# Beer's law experiment - parameters

• fog37

#### fog37

Hello everyone,
I am planning to build a device to test Beer's law for a specific solution and obtain the molar concentration of the solution. Beer's law presumes that the input and output light intensities are related by an exponential law.

I need to know:
1. The sample path length ##\ell##. Easy to know.
2. The substance extinction coefficient ##\epsilon##. This is unique for each substance. How can I find it out? What if I had a mixture like water and algae?
3. The ratio between the input and output light intensities: ##I_{f} / I_{0}##
The molar concentration ##c## is what I am trying to determine.

• What if the relation between the input and output intensities was not exponential?
• Also, what about the "wavelength" of the light intensity? The ratio ##I_{f} / I_{0}## may be wavelength dependent while the molar concentration ##c## is the investigated solution is fixed. So which wavelength should we pick?

The substance extinction coefficient ϵϵ\epsilon. This is unique for each substance.

And depends on the wavelength. Typical approach is to register a curve of ϵ vs λ and choose the optimal value. Typically the one with the largest ϵ value, as this gives best sensitivity, but sometimes (when we deal with mixtures) we choose other wavelengths to avoid interference.

How can I find it out? What if I had a mixture like water and algae?

Algae is not a substance.

Can't help you with building the spectrophotometer, but it doesn't sound trivial. Light sources and light sensors are not necessarily linear so you either need to choose them very carefully or to compensate, which requires precise calibration.

Thank you Borek.

Why do we choose the wavelength that is the most absorbed, hence has the largest extinction coefficient ##\epsilon##? Because that gives the most contrast if we change the mixture's concentration ##c##?

As I wrote - it gives best sensitivity. That means both relatively large differences in the signal when changing concentrations and signal becomes detectable at low concentrations, making it possible to analyze more diluted samples.

Also because that is where the variation of ε with λ is lowest, so it is less sensitive to errors in wavelength calibration (or small changes in the position of the absorption peak as a function of concentration) than a wavelength on the slope of a peak. (NB You should always run a full spectrum of each sample, to check for consistency - or the accidental presence of contaminants - not just measure ε at a particular wavelength. And of course you don't measure ε, you measure absorbance. Do you know how to translate that into ε for your samples?)

Thank you mjc123. I see how the extinction factor ##\epsilon## can vary with wavelength. Why is the variation the smallest at the wavelength ##\lambda## with the largest absorption? because it is an absorption peak so in that neighborhood the slope, i.e. the rate of change, is more or less horizontal?

Yes, just a simple math.

The Beer-Lambert part of this is simple. Building a fixed frequency device: not simple (but possible, if you can determine the proper freq and can find a compatible lamp/receiver combination) - you'll have to learn a lot about lamps, receivers, temperature regulation, electronics, noise... Building device upon which one can 'run a spectrum': You'll need a lab assistant named Sancho Panza.