Instrumental Errors A 1975 paper in Analytical Chemistry derived a model for error estimation in absorbance spectroscopy The model is based on the eqn below (derivation from Beer s Law on pg. 343 of text) Absorption Spectroscopy: Case I Error Case I error considers low quality detectors thermal noise is present (amount depends on temperature and quality) and predominates shot (quantum) noise is always present if the detector is of low quality, most other sources of error (other part of the instrument, placement error, etc.) are insignificant Absorption Spectroscopy: Case I Error Why does this happen?? Let s do the math! low absorbance at low A, P P 0, since A = log P 0 - log P, the difference between the log s is very small and uncertainty increases detector is trying to distinguish between a small change on top of the full power of P 0 if there is any noise (thermal or shot noise) then the noise is amplified at low absorbance Case I Error A = log P 0 - log P = - log (P/P 0 ) s T= 0.001 or 0.1% Case I Error high absorbance at high A, P 0, since A = log P 0 - log P, log P detector is receiving very little signal, so the dark current of the detector becomes significant dark current the current the detector outputs when exposed to no photons again, the noise is magnified the noise is magnified at low absorbance values 1
Case I Error A = log P 0 - log P s T= 0.001 or 0.1% Case I Error you will study these errors during the Instrumental Error lab What can you surmise about the detectors of these two instruments? Absorption Spectroscopy: Case II Error Case II Error Case II error considers medium quality detectors thermal noise and dark current are very low shot (quantum) noise is always present and is proportional to the photocurrent (I) The noise should increase when I is low or high? high Is I high at high or low absorbance? low Absorption Spectroscopy: Case III Error Case III error considers high quality detectors dark current, thermal and shot noise are very low the dominant noise source is flicker (1/f) noise Errors in Absorption Spectroscopy Case I error: noisy detector the detector has a large amount of dark current, which becomes significant when the absorption is high thermal noise plagues measurement shot noise are minor cheap UV-vis detectors or any thermal detectors Case II error: shot noise limited shot noise plagues better detectors small noise gets amplified at high Abs Case III error: virtually noise free detector does not limit the precision flicker noise in the source and/or placement error are the largest errors 2
Pre-Lab Problem CAPA set #7 in class chem380l Use Instrumental Error Excel template on web % Transmission values for a slit width of 0.30 mm conc.(g/ml) rep.1 rep.2 rep.3 rep.4 rep.5 rep.6 0.1314 19.72 19.26 19.69 20.37 20.03 20.52 0.0329 59.56 59.13 59.39 59.29 58.71 59.62 0.0131 81.11 81.75 81.79 79.23 82.31 81.60 0.0026 85.11 94.39 95.21 95.23 93.70 92.75 Spectra absorbance vs. wavelength (or frequency or wavenumber) is known as a spectrum (plural is spectra) spectral properties of an analyte depend on solvent, phase, temperature, ph, ionic strength, etc. Spectra When a sample is a mixture, narrow absorptions = high resolution = a more selective measurement Think about the AA compared to the Analysis of Mixtures experiment. Absorption Spectrum polar solvents = strong interactions = broaden spectrum Resolution and Phase This is an aqueous solution. Why are the absorptions so narrow? gas phase UV-vis spectra are highly structured condensed phase spectra have broad peaks and are sometimes unresolved 3
f orb e - are core e - = little interaction with solvent = narrow spectrum Slit Width Some instruments have slits that limit the amount and color of light entering the sample Slits affect the following the monochromicity of the light and therefore the sensitivity and the resolution the amount of light and therefore the SNR Slit Width and SNR You will see this in the lab Beer s Law Worksheet Slit Width 4
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Slit Width Smaller slits on the monochromator means Higher resolution (good!) Higher sensitivity (good!) Lower SNR (bad!) Review Why higher resolution? Why higher sensitivity? Why lower SNR? Spectroscopic Methods absorption spectroscopy does not work if molecules do not absorb light (duh!) UV-Vis native absorption in organic systems -bonds, conjugated systems weakly held electrons can absorb UV-vis UV-Vis native absorption in inorganic systems metal complexes where d subshell e - do the absorbing if there is no native absorption, then analyte must be derivatized 9
M.O. Diagrams * He 1s He 1s Absorption Transitions Organic molecules transitions require vacuum UV (high energy) not the focus of UV-vis absorption spectroscopy transitions require 150-250 nm not a common absorption and transitions require 200-700 nm the commonly observed absorption n e - stabilized by polar solvents; blue shifts usually e - destabilized by polar solvents; red shifts Inorganic molecules d de transitions in metal complexes affected by solvent and ligand Absorption Transitions -Quiz Identify the transition in the following molecules all but f f transitions HoCl 3 f f all but d d transitions d d f f 10