Chemical reaction equations are in the unit "moles". If you wanted to, you could, with a balanced chemical reaction equation, convert to mass by using the molar mass and the associated moles and numbers of atoms and then show that the mass is equivalent on both sides of the equation. But since the mass of each element is the same on one side of the equation as the other, and since there are equivalent numbers of element atoms on each side as the other, then it seems sort of trivial to say the mass is the same.
Hope this helps!