Quantitative analysis errors

Although the most sensitive line for cadmium in the arc or spark spectmm is at 228.8 nm, the line at 326.1 nm is more convenient to use for spectroscopic detection. The limit of detection at this wavelength amounts to 0.001% cadmium with ordinary techniques and 0.00001% using specialized methods. Determination in concentrations up to 10% is accompHshed by solubilization of the sample followed by atomic absorption measurement. The range can be extended to still higher cadmium levels provided that a relative error of 0.5% is acceptable. Another quantitative analysis method is by titration at pH 10 with a standard solution of ethylenediarninetetraacetic acid (EDTA) and Eriochrome Black T indicator. Zinc interferes and therefore must first be removed. 

If there is any doubt as to the purity of the reagents used, they should be tested by standard methods for the impurities that might cause errors in the determinations. It may be mentioned that not all chemicals employed in quantitative analysis are available in the form of analytical reagents the purest commercially available products should, if necessary, be purified by known methods see below. The exact mode of drying, if required, will vary with the reagent details are given for specific reagents in the text. 

The function of the analyst is to obtain a result as near to the true value as possible by the correct application of the analytical procedure employed. The level of confidence that the analyst may enjoy in his results will be very small unless he has knowledge of the accuracy and precision of the method used as well as being aware of the sources of error which may be introduced. Quantitative analysis is not simply a case of taking a sample, carrying out a single determination and then claiming that the value obtained is irrefutable. It also requires a sound knowledge of the chemistry involved, of the possibilities of interferences from other ions, elements and compounds as well as of the statistical distribution of values. The purpose of this chapter is to explain some of the terms employed and to outline the statistical procedures which may be applied to the analytical results. 

The relative error is the absolute error divided by the true value it is usually expressed in terms of percentage or in parts per thousand. The true or absolute value of a quantity cannot be established experimentally, so that the observed result must be compared with the most probable value. With pure substances the quantity will ultimately depend upon the relative atomic mass of the constituent elements. Determinations of the relative atomic mass have been made with the utmost care, and the accuracy obtained usually far exceeds that attained in ordinary quantitative analysis the analyst must accordingly accept their reliability. With natural or industrial products, we must accept provisionally the results obtained by analysts of repute using carefully tested methods. If several analysts determine the same constituent in the same sample by different methods, the most probable value, which is usually the average, can be deduced from their results. In both cases, the establishment of the most probable value involves the application of statistical methods and the concept of precision. 

It is crucial in quantitative GC to obtain a good separation of the components of interest. Although this is not critical when a mass spectrometer is used as the detector (because ions for identification can be mass selected), it is nevertheless good practice. If the GC effluent is split between the mass spectrometer and FID detector, either detector can be used for quantitation. Because the response for any individual compound will differ, it is necessary to obtain relative response factors for those compounds for which quantitation is needed. Care should be taken to prevent contamination of the sample with the reference standards. This is a major source of error in trace quantitative analysis. To prevent such contamination, a method blank should be run, following all steps in the method of preparation of a sample except the addition of the sample. To ensure that there is no contamination or carryover in the GC column or the ion source, the method blank should be run prior to each sample. 

In practice, it is probable that both of the effects discussed contribute to the overall peak asymmetry. Unfortunately, peak asymmetry varies in extent from the very obvious to the barely noticeable and because of this, peak asymmetry is often dismissed as the normal shape of a single solute peak. Such an assumption can cause serious errors in both qualitative and quantitative analysis. 

Royston, G. C., Comments on Unrecognized Systematic Errors in Quantitative Analysis in Gas Chromatography, Ana/. Chem. 50, 1978, 1005. 

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. 

XRF nowadays provides accurate concentration data at major and low trace levels for nearly all the elements in a wide variety of materials. Hardware and software advances enable on-line application of the fundamental approach in either classical or influence coefficient algorithms for the correction of absorption and enhancement effects. Vendors software packages, such as QuantAS (ARL), SSQ (Siemens), X40, IQ+ and SuperQ (Philips), are precalibrated analytical programs, allowing semiquantitative to quantitative analysis for elements in any type of (unknown) material measured on a specific X-ray spectrometer without standards or specific calibrations. The basis is the fundamental parameter method for calculation of correction coefficients for matrix elements (inter-element influences) from fundamental physical values such as absorption and secondary fluorescence. UniQuant (ODS) calibrates instrumental sensitivity factors (k values) for 79 elements with a set of standards of the pure element. In this approach to inter-element effects, it is not necessary to determine a calibration curve for each element in a matrix. Calibration of k values with pure standards may still lead to systematic errors for unknown polymer samples. UniQuant provides semiquantitative XRF analysis [242]. 

Quantitative analysis of multicomponent additive packages in polymers is difficult subject matter, as evidenced by results of round-robins [110,118,119]. Sample inhomogeneity is often greater than the error in analysis. In procedures entailing extraction/chromatography, the main uncertainty lies in the extraction stage. Chromatographic methods have become a ubiquitous part of quantitative chemical analysis. Dissolution procedures (without precipitation) lead to the most reliable quantitative results, provided that total dissolution can be achieved follow-up SEC-GC is molecular mass-limited by the requirements of GC. Of the various solid-state procedures (Table 10.27), only TG, SHS, and eventually Py, lead to easily obtainable accurate quantitation. 

