scholarly journals A method for determining stoichiometric coefficients using minors of a matrix

Author(s):  
Rainier Lombaard

Spinel materials often have complex structures and as a result, balancing of reactions with these compounds by traditional methods become very time consuming. A method to calculate the stoichiometric coefficients for chemical reactions using first a modified matrix-inverse method and then an optimised method is proposed. Both methods are explored using linear algebra and the result demonstrated using a typical chromite reduction reaction.

2022 ◽  
Author(s):  
Rainier Lombaard

Spinel materials often have complex structures and as a result, balancing of reactions with these compounds by traditional methods become very time consuming. A method to calculate the stoichiometric coefficients for chemical reactions using first a modified matrix-inverse method and then an optimised method is proposed. Both methods are explored using linear algebra and the result demonstrated using a typical chromite reduction reaction.


2022 ◽  
Author(s):  
Rainier Lombaard

Spinel materials often have complex structures and as a result, balancing of reactions with these compounds by traditional methods become very time consuming. A method to calculate the stoichiometric coefficients for chemical reactions using first a modified matrix-inverse method and then an optimised method is proposed. Both methods are explored using linear algebra and the result demonstrated using a typical chromite reduction reaction.


2021 ◽  
Author(s):  
Rainier Lombaard

The motivation of this study was the investigation into the metallothermic reduction of chromite ores. Spinel materials have complex structures and as a result, balancing of the reduction reactions by traditional methods become very time consuming. A method to calculate the stoichiometric coefficients for chemical reactions using first a modified matrix-inverse method and then a new optimised method is proposed. The mathematical basis of both methods is explored using matrix algebra and then demonstrated using a typical chromite reduction reaction.


Author(s):  
Ahmadreza Amini ◽  
Ko-ichiro Ohno ◽  
Takayuki Maeda ◽  
Kazuya Kunitomo ◽  
Keiichiro Kashimura

Microwave irradiation is an energy-efficient and a rapid-heating method to decrease the activation energy of chemical reactions via both thermal and non-thermal effects of microwave photons 1). Recently, hydrogen-reduction during microwave heating has been proposed for magnetite reduction to combine the advantages of microwave irradiation and using H2 as a reducing agent during iron production 2). In the present study, as a novel idea, the traditional microwave heating system was equipped with thermobalance to investigate the kinetics of H2-reduction of FeS-CaO mixture (FeS(s) + CaO(s) + H2(g) = Fe(s) + CaS(s) + H2O(g)) under microwave heating at 2.45 GHz to further mitigate CO2 emission and prevent SO2 release during iron production from a sulfide mineral. Microscope observations revealed that the un-reacted core model can be employed for such a kinetic study. Linearity (R2) of different rate-controlling mechanisms after a 10-minute reduction reaction demonstrated that the gas diffusion in micropores of reduced metallic Fe is a dominant rate-controlling mechanism while the interfacial chemical reaction is progressed rapidly. This is attributed to extraordinary effects of microwave irradiation on speeding up the chemical reactions 3), while the formation of Fe shell on the surface of FeS/FeO particles decreases the accessibility of gas to un-reacted parts, resulting in a lower rate of gas diffusion in micropores. Moreover, the diffusion coefficients (De) at 460, 570, and 750 °C were calculated from the plot of the gas diffusion, as illustrated in Fig. 1, wherein the X is reduction degree: where Wi (g) is the initial weight of the sample, Wt (g) is the weight of the sample after treatment for t seconds, Wht (g) is the weight change of the sample owing to the dehydration reaction, and WO (-) is the stoichiometric weight ratio of oxygen in the sample, which is 0.111. Consequently, the activation energy of 22.3 kJ.mol-1 was attained from the Arrhenius equation for the hydrogen-reduction reaction of FeS-CaO mixture under microwave heating.


2008 ◽  
Vol 84 (1) ◽  
pp. 63-72 ◽  
Author(s):  
DRAGANA S. CVETKOVIĆ-ILIĆ

AbstractIn this article we consider Re-nnd solutions of the equation AXB=C with respect to X, where A,B,C are given matrices. We give necessary and sufficient conditions for the existence of Re-nnd solutions and present a general form of such solutions. As a special case when A=I we obtain the results from a paper of Groß (‘Explicit solutions to the matrix inverse problem AX=B’, Linear Algebra Appl.289 (1999), 131–134).


2019 ◽  
Vol 7 (1) ◽  
pp. 170-190 ◽  
Author(s):  
Yusran Yusran ◽  
Xinyu Guan ◽  
Hui Li ◽  
Qianrong Fang ◽  
Shilun Qiu

Abstract Covalent organic frameworks (COFs) have been at the forefront of porous-material research in recent years. With predictable structural compositions and controllable functionalities, the structures and properties of COFs could be controlled to achieve targeted materials. On the other hand, the predesigned structure of COFs allows fruitful postsynthetic modifications to introduce new properties and functions. In this review, the postsynthetic functionalizations of COFs are discussed and their impacts towards structural qualities and performances are comparatively elaborated on. The functionalization involves the formation of specific interactions (covalent or coordination/ionic bonds) and chemical reactions (oxidation/reduction reaction) with pendant groups, skeleton and reactive linkages of COFs. The chemical stability and performance of COFs including catalytic activity, storage, sorption and opto-electronic properties might be enhanced by specific postsynthetic functionalization. The generality of these strategies in terms of chemical reactions and the range of suitable COFs places them as a pivotal role for the development of COF-based smart materials.


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