Answer:
The law of multiple proportions states that when two elements combine to form more than one compound, the mass ratios of the elements in the compounds can be expressed as small whole numbers.
Let's assume that the metal M combines with oxygen to form two different oxides, which are represented by the formulas MOx and MOy, where x and y are the number of oxygen atoms in each oxide.
According to the problem, the two oxides contain 11.1% and 20.0% of oxygen, respectively. We can convert these percentages to mass ratios as follows:
Mass ratio of oxygen in MOx = 11.1 g / 100 g of oxide
Mass ratio of oxygen in MOy = 20.0 g / 100 g of oxide
We can simplify these ratios by dividing each by their lowest common factor, which is 1.1:
Mass ratio of oxygen in MOx = 10 g / 91 g of oxide
Mass ratio of oxygen in MOy = 20 g / 100 g of oxide = 20 g / 91 g of oxide
These ratios can be expressed as small whole numbers by multiplying them by a factor that makes the denominator equal to a whole number. We can multiply the ratio for MOx by 10 to get:
Mass ratio of oxygen in MOx = 100 g / 910 g of oxide
We can multiply the ratio for MOy by 5 to get:
Mass ratio of oxygen in MOy = 100 g / 910 g of oxide
Now we can see that the mass ratios of oxygen in the two oxides are in a small whole number ratio of 1:1, which is consistent with the law of multiple proportions. This means that the metal M forms two different oxides in a ratio of small whole numbers, and that the composition of the oxides is determined by the ratio of the masses of the elements involved.
Step-by-step explanation: