How to use Beer-Lampert law without knowing pathlength?

rawr18

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.

tex43

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

rawr18

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?

Borek

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.

tex43

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.

DrDu

Maybe you can use some absorption of your solvent for calibration?

DrDu

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).

tex43

Here's a dopy question - how do you get to display the originally posted questions when answering?

tex43

Hang on! I think I may have it! You just click "quote" right?

Borek

Yes.