In-class Questions: General Background on Molecular Spectroscopy
- Page ID
- 111917
Electromagnetic Radiation
- What is the relationship between the energy (E) and frequency (\(\nu\)) of electromagnetic radiation?
Students usually remember the equation that E = h\(\nu\) without any prompting on my part and determine that there is a direct proportionality between the two.
- What is the relationship between the energy and wavelength (\(\lambda\)) of electromagnetic radiation?
Students usually remember that c = \(\lambda\nu\) without any prompting on my part and determine that there the energy and wavelength of radiation are inversely proportional.
- Write the types of radiation observed in the electromagnetic spectrum going from high to low energy. Also include what types of processes occur in atoms or molecules for each type of radiation.
The students’ individual ability to identify all the different types of electromagnetic radiation and rank them in energy usually varies widely. Within a group most are able to generate a complete or close to complete list and rank those that they are most familiar with. One of the most perplexing to most students is where to put microwave radiation in the energy ranking.
Identifying the types of processes that occur in atoms or molecules for each type of radiation presents more difficulties.
What type of process do you already know about in molecules and what radiation produces them?
Within groups they can determine that UV/VIS involves transitions of valence electrons and IR corresponds to molecular vibrations. Many are familiar with the idea of a nuclear spin flip from their organic chemistry course, although they may or may not remember that RF radiation is used to excite nuclear spin flips. Some know that it is possible to rotationally excite molecules, although they often do not know that rotational excitation occurs in the microwave region of the spectrum. It is uncommon for them to know what processes occur with \(\gamma\)-rays and X-rays. Many are not familiar with the idea of an electron spin flip in paramagnetic substances and that it occurs in the microwave region of the spectrum.
At this point, I briefly discuss the difference between absorbance and emission. I also discuss how different spectroscopic methods are of different utility for compound identification and compound quantification. Some techniques (e.g., NMR spectroscopy) are useful for interpretation and identification, whereas others (e.g., IR spectroscopy) are useful for identification but not that amenable to interpretation and instead require use of a computer library to determine the best match.
I then go over the basic design of an absorption spectrophotometer and present them with the following series of questions on Beer’s Law.
Beer’s Law
- What factors influence the absorbance that you would measure for a sample? Is each factor directly or inversely proportional to the absorbance?
Students quickly realize that the absorbance relates to the concentration and that it is a direct proportion. They often do not think of path length as a variable, I suspect because they are given specific cuvettes to use in any prior measurement they have performed and then don’t think the path length is something they could adjust.
What would be the effect of increasing the path length?
This is usually sufficient for them to see that there ought to be a direct relationship between path length and absorbance. Some students are familiar with the concept of an extinction coefficient from other courses, but rarely do they have an exact understanding of the meaning of the extinction coefficient. I indicate that molar absorptivity is another term for the extinction coefficient and at this point we can write Beer’s Law on the board.
How would you measure a spectrum and draw an example of a UV/VIS absorbance spectrum of a chemical species?
Someone in each group usually has enough prior experience and knows that recording a spectrum involves measuring the absorbance as the wavelength is scanned. If so, they can draw a spectrum where the absorbance varies with wavelength so that there are regions of high absorbance and regions of low absorbance. Some may think of an atomic (line) spectrum whereas others think of a molecular absorbance spectrum, and I clarify that they are different but that we can consider the nature of the extinction coefficient using either of them. I also prompt them to consider the concentration and path length when someone records a spectrum, and they realize that both are fixed.
Explain why the absorbance is high in some regions and low in others (or that lines in an atomic emission spectrum have different intensities).
They can usually rationalize that chemical species have the ability to absorb some wavelengths of light and not others, and when pushed on the differences in intensities of lines in an atomic emission spectrum, that some transitions must have a higher likelihood of occurrence than others. They sometimes wonder whether the difference in intensities reflects differences in the detector response, so it is important to point out that it is a fundamental process taking place in the chemical species. At this point, we can now discuss how the extinction coefficient or molar absorptivity is a measure of the probability that a particular wavelength of light can be absorbed. We discuss the aspect of energy transitions and that different transitions within a chemical species have different probabilities of occurrence. I introduce the idea of selection rules and that it is appropriate to talk about the degree to which a transition is allowed. I also introduce the idea that there are some transitions that are not allowed or forbidden.
- If you wanted to measure the concentration of a particular species in a sample, describe the procedure you would use to do so.
The groups’ first response to this is often rather superficial. They tend to think more of putting the sample into a cuvette, measuring the absorbance and somehow equating that with concentration without explicitly stating that you first need to select a wavelength to use and prepare a standard curve.
Referring back to the spectra from the problem above that are still on the board, I point out that the analyst must set a wavelength.
Which wavelength would you choose?
They usually see right away that \(\lambda\)max is the preferable one and that with the highest molar absorptivity would provide the largest response. I also push them to examine how \(\lambda\)max would provide the lowest possible detection limits of any of the wavelengths.
Can you imagine a situation where you would not use \(\lambda\)max for the analysis?
Most groups quickly realize that you would need a different wavelength if the sample had another substance in it that absorbed at \(\lambda\)max.
Having selected the proper wavelength, how would you relate the absorbance of the sample with an unknown concentration to the actual concentration?
