Balancing Chemical Equations

For users with the Mathcad browser: (10 KB, ver. 5.0)

For the chemical reaction: by balancing we mean finding the least integer solutions for a, b, c, d and e.

In mathematics, such equations involving more than one variable in which the coefficients of the variables are integers and only integral solutions are sought, are known as Diophantine equations. From the given chemical equation several linear equations can be written:

2a = 2c to balance Na
4a = c + e to balance S
6a + 2b = 4c + d + 4e to balance O
2b = 2d + 2e to balance H
Such a set of linear equations can be solved in Mathcad with the Given/Find functions.

Try balancing the following reaction:

HClO3 + SnS + As2S3 + H2O   ——>   Sn3(AsO4)4 + H2SO4 + HCl

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