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## AP®︎/College Chemistry

### Course: AP®︎/College Chemistry>Unit 3

Lesson 13: Beer–Lambert law

# Worked example: Calculating concentration using the Beer–Lambert law

The Beer–Lambert law relates the absorption of light by a solution to the properties of the solution according to the following equation: A = εbc, where ε is the molar absorptivity of the absorbing species, b is the path length, and c is the concentration of the absorbing species. In this video, we'll use the Beer–Lambert law to calculate the concentration of KMnO₄ in an unknown solution. Created by Sal Khan.

## Want to join the conversation?

• At he said 'spectrometer', we he soon corrected. I wonder, what is the difference between spectrometer and a spectrophotometer? •  A spectrometer is 'An apparatus used for recording and measuring spectra, esp. as a method of analysis.'. However, a spectrophotometer is ;An apparatus for measuring the intensity of light in a part of the spectrum, esp. as transmitted or emitted by particular substances.;,
Hope that helped!
• What is the purpose of knowing that the solution was measured at 540nm? and was it just coincidence that epsilon = 5.40? • Is mole spelled mole or mol? Sal spells it both ways. • mole is the word used to describe Avogadro's number of particles. mol is the SI symbol for the unit. It is not an abbreviation.
In SI, you use words with words but symbols with numbers. Thus, you would write "two moles" but "2 mol". Note that symbols are not pluralized : it is incorrect to write "2 mols".
• what if the length was not given? how do i find the molar concentration? • How did Sal get liter per cm times mole? also how can you have a liter per mole? And why did Sal do mole per liter at the end instead of liter per mole? I'm really confused. • You're probably referring to the unit of the epsilon constant. Usually, constants have complicated units in order to make sure that the answer has the correct unit and that the other units are cancelled out.

So according to the Beer-Lambert law, absorbance equals epsilon times length of container (or the length that the light has to travel through to pass through the solution) times concentration. The unit of concentration is molarity, which is moles over liter. The unit of length can be centimeters. Absorbance has no unit. If you would try to multiply the units of epsilon, length, and concentration, you should get the unit for absorbance which has no unit. Multiplying liter per cm times mole, cm, and mole per liter would result to all units cancelling out, resulting in no unit.

Sal wanted to find concentration, so he used moles per liter.
• I just realized something. At , Sal says that the length of the vial is 1 centimeter, while the problem says that it is 1.0 centimeter. When he gets to his final answer at , he reports the answer to three significant digits. Since the length of the vial only had 2 significant digits, shouldn't the answer be 0.010, instead of 0.0998? Thanks for the input. • How do you measure the absorbency of a solution without knowing the concentration? • You just need to know the intensities of the light before and after it passes through the solution.

You first need to find the transmittance of the solution, which is the intensity of the light after it passes through the solution divided by the intensity of the incident light, which is the light before it enters the solution. Then you just get the negative log of the transmittance (use base 10) in order to get the absorbency.

Unless the solution has zero transmittance, then the absorbency should be a positive number. I'm not sure what will be the absorbency of a solution with zero transmittance (probably infinite?)
• Will the absorbance be zero when Molarity is zero? Does pure water absorb some light? • Yes, water will absorb and scatter some light. So, what we do with a spectrophotometer is use what is called a "blank". The blank will NOT contain the substances whose absorbance we're interested in (most of the time the blank is water plus the indicator). And we just treat the absorbance of this blank as if it were 0. This is known as "zeroing out" or sometimes as "blanking out" the spectrophotometer. The way that you do this depends on how sophisticated the method you're using is.

So, the answer to the question is that we have to declare something to be 0 absorbance. So, normally we would treat a cuvette containing 0 M of the substance we're interested in as having 0 absorbance -- we just tell the spectrophotometer to treat that as 0. But, strictly speaking, no, it is not actually 0 absorbance.
• At , Sal explains that we've proven the Beer-Lambert law to be true because we can see that the relationship of the points is linear. The points in the table, though, do not form a straight line - calculating the slope by using different pairs of the coordinates yields slightly different slopes for each pair of coordinates, and if the relationship was linear, based on the first set of coordinates, the last coordinate would be (.15, .81) rather than .(.15,.84). So is it the case that the Beer-Lambert relationship is "almost' linear or is the discrepancy due to imperfection in measuring instruments. Thanks.

James Knight • Beer-Lambert is only approximately true. I wouldn't trust it for any absorbance greater than 0.400 myself. (My research required much better accuracy and precision than I student would need, so you might get away with a little higher.)

Depending on many circumstances, the curve of absorbance vs. concentration begins to flatten out above 0.3 absorbance.

The way that we accommodate for this is to analyze standards of known concentrations, and only use those that are within what is called "the linear range" -- in other words where Beer-Lambert applies. 