At this point, they realize the need to examine a sample with a known concentration and some students realize that they will need a standard curve with several concentrations whereas others may think only one known concentration is acceptable.
We can then discuss the concept of a blank solution and examine how a standard curve ought to be a linear plot that goes through the origin. We also examine how the slope of the standard curve can be used to determine the molar absorptivity.
- Suppose a small amount of stray radiation (PS) always leaked into your instrument and made it to your detector. This stray radiation would add to your measurements of Po and P. Would this cause any deviations to Beer's law? Explain.
It is helpful to draw a picture on the board that shows a basic design of the spectrophotometer and indicates Po, P and Ps.
Consider the situation of a sample with a high concentration and another sample with a low concentration of analyte, and think about the relative magnitudes of the different terms at these different conditions.
It can also be useful to indicate on the board the way in which the stray radiation gets incorporated into the expression for the absorbance [A = log(Po + Ps)/(P + Ps)], and to examine these terms at the extremes of high and low concentrations. At this point, the groups can usually rationalize that the (P + Ps) term will approach Ps or a constant as the concentration of analyte is increased. When asked to draw the standard curve that would be observed, they can draw one that shows a negative deviation at higher concentrations.
- The derivation of Beer's Law assumes that the molecules absorbing radiation don't interact with each other (remember that these molecules are dissolved in a solvent). If the analyte molecules interact with each other, they can alter their ability to absorb the radiation. Where would this assumption break down? Guess what this does to Beer's law?
Groups usually realize that the molecules are more likely to interact with each other at high concentration.
- Beer's law also assumes purely monochromatic radiation. Describe an instrumental set up that would allow you to shine monochromatic radiation on your sample. Is it possible to get purely monochromatic radiation using your set up? Guess what this does to Beer's law.
What is meant by “purely monochromatic radiation”?
We have not yet discussed the specific details of a monochromator, but based on earlier discussion related to selecting a \(\lambda\)max value, they already know that some form of wavelength selection device is necessary. They are familiar with the ability of a prism to disperse radiation. I point out that gratings are more commonly used and that we will discuss gratings in more detail later in the course. With a drawing of a prism on the board, and prompted as to how they would direct only one wavelength on a sample, they realize that it will be necessary to use a slit that blocks out the unwanted wavelengths, but that the radiation passing through the device will never be purely monochromatic. At this point, without explaining it further, I indicate that polychromatic light will lead to negative deviations from Beer’s Law, especially at higher concentrations.
- Is there a disadvantage to reducing the slit width?
What varies as one goes from a wide to a narrow slit width?
The groups realize that a wide slit width gives more power (and I point out how we will equate the number of photons with power) and a wider range of wavelengths, whereas a narrow slit width gives fewer photons and a smaller range of wavelengths.
Do you want high or low source power?
Based on our prior discussion of the effect of stray radiation they usually realize that higher power is desirable. This is also a useful time to further introduce the presence of noise and discuss how the signal-to-noise ratio is an important consideration in spectroscopic measurements. They realize that this argues for the use of wide slits.
Is there any situation where you would want to use a small slit width?
The groups can usually figure out that the ability to distinguish two nearby peaks is improved with smaller slit widths. This allows us to discuss what is meant by “resolution” in spectroscopic measurements.
Finally, we can examine Figure 1.5 to look at the effect of polychromatic radiation on the deviation from Beer’s law. I also draw Figure 1.6 on the board and ask what wavelength they would use for the analysis and to justify why. They readily appreciate that the broader region is better for use because of the prior discussion about deviations to Beer’s Law and because slight changes in the setting of the monochromator will have less significant effects on the measured absorbance.
- Consider the relative error that would be observed for a sample as a function of the transmittance or absorbance. Is there a preferable region in which to measure the absorbance? What do you think about measuring absorbance values above 1?
Examine separately the extent of error that would occur at low and high concentration.
Groups can usually determine that the error at the extremes of concentration is more pronounced and there must be some mid-range absorbance measurements where the error is minimized.
Determine the percent transmittance that gives an absorbance value of 1 and consider the likelihood that negative deviations to Beer’s law occur in this region?
They can figure out that an absorbance of 1 equals only 10% transmittance and realize that negative deviations are likely to occur, enhancing the error of the measurement and reducing the number of significant figures that could be measured. I also discuss with them whether it would ever be acceptable to use a non-linear standard curve.
It is ever acceptable to extrapolate a standard curve to higher concentrations?
They have enough understanding to determine that the possible onset of negative deviations to Beer’s Law means that one cannot reliably extrapolate to higher concentrations.
- What are some examples of matrix effects and what undesirable effect could each have that would compromise the absorbance measurement for a sample with an unknown concentration?
After describing to the class what is meant by a matrix effect, groups are given a few minutes to discuss this question and I have them report out on what they identified. In the aggregate the class is usually to arrive at important variables such as pH, the possibility that other species might absorb at \(\lambda\)max, and the possibility that another species interacting with the analyte could alter the value of \(\lambda\)max. Prompting may be required to have them consider scatter from suspended particulate matter and that the solvent may have an effect as well.
Are there any special constraints that must be considered in selecting a buffer?
They can usually identify that the buffer can’t absorb at \(\lambda\)max.