Question

How is the law of definite composition related to the law of multiple proportions?

Answer 1

Hint: To determine the relation between the law of definite composition and law of multiple proportions we should what is the law of definite composition and law of multiple proportions. The law of definite proportions, as the name indicates is a law that states about the definite ratio of masses of elements in a compound. Law of multiple proportions as the name indicates is a law that states about the ratio of an element in two compounds formed by the same elements.

Complete step by step answer:
Law of definite composition: The elements combine to form compounds. The compounds have elements in a fixed and constant ratio by mass and the ratio does not depend upon the preparation method of the source of the compounds.

For example, consider water, we can take water from anywhere. The ratio of oxygen and hydrogen in water by mass will always be $16:2$ or $8:1$. So, the chemical formula of water will be ${\text{H}}_{\text{2}}\text{O}$. The ratio of oxygen and hydrogen will not change.
So, according to the law of definite composition the ratio of oxygen and hydrogen in water will be $8:1$ always.

Law of multiple proportions: When elements form more than one compound. The ratio of one element in both or all the compounds will be in whole number ratio by mass.
Now, hydrogen and oxygen elements form hydrogen peroxide also. The formula of hydrogen peroxide is ${\text{H}}_{\text{2}}{\text{O}}_{\text{2}}$. The ratio of oxygen and hydrogen in hydrogen peroxide is $32:2$ or $16:1$.
So, according to the law of multiple proportions the ratio of mass of oxygen in both compounds will be in a ratio.
$$\Rightarrow {\displaystyle \frac{{\text{H}}_{\text{2}}{\text{O}}_{\text{2}}}{{\text{H}}_{\text{2}}\text{O}}}={\displaystyle \frac{16}{8}}$$
$$\Rightarrow {\displaystyle \frac{{\text{H}}_{\text{2}}{\text{O}}_{\text{2}}}{{\text{H}}_{\text{2}}\text{O}}}={\displaystyle \frac{2}{1}}$$
Oxygen ratio in, $${\text{H}}_{\text{2}}{\text{O}}_{\text{2}}:{\text{H}}_{\text{2}}\text{O}$$
$$2:1$$.
Therefore, law of definite composition and law of multiple proportions both tells the ratio by mass of elements in compounds.

Note: Law of definite composition is used for the determination that the given masses ratio represents the same compound or not. If we are calculating the ratio of oxygen and hydrogen in any reaction, if we get oxygen and hydrogen in $8:1$ by mass we can say the compound will be water. If the ratio comes to $16:1$ we can the compound is not water. The compound will have the formula HO so, it will be hydrogen peroxide ${\text{H}}_{\text{2}}{\text{O}}_{\text{2}}$.