# How do you use the Beer-Lambert Law to perform quantitative analysis?

### A = a*b*c

Let’s look at the Beer-Lambert law and explore its significance. This is important because people who use the law often don’t understand it, even though the equation representing the law is straightforward. So far we have considered only the amount of light entering and exiting the sample. There are three other important factors related to the sample that define the absorbance.

These factors are:

• the path length of the sample (represented by b)
• the concentration of the sample (represented by c)
• the extinction coefficient of the sample (represented by a). Sometimes a is also called the molar absorptivity.

The extinction coefficient is a physical property of the molecular bonding (chemical structure) of the sample compound. The same molecule will always have the same value for a at the specified wavelength. For example, a weakly absorbing peak (n to pi* bonding) may have a a value of only 1000; whereas, a strongly absorbing peak (pi to pi* bonding) can have values of 600,000 Values for a can range from several 100 to 1,000,000. The important feature of the a value is that it is a constant for the unique chemistry of the sample and will only change when the chemistry changes.

The reason why we prefer to express the law as absorbance (rather than %T) with this equation... A = a*b*c

is because absorbance is directly proportional to the other parameters, as long as the law is obeyed. The take home message is that

• if I double the path length of the sample, I double the absorbance value and
• if I double the concentration of the sample, I double the absorbance value.

Concentration and path length have a linear proportion relationship with the absorbance value.

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