In H₂O and H₂O₂, hydrogen and oxygen combine in different proportions. If 2 g of hydrogen combines with 16 g of oxygen in H₂O and with 32 g in H₂O₂, what does this illustrate?

This example illustrates the law of multiple proportions because we have two different compounds (H₂O and H₂O₂) formed from the same elements (hydrogen and oxygen).

In H₂O, 2 grams of hydrogen combine with 16 grams of oxygen, whereas in H₂O₂, 2 grams of hydrogen combine with 32 grams of oxygen.

According to the law of multiple proportions, when two elements (in this case, hydrogen and oxygen) form more than one compound, the different masses of one element (oxygen here) that combine with a fixed mass of the other (hydrogen) will be in a ratio of small whole numbers.

Here, the ratio of the masses of oxygen (16 g in H₂O to 32 g in H₂O₂) that combine with 2 g of hydrogen is 1:2, which is a simple whole-number ratio, satisfying the law of multiple proportions.