The Beer-Lambert Law
Introduced| English |
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| absorbance/əbˈsɔːbəns/ |
Reading concentration from colour
- A deeper-coloured drink usually means a stronger mix.
- Shine light through it and more colour absorbs more light.
- Measure how much light is swallowed and you know the strength.
- One tidy equation turns absorbed light into concentration.
The absorbance equation
- Absorbance 吸光度 grows with concentration:
- $\varepsilon$ is how strongly the substance absorbs, $b$ the path length, and $c$ the concentration.
With $\varepsilon = 300$, $b = 1\ \text{cm}$, $c = 0.002\ \text{M}$, the absorbance $A$?
$A = \varepsilon b c = 300\times1\times0.002 = 0.6$.
Absorbance tracks concentration
- With everything else fixed, $A$ is directly proportional to $c$.
- Double the concentration and the absorbance doubles.
- A plot of $A$ versus $c$ is a straight line through the origin.
With path length and wavelength fixed, absorbance is proportional to...
$A = \varepsilon b c$, so $A \propto c$ when the rest is fixed.
Doubling the concentration doubles the absorbance (in the linear range).
$A$ is directly proportional to $c$, so it doubles too.
Finding an unknown
- Measure $A$ for known concentrations to draw a calibration line.
- Read an unknown's concentration off that line from its $A$.
- This is how a spectrophotometer measures a sample.
A calibration plot of absorbance versus concentration is...
$A = \varepsilon b c$ is linear in $c$, passing through the origin.
A ____ measures a sample's absorbance to find its concentration.
A spectrophotometer reads absorbance and applies the Beer-Lambert law.
A solution has $\varepsilon = 200$, path length $b = 1\ \text{cm}$, and $A = 0.6$.
- $c = \dfrac{A}{\varepsilon b} = \dfrac{0.6}{200 \times 1}$.
- $c = 0.003\ \text{M}$.
The Beer-Lambert law
Absorbance is proportional to concentration - the basis of a calibration curve.
With $\varepsilon = 100$, $b = 1\ \text{cm}$, and $A = 0.5$, the concentration (in M)?
$c = A/(\varepsilon b) = 0.5/(100\times1) = 0.005\ \text{M}$.
Absorbance is directly proportional to concentration only over a limited range -- very concentrated solutions bend the line. Keep the path length and wavelength fixed when you compare samples. And use the wavelength the substance absorbs most strongly for the best sensitivity.
The Beer-Lambert law says absorbance $A = \varepsilon b c$, so $A$ is directly proportional to concentration when path length and wavelength are fixed. A plot of $A$ versus $c$ is a straight line, and reading an unknown's $A$ against a calibration line gives its concentration.