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Index/Organic chemistry/ORG-17

ORG-17

Beer–Lambert (organic) A = ε l c

A = ε l c. Absorbance of a chromophore in a cuvette.

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SpectroscopyBeer–Lambert

Governing equation

A=εℓcA=\varepsilon \ell c

c∈[1×10−8,0.01]c \in \left[1\times 10^{-8}, 0.01\right]

where

\varepsilon
Molar absorptivity (L mol^{-1} cm^{-1})
\ell
Path (cm)
c
Concentration (mol/L)
A
Absorbance (—)

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ORG-17 · spectrum
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①

Governing law — red

A=εℓcA=\varepsilon \ell c

c∈[1×10−8,0.01]c \in \left[1\times 10^{-8}, 0.01\right]

c=1×10−8c = 1\times 10^{-8}A=1.2×10−4A = 1.2\times 10^{-4}

②

Domain of the variable — blue

cmin⁡=1×10−8,cmax⁡=0.01c_{\min} = 1\times 10^{-8},\quad c_{\max} = 0.01

c∈[1×10−8,0.01]c \in \left[1\times 10^{-8}, 0.01\right]

c=1×10−8c = 1\times 10^{-8}c=1×10−8c = 1\times 10^{-8}

③

Response curve — green

A=εℓcA=\varepsilon \ell c

c∈[1×10−8,0.01]c \in \left[1\times 10^{-8}, 0.01\right]

c=1×10−8c = 1\times 10^{-8}A=1.2×10−4A = 1.2\times 10^{-4}

④

Rate of change — amber

dAdc\frac{\mathrm{d}A}{\mathrm{d}c}

c∈[1×10−8,0.01]c \in \left[1\times 10^{-8}, 0.01\right]

c=6.29×10−5c = 6.29\times 10^{-5}A′=12000A^{\prime} = 12000

Lecture brief

Historical brief

Hammett (1937) and Taft linear free-energy, E-factor green metrics, Woodward–Fieser UV and Claisen equilibria are how organic chemistry became predictive. The lab is substituent, waste and tautomer. This sheet (ORG-17 — Beer–Lambert (organic) A = ε l c) is the form associated with Beer–Lambert. Working symbols: ε\varepsilon, ℓ\ell, cc →\rightarrow AA. ε is the molar absorptivity (L mol⁻¹ cm⁻¹). Linear only in the dilute, non-scattering limit.

Purpose

Purpose: compute AA from ε\varepsilon, ℓ\ell, cc in Organic chemistry via A=εℓcA=\varepsilon \ell c A = ε l c. Absorbance of a chromophore in a cuvette. Use it when a real organic chemistry question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given ε=12000.000 Lmol−1cm−1\varepsilon = 12000.000\,\mathrm{L mol^-1 cm^-1}, ℓ=1.000 cm\ell = 1.000\,\mathrm{cm}, c=5.000e−5 mol/Lc = 5.000e-5\,\mathrm{mol/L}, the governing relation A=εℓcA=\varepsilon \ell c yields A=0.6000 —A = 0.6000\,\mathrm{—}. 1 cm path default, single wavelength. Move a slider: the numbers are this situation, not a canned story.

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Outputs

  • Absorbance A0.6000 —
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ORG-17 · spectrum
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Narration of this film

1 cm path default, single wavelength.

ε is the molar absorptivity (L mol⁻¹ cm⁻¹). Linear only in the dilute, non-scattering limit.

Reading speed

Watch on YouTube