Final answer:
In a chemical equation, the number of atoms of each kind and the sum of the masses of all substances must be the same on both sides due to the law of conservation of mass.
Step-by-step explanation:
The quantities that must always be the same on both sides of a chemical equation are crucial for the balance of the equation and follow the law of conservation of mass. The correct answers that apply here are that the number of atoms of each kind and the sum of the masses of all substances involved must remain constant. This is because in any closed system, no atoms are lost or gained in a chemical reaction; they are simply rearranged. The number of atoms of each element must be the same on both sides of the equation to ensure that matter is conserved. When it comes to the number of molecules or moles, these may vary depending on the coefficients used to balance the equation. Therefore, the option regarding the number of molecules doesn't necessarily apply, but the ones regarding the number of moles and the sum of masses do, as they relate directly back to the conservation of atoms.