Spectroscopy and Beer's law

Light comes in packets of energy, photons; the shorter the wavelength, the more energy each carries. Molecules absorb only photons whose energy matches a jump they can make: ultraviolet and visible light move electrons, infrared makes bonds stretch and bend. Which wavelengths are absorbed is a fingerprint, and how much is absorbed tells you how much is there.

A spectrophotometer shines a beam through a sample in a small clear container (a cuvette) and measures how much gets through. Transmittance, T, is the fraction that gets through. Absorbance, A = −log₁₀ T. A = 1 means 10% gets through; A = 2 means 1%.

The Beer–Lambert law says absorbance is proportional to concentration: A = ε × b × c. Here ε (epsilon) is how strongly that substance absorbs at that wavelength, in L/(mol·cm); b is the path length through the sample, usually 1 cm; c is the concentration in mol/L. With ε = 15,000 L/(mol·cm), b = 1 cm and A = 0.45: c = 0.45 ÷ 15,000 = 3.0 × 10⁻⁵ M.

In practice you rarely trust a book ε. You measure standards, solutions of known concentration, and plot absorbance against concentration: a calibration curve. Fit a straight line, then read unknowns off it. If the line is A = 0.20 × c (c in mg/L), an unknown with A = 0.50 is 2.5 mg/L. Stay inside the range of your standards, because the law bends at high absorbance (above about 1).

Always measure a blank (the solvent alone) first and zero the instrument on it, so you only count what the analyte absorbs. Pick the wavelength where the analyte absorbs most and other things little.