[agent1594]

In spectrophotometry, wavelength of maximum absorption(λ_max) is used instead of using the whole spectrum.

Here are some questions that came into my mind.

1. What is the reason for using λ_max?

my reasoning: Beer-Lambert law is satisfied in the 0.2-0.7 absorbance range. λ_max gives the highest absorbance for a given concentration. This will take the absorbance value toward 0.7. If it goes over 0.7, we can dilute the sample and take readings. But if we used some other wavelength other than λ_max, absorbance may drop below 0.2 and there's no way to increase the concentration of the sample to increase the absorbance. So we always stick with  λ_max.

2. Why we only use λ_max instead of full spectrum?

my reasoning: If the full spectrum is used, lots of incident rays are transmitted without being absorbed since the solution absorb mainly λ_max. I increases while I₀ remains same. And by the equation A=log₁₀(I₀/I), absorbance may drop below 0.2.

3. What determines the intensity of a color(pale vs bright)?
Is it the amplitude of a light wave or wavelength(like red color has many wavelengths in its range 630-750nm )?
Does the molar absorption coefficient(ε) have anything to do with the color of the sample?

4. Why we make Fe(SCN)₆^3- when determining Fe³⁺ concentration?

my reasoning: Molar absorption coefficient(ε) of Fe³⁺ is low that it gives an absorbance above 0.2 only in higher Fe³⁺ concentrations. But the complex has a higher ε, thus will give an absorbance between 0.2-0.7.

Can someone correct me?
Thanks!

[Borek]

1. What is the reason for using λ_max?

Think in terms of sensitivity.

2. Why we only use λ_max instead of full spectrum?

Think in terms of specificity of the method.

Actually for some simple cases it is possible to use "full spectrum", it is just much less universal approach.

3. What determines the intensity of a color(pale vs bright)?

Define what you mean by intensity.

Why we make Fe(SCN)₆^3- when determining Fe³⁺ concentration?

my reasoning: Molar absorption coefficient(ε) of Fe³⁺ is low that it gives an absorbance above 0.2 only in higher Fe³⁺ concentrations. But the complex has a higher ε, thus will give an absorbance between 0.2-0.7.

That's correct - Fe/SCN complex gives much higher sensitivity and makes teh determination much easier.

Please note: most of your reasoning based on the "0.2-0.7" range is wrong. Yes, it is the best range to use, but there are three factors that vary - and if the need be we can easily either dilute the sample, or use a longer cuvette to keep the absorbance in the correct range. λmax is a given, we choose it for the highest sensitivity only.

[Corribus]

Actually for some simple cases it is possible to use "full spectrum", it is just much less universal approach.

In most cases it simply comes down to analysis time. In principle what you want is the integrated area underneath the entire transition. However if the transition only changes intensity and not line-shape, then the intensity at the peak maximum is linearly proportional to the peak area, and you lose nothing by just measuring the peak intensity at the maximum wavelength. It is much quicker just to take an intensity measurement at a single point than to record an entire spectrum, and simple instruments are designed this way.

That said, it should typically be confirmed that the peak shape isn't changing before single point measurements are taken. If the peak shape is changing, it can tell you that additional things are going on, and recording data (kinetics say) at a single wavelength can mask this important information and lead to erroneous conclusions.

[Babcock_Hall]

I seem to recall a similar question a couple of years ago.  I may have raised the argument that near λ_max one may see better adherence to the Beer-Lambert law; however, my imperfect memory of the thread is that this argument might be a bit simplistic.

[Corribus]

Too simplistic, I would say. The peak maximum is also the strongest absorbing point, and therefore is mostly likely to be in the nonlinear range, so it could also be less likely to adhere to Beer-Lambert. It all depends.

[Babcock_Hall]

Suppose that the highest level of absorbance is within the linear range and that spectrophotometers provide light that is not truly monochromatic.  Then what will happen?

[Corribus]

It depends on the nature of the spectral transition. If the transition arises strictly between two electronic states, then (removing instrument from the equation) I can't think of a mechanism whereby the peak maximum would have a different Beer-Lambert behavior than an off-center wavelength. Of course most peaks in the UV-Vis spectrum are superpositions of multiple transitions, and the lambda max may not even be the maximum of any of the individual components. Different transitions can in principle have differing nonlinear absorption effects, although most UV-Vis experiments I wouldn't imagine use a powerful enough light source to really observe these effects strongly.  (Similarly, concentration can affect different transitions to different degrees - much more likely to be observed in a UV-Vis experiment.)

Regarding the monochromaticity, the important condition is not the absolute monochromaticity per se but the spectral bandwidth of the incident light versus that of the spectral transition.  If the bandwidth of the incident light is very broad, and you excite on the slope of the absorption band where the extinction coefficient varies considerably as a function of small changes in wavelength, you can inaccurate measurements of absorptivity (e.g., extinction coefficient) because of nonuniform absorption of different incident light wavelengths - particularly at high concentrations. For this reason it is best to measure the extinction coefficient at the peak maximum as a general rule.  But honestly for most good UV-Vis instruments I wouldn't say that this is not a huge problem because of (1) the broadness of most electronic transitions and (2) the standard practice for measuring extinction coefficients is to use low concentration and narrow excitation slits so that you are most likely to be in the range where the B-L law applies. The exception would of course be very narrow transitions, such as some lanthanide complexes, maybe.  But I guess if you want to be technical, then yes the Beer-Lambert Law fails to a greater degree as you excite farther away from the areas of the spectra that have constant absorptivity, which is most cases is far away from the lambda max value.

[Babcock_Hall]

Corribus,

Thank you for a very thoughtful reply.  An older textbook on analytical chemistry (Peters, Hayes, Hieftje, Chemical Separations and Measurements) dealt with a similar situation.  They show an absorption spectrum with a tall, narrow peak and a shorter, broader peak in Figure 19-17.  They discuss which λ_max to use in terms of sensitivity (the tall, narrow peak is better on that criterion) and in terms of a variation in the frequency selector and also in terms of Beer's law.  "Because a slight wavelength shift is not uncommon in absorption spectrophotometers, it is better to choose a wavelength for analysis which lies in the central portion of a brand band rather than one either at the top of a sharp peak or on the sloping side of a peak or band.  In addition, the use a broad absorption band will minimize deviations from Beer's law caused by molar absorptivity over the range of wavelengths incident on the sample."  What I am taking away from this conversation is that the choice may depend on the particulars of the data collection (what the band width is), of the absorbance spectrum itself, and perhaps also the purpose of the measurement.

[Corribus]

This all supposes, also, that you are only interested in UV-Vis as a way to measure concentration. Other applications may require you to use peaks that otherwise would not be the ideal choice. The important thing is to be cognizant of the limitations of the measurement so you can avoid inaccuracies in your measurements. So, it's good to keep in mind what might be a problem with exciting into a very narrow absorption band, and adjust your method accordingly (changing your incident light bandwidth, for example).