Element Variables and the Solution of Complex Chemical Equilibrium Problems

1989 ◽  
Vol 68 (1-3) ◽  
pp. 35-48 ◽  
Author(s):  
Keith Meintjes ◽  
Alexander P. Morgan
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Antonios Bakolis ◽  
Dimitrios Stamovlasis ◽  
Georgios Tsaparlis

Abstract A crucial step in problem solving is the retrieval of already learned schemata from long-term memory, a process which may be facilitated by categorization of the problem. The way knowledge is organized affects its availability, and, at the same time, it constitutes the important difference between experts and novices. The present study employed concept maps in a novel way, as a categorization tool for chemical equilibrium problems. The objective was to determine whether providing specific practice in problem categorization improves student achievement in problem solving and in conceptual understanding. Two groups of eleventh-grade students from two special private seminars in Corfu island, Greece, were used: the treatment group (N = 19) and the control group (N = 21). Results showed that the categorization helped students to improve their achievement, but the improvement was not always statistically significant. Students at lower (Piagetian) developmental level (in our sample, students at the transitional stage) had a larger improvement, which was statistically significant with a high effect size. Finally, Nakhleh’s categorization scheme, distinguishing algorithmic versus conceptual subproblems in the solution process, was studied. Dependency of problem solving on an organized knowledge base and the significance of concept mapping on student achievement were the conclusion.


1973 ◽  
Vol 21 (1) ◽  
pp. 240-246 ◽  
Author(s):  
K. O. Kortanek ◽  
W. O. Rom ◽  
A. L. Soyster

Author(s):  
Adrian Bonilla-Petriciolet ◽  
Ma. del Rosario Moreno-Virgen ◽  
Juan Jose Soto-Bernal

Phase equilibrium calculations in systems subject to chemical reactions play a major role in the design of reactive separation schemes including chemical reaction engineering. Basically, these calculations involve the global minimization of Gibbs free energy constrained by the material balances and chemical equilibrium restrictions. However, Gibbs free energy function is non-convex, highly non-linear with many decision variables, and may have several local minimums including trivial and nonphysical solutions. In these conditions, conventional numerical methods are not suitable for solving reactive phase equilibrium problems. Recently, there has been a significant and increasing interest in the development of global strategies for reliably solving reactive phase equilibrium problems subject. Harmony search (HS) is a global stochastic optimization method, which has been conceptualized using the musical process of searching for a perfect state of harmony. Until now, HS has been successfully applied to solve various engineering and optimization problems. However, there are few studies concerning the application of this optimization method for chemical engineering calculations. To the best of our knowledge, the performance of HS for solving reactive phase equilibrium problems has not yet been reported. Therefore, this paper introduces the application of HS-based algorithms to the constrained global minimization of Gibbs free energy in reactive systems. Specifically, we have studied the performance of three variants of HS in reactive phase equilibrium calculations. Our results are useful to identify the capabilities and relative strengths of HS with respect to other stochastic optimization methods for the simultaneous calculation of physical and chemical equilibrium.


1959 ◽  
Vol 36 (10) ◽  
pp. 485 ◽  
Author(s):  
John W. Swinnerton ◽  
Warren W. Miller

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