By Jack Brubaker
Updated Aug 30, 2022
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In analytical chemistry, the ultraviolet‑visible (UV‑Vis) spectrometer is the standard tool for quantifying how much light a sample absorbs. The amount of absorption—captured as absorbance (A)—depends on three key variables: the sample’s concentration (c), the path length of the cuvette (l), and the molar absorption coefficient (ε), also known as the molar extinction coefficient. The relationship is expressed by Beer’s Law: A = εcl. To solve for any one of these variables, the other three must be known.
Use the absorbance spectrum produced by your UV‑Vis instrument. The spectrum plots absorbance versus wavelength (nm). Peaks on the graph indicate wavelengths where the compound absorbs most strongly; select the peak that best matches your analytical goal.
Determine the molarity (M) of the solution with the formula:
M = (grams of solute) ÷ (molecular weight in g mol⁻¹) ÷ (liters of solution).
For example, dissolving 0.10 g of tetraphenylcyclopentadienone (MW = 384 g mol⁻¹) in 1.00 L of methanol gives:
M = 0.10 g ÷ 384 g mol⁻¹ ÷ 1.00 L = 2.6 × 10⁻⁴ M.
The cuvette’s optical path length is usually 1.0 cm, though other lengths are available—particularly for gaseous samples. The path length is often printed on the absorbance spectrum or on the cuvette itself.
Rearrange Beer’s Law to isolate ε:
ε = A ÷ (c × l)
Using the tetraphenylcyclopentadienone example: two peaks appear at 343 nm (A = 0.89) and 512 nm (A = 0.35). With a 1.0 cm cuvette and a concentration of 2.6 × 10⁻⁴ M, the coefficients are:
ε(343 nm) = 0.89 ÷ (2.6 × 10⁻⁴ × 1.0) ≈ 3423 L mol⁻¹ cm⁻¹
ε(512 nm) = 0.35 ÷ (2.6 × 10⁻⁴ × 1.0) ≈ 1346 L mol⁻¹ cm⁻¹
