/L, and 100.0 mL is 0.1000 L. Moles of dye = 5.00 × 10⁻⁶ mol/L × 0.1000 L = 5.00 × 10⁻⁷ mol.

  • Point 3 Converts both units and multiplies concentration by volume in liters.

(d) Higher. The fingerprint scatters some light, so less light reaches the detector, and the instrument reads that as extra absorbance.

  • Point 4 States that the absorbance reading is higher than it should be.

(e) Too high. A higher absorbance divided by the same slope, 0.0520 per μM, gives a higher concentration than the true value.

  • Point 5 Carries the higher absorbance through the calibration to a concentration that is too high.