Lambert plots

The absolute values of the absorption cross sections of HCHO have been somewhat controversial. This appears to be due to a lack of sufficient resolution in some studies as discussed in Chapter 3.B.2, if the spectral resolution is too low relative to the bandwidth, nonlinear Beer-Lambert plots result. The strongly banded structure means that calculations of the photolysis rate constant require actinic flux data that have much finer resolution than the 2- to 5-nm intervals for which these flux data are given in Chapter 3 or, alternatively, that the measured absorption cross sections must be appropriately averaged. One significant advantage of the highly structured absorption of HCHO is that it can be used to measure low concentrations of this important aldehyde in the atmosphere by UV absorption (see Sections A.ld and A.4f in Chapter 11.). 

Figure 23.5 Beer-Lambert plot of absorbance A against concentration c...

An example of a Beer-Lambert plot is shown in Fig. 20.34. This shows the aborbance of 4-nitrophenoi (C6H4OHNO2) in ethanoi soiution at a waveiength of 312 nm. The ceii pathlength was 1.0 cm. Caicuiate the moiar absorption coefficient of 4-nitrophenoi at 312 nm. 

Rg. 20.34 Beer-Lambert plot for 4-nitrophenol in ethanol solution at 312 nm. 

It is possible to purchase variable-pathlength liquid transmission cells, which commonly have a pathlength that can be varied between 5 pm and 5 mm. A suitable sample must be chosen, preferably a neat solvent that has relatively wide peaks, the resolution of the spectrometer must be set so that the resolution parameter, p, is no greater than 0.5, and a Norton-Beer medium apodization function should be applied. A series of measurements at increasing pathlengths should yield a linear Lambert plot if the instrument is functioning correctly. Some instruments will exhibit linear Lambert plots up to 4 AU however, this is unusual, and an acceptable... 

Harrington and Sundheim report that in molten KSCN, C0CI2, CoBr2, and Co(SCN)2 produce identical spectra. In fact, a Beer-Lambert plot of data obtained with the three salts produced a straight line. It was concluded that, since no evidence for mixed complexes was obtained, the species present was a tetrahedral Co(SCN) complex. Recent work by Egghart has confirmed the tetrahedral nature of the cobalt thiocyonate complex which is suggested to involve Co-N bonding. 

Lambert and coworkers,7 18 25 who were first to study this interesting system, have shown that the nature of the anion (nitrate or carbonate) formed on the catalyst surface in presence ofNa+ plays an important role in the sharpness of the volcano plot obtained upon varying Uwr.-... 

One-dimensional data are plotted versus an experimental variable a prime example is the Lambert-Beer plot of absorbance vs. concentration, as in a calibration run. The graph is expected to be a straight line over an appreciable range of the experimental variable. This is the classical domain of linear regression analysis. 

Fig. 4.13. Evidence for the presence of 5 2 per cent 6Li in the warm halo subdwarf HD 84937 with [Fe/H] = -2.4, 7 = 6090 K. The left panel shows synthesized profiles for 0, 5 and 10 per cent 6Li with the observational points on an absolute wavelength scale in the rest frame of the stellar photosphere. The right panel shows the central wavelengths of the doublets of each isotope and a deviation plot for the three hypotheses on 6Li/7Li. Adapted from Smith, Lambert and Nissen (1993).

A valuable means of comparing two or more methods with regard to precision, conformity to the Beer-Lambert law and the range of concentrations usefully measured is to plot calibration data in the form of... 

Fig. 2. Arrhenius plots for the decomposition of dimethyl zinc. 1, Price and Trotman-Dickenson solid line, 16 torr toluene dotted line, 5 torr toluene 2, Lambert, approx. 760 torr (cyclohexane +7 % alkyl) 3, composite curve obtained from rate coefficients of Price and Trotman-Dickenson corrected to infinite pressure and from Lambert s values. The composite curve has been displaced upwards by 2.0 log units. Open circles Topor, 22-24 torr (argon+2.4 torr dimethyl zinc). 

