[Chewbie]

Good evening.

I have a unit question regarding molar absorptivity in Beer's law.

In lab, I measured the lambda max of a solution as 501.1 nm. Molar absorptivity in Beer's law requires the units M^-1 cm^-1.
Is there a way to convert from nm to M^-1 cm^-1?

I've searched far and wide and haven't found an answer to the issue.

edit: My instructor told me during lab that the measured lambda max is indeed the value to use for molar absorptivity.

[Borek]

Please get back to the Beer's law theory. Lambda max and molar absorptivity are two separate parameters, each with its own units.

edit: My instructor told me during lab that the measured lambda max is indeed the value to use for molar absorptivity.

That's completely wrong. Either you misunderstood each other or you should look for another instructor.

[Babcock_Hall]

Perhaps what the instructor meant was that one should use the molar absorptivity at λ_max.  I have seen this sort of issue come up before.  The values of molar absorptivity at other values of λ are necessarily smaller.

[Consequentium]

Good evening.

I have a unit question regarding molar absorptivity in Beer's law.

In lab, I measured the lambda max of a solution as 501.1 nm. Molar absorptivity in Beer's law requires the units M^-1 cm^-1.
Is there a way to convert from nm to M^-1 cm^-1?

I've searched far and wide and haven't found an answer to the issue.

edit: My instructor told me during lab that the measured lambda max is indeed the value to use for molar absorptivity.

Are you sure you didn't misunderstand it as you being able to use λ to get the molar absorptivity? Beer's Law is usually expressed as

A=εLc

You have A in terms of either λ absorbed or transmitted. Do you know what the concentration of what you're measuring is? The pathlength? Is this from a dataset or a problem? If all you have is a wavelength, the you need more information. Look for assumptions implied by the problem or lab assignment (this might mean checking your procedure). That's something I've seen before.

Edit: I should clarify that when I say "or transmitted," I've seen questions that ask to convert absorbance to transmittance and vice versa. Not that A is transmittance.

[Doc048]

The following is an excerpt from Cataldo, et. al.;Determination of the Integrated Molar Absorptivity and Molar Extinction Coefficient of Hydrogenated Fullerenes at http://www.iac.es/preprints/files/PP12062.pdf. This might be helpful in shedding some light on your question.

Molar Absortivity and the Molar Extinction Coefficient
If Iₒ is the incident intensity (radiant power) of monochromatic radiation entering a sample and I the intensity after passing throught he sample, then the logarithm of the ratio Iₒ/I is the absorbance A (1):
                                                                            A = Log[Iₒ/I] = єbc                                                        Equation 1
According to the Beer-Lambert Law, the absorbance is directly proportional to the thickness b (or, optical path length) and the concentration c of the absorbing molecules in the infrared beam in moles/liter ( = Molarity ). This is, also true for UV-Vis Spectrophotometry as well.  As shown in equation 1, the proportionality constant linking absorbance with the optical path length and with concentration is є, known as the molar absorptivity or more commonly known in the literature as 'molar extinction coefficient' whose typical physical dimensions are L▪cm⁻¹▪mol⁻¹.

Centimeters (cm) can be converted to nanometers (nm) but Molarity is a mass (moles) per unit volume (liters) term and represents different fundamental quantities.  Would be like trying to convert inches into pounds. Not going to happen.  :-)

1.   Colthup, N.B., Daly, L.H., and Wiberley, S.E. (1990) Introduction to Infrared and Raman Spectroscopy, 3rd. ed., Academic Press: SanDiego, pp. 100 – 103.