Computer Algorithm Design and Linear Algebra: How to Solve Chemical Equations as Linear Systems

Overview

Objectives/Goals The objective of my project is to design algorithms based on concepts of linear algebra and apply the algorithms to solve chemical equations. Methods/Materials A standard C or C++ compiler is required for the project. I used Microsoft#s Visual C++ compiler on a Dell Dimension 8100 PC running a 1.4 Ghz Processor with 384 megabytes of SDRAM on Microsoft#s Windows ME operating system. I did research from a number of references on specific topics of linear algebra to help me design effective algorithms to complete the design of the program. Once the design of the program was developed I began the actual coding process. I ran through multiple releases of my program and developed better #input# algorithms until I finished the final program. Results Algorithms designed based on principles of linear algebra can be effectively applied to balancing chemical equations set up as a system of linear equations. Conclusions/Discussion The algorithms performed their functions as designed. The only problem came from balancing double replacement reactions because the polyatomic ions involved in double replacement reactions usually have more than one element. As a result an extra equation is added to the system of linear equations. The solution to the problem is to count a polyatomic ion as a single element instead of counting each individual element that makes up the polyatomic ion.

Competition history

• CSEF 2002 Mathematics & Software · Entry S1213

Resources

• CSEF project summary ↗

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