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It is known that the temperature of crystallization during the synthesis of zeolite is one of the most important process parameters. However, during the research work on the synthesis of zeolite 13X and the introduction of this material into regular industrial production, it was noticed that the heating rate of the starting reaction suspension can have an equally important influence. This influence can be so pronounced that a difference of just a few minutes in reaching the crystallization temperature can make a significant difference in product quality, affect the presence of other phases in the crystal, or even determine the direction of zeolite crystallization. Therefore, the aim of this work was to show the influence of the heating rate on the quality of the obtained 13X zeolite powders. The obtained samples were analysed in terms of crystallinity (by X-ray diffraction), chemical composition, granulometry and specific surface area (by Brunauer-Emmett-Teller analysis), and regarding water and CO2 adsorption capacities. Additionally, scanning electron microscopy analysis of the samples showed the morphological characteristics of different 13X zeolite powders. The analysis results of the obtained powders confirmed the influence of the heating rate and helped to define the optimal synthesis parameters i.e. the initial temperature and heating time, that resulted in stable product quality.

This paper presents research on hydrodynamics and mass transfer in a packed absorption column. Experimental data on dry column pressure drop, flooding point, and efficiency of absorption of CO2 in water is obtained on a lab-scale absorption column packed with Raschig rings. Auxiliary parts of equipment together with chemical analyses provide simple monitoring and collecting the data. All obtained data were used to test different mathematical models for a given problem, i.e. for determination of the dry column pressure drop, flooding point and the overall gas transfer unit height. For dry column pressure drop, models developed primarily for packed columns described the data the best, with the Billet model generating a 6.54 % mean error, followed by Mackowiak and Stichlmair models. In flooding point calculations, empirical models were tested and models of Lobo, Leva and Takahshi gave the best results. Mass transfer (absorption) experiments gave expected results, since absorption efficiency increased with the increase in the liquid/gas flow rate ratio, i.e. with approaching the flooding point. The Onda’s model was used to calculate partial mass transfer coefficients in liquid and gas phases based on which the height of the overall gas transfer unit was estimated and subsequently compared with the experimental data. Deviation of calculated and experimental results for the height of the overall gas transfer unit is in the expected range of 0-20 %, with mean value of 15.5 %. In conclusion, the available models for determination of the investigated hydrodynamics and mass transfer parameters in packed absorption columns gave adequate results in comparison to the experimental values.

In a semi-ideal gas, entropy changes cannot be determined through the medium specific heat capacity in a manner as determined by the change of internal energy and enthalpy, i.e. the amount of heat exchanged. Taking this into account, the authors conducted two models through which it is possible to determine the change in the specific entropy of a semi-ideal gas for arbitrary temperature interval using the spread sheet method, using the mean values of the appropriate functions. The idea is to replace integration, which occurs here in evitably, with mean values of the previous functions. The models are derived based on the functional dependence of the actual specific heat capacity on the temperature. The theorem used is that of the mean value of a function as well as the mathematical properties of the definite integral. The mean value of a fractional function is determined via its integrand while the logarithmic functions were performed by applying a suitable transformation of the differential calculus. The relations derived relation, using the computer program, have enabled the design of appropriate thermodynamic tables through which it is possible to determine the change in entropy of arbitrary state changes in an efficient and rational manner, without the use of calculus or finished forms. In this way, the change in the entropy of a semi-ideal gas is determined for an arbitrary temperature interval using the method which is analogous to that applied in determining the change of internal energy and enthalpy or the amount of heat exchanged, which was the goal of the work. Verification of the proposed method for both the above functions was performed for a a few characteristic semi-ideal gases where change c(T) is significant, for the three adopted temperature intervals, for the characteristic change of state. This was compared to the results of the classical integral and the proposed method through the prepared tables. In certain or special cases, it is possible to apply the presented method also in determining the change in entropy of the real gas. Apart from that, the paper shows that the change in entropy for the observed characteristic case can be represented or graphically determined using the planimetric method of diagrams with suitably selected coordinates.

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.

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.

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.

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.