## Balancing Chemical Equations

For users with the
Mathcad browser: wmc-ce1.mcd (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:

HClO_{3} + SnS + As_{2}S_{3} + H_{2}O ——>
Sn_{3}(AsO_{4})_{4} + H_{2}SO_{4} + HCl

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