CALIFORNIA STATE SCIENCE FAIR
2002 PROJECT SUMMARY
Ap2/02
Name(s) Project Number
Project Title
Abstract
Summary Statement
Help Received
Sahand N. Negahban
Computer Algorithm Design and Linear Algebra: How to Solve
Chemical Equations as Linear Systems
S1213
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.
This project explores concepts in both linear algebra and algorithm development and their applications to
solving chemical equations.
My dad supplied a few of the books that I used for my research. My mom helped me purchase the
compiler. Mr. Robert Ferazzi helped test the program.
