Final answer:
Compound I and Compound II are different because they have different mass ratios of hydrogen to oxygen, which is consistent with the law of definite proportions.
Step-by-step explanation:
To determine whether Compound I and Compound II are the same, we should calculate the mass ratios of hydrogen to oxygen in both compounds and compare them. For Compound I, we have 15.0 g of hydrogen and 120.0 g of oxygen, which gives us a ratio of 1:8 (when simplified from 15:120). In contrast, Compound II contains 2.0 g of hydrogen and 32.0 g of oxygen, resulting in a ratio of 1:16 (when simplified from 2:32). Since the mass ratios of hydrogen to oxygen in both compounds are different, we can conclude under the law of definite proportions that these are two different compounds.