Error in absorbance measurement

Figure 11.23—Average curves representing each of the instrumental causes of error in absorbance measurements and the global curve (4) resulting from their sum (see text).

Not only can errors in absorbance measurements arise from non-linearity in the detector circuitry, but distortion in the linearity of the position of channel detector elements can lead to a corresponding distortion of the measured intensity profile. The geometric distortion of the SIT vidicon, as stated in the specification sheet supplied by the OMA manufacturer, is typically 2 channels between channels 100 and 400 for a 2.5 mm high image centered on the tube. This distortion is sufficient to require correction of data obtained for experiments with steep concentration gradients in our system. 

Fig. 4.14. Relative error in absorbance measurement for increasing absorbance values. Parameter is an increasing stray light (A) 0.075% (B) 0.05%, (C) 0.025%, (D) 0.01%, (E)...

Anderson RJ and Griffiths PR (1975) Errors in absorbance measurements in infrared Fourier transform spectrometry because of limited instrument resolution. Analytical Chemistry 47 2339-2347. 

Figure 10 shows the absorbance response of an indicator to pH change. As can be seen, with the use of an indicator, the pH measurements can be made only over a range of about two pH units, i.e. pKa 1. Beyond this range, the change in absorbance with pH becomes small and the error in pH measurements will be large. 

As shown in Figure 20, the excitation spectrum for pyropheophorbide fluorescence does not appear to include any significant contribution from light absorbed by the carotenoid moiety. Quantitatively, singlet energy transfer must be less than ca. 7%, which is the limit of error in these measurements. 

Absorption by the flame atomizer itself as well as by concomitants introduced into the flame or electrothermal atomizer can cause serious problems in atomic absorption. Rarely are there interferences from absorption of the analyte line by other atoms since the hollow-cathode lines are so narrow. Molecular species can absorb the radiation and cause errors in AA measurements, however. 

The theoretical bases of differential spectrophotometry have been presented [22]. The relative error of absorbance measurement is 0.2-0.5%, and is less in differential spectrophotometry [25-28] than in the regular method. Hence, the precision of differential spectrophotometry is comparable with that of gravimetric and titrimetric methods. This fact enables the technique to be applied in the determination of higher contents of the analytes. 

The effects of systematic errors are of two kinds. A constant shift in the wave numbers of the lines of a band—produced, for example, by an alignment error in the measuring process-can be absorbed into the band origin and, hence, into the vibrational intervals of the molecule. 

Figure 9.28 Relative errors in quantitative UV spectrometry. Curves representing the average of each of these errors (1 to 3) in absorbance measurements, as well as the relative standard deviation (RSD) of concentration determination as a function of absorbance resulting from their sum (4).

For transparent substrates, the spread of incident angles around the average value for the central incoming ray affects the p-polarized absorbance as shown in Fig. 3.70 for spreads of 0, 8°, and 16°. When the angle of incidence is near the Brewster angle, the error in the measured absorbance increases abruptly due to the uncertainty in the beam convergence. 

It is important to use different monitors for the resonance and thermal fluxes, and to use positions of different < o/< ep ratios because the error in the measured < o/< ep ratio is proportional to CR — 1) (see Eq. (38.28)) and this error will be greater under conditions where CR is near unity (in which case CR — 1 approaches 0). In order to minimize the errors in the experimental value of o/ep> it is necessary to use a resonance flux monitor with a large Jo/o o ratio to minimize thermal absorption and the significance of uncertainties in the cutoff. On the other hand, a nearly 1/v thermal flux monitor should be used to minimize epithermal absorption. This source of error may also be reduced by irradiating in a position with a higher thermal to resonance flux ratio. For an unknown sample of low cadmium ratio, only this latter approach will minimize the uncertainty. It has been customary to report values of (To and Iq rather than Cth and Iq since experimental data. These distinctions have not usually been made clear, probably because tbe difference between (To and (7th is small for a 1/v absorber. 

Noise is rarely the only cause of error in the measurement of an intense absorption band. In Chapter 8, it was shown that the 0% line of many FT-IR spectrometers can be in error by as much as 0.1% (or more if an MCT detector is used for the measurement) [1]. Indeed, most manufacmrers of FT-IR spectrometers rarely specify the ordinate scale accuracy as being better than 0.1 %T. The limited photometric accuracy of FT-IR spectrometers in the region of 0% transmittance reinforces the recommendation made in the preceding paragraph that the peak absorbance of strong bands be held below 0.7 AU whenever possible. 

