Applications of Derivatives

Why do we care about derivatives in a chemistry course There are several reasons  

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The application of derivatives is not without problems, however, especially when the concern is to accurately represent the derivative of a given data spectrum. Therefore understanding the nature of the problems encountered, so that the proper decisions can be made regarding how the derivative should be calculated is crucial to obtaining optimum results. 

Hearn, M.T., M.I. AgnUar, T. Nguyen, and M. Fridman, High-performance liquid chromatography of amino acids, peptides and proteins. LXXXTV. Application of derivative spectroscopy to the study of column residency effects in the reversed-phase and size-exclusion liquid chromatographic separation of proteins. J Chromatogr, 1988. 435(2) 271-84. 

E.E. Mason, "Application of Derivative Differential Thermal Analysis to Military High Explosives . NAVWEPS Rept 6996... 

Another common application of derivatives is to generate a simple approximation to some complicated function /(x). We can rearrange Equation 2.1 and substitute y =... 

Because of the polyfunctional character of aconitic acid, it being both an unsaturated acid and a polybasic acid, the compound can undergo a variety of chemical reactions. Application of derivatives obtained by such reactions has aroused considerable interest in the plasticizer, wetting agent and resin manufacturing fields. 

In conclusion, it is necessary to add that a number of the problems mentioned, caused by adsorption in the chromatographic system, may be solved by new technological procedures for the preparation of columns and whole systems. Modern sorbents and procedures for deactivation have partly solved the initial difficulties in some instances, but the field is still wide enough for useful applications of derivatives. 

Gas chromatographic analysis proper does not differ from the conventional procedure in its arrangement for derivatives, as the derivatives used are often common compounds which can, in other circumstances, be the object of analysis themselves (e.g., carboxylic acids versus esters). It is beyond the scope of this book to deal with the detailed theory and instrumentation of GC and readers are referred elsewhere [23—25] only some peculiarities introduced into GC as a result of the application of derivatives will be discussed here. 

Another approach involves the application of derivative linear sweep voltammetry or DCV [Fig. 10(b)]. These techniques allow a precision of the order of 0.2 mV to be realized during peak potential measurements [29-31,36]. The feature giving the high precision is that the peak potential is measured at the point where the steeply descending first derivative crosses zero. 

Analytical applications of derivative spectroscopy are numerous and generally owe their popularity to the apparent higher resolution of the differential... 

The application of derivative spectrophotometry allows the determination of Co in the presence of Fe [2] and Fe, Ni and Cu [3]. 4-(2-Pyridylazo)resorcinol and l,5-bis(di-2-pyridylmethylene) thiocarbonohydrazide were used as chromogenic reagents. The method [3] was applied to the determination of Co in alloys and biological materials. Cobalt(II) in steels has been determined with the use of 4-(2-pyridylazo)resorcinol and xylometazoline hydrochloride [4]. 

An important application of derivative spectroscopy lies in the determination of analytes in turbid media. Turbid solutions usually present a continuous increase of the absorbance towards shorter wavelengths and, as a consequence, do not produce any sudden spectral change either in the first or in the second derivative spectrum. Phenol determination in wastewater was one of the first practical applications of the derivative spectroscopy in turbid media [19], Another study, more recent, deals with the evaluation of the second-derivative determination of nitrate and total nitrogen [20],... 

Application of Derived Rate Constant Expression to Sunlight... 

The application of derivative techniques to spectroscopy is very useful when signal overlap or interference exits and it offers a powerful tool for both qualitative and quantitative analysis of components in pharmaceutical [11, 12], biomedical [13, 14] and food analysis [15, 16],... 

Fig. 4. The application of derivative spectrophotometry for analysis of cephem analogs [15-16].

Basic Principles and Analytical Application of Derivative Spectrophotometry... 

Derivative spectrophotometry (DS) has found a wide application in quantitative chemical analysis. As the latest applications have been gathered and described in reviews published previously [8,9], this pwt is focused on the recent use of DS. Based on scientific literature the following fields of application of derivative spectrophotometry can be distinguished ... 

An interesting application of derivative sp>ectrophotometiy was described by Wu and Zivanovic [46], They proposed the use of the first derivative spectra for determination of the degree of acetylation of chitin and chitosan. They employed the evaluated procedure for commercial samples. 

The provided short review shows good and bad sides of derivative spectrophotometry. It has mainly found application in pharmaceutical analysis for control of pharmaceuticals. It gives good results for samples with well defined composition. A main compound usually is present in its commercial forms at a relatively high level, convenient for sp>ectrophotometric determination. An application of derivative sp>ectrophotometry simplified procedure and allows to determine an active compoimd in presence of matrix (others ingredients, its degradation products) without paimaiy sample pjrepjaration. 

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