Youden Two-Sample Method

The results obtained when testing materials, equipment and procedures are not generally identical. Factors that influence the magnitude of the results are not fully controllable. As such, the interpretation and analysis of results must take into account the variations caused by numerous and random unavoidable causes. Intercomparison exercises are considered of being of importance, as they do allow the examination of the analytical process and their generated results. Youden plot is particularly aimed at interlaboratory comparisons. The raw results provided by the participating laboratories are treated by a statistical method applied by the centre performing the trial. In order to materialize this, two similar materials with small differences in the concentration of the characteristics are required. The advantage of Youden analysis is its ability to separate the random errors with a minimum effort by participants in the design from the point of view of the analytical requirement. This book chapter illustrates the method that has been applied to elaborate on data covering a diverse scientific field: polyunsaturated fatty acids in fat and oils, total blood cholesterol and aspirin in pharmaceutical preparations. Finally, liquid chromatography with tandem mass spectrometry detector has been applied to the determination of an emerging contaminant, methylparaben (MeP), in surface waters

Intersecting Straight Lines: Titrimetric Applications

Plotting two straight line graphs from the experimental data and determining the point of their intersection solve a number of problems in analytical chemistry (i.e., potentiometric and conductometric titrations, the composition of metal-chelate complexes and binding interactions as ligand-protein). The relation between conductometric titration and the volume of titrant added lead to segmented linear titration curves, the endpoint being defined by the intersection of the two straight line segments. The estimation of the statistical uncertainty of the end point of intersecting straight lines is a topic scarcely treated in detail in a textbook or specialized analytical monographs. For this reason, a detailed treatment with that purpose in mind is addressed in this chapter. The theoretical basis of a variety of methods such as first-order propagation of variance (random error propagation law), Fieller’s theorem and two approaches based on intersecting confidence bands are explained in detail. Several experimental systems described in the literature are the subject of study, with the aim of gaining knowledge and experience in the application of the possible methods of uncertainty estimation. Finally, the developed theory has been applied to the conductivity measurements in triplicate in the titration of a mixture of hydrochloric acid and acetic acid with potassium hydroxide

Fitting Models to Data: Residual Analysis, a Primer

The aim of this chapter is to show checking the underlying assumptions (the errors are independent, have a zero mean, a constant variance and follows a normal distribution) in a regression analysis, mainly fitting a straight‐line model to experimental data, via the residual plots. Residuals play an essential role in regression diagnostics; no analysis is being complete without a thorough examination of residuals. The residuals should show a trend that tends to confirm the assumptions made in performing the regression analysis, or failing them should not show a tendency that denies them. Although there are numerical statistical means of verifying observed discrepancies, statisticians often prefer a visual examination of residual graphs as a more informative and certainly more convenient methodology. When dealing with small samples, the use of the graphic techniques can be very useful. Several examples taken from scientific journals and monographs are selected dealing with linearity, calibration, heteroscedastic data, errors in the model, transforming data, time‐order analysis and non‐linear calibration curves

Thermodynamic Modelling of Dolomite Behavior in Aqueous Media

The compact thermodynamic approach to the systems containing calcium, magnesium, and carbonate species is referred to dissolution of dolomite, as an example of nonequilibrium ternary salt when introduced into aqueous media. The study of dolomite is based on all attainable physicochemical knowledge, involved in expressions for equilibrium constants, where the species of the system are interrelated. The species are also involved in charge and concentration balances, considered as constraints put on a closed system, separated from the environment by diathermal walls. The inferences are gained from calculations performed with use of an iterative computer program. The simulated quasistatic processes occurred under isothermal conditions, started at a preassumed pH0 value of the solution where dolomite was introduced, and are usually involved with formation of other solid phases. None simplifying assumptions in the calculations were made

Up-To-Date Analysis of the Extraction Methods for Anthocyanins: Principles of the Techniques, Optimization, Technical Progress, and Industrial Application