In Section 9.1 we saw that Beer s law states that absorbance at any wavenumber is a linear function of concentration for a single component. Errors in the measurement... 

In the process of performing a spectrophotometric determination of Ee, an analyst prepares a calibration curve using a single-beam spectrometer, such as a Spec-20. After preparing the calibration curve, the analyst drops the cuvette used for the method blank and the standards. The analyst acquires a new cuvette, measures the absorbance of the sample, and determines the %w/w Ee in the sample. Will the change in cuvette lead to a determinate error in the analysis Explain. 

Assays using equiUbrium (end point) methods are easy to do but the time requited to reach the end point must be considered. Substrate(s) to be measured reacts with co-enzyme or co-reactant (C) to produce products (P and Q) in an enzyme-catalyzed reaction. The greater the consumption of S, the more accurate the results. The consumption of S depends on the initial concentration of C relative to S and the equiUbrium constant of the reaction. A change in absorbance is usually monitored. Changes in pH and temperature may alter the equiUbrium constant but no serious errors are introduced unless the equihbrium constant is small. In order to complete an assay in a reasonable time, for example several minutes, the amount and therefore the cost of the enzyme and co-factor maybe relatively high. Sophisticated equipment is not requited, however. 

The molecular absoi ption spectra, registered at a lower temperature (e.g. 700 °C for iodide or chloride of potassium or sodium), enable one to find the absorbance ratio for any pair of wavelengths in the measurement range. These ratios can be used as a correction factor for analytical signal in atomic absoi ption analysis (at atomization temperatures above 2000 °C). The proposed method was tested by determination of beforehand known silicon and iron content in potassium chloride and sodium iodide respectively. The results ai e subject to random error only. 

The last elements of realism we will add to the data is random error or noise. In actual data there is noise both in the measurement of the spectra, and in the determination of the concentrations. Accordingly, we will add random error to the data in the absorbance matrices and the concentration matrices. 

Whole cell OPH activity was measured by following the increase in absorbancy of p-nitrophenol from the hydrolysis of substrate (0.1 mM Paraoxon) at 400 nm (sm = 17,000 M cm ). Samples of culture (1 ml) were centrifuged at 10,000 g and 4 C for 5 min. The cells were washed, resuspended with distilled water, and 100 pi was added to an assay mixture containing 400 pi 250 mM CHES [2-(N-cyclohexylamino)ethane-sulfonic acid] buffer, pH 9.0, 100 pi 1 mM Paraoxon, and 400 pi distilled water. One unit of OPH activity was defined as pmoles Paraoxon hydrolyzed per min. Each value and error bar represents the mean of two independent experiments and its standard deviation. 

The accuracy and precision of carotenoid quantification by HPLC depend on the standard purity and measurement of the peak areas thus quantification of overlapping peaks can cause high variation of peak areas. In addition, preparation and dilution of standard and sample solutions are among the main causes of error in quantitative analysis. For example, the absorbance levels at of lutein in concentrations up to 10 mM have a linear relationship between concentration and absorbance in hexane and MeOH on the other hand, the absorbance of P-carotene in hexane increased linearly with increasing concentration, whereas in MeOH, its absorbance increased linearly up to 5 mM but non-linearly at increasingly higher concentrations. In other words, when a stock solution of carotenoids is prepared, care should be taken to ensure that the compounds are fuUy soluble at the desired concentrations in a particular solvent. 

It can be shown [4] that the innovations of a correct filter model applied on data with Gaussian noise follows a Gaussian distribution with a mean value equal to zero and a standard deviation equal to the experimental error. A model error means that the design vector h in the measurement equation is not adequate. If, for instance, in the calibration example the model was quadratic, should be [1 c(j) c(j) ] instead of [1 c(j)]. In the MCA example h (/) is wrong if the absorptivities of some absorbing species are not included. Any error in the design vector appears by a non-zero mean for the innovation [4]. One also expects the sequence of the innovation to be random and uncorrelated. This can be checked by an investigation of the autocorrelation function (see Section 20.3) of the innovation. 

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