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|
Try balancing the following reaction:
HClO3 + SnS + As2S3 + H2O > Sn3(AsO4)4 + H2SO4 + HCl