True peak absorbance

No matter what type of spectrometer is used, a measured spectrum is always slightly different from the true spectrum because of the measurement process, and it is important to recognize that instrumental effects often determine how well Beer s law is obeyed for any chemical system. For example, when a monochromator is used to measure a spectrum, the true spectrum is convolved with the spectrometer s slit function. The effect of this convolution is to decrease the intensity and increase the width of all bands in the spectrum. The convolution of Lorentzian absorption bands with a triangular slit function was reported over 50 years ago in a classic paper by Ramsay [1]. Ramsay defined a resolution parameter, p, as the ratio of the full width at half-height (FWHH) of the slit function to the true FWHH of the band. He showed how the measured, or apparent, absorbance, A, at the peak of a Lorentzian band varied as a function of the true peak absorbance, peak> resolution parameter. Not surprisingly, Ramsay showed that as... 

Figure 8.1. Variation of the measured, or apparent, absorbance, Ap, at the peak of a Lorentzian band as a function of the true peak absorbance, Ap j, plotted on a logarithmic scale for Lorentzian bands measured with no apodization (boxcar truncation). A, p = 0 B, p = 1.0 C, p = 3 D, p = 10 E, p = 25 F, p = 50. (Reproduced from [2], by permission of the American Chemical Society copyright 1975.)...

From equation 5, it is apparent that each shell of scatterers will contribute a different frequency of oscillation to the overall EXAFS spectrum. A common method used to visualize these contributions is to calculate the Fourier transform (FT) of the EXAFS spectrum. The FT is a pseudoradial-distribution function of electron density around the absorber. Because of the phase shift [< ( )], all of the peaks in the FT are shifted, typically by ca. —0.4 A, from their true distances. The back-scattering amplitude, Debye-Waller factor, and mean free-path terms make it impossible to correlate the FT amplitude directly with coordination number. Finally, the limited k range of the data gives rise to so-called truncation ripples, which are spurious peaks appearing on the wings of the true peaks. For these reasons, FTs are never used for quantitative analysis of EXAFS spectra. They are useful, however, for visualizing the major components of an EXAFS spectrum. 

Take 10 mL of commercial propan-2-ol and dilute to 100 mL with carbon tetrachloride in a graduated flask. Record the infrared spectrum and calculate the absorbance for the peak at 1718 cm-1. Obtain a value for the acetone concentration from the calibration graph. The true value for the acetone in the propan-2-ol will be 10 times the figure obtained from the graph (this allows for the dilution) and the percentage v/v value can be converted to a molar concentration (mol L-1) by dividing the percentage v/v by 7.326 e.g. 1.25 per cent v/v = 1.25/7.326 = 0.171 molL-1. 

The kinetic determination of any concentration as a function of time yields k, as in Eqs. (3-61) and (3-63). This is true no matter whether one follows [A] or [P],. The latter point, although correct, can sometimes seem illogical. Suppose one measures the buildup of P2 (say), by monitoring an infrared peak, an ultraviolet band, or an NMR signal. Assume that neither A nor any product other than P2 contributes to the signal. Surely then, will it not be k2 that is obtained from the kinetic analysis The answer is no. Consider the result from Eq. (3-63), which gives the concentration of the one product in terms of its absorbance (per unit optical path) and molar absorptivity (62) ... 

It follows, that if the detector was to be effective and produce the true Gaussian form of the eluted peak then, (Ca), must at all times be unity and consequently the detector must have the same plate capacity as that of the column. This means that the detector must employ the same absorbant, have the same geometry and be packed to give the same plate height as the column. It is obvious to accomplish this, the column must also be the detecting cell and the temperature sensing element must be placed in the column packing itself. 

Finally, two related studies can be mentioned here. It was noted that when a quartz plate was immersed overnight in a solution of Pb(C104)2 and poly(vinyl alcohol) through which H2S had been bubbled, a film formed on the plate parallel with formation of a colloidal PbS sol [47]. The film was extremely thin (maximum absorbance of <0.015 at 400 nm). The absorption spectrum of this film was similar to that of the PbS sol and consisted of several absorption peaks with an absorption onset of ca. 630 nm (1.97 eV). It is not clear that this is the true bandgap onset, for the same reasons as discussed previously (weak absorption close to the bandgap). The XRD crystal size of the precipitate was ca. 3 nm. 

It is often simpler to express the rate law in terms of directly measured physical properties (PP), such as absorbance, NMR peak areas, or conductivity, provided the chosen PP is linearly related to the concentration. For example, Equation 8.7 can be recast in terms of absorbance as shown in Equation 8.9, where Abs is absorbance. Regardless of the rate law, it will always be true that the ratio [A]/[A]0 = (PP/ — PPinf)/ (PP0 — PPinf), where subscripts 0, t, and inf refer to initial time (time zero), time t, and infinitely long time, that is, after the reaction had reached completion. Both [A]/[A]0 and (PP/ — PPinf)/(PP0 — PPinf) represent the fraction of the reaction that remains to be completed at time t. The somewhat more complicated rate expression in terms of physical property arises from the fact that the value of the physical property, unlike the concentration of reactant A, does not necessarily decrease to zero at the end of the reaction. For example, both the formation of absorbing products or a nonzero baseline will affect the absolute absorbance readings throughout the reaction, but not the ratio (Abs/ — Absinf)/(Abs0 — Absinf). 

The two Ma papers do not discuss the visual appearance of their spectral samples. However, the absorbance levels they report are very low (compared to the peak spectral absorptions of in-vivo photoreceptor cells which are in the 80% range). The measurement of absorbance values in simple spectral cells may not be meaningful due to the fact the sample material does not participate in a true solution. 

A pH-sensitive dye induces two different absorption spectra for the protonated (AH+) and deprotonated (A) forms. This means that at low pHs, we observe an absorption spectrum of the protonated form only, while at a high pHs only the absorption spectrum of the deprotonated form is recorded. However, this is not always true, since many dyes can absorb in both forms, protonated and deprotonated. The absorption spectra maxima of the two forms are different. The protonated form displays an absorption spectrum with a peak that is shifted toward short wavelengths in comparison with the absorption spectrum of the deprotonated form of the dye. 

---