Beer’s law deviations

Spectroscopic instruments in the UV and visible regions are usually equipped with one or more devices to restrict the radiation being measured to a narrow band that is absorbed or emitted by the analyte. Such devices greatly enhance both the selectivity and the sensitivity of an instrument. In addition, for absorption measurements—as we saw in Section 24C-2—narrow bands of radiation greatly diminish the chance of Beer s law deviations due to polychromatic radiation. Many instruments use a monochromator or filter to isolate the desired wavelength band so that only the band of interest is detected and measured. Others use a spectrograph to spread out, or disperse, the wavelengths so that they can be detected with a multichannel detector. 

Rozou, S. Antoniadou Vyza, E. An improved HPLC method overcoming Beer s law deviations arising from... 

Application of the Matrix Method to Mixtures Involving Beer s Law Deviations... 

In industrial control analysis the components in many mixtures vary over relatively narrow concentration ranges. Suppose the components of such a mixture have Beer s law deviations approximating Fig. 1. The equation for the dotted line in. Fig. 1 is... 

A graphical method of successive approximation which uses no matrix in the calculations has been described by L. V. Daasch. This method also should work when Beer s law deviations occur. 

This full-spectrum method improves the precision over those that use only a few wave numbers. Corrections can be added for Beer s law deviations or fitting spectral baselines. However, all components present must be included in the calibration mixtures. 

Calibration curves showing positive and negative deviations from Beer s law. 

According to Beer s law, a calibration curve of absorbance versus the concentration of analyte in a series of standard solutions should be a straight line with an intercept of 0 and a slope of ab or eb. In many cases, however, calibration curves are found to be nonlinear (Figure 10.22). Deviations from linearity are divided into three categories fundamental, chemical, and instrumental. 

Chemical Limitations to Beer s Law Chemical deviations from Beer s law can occur when the absorbing species is involved in an equilibrium reaction. Consider, as an example, an analysis for the weak acid, HA. To construct a Beer s law calibration curve, several standards containing known total concentrations of HA, Cmt, are prepared and the absorbance of each is measured at the same wavelength. Since HA is a weak acid, it exists in equilibrium with its conjugate weak base, A ... 

Stray radiation is the second contribution to instrumental deviations from Beer s law. Stray radiation arises from imperfections within the wavelength selector... 

For small concentrations of analyte, Pstray is significantly smaller than Pq and Py, and the absorbance is unaffected by the stray radiation. At higher concentrations of analyte, however, Pstray is no longer significantly smaller than Py and the absorbance is smaller than expected. The result is a negative deviation from Beer s law. 

The emission spectrum from a hollow cathode lamp includes, besides emission lines for the analyte, additional emission lines for impurities present in the metallic cathode and the filler gas. These additional lines serve as a potential source of stray radiation that may lead to an instrumental deviation from Beer s law. Normally the monochromator s slit width is set as wide as possible, improving the throughput of radiation, while being narrow enough to eliminate this source of stray radiation. 

A study of the effect of substitution patterns in oxadiazoles and isoxazoles and their effect on the UV spectra in the lO -lO M concentration range was performed. Hypso-chromic effects and deviations from Beer s law were observed and were believed to be associated with antiparallel, sandwich-type self-association via dipole-dipole interactions. Beer s law is followed when the molecular dipole moments are small or when self-association is sterically hindered. 

Typical standard curves for a technical grade of parathion are shown in Figure 3. Beer s law is followed within the range 10 to 400 micrograms of parathion per milliliter of dyed solution. Deviation becomes apparent outside this range, under the conditions of test. 

Niclosamide and its dosage forms were spectrophotometrically estimated by reaction with aqueous 4-aminophenazone in the presence of ammonia and measurement of absorbance of the resulting oxidative coupling product at 520 nm [50], Beer s law was obeyed in the concentration range 1.25-10.0 pg/mL the relative standard deviation was 1.51% and the recovery 98.9 99.6%. Dosage form excipients did not interfere. 

Our first chapter in this set [4] was an overview the next six examined the effects of noise when the noise was due to constant detector noise, and the last one on the list is the first of the chapters dealing with the effects of noise when the noise is due to detectors, such as photomultipliers, that are shot-noise-limited, so that the detector noise is Poisson-distributed and therefore the standard deviation of the noise equals the square root of the signal level. We continue along this line in the same manner we did previously by finding the proper expression to describe the relative error of the absorbance, which by virtue of Beer s law also describes the relative error of the concentration as determined by the spectrometric readings, and from that determine the... 

There are no known exceptions to the Lambert law for homogeneous samples. Beer s law is a limiting case applicable only to dilute solutions and monochromatic radiation. Deviations may be observed in practice, but these are all apparent in the sense that the limiting conditions have been contravened either chemically or instrumentally. Such deviations show as a curvature of the calibration graph, but this does not necessarily preclude the use of a particular method unless the deviation is non-reproducible. Apparent deviations may be summarized as follows ... 

You should have noticed that the Beer s law plot constructed in Experiment 19 is linear between concentrations of 1 and 4 ppm Fe. At some point beyond 4 ppm, there will be a deviation from Beer s law. Design and conduct an experiment that will precisely determine the concentration at which this occurs. 

Deviations from Beer s law are in evidence when the Beer s law plot is not linear. This is probably most often observed at the higher concentrations of the analyte, as indicated in Figure 8.10. Such deviations can be either chemical or instrumental. 

A deviation from Beer s law refers to the linear relationship between absorbance and concentration becoming nonlinear, as in Figure 8.10. 

The optimum working range for percent transmittance (to avoid instrumental deviations from Beer s law) is between 15 and 80%, which corresponds to an absorbance range of 0.10 to 0.82. 

Microgram amounts of pertechnetate can be determined by measuring the extinction of its colored complex with toluene-3,4-dithiol in 2.5 N hydrochloric acid after extraction into carbon tetrachloride . One hour must be allowed for the development of the color. The molar extinction coefficient at 450 nm is 15,000. Beer s law is followed over the range of 1.5 to 16.5 fig Tc per ml. The overall error does not exceed a standard deviation of 5%. Because many cations interfere, an initial separation of technetiiun is necessary. 

As was pointed out in Section 4.2.1, the plot of absorbance versus concentration becomes less than linear beyond a threshold concentration due to non-negfigible interactions between absorbing molecules. The baseline shifts discussed above may equally give rise to deviations from Beer s Law. Upstone discusses fluorescence (which may be removed by inserting a cutoff filter between sample and detector) and peak shifts due to changes in pH. ... 

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