Beer’s Law

The key equation for making UV-Vis absorption experiments quantitative is

Beer’s Law:

where A is the absorption of the sample, ε is the molar absorptivity, l is the path

length of the sample, and c is the concentration of the absorbing molecule in the

sample.

The molar absorptivity, ε, is a measure of how well a particular molecule absorbs

a particular wavelength of light. The wavelengths where a molecule absorbs large

amounts of light have high molar absorptivity, and the wavelengths where the

molecule does not absorb light have zero molar absorptivity. The molar

absorptivity is a property of a molecule and changes as the wavelength changes.

Typical units of molar absorptivity are .

The path length, l, is determined by the sample holder and is usually consistent

from one measurement to the next. In our experiments the path length is

determined by what cuvette is used. This will typically be 1 cm for most UV-Vis

spectrophotometers.

The concentration, c, is typically expressed as a molarity. It is the concentration

of the molecule that is absorbing the light.

The absorbance, A, is a measure of how much light made it through the sample.

It is calculated by taking the negative log base 10 of the fraction of light that

made it through the sample at a certain wavelength.

We can consider a few scenarios to understand how absorbance is calculated. If

50% of the light makes it through the sample - meaning that when we measure

the sample half as much light comes through as compared with the

measurement of the blank - then the absorbance would be equal to

-log(0.50)=0.30. If 100% of the light makes it through the sample, then the

absorbance would be equal to -log(1)=0. Absorbance is a logarithmic scale,

which means that when the absorbance doubles, the amount of light making it

through the sample is 10 times smaller! An absorbance of 1 means that 10% of

the light made it through the sample. An absorbance of 2 means that 1% of the

light made it through the sample.

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