How to use Beer-Lampert law without knowing pathlength?

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Discussion Overview

The discussion revolves around the application of Beer's Law in the context of ATR-IR spectroscopy, specifically addressing the challenge of determining concentration without knowing the pathlength. Participants explore methods for calibration and the implications of using absorbance data from FT-IR graphs.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant notes the formula for Beer's Law and expresses confusion about the pathlength in ATR-IR spectroscopy, questioning the interchangeability of penetration depth and pathlength.
  • Another participant suggests that without the pathlength, Beer's Law cannot be applied, proposing the construction of a calibration curve as an alternative method to determine concentration.
  • There is a query about the feasibility of creating a calibration curve after data collection, with responses indicating that prior concentration data is necessary for such a curve.
  • One participant proposes using the absorption of the solvent for calibration purposes.
  • Another participant advises consulting the instrument manual for information on the incident angle and refractive indices, suggesting that the solvent's refractive index could be used if the substance is diluted.

Areas of Agreement / Disagreement

Participants generally agree that knowing the pathlength is crucial for applying Beer's Law, and there is a consensus that calibration curves are necessary for determining concentration. However, there is disagreement on the possibility of creating a calibration curve after data collection, with some asserting it is not feasible without prior concentration measurements.

Contextual Notes

Participants express uncertainty regarding the definitions and applicability of penetration depth versus pathlength, as well as the specific parameters needed for ATR-IR spectroscopy calculations.

Who May Find This Useful

Researchers and students working with ATR-IR spectroscopy, particularly those interested in absorbance measurements and calibration techniques.

rawr18
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So I did an experiment today using ATR-IR spectroscopy, thus I didn't know what the exact pathlength was (I should have just used traditional FT-IR!). Anyhow, I know that Beer's Law states that:

A(Absorbance)= a(wavelength) * b (pathlength) * c (concentration)

I know absorbance and wavelength, and am trying to find the concentration of my sample. However, I have no idea what the pathlength was since I used ATR. I looked up a formula online for penetration depth (which may be interchangeable with pathlength, not really sure), and it read:

dp= λ / 2(π)(n1) sqrt(sin^2θ - (n2/n1)^2)

I'm just confused as how to find the incident angle, ATR crystal refractive index and sample refractive index?

Any help would be much appreciated! thanks.
 
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Without the path length the Beer-Lambert law is redundant. One way round your problem would be to construct a calibration curve for your substance vs absorbance and then simply read off your concentration at the appropriate absorption
 
Thanks Text, is there a way to create a calibration curve AFTER the analyses have been done? I already have my data in the form of FT-IR graphs, how can I create a calibration curve?
 
rawr18 said:
is there a way to create a calibration curve AFTER the analyses have been done

If you have not recorded signals for different concentrations - no. If you did - it is not different from calibration curve for any other type of measurement.
 
Thanks Text, is there a way to create a calibration curve AFTER the analyses have been done? I already have my data in the form of FT-IR graphs, how can I create a calibration curve?

Make solutions with a range of concentrations which include your estimated value and measure their absorbances. Then plot concentration vs absorbance.
 
Maybe you can use some absorption of your solvent for calibration?
 
rawr18 said:
I'm just confused as how to find the incident angle, ATR crystal refractive index and sample refractive index?


For the first two, RTFM of the instrument. For the latter one, if your substance is diluted, you can probably use the index of the pure solvent (in the IR, of course).
 
Here's a dopy question - how do you get to display the originally posted questions when answering?
 
Hang on! I think I may have it! You just click "quote" right?
 
  • #10
tex43 said:
Hang on! I think I may have it! You just click "quote" right?

Yes.
 

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