First the Beer-Lambert Law is tested with the solutions of known composition at max of solution by plotting (absorbance) versus concentration as shown in Fig. 1.9. The concentration range for which the plot is a straight line is determined and method is applied within this concentration range. 

To check that phenol was not self-associated at the concentration used, Sousa Lopes andThompson repeated the calibration experiments (i.e., the study of the temperature variation of el) for several phenol concentrations. Good linear plots of A against c at each temperature were observed, indicating that the Lambert-Beer law is valid and that the self-association is negligible. 

Concentrations in the region of 0.1 mol 1 1 are often convenient but it obviously depends upon such factors as the amount of substance available, the cost, the solubility, etc. From this stock solution, a series of accurate dilutions are prepared using volumetric glassware and the absorbance of each dilution measured in a 1-cm cuvette at the wavelength of maximum absorbance for the compound. A plot of absorbance against concentration will give an indication of the validity of the Beer-Lambert relationship for the compound and a value for the molar absorption coefficient may be calculated from these individual measurements or from the slope of the linear portion of the graph ... 

The analysis of a range of known concentrations of the test substance is necessary to validate the Beer-Lambert relationship. If the plot of absorbance values against concentration results in a straight line then either of the two previously outlined methods may be used. If, however, the resulting graph shows a curve instead of a straight line then the implication is that the actual value for the molar absorption coefficient is dependent to some extent upon the concentration of the compound and as a result invalidates both methods. In such circumstances a graphical plot (calibration curve) will be needed. 

In six-membered heterocycles Lambert and co-workers (143,164) noticed a clear electronegativity dependence of C(4) resonances (Figure 4), the slopes in the plots being - 5.3 for 52 and - 3.5 ppm/electronegativity unit for 53 (Scheme 22). 

Fig. 1.3 Second-order kinetic plot for decay of RefCO) obtained by flash photolysis of 120 pM RejlCOlm with 10 mM CO in isooctane. (CO slows further reactions of RelCO) ) At X = 535 nm, the molar absorbance coefficient, 8m of Re(CO)5 is 1.0 x lO lVf cm". Since therefore from Beer-Lambert law (Df-Df) = [A]e ,l, where D s are optical absorbances and 1 is the path length (10 cm), the slope of Fig. 1.3 is 2k/s and 2k therefore equals (5.3 x lO KlO lflO) = 5.3 x lO M- s". Ref. 25. Reproduced with permission of the Journal of the American Chemical Society. 1982, American Chemical Society.

Practical Considerations. Typical absorption assay methods utilize ultraviolet (UV) or visible (vis) wavelengths. With most spectrophotometers, the measured absorbance should be less than 1.2 to obtain a strictly linear relationship (/.c., to obey the Beer-Lambert Law). Nonlinear A versus c plots can result from micelle formation, sample turbidity, the presence of stray light (see below), bubble formation, stacking of aromatic chromophores, and even the presence of fine cotton strands from tissue used to clean the faces of cuvettes. One is well advised to confirm the linearity of absorbance with respect to product (or substrate) concentration under the exact assay conditions to be employed in... 

Figure 11.18—Beer-Lambert s law. Representation of absorbance and a plot showing the linearity of absorbance for solutions containing an increasing amount of potassium permanganate.

A standard curve for the data is plotted in Figure 2.6 on page 45. Note the linearity, indicating that the Beer-Lambert law is obeyed over this con-... 

Fig. 10. The Lambert-Salter plot. Relation between Z1>0 and vmln for simple polyatomic molecules at 300 °K. Values listed in order from the bottom upwards. O, molecules containing no hydrogen atom C,Ft CF,Br, CF,BrCl CF,C1, CFC1S CClt CF,Br CF,C1 SF, CF, CS, NsO COS Cl, CO,. , molecules containing one hydrogen atom CHC1,F CHC1, CHC1F, CHF,. , molecules containing two or more hydrogen atoms CH,C1F CH,I CH,F, CH,Br C,H, CH,C1 C,H,0 C,H, cyclo-C,H, CH,F CH(. , deuterated molecule CD,Br.

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