Uncertainties spectrophotometric

Spencer and Brewer [111] have reviewed methods for the determination of silicate in seawater. Various workers [209-212] have studied the application of molybdosilicate spectrophotometric methods to the determination of silicate in seawater. In general, these methods give anomalous results due, it is believed, to erratic blanks and uncertainty regarding the structure of the silicomolybdate formed. 

COMPOUNDING OF ERRORS. Data collected in an experiment seldom involves a single operation, a single adjustment, or a single experimental determination. For example, in studies of an enzyme-catalyzed reaction, one must separately prepare stock solutions of enzyme and substrate, one must then mix these and other components to arrive at desired assay concentrations, followed by spectrophotometric determinations of reaction rates. A Lowry determination of protein or enzyme concentration has its own error, as does the spectrophotometric determination of ATP that is based on a known molar absorptivity. All operations are subject to error, and the error for the entire set of operations performed in the course of an experiment is said to involve the compounding of errors. In some circumstances, the experimenter may want to conduct an error analysis to assess the contributions of statistical uncertainties arising in component operations to the error of the entire set of operations. Knowledge of standard deviations from component operations can also be utilized to estimate the overall experimental error. 

This paper has examined the role of calibration and evaluation of measurement uncertainty in clinical laboratories arising from the request for traceability assurance. To produce results which are accurate and reliable within the stated uncertainty, all uncertainties of the quality measurement process and the traceability chain should be demonstrated. Also, the quality of a spectrophotometric result depends critically on RMs and photometric systems whose traceability have been properly demonstrated. 

It is well known that outside the pH range almost all predeterminations for unexcited molecules have been based on the Hammett indicator method (Hammett and Deyrup, 1932). Even in concentrated acid (or alkaline) solutions, where uncertainties in the value of b//bh become very serious, it is easy to measure the ratio of protonated to unprotonated indicator concentrations spectrophotometrically when the absorption peaks are sufficiently resolved. The difficulty arises in trying to extrapolate beyond the measurable [BH+]/[B] range to zero electrolyte concentration. Hammett and Deyrup assumed that the activity coefficient ratios of the type /b//bh+ were very similar for different indicators in the same acid solution. For the equilibrium (51) between two indicators A and B, a comparison of the concentration ratios [BH+]/[B] and [AH+]/[A] over an acidity range in which both could be measured would lead to a direct estimate of the difference in p-K-values using (52) and (53). Beginning with 4-nitroaniline, which is about half-... 

Figure 7.6 was obtained by carrying out electrolysis experiments at extremely low chloride concentrations. Both curves show a tendency of chlorine formation and destruction in terms of a spectrophotometrical DPD signal. Even if there are some uncertainties with respect to the DPD method (see Sect. 7.3.3.7) these results support the second theory (2). 

Noise in UV-vis spectrophotometry refers to uncertainties caused in the measurement of the absorbance signal. Essentially, there are two sources of noise. One isdependent on the source intensity (Schott noise) and the other independent of it. The effect of noise in spectrophotometric measurement can be significantly reduced if the concentration of the analyte is adjusted such that measured absorbance is between 0.3 and 1.2 absorbance units. A significant source of noise in double-beam instruments arises when sample and reference cells are not positioned properly. Minor imperfections in the cells cause reflections and scattering... 

It should be noted that when we used methods of measurement needing inorganic reference materials for calibration (such as flame photometry or atomic absorption spectrometry) the uncertainty due to the reference materials was considerably lower than that due to the photometric device. On the contrary, when we used a clinical reference material certified for its glucose concentration with a 10% (rel) uncertainty, this uncertainty exceeded twice the uncertainty due to the spec-trophotometric device. When we determined Mg by a spectrophotometric method with Titan Yellow, we found that the uncertainty due to the reference material was approximately twice that due the device, as we used a very accurate spectrophotometer. 

Spreadsheet Summary In the first exercise in Chapter 12 of Applications of Microsoft Excel in Analytical Chemistry, a spreadsheet is developed to calculate the molar absorptivity of permanganate ion. A plot of absorbance versus permanganate concentration is constructed, and least-squares analysis of the linear plot is carried out. The data are analyzed statistically to determine the uncertainty of the molar absorptivity. In addition, other spreadsheets are presented for calibration in quantitative spectrophotometric experiments and for calculation of concentrations of unknown solutions. 

The accuracy and precision of spectrophotometric analyses are often limited by the indeterminate error, or noise, associated with the instrument. As pointed out in Chapter 25, a spectrophotometric absorbance measurement entails three steps a 0% T adjustment, a 100% T adjustment, and a measurement of % 7i The random errors associated with each of these steps combine to give a net random error for the final value obtained for T. The relationship between the noise encountered in the measurement of T and the resulting concentration uncertainty can be derived by writing Beer s law in the form... 

Uncertainties in spectrophotometric concentration measurements depend on the magnitude of the transmittance (absorbance) in a complex way. The uncertainties can be independent of 7) proportional to V -E T, or proportional to T. 

A spectrophotometric analysis was performed with a manual instrument that exhibited an absolute standard deviation in transmittance of 0.003 throughput its transmittance range. Calculate the relative standard deviation in concentration that results from this uncertainty when the analyte solution has an absorbance of (a) 1.000 and (b) 2.000. 

The photometric calibration also contributes to the uncertainty of the measured spectrum. Flux standard stars are typically measured at widely spaced wavelengths (50 A is common), and the sensitivity function of the instrument is determined by fitting a low-order polynomial or spline to the flux points. Such fits inevitably introduce low-order wiggles in the sensitivity function, which will vary from star to star. Based on experience, the best spectrophotometric calibration yield uncertainties in the relative fluxes of order 2-3% for widely-spaced emission lines the errors may be better for ratios of lines closer than 20 A apart. Absolute fluxes have much higher uncertainties, of course, especially for narrow-aperture observations of extended objects. 

The accuracy and precision of spectrophotometric analyses arc often limited by the uncertainties or noise associated with the instrument. A general discussion of instrumental noise and signal-to-noise optimLaiion is found in Chapter 5. 

Primary kinetic hydrogen-deuterium isotope effects are usually calculated from the ratio of the rates of elimination of isotopically labelled substrates. An uncertainty in rate coefficients of 2% arises from a titrimetric determina-tion23.26,4o whereas a spectrophotometric approach, usually the monitoring of the olefin concentration under conditions of first-order kinetics, gives an improved precision During attainment of the transition state, a... 

Absorption spectroscopy based on ultraviolet and visible radiation is one of the most useful tools available to the scientist for quantitative analysis. Important characteristics of spectrophotometric and photometric methods include (1) wide applicability to both organic and inorganic systems, (2) typical detection limits of 10" to 10 M (in some cases, certain modifications can lead to lower limits of detection), (3) moderate to high selectivity, (4) good accuracy (typically, relative uncertainties are 1% to 3%, although with special precautions, errors can be reduced to a few tenths of a percent), and (5) ease and convenience of data acquisition. 

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