For quantitative analysis of protein concentration the colorimetric Bradford-assay [147] is most commonly used. Here another Coomassie dye, Brilliant Blue G-250, binds in acidic solutions to basic and aromatic side chains of proteins. Binding is detected via a shift in the absorption maximum of the dye from 465 nm to 595 nm. Mostly calibration is performed with standard proteins like bovine serum albumin (BSA). Due to the varying contents of basic and aromatic side chains in proteins, systematic errors in the quantification of proteins may occur. 

Instrumentation. Sample Preparation. Qualitative and Quantitative Analysis. Interferences and Errors Associated with the Excitation Process. Applications of Arc/Spark Emission Spectrometry. 

Part—I has three chapters that exclusively deal with General Aspects of pharmaceutical analysis. Chapter 1 focuses on the pharmaceutical chemicals and their respective purity and management. Critical information with regard to description of the finished product, sampling procedures, bioavailability, identification tests, physical constants and miscellaneous characteristics, such as ash values, loss on drying, clarity and color of solution, specific tests, limit tests of metallic and non-metallic impurities, limits of moisture content, volatile and non-volatile matter and lastly residue on ignition have also been dealt with. Each section provides adequate procedural details supported by ample typical examples from the Official Compendia. Chapter 2 embraces the theory and technique of quantitative analysis with specific emphasis on volumetric analysis, volumetric apparatus, their specifications, standardization and utility. It also includes biomedical analytical chemistry, colorimetric assays, theory and assay of biochemicals, such as urea, bilirubin, cholesterol and enzymatic assays, such as alkaline phosphatase, lactate dehydrogenase, salient features of radioimmunoassay and automated methods of chemical analysis. Chapter 3 provides special emphasis on errors in pharmaceutical analysis and their statistical validation. The first aspect is related to errors in pharmaceutical analysis and embodies classification of errors, accuracy, precision and makes... 

Precision and accuracy Quantitative analysis by NMR is very precise with relative standard deviations for independent measurements usually much lower than 5%. The largest errors in NMR measurements are likely due to sample preparation, not the NMR method itself. If a good set of standards is available and all NMR measurements for the test and standard samples are performed under the same acquisition conditions, the quantitative results can be readily reproduced on different instruments operated by different analysts at different times. Therefore, good intermediate precision can also be achieved. An accurate quantitative NMR assay will require accurately prepared standards. The accuracy of an NMR assay can be assessed, for example, by measuring an independently prepared standard or an accurate reference sample with the assay. In many cases, a spike recovery experiment can also be used to demonstrate the accuracy of an NMR assay. 

Quantitative analysis relies on a highly probable mechanistic hypothesis and determines as many as possible kinetic, thermodynamic, and/or transport parameters for the various steps. This is often a complex problem, since the values of the parameters are usually correlated, their relation to experimental data is nonlinear, and the data contain artifacts and statistical errors [40, 41]. 

Quantitative analysis using peak areas. Error estimates are based on experimental reproducibility of duplicate runs. 

A quantitative analysis is not a great deal of use unless there is some estimation of how prone to error the analytical procedure is. Simply accepting the analytical result could lead to rejection or acceptance of a product on the basis of a faulty analysis. 

For quantitative analysis by either the external or internal standard methods, HPLC requires the use of calibration solutions that are injected under identical conditions. Thus to fully identify quantitative effects, calibration solutions plus standard solutions need to be analysed for each experiment in a ruggedness test. As duplicate determinations are required for the estimation of standard errors a single experiment can consist of up to six chromatographic experiments as shown below. 

X-Ray Photoelectron Spectrometry. X-ray photoelectron spectrometry (XPS) was applied to analyses of the surface composition of polymer-stabilized metal nanoparticles, which was mentioned in the previous section. This is true in the case of bimetallic nanoparticles as well. In addition, the XPS data can support the structural analyses proposed by EXAFS, which often have considerably wide errors. Quantitative XPS data analyses can be carried out by using an intensity factor of each element. Since the photoelectron emitted by x-ray irradiation is measured in XPS, elements located near the surface can preferentially be detected. The quantitative analysis data of PVP-stabilized bimetallic nanoparticles at a 1/1 (mol/mol) ratio are collected in Table 9.1.1. For example, the composition of Pd and Pt near the surface of PVP-stabilized Pd/Pt bimetallic nanoparticles is calculated to be Pd/Pt = 2.06/1 (mol/ mol) by XPS as shown in Table 9.1.1, while the metal composition charged for the preparation is 1/1. Thus, Pd is preferentially detected, suggesting the Pd-shell structure. This result supports the Pt-core/Pd-shell structure. The similar consideration results in the Au-core/Pd-shell and Au-core/Pt-shell structure for PVP-stabilized Au/Pd and Au/Pt bimetallic nanoparticles, respectively (53). 

For a more quantitative analysis of the errors involved, artificial data will be addressed first. To see the effects of truncation and restoration of a single spectral line, we shall first consider a monochromatic electromagnetic... 

Schierle and Otto [63] used a two-layer perceptron with error back-propagation for quantitative analysis in ICP-AES. Also, Schierle et al. [64] used a simple neural network [the bidirectional associative memory (BAM)] for qualitative and semiquantitative analysis in ICP-AES. 

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