Nowadays, food industries are concerned about satisfying legal requirements related to waste policy and environmental protection. In addition, they take steps to ensure food safety and quality products that have high nutritional properties. Anthocyanins are considered high added-value compounds due to their sensory qualities, colors, and nutritional properties; they are considered bioactive ingredients. They are found in high concentrations in many by-products across the food industry. Thus, the non-conventional extraction techniques presented here are useful in satisfying the current food industry requirements. However, selecting more convenient extraction techniques is not easy. Multiple factors are implicated in the decision. In this review, we compile the most recent applications (since 2015) used to extract anthocyanins from different natural matrices, via conventional and non-conventional extraction techniques. We analyze the main advantages and disadvantages of anthocyanin extraction techniques from different natural matrices and discuss the selection criteria for sustainability of the processes. We present an up-to-date analysis of the principles of the techniques and an optimization of the extraction conditions, technical progress, and industrial applications. Finally, we provide a critical comparison between these techniques and some recommendations, to select and optimize the techniques for industrial applications

“Why Not Stoichiometry” Versus “Stoichiometry—Why Not?” Part II: GATES in Context with Redox Systems

<div><p>Redox equilibria and titration play an important role in chemical analysis, and the formulation of an accurate mathematical description is a challenge. This article is devoted to static and (mainly) dynamic redox systems; the dynamic systems are represented by redox titrations. An overview addresses earlier approaches to static redox systems (redox diagram plots, including Pourbaix diagrams) and to titration redox systems, thereby covering a gap in the literature. After this short review, the generalized approach to electrolytic systems (GATES) is introduced, with generalized electron balance (GEB) as its inherent part within GATES/GEB. Computer simulation, performed according to GATES/GEB, enables following the changes in potential and pH of the solution, together with chemical speciation at each step of a titration, thus providing better insight into this procedure. The undeniable advantages of GATES/GEB over earlier approaches are indicated. Formulation of GEB according to two approaches (I and II) is presented on the respective examples. A general criterion distinguishing between non-redox and redox systems is presented. It is indicated that the formulation of GEB according to Approach II does not need the knowledge of oxidation degrees of particular elements; knowledge of the composition, expressed by chemical formula of the species and its charge, is sufficient for this purpose. Approach I to GEB, known also as the “short” version of GEB, is applicable if oxidation degrees for all elements of the system are known beforehand. The roles of oxidants and reductants are not ascribed to particular components forming a system and to the species thus formed. This is the complete opposite of earlier approaches to redox titrations, based on the stoichiometric redox reaction, formulated for this purpose. GEB, perceived as a law of matter conservation, is fully compatible with other (charge and concentration) balances related to the system in question. The applicability of GATES/GEB in optimization a priori of chemical analyses made with use of redox titration is indicated. The article is illustrated with many examples of static and dynamic redox systems. The related plots are obtained from calculations made according to iterative computer programs. This way, GATES/GEB enables seeing details invisible in real experiments.</p></div

“Why Not Stoichiometry” versus “Stoichiometry—Why Not?” Part III: Extension of GATES/GEB on Complex Dynamic Redox Systems

<div><p>In the third part of a series of articles issued under a common title, some examples of complex dynamic redox systems are presented and considered from analytical and physico-chemical viewpoints; the analysis is a leitmotiv for detailed, physico-chemical considerations. All attainable physico-chemical knowledge is involved in algorithms applied for resolution of the systems, realized with use of iterative computer programs. The first redox system (System I) is related to titration of FeSO₄ + H₂C₂O₄ with KMnO₄ solution in acidic (H₂SO₄) medium, where simultaneous determination of both analytes from a single curve of potentiometric titration is possible. The possibility of the formation of precipitates (<b>FeC₂O₄</b> and/or <b>MnC₂O₄</b>) in this system is taken into considerations. The second system (System II) relates to the complete analytical procedure involved in the iodometric determination of Cu; four consecutive steps of this analysis are considered. As a reasonable tool for explanation of processes occurring during simulated redox titration, speciation diagrams are suggested. This explanation is based on graphical presentation of results obtained from the calculations. The calculations made for this purpose are performed in accordance with principles of the generalized approach to electrolytic systems (GATES) with generalized electron balance (GEB) or GATES/GEB and realized with use of iterative computer programs offered by MATLAB. The reactions proceeding in this system can be formulated, together with their efficiencies, at any stage of the titration. Stoichiometry is considered as the derivative concept when put in context with GATES/GEB. The article illustrates the enormous possibilities and advantages offered by GATES/GEB.</p></div