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The Law of Constant Composition (or Law of Definite Proportions) states that a chemical compound always contains the same proportion of elements by mass, regardless of the amount of the compound or its source. This law was formulated by Joseph Proust in the early 19th century and is a fundamental concept in chemistry.

Moles are a unit of measurement used to express the amount of a chemical substance, defined as the amount of substance that contains as many particles as there are atoms in 12 grams of pure carbon-12. It is a convenient way to count atoms, molecules, or ions in a sample of a substance. The number of particles in one mole of any substance is approximately \(6.022 \times 10^{23}\) particles (Avogadro's number).

The mass of an element in a compound can be determined by multiplying the number of moles of that element by its atomic mass. Using the mole concept, the relative numbers of atoms in a compound can be directly related to the relative masses of the constituent elements. Since the number of moles of an element in a compound is proportional to the mass of the element, it follows that the ratio of masses of the elements in a compound is equivalent to the ratio of the number of moles (and thus the number of atoms) of each element.

Let's use water as an example to further illustrate this relationship. In one mole of water, there are 2 moles of hydrogen atoms (H) and 1 mole of oxygen atoms (O). The atomic mass of hydrogen is approximately 1 g/mol, and that of oxygen is 16 g/mol. Consequently, in one mole of water, there are 2 grams of hydrogen and 16 grams of oxygen. The ratio of the masses of hydrogen to oxygen in water is 2:16 or 1:8. This ratio also represents the relative numbers of hydrogen to oxygen atoms in the compound water. This property holds true regardless of the amount of water or its source, supporting the Law of Constant Composition. In conclusion, the relative masses of the constituent elements of a compound are related to the relative numbers of each kind of atom present by maintaining a fixed ratio, in agreement with the Law of Constant Composition.