Final answer:
In binary ionic compounds, the ratio of elements is determined by their oxidation numbers to ensure electrical neutrality and adherence to the law of conservation of matter.
Step-by-step explanation:
In a binary ionic compound, the ratio of elements is based on the element's oxidation number. This is because the compound must be electrically neutral, meaning the total number of positive charges from the cations must equal the total number of negative charges from the anions. For instance, in aluminum oxide (Al2O3), there are two aluminum cations (Al3+) for every three oxide anions (O2−), which results in a neutral compound [(2 × +3) + (3 × −2) = 0]. The correct ratio of ions ensures that the number of electrons lost is equal to the number of electrons gained, satisfying the law of conservation of matter.