i wasn't being sarcastic =) i rediscover stuff all the time, and it always feels nice.
this is really long.. sorry, but you asked a lot =)
resolving the components of a sample: yes, although UV/VIS isn't very good at it. assuming you tried to get out the impurities first, you would get a curve with several peaks, and those numbers are enough to identify the substance. especially if you only have a few possibilities.
far from pure: filter it, neutralize it and dissolve the residue in something non-polar.
could you do it accurately with cheap equipment at home: well, it's not something every candy kid would be able to do... but it may work. probably worth trying, you could get some semi-interesting results from it.=)
to clarify.. what i think you want to do, is split a white light source with a diffraction grating, then move the sample and photodiode across the spectrum and measure the absorbances, right? (or maybe you want to move the diffraction grating; same idea). this is the usual means of doing it. a white light (tungsten filament) is split with a prism or diffraction grating, a narrow band of wavelengths passed through a slit, and the absorption measured with a photodiode... so you've basically got it.
stuff like the vibrational modes of C-O, C=O, H-O, Si=0: that's IR, not UV/VIS. IR is useful and fun, but it requires a laser... btw, Si=O is very rare; double bonds with silicon are very, very hard to form (but possible). im guessing you're talking about silica gel, which actually only has Si-O-Si bonds, and Si-OH bonds.
metal oxides from (eg) water: you want to use distilled water, right? =)
the glass surrounding the sample: no! glass is amorphous and interferes with light. UV/VIS requires a quartz cuvette, which is always 1x1 cm internally to simplify the path length (l) in the calculation.
Bond strengths and therefore absorption wavelengths would naturally vary depending upon their environments, O=C=O being different from CH2=0, but would you be able to pick that up?
yes, because you run a background sample with just the solvent, then subtract that from the specimen. air is a big problem with IR because carbon dioxide is IR-active. the background takes care of it though.
Is there any hope of achieving a suitable balance using a ruler and a protractor as measuring devices?
using the tech sheet for the diffraction grating and some optics equations you could work out the distance-length-angle relationship of the spectrum. you're not going to get perfect results anyway so it should work if you use a ruler and protractor. your biggest problem is going to be restricting the wavelengths that impinge on the sample simultaneously. somehow, you'll need to find a way to focus a narrow section of the visible light spectrum on your sample at once. remember, that quartz cuvette is going to be 1 cm wide, so the spectrum will have to be on that kind of scale.
if I can't tell the difference between MDMA and PMA then it aint worth doing.
i'm not *sure* about that...i calculated some orbitals and they do seem to have very similar differences in energy, but you might be able to get some results. especially if you used Mandelin derivatives.
Also, I wouldn't want to be messing around calculating absorption coefficients if I could help it. Anyone know any nice URLs where this sort of data can be gotten/derived? (I know it's a long shot!)
you can look up electron transition energies here:
http://webbook.nist.gov/chemistry/
and this is a link to a database with information on 125 compounds, not including anything interesting, but at least you can see how the spectra work. the site also has several examples explaining the theory behind it.
http://www.omlc.ogi.edu/spectra/PhotochemCAD/html/du98.html
you can calculate the extinction coefficient with A = ecl if you know the concentration, or you can calculate the concentration if you know the extinction coefficient (A is measured, l is given as 1 cm). on the other hand, you don't necessarily need that at all. just the absorption curve and the peak wavelength will be characteristic of the substance. knowing epsilon would be useful because then you could determine the exact composition of the mixture in the pill...but you'd still need a scale to determine what fraction of the pill you sampled.
important limitations of UV/VIS
your setup would only work for visible light since it depends on a measurement of the spectrum. obviously, if a compound is colorless, it will not have any transitions in the visible light range. but i believe the *substance of primary interest* is yellow, right?
Any quantitative information on doing this from first principles would be helpful. (Definitely a long shot).
not at all! remember, UV/VIS spectra are a result of molecular orbital transitions. therefore:
E_transition = E_excited - E_ground-state
the energy values can be determined by several methods, all of which are approximations for the E term in the Schroedinger equation. for example, MNDO, or the extended Huckel method. there's a bit more to it than that, of course, because the MO energies of every molecule are different. in the event you want to know more about that (warning: hardcore math!) a quantum or physical chemistry textbook will tell you more than humanity deserves to know. you'll find you can use the particle-in-a-box model to predict a lot of things, including bond length, bond energy, and orbital energy, with some degree of accuracy. especially the energy part:
E = n²²² / 4 ma²
(where n = principal quantum number, h-bar = Planck's constant / 2 pi, m = mass, a = length of the box)
anyway.. you'll need to use a puter program of some kind to actually calculate the orbitals. hypercube's hyperchem suite is really good for it (it even calculates symmetry, which is an evil, evil bitch) and has a 20-day demo (but no crack and it's damned expensive). then, you need to understand what transitions are allowed. once youve got the transition energies worked out, you know the peak absorption wavelengths (recall E = hv = hc/wavelength, which you probably know if you've followed this far)... the curve will be somewhat normally distributed around this; the shape and amplitude is related to quenching and intricate matters of how electrons actually undergo transitions
(triplet states, singlet states, stokes shift, that kinda stuff.). that's basically how it works. i might be able to go into more detail if you want...
anyway, all of that goes into determining what the molar extinction coefficient epsilon is (whether or not you know it). that goes into the beer-lambert equation A = ecl, and that's how you interpret the results.
diffraction gratings.. heh.. one time some candykid put those trippy glasses on me and gave me an involuntary lightshow. i felt violated. i just stood there explaining that i wasn't on e, and started talking about diffraction gratings. i think it's kind of ironic that when niels bohr looked at the emission spectrum of hydrogen, he saw the first hints of quantum mechanics, and when candies look at glowsticks, it's trippy and fun.
you may draw analogies with how the average raver treats electronic music, then try to explain to them how a square-wave bassline is an infinite series of sinusoidal harmonics, and how that somehow makes the Sounds deeper and more universal than any other human music. they will, most likely, say it's like disco, or about plur.
unfortunate.