Determination of stoichiometric coefficients by the matrix method

The problem of calculating stoichiometric coefficients in a chemical equation can be solved by standard methods and the method of multidimensional vector space, but good knowledge of vector algebra is required. In this paper, the authors proposed a matrix method and other treatment of the problem was given as the authors' own interpretation. A matrix was formed in the form of base using all the elements which take place in a chemical reaction, after which the matrixes of all the chemical compounds were determined based on numerical indexes and element symbols. This approach enables the setting of a principal matrix equation based on a mathematical approach. The solutions of this matrix equation are the desired stoichiometric coefficients that form a balanced equation. A new approach to tabular solving is presented. This method, compared to existing standard methods, is faster, simpler, and more effective, especially for complex chemical equations. The method was tasted on examples from inorganic chemistry and metallurgy

A model for reliability analysis and calculation applied in an example from chemical industry

The subject of the paper is reliability design in polymerization processes that occur in reactors of a chemical industry. The designed model is used to determine the characteristics and indicators of reliability, which enabled the determination of basic factors that result in a poor development of a process. This would reduce the anticipated losses through the ability to control them, as well as enabling the improvement of the quality of production, which is the major goal of the paper. The reliability analysis and calculation uses the deductive method based on designing of a scheme for fault tree analysis of a system based on inductive conclusions. It involves the use standard logical symbols and rules of Boolean algebra and mathematical logic. The paper eventually gives the results of the work in the form of quantitative and qualitative reliability analysis of the observed process, which served to obtain complete information on the probability of top event in the process, as well as objective decision making and alternative solutions

Determination of the number of radicals in the initial chain reactions by mathematical methods

Starting from the fact that the real mechanism in a chemical equation takes places through a certain number of radicals which participate in simultaneous reactions and initiate chain reactions according to a particular pattern, the aim of this study is to determine their number in the first couple of steps of the reaction. Based on this, the numbers of radicals were determined in the general case, in the form of linear difference equations, which, by certain mathematical transformations, were reduced to one equation that satisfies a particular numeric series, entirely defined if its first members are known. The equation obtained was solved by a common method developed in the theory of numeric series, in which its solutions represent the number of radicals in an arbitrary step of the reaction observed, in the analytical form. In the final part of the study, the method was tested and verified using two characteristic examples from general chemistry. The study also gives a suggestion of a more efficient procedure by reducing the difference equation to a lower order

Graphic constructions of characteristic diagrams in chemical engineering and the application of differential geometry

Starting from the experimental concentration-time ( cA,t diagram this work gives the construction of the rate of reaction-time (rA,t diagram using the pure graphic method. The diagram was constructed based on the constructed tangents in arbitrary points of the starting diagram by drawing lines parallel to them in the predetermined pole. The evidence of the construction was derived using differential geometry, i.e. the main theorem of differential calculus. Differential properties between the observed values were used in the method. Starting from the analytic relations rA = rA(t) and cA = cA(t), which can be very complex (polynomes of the n-th order), and, eliminating time t in order to give a full description of the process, we obtain the analytical relation rA = rA(cA), which is then graphically represented. Hoewever, this elimination of time can also be done graphically, in a relatively simple way. After that, through the use of the integral calculus, it was shown that concentration increase in a time interval is proportional to the (rA,t) diagram surface area. Using a similar procedure, further in the paper, it was shown that the time increase is proportional to the (1/rA, cA) diagram surface area. In order for the method to be applicable in practice, we have derived relations for appropriate coefficients of proportionality. Verification of the method is illustrated by the two characteristic examples from chemical kinetics at different monotonies of the starting experimental functions

Photocatalytic degradation of methylene blue under natural sunlight using iron titanate nanoparticles prepared by a modified sol-gel method

The aim of this work was to synthesize semiconducting oxide nanoparticles using a simple method with low production cost to be applied in natural sunlight for photocatalytic degradation of pollutants in waste water. Iron titanate (Fe2TiO5) nanoparticles with an orthorhombic structure were successfully synthesized using a modified sol-gel method and calcination at 750 degrees C. The as-prepared Fe2TiO5 nanoparticles exhibited a moderate specific surface area. The mesoporous Fe2TiO5 nanoparticles possessed strong absorption in the visible-light region and the band gap was estimated to be around 2.16 eV. The photocatalytic activity was evaluated by the degradation of methylene blue under natural sunlight. The effect of parameters such as the amount of catalyst, initial concentration of the dye and pH of the dye solution on the removal efficiency of methylene blue was investigated. Fe2TiO5 showed high degradation efficiency in a strong alkaline medium that can be the result of the facilitated formation of OH radicals due to an increased concentration of hydroxyl ions