Balancing chemical reactions is consistent with which scientific law?

Balancing chemical reactions is consistent with Lavoisier's law of conservation of mass.

Explanation:

When a chemical reaction happens, involves the exchange of electrons between the different elements inside the compounds that participate in the reaction.

But the elements themselves (that form the compounds) are not affected , so the elements that are after the reaction should be the same ones that before it happens.

Therefore the total mass of an element (sum of the mass of all the atoms of an element that appears before the reaction) should be the same as the total mass of the element after the reaction. And this should be true for each element.

Lets take this example of a balanced chemical reaction

the number of N atoms at the beggining is 2 ( 2 N atoms attached to themselves) and after the reaction are 2 N also ( each one bonded to an ammonia molecule)

The same should happen with H : 3 gas molecules x 2 atoms of H per gas molecule (H2) = 6 and after the reaction 2 ammonia molecules x 3 atoms of H per ammounia molecule = 6

The equation is balanced only when all the elements are balanced

Note: Strictly speaking, the sum of energy and mass is conserved. But the correction is so insignificant for chemical reactions that in the majority of cases is not taken into account.