How does mass balance apply in a chemical equation?
By the principle of conservation of mass: GARBAGE IN EQUALS GARBAGE OUT.
Mass is CONSERVED in every chemical reaction. If I start with 10 g of reactant (from all sources) AT MOST I can get 10 g of product; in practice, I can't even get that; I am going to lose something on handling.
Let's take a simple example, the combustion of methane, on which our industrial society depends:
This balanced equation says in fact that 16 g of methane gas reacts with 64 g dioxygen gas to give 44 g of carbon dioxide gas and 36 g water vapour. (From where am I getting these numbers?) The mass of the products is PRECISELY EQUAL to the mass of the reactants. If the masses were not equal, I would know that I have made an error in my arithmetic, and would have to try again.
Every chemical reaction ever performed is known to follow the principle of conservation of mass; which is, I suppose, why educators insist that chemical equations be stoichiometrically balanced.