Final answer:
The law of conservation of matter requires that there be equal numbers of atoms of each element in the reactants and products of a balanced chemical equation.
Step-by-step explanation:
The scientific law that requires equal numbers of atoms of each element in both the reactants and the products in a balanced chemical equation is the law of conservation of matter. This law states that matter cannot be created or destroyed in an isolated system. Therefore, during a chemical reaction, the mass and the number of atoms of each element must remain constant. Balancing a chemical equation ensures that there are the same number of atoms for each element on both sides. Coefficients can be added in front of reactants and products to achieve this balance, while maintaining the correct stoichiometric ratios outlined by the equations.