Beer’s Law and AP Exam 2003, 5b

September 20, 2006
Categories: AP | AP TOPIC 04

Here is a question I recently posed on the AP Listserv;

“OK, here’s a question that has been bothering me for sometime. I can SEE how the answer that makes sense is 510 nm, but….

1. As long as there is some significant degree of absorbance, does it really matter which wavelength of light is used?

2. I appreciate that the official scoring standards offer a range of answers from 490-520 nm, but why not 480, 470, 460-530, 540, 550 etc?

3. Is there some arbitrary (or non-arbitrary) cut-off of approx. 30% transmittance that is crucial in this experiment and others using colorimetry? If so, WHY?

4. Wouldn’t ANY (reasonable*) wavelength of light produce a linear relationship in the graph in part (c) anyway?

*I guess my question is coming down to the central idea of what range of wavelengths is acceptable in these experiments and why? I think I *know* that there has to be *some* absorbance (otherwise the light just passes through and the experiment is meaningless), but where (and why) is the boundary?”

Here are a couple of responses that I thought might be useful to share – thanks guys, you know who you are!

You are correct that you could do the study at any wavelength where there is significant absorbance, with the emphasis on significant.  Due to limitations in detectors and electronics, typical spectrophotometers only give a linear response in the range of 0.2 to 0.8 absorbance.  If you pick a wavelength where the absorbance isn’t very great, you can’t do very many dilutions before you run into this lower end of absorbance.  Also, if you cut the concentration in half and you are at a wavelength where the absorbance is 0.8, the absorbance will fall to 0.4, a pretty significant drop.  If you are at a wavelength where the absorbance is only 0.2 and you cut the concentration in half, assuming you could get a linear response, the absorbance would only drop to 0.1, not as significant of a drop.  With less drastic dilutions at this wavelength, your absorbances are so close together that you approach or exceed the limits of being able to accurately distinguish between the different readings.  In short, the quality of the results will suffer if you do the study too far off of the peak, where you get the maximum change in absorbance per dilution.

AND

1.  In theory, any wavelength could be used, but the choice of wavelength depends on the limit of detection of the instrument and whether or not Beer’s Law is truly linear over the range of concentrations at that wavelength.  Plus, the signal to noise ratio is highest here.  One would figure that anyone teaching spectroscopic techniques would hit those points.  These concepts are inherent in the word “optimum,” at least from the analytical point of view.  Most likely, CB expects that most chemistry teachers who teach spec use
mention that you use the wavelength of highest absorption without going into detail why.  This is not advisable, I think.

2. Again, “optimum”.

3. No, but see #1.  Low S/N ratios cause problems.  Is this beyond the scope of AP chem?  I think we are in an area which cannot be competently handled by many AP chem teachers.

4. Not necessarily.  Beer’s law is a harsh mistress.

The worst thing about this question is the presentation of two graphs, which could imply that both should be consulted. At least they are consistent.  I know they put both to accommodate students who could read one but not the other.

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