15,000
L/(mol·cm)
150
4.176
15,000
L/(mol·cm)
150
4.176
The Molar Absorptivity Calculator determines the molar absorptivity (extinction coefficient, ε) of a substance from its absorbance, path length, and concentration using Beer's law. Molar absorptivity is an intrinsic property of a molecule that quantifies how strongly it absorbs light at a specific wavelength. It is measured in units of L/(mol·cm) and is essential for identifying compounds, quantifying concentrations, and characterizing chromophores in UV-Vis spectroscopy. Values range from less than 10 for forbidden transitions (such as d-d transitions in transition metal complexes) to over 100,000 for strongly allowed π→π* transitions in conjugated organic molecules. Knowing ε enables the determination of unknown concentrations from simple absorbance measurements and is crucial for designing spectrophotometric assays in clinical, pharmaceutical, and environmental chemistry.
Molar absorptivity is calculated by rearranging Beer's law:
$$\varepsilon = \frac{A}{l \cdot c}$$
where A is the measured absorbance (dimensionless), l is the optical path length in cm, and c is the molar concentration in mol/L. The resulting units are L/(mol·cm), sometimes written as M⁻¹cm⁻¹. The logarithm of epsilon is also provided:
$$\log_{10}(\varepsilon) = \log_{10}\left(\frac{A}{lc}\right)$$
This is commonly reported in organic chemistry literature because log(ε) values typically range from 1 to 5, making comparisons easier. For reference, the specific absorptivity (a) uses concentration in g/L instead of mol/L: a = A/(l·c_g), which is useful when the molecular weight is unknown.
Accurate determination of ε requires: (1) precise knowledge of concentration, (2) absorbance in the linear range (0.1–1.0), (3) monochromatic light, and (4) a well-characterized solution with no interfering species.
The magnitude of molar absorptivity reveals the nature of the electronic transition. Very high ε values (>10,000) indicate spin-allowed, symmetry-allowed transitions such as π→π* in conjugated systems. Moderate values (100–10,000) are typical of n→π* transitions in carbonyls. Very low values (<100) indicate formally forbidden transitions such as d-d transitions in octahedral metal complexes or spin-forbidden transitions. The log(ε) value is widely reported in chemical databases and can be used to classify transition types at a glance: log(ε) > 4 indicates a strong transition, 2–4 indicates moderate, and < 2 indicates weak/forbidden.
Inputs
Results
A dye with A = 0.75 at 50 μM concentration in a 1 cm cuvette has ε = 15,000 L/(mol·cm), typical of azo dyes and indicators with extended conjugation. The log(ε) = 4.18 confirms a strongly allowed electronic transition.
Inputs
Results
A Cu²⁺ aqua complex with A = 0.25 at 0.05 M has ε = 5 L/(mol·cm), characteristic of Laporte-forbidden d-d transitions. The log(ε) < 1 confirms this is a very weak absorption.
Common values: isolated C=C (π→π*) ε ≈ 10,000; benzene (π→π*) ε ≈ 200–8,000 depending on band; C=O (n→π*) ε ≈ 10–100; conjugated dienes (π→π*) ε ≈ 10,000–25,000; extended conjugated systems (β-carotene) ε > 100,000. Transition metal d-d transitions typically give ε = 1–100.
Molar absorptivity varies with wavelength because different wavelengths excite different electronic transitions with different probabilities. The absorption spectrum is essentially a plot of ε vs. wavelength. The wavelength of maximum absorption (λ_max) corresponds to the peak ε value and is used for quantitative measurements.
Yes. Solvent effects can shift both the wavelength (solvatochromism) and intensity of absorption bands. Polar solvents can stabilize excited states differently than ground states, shifting π→π* transitions to longer wavelengths (bathochromic shift) and n→π* transitions to shorter wavelengths (hypsochromic shift).
Molar absorptivity (ε) uses molar concentration (mol/L) and has units L/(mol·cm). Specific absorptivity (a) uses mass concentration (g/L) and has units L/(g·cm). They are related by: ε = a × M, where M is the molar mass (g/mol). Specific absorptivity is used when molecular weight is unknown.
Quantum mechanical selection rules determine transition probabilities. Transitions that are both spin-allowed (ΔS = 0) and Laporte-allowed (change in orbital angular momentum quantum number) have high ε values. Forbidden transitions (d-d in centrosymmetric complexes, spin-forbidden transitions) have much lower ε values but can still be observed weakly.
log(ε) provides a compact classification: log(ε) > 4 = strong, fully allowed transition (π→π* in conjugated systems); log(ε) = 2–4 = moderately allowed (n→π*, charge transfer); log(ε) = 1–2 = weak, partially forbidden (d-d in non-centrosymmetric complexes); log(ε) < 1 = very weak, forbidden transition.
Since ε = A/(lc), errors in concentration directly propagate to ε. A 1% error in concentration causes a 1% error in ε. For reliable ε determination, use analytically pure compounds, accurate volumetric equipment, and verify concentration by an independent method if possible. Typically, ε values are reported to 3–4 significant figures.
Molar absorptivity from absorption spectroscopy is used in fluorescence calculations, particularly in the relationship F = 2.303 × I₀ × ε × l × c × Φ_f, where Φ_f is the fluorescence quantum yield. However, ε should be determined from absorption, not emission measurements.
Water is remarkably transparent in the visible region (ε < 0.01 at 400–700 nm). It begins absorbing significantly in the near-IR (ε ≈ 0.7 at 960 nm, ε ≈ 5 at 1450 nm) and has strong absorption bands in the mid-IR due to O-H stretching and bending vibrations.
Proteins are routinely quantified using A₂₈₀ (absorbance at 280 nm), which arises from tryptophan (ε = 5,500), tyrosine (ε = 1,490), and cystine (ε = 125) residues. The molar absorptivity of a protein can be predicted from its amino acid sequence using the Pace equation: ε₂₈₀ = 5500×n_Trp + 1490×n_Tyr + 125×n_Cys-Cys.
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