Question: Does the Beer Lambert law apply to the opacity of reagents?

warren is asking a question about spectrometry: Subscribe to answer questions on this topic

warren asked on November 20, 2017 21:41
250 | 2 answers | #15212

I guess it depends on if the reagent color change is linearly related to the concentration of the target compound (say, nitrate).

(originally asked here)

Beer's Law determines the relationship between opacity and concentration. According to Beer's Law, if you double the concentration of a liquid, you should see double the opacity -- that is, it'll be twice as dark when you shine light through it. Here's some work people have shared to demonstrate this:

Title Author Updated Likes
Can a DIY spectrometer be used to measure water turbidity? @warren 12 months ago
Draft: Find the concentration of a liquid with a DIY spectrometer @warren about 1 year ago
Does the Beer Lambert law apply to the opacity of reagents? @warren about 1 year ago
Mini spectrophotometer - how does this deviate from the Beer-Lambert law? @FoxClass over 2 years ago
CCD Photodiode Array Spectrometer @bhickman about 5 years ago
Using the Spectroscope for Analysis of Concentration (Beer's Law) @straylight over 5 years ago
Does Coffee Obey Beer's Law? A Spectrometric Investigation @akjeff91 over 5 years ago
Attempt at Quantitative Analysis for Desktop Spectrometer @ben.alley43 over 5 years ago


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2 Answers

Copying in answer from @stoft, here:

It is my understanding that Beer's law is not the relationship between reagent's effect on color, but is the property of light passing through a uniform substance and the attenuation of that light with distance -- which is linear assuming the substance is uniform. So, if you had some chemical reaction, which was not linear with the concentration of reagent, that non-linearity would appear in a plot of the measured attenuation (from the spectral data) as the concentration changed. The Beer's Law linearity you are relying on is that given that the sample containers are all "identical" then the path-length for light is "identical" and therefore (with all else held constant - like the light source, camera exposure, etc) then the measurements of relative intensity will be directly related (linear or non-linear) with the concentration. [Note: Realize that there are many possible components to the issue of measurement stability and that the default PLab stuff is only a first step. You might find some of my PLab notes on spectrometer stability, noise, time-averaging, calibration and uncertainty of interest.] It's all in the numbers to estimate measurement limits vs your requirements.

Just to clarify here, I believe to sum up we can say that:

IF a reagent reacts linearly (for example, if doubling the concentration of the thing the reagent reacts to DOUBLES the opacity of the reagent)

...then YES, you can use the principle of Beer's Law to determine concentration of what the reagent is reacting to.

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Also noting that @ygzstc cited some work supporting the use of the area under the curve in a spectrum data reading instead of intensity at one wavelength, as a possibly better measure of concentration:

Yes the Beer-Lambert Law is based on -log(I/Io) but it's applicable for a single wavelength value. ( And this law has many limitations. Recent research showed that the area under the peak is much more stable indication of concentration variations ( Hope this is helpful...

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