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The Law of Multiple Proportions

The Law of Multiple Proportions states that any two compounds formed from the same elements can be described by the mass ratio of one element to another. This is a relatively simple concept, but it is the basis of understanding more complex concepts when quantifying chemical reactions.

For example, take two common gases: carbon monoxide and carbon dioxide

If you know a compound’s molecular formula, then you can determine the mass ratio between the constituent elements.

The reverse is also true.

The law of multiple proportions states that if elements form more than one compound between them, then the ratio of masses of the second element when combined with a fixed amount of the first, will be a small whole number ratio.

This may seem complicated, so let's break down an example. Carbon can react with oxygen in order to make 2 different compounds. 10 grams of carbon can either react with 13.3 grams of oxygen, or 26.6 grams of oxygen. Comparing these two masses of oxygen, $$26.6:13.3 = 2:1$$ Thus, carbon can combine with oxygen in either a 1 to 1 ratio or a 1 to 2 ratio.

The discovery of the law of multiple proportions helped to create the atomic theory, and to develop stoichiometry.

John Dalton's first new idea for his atomic theory, the Law of Multiple Proportions, describes the mass ratios in which the same elements combine to form different compounds.

$CO$ and $CO_{2}$ are both common compounds made of C and O. In modern times, we know them by their molecular formula, and understand that $CO$ is literally one C bonded to one O, while $CO_{2}$ is one C bonded to two Os. However, in the early 1800s, when Dalton was developing his understanding of chemistry, all scientists knew was that when C and O are mixed, multiple compounds are created. The bridge between understanding that C and O can form different substances together, and that those substances are literally combinations of individual atoms of C and O bonded together in specific ratios, was Dalton's Law of Multiple Proportions- the mass ratios of an element in two different compounds composed of the same elements are small whole numbers.

In this example, a mole of $CO_{2}$ will have 32.00 g of O, while a mole of $CO$ will have 16.00. Therefore, the ratio is 2:1, because those numbers correspond to the actual count of atoms of a certain element found in the molecule of a compound.

(Video) Chemistry 5.8b Law of Multiple Proportions

by IsaacsTEACH

This video will teach you about the Law of Multiple Proportions and why the numbers work out the way they do. This law may seem confusing at first, but this video breaks it down line by line and works with the example of $CO$ and $CO_2$ to help you really understand it.