Chemistry · General chemistry II · Worked example
Find a concentration from a calibration curve
Standards of a dye give the absorbances below. An unknown sample reads A = 0.350. Find its concentration.
Tabulate the standards
Each standard pairs a known concentration with its measured absorbance at the same wavelength.
| c (µmol/L) | 0 | 2.00 | 4.00 | 6.00 | 8.00 |
|---|---|---|---|---|---|
| A | 0.002 | 0.151 | 0.302 | 0.449 | 0.601 |
Fit a straight line
A least-squares line through the five points has slope 0.0748 per µmol/L and intercept 0.0018. It fits closely: R² = 0.99998, and no point lies more than 0.002 from the line.
Solve for the unknown
Set A = 0.350 and solve for c.
Check the range
The unknown’s absorbance, 0.350, lies inside the range of the standards, 0.002 to 0.601, so reading it from the line is justified.
Result
About 4.66 µmol/L.
Your turn
Another sample reads A = 0.525 on the same line. Find its concentration.
Show the answer and explanation
6.99 µmol/L.
c = (0.525 − 0.0018)/0.0748 = 6.99 µmol/L. Its absorbance is still inside the range of the standards.
Keep exploring
In Photons & spectrophotometry, set the dilution factor to 10, as if the sample had been diluted tenfold before measuring. The original sample is 46.6 µmol/L.
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