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Law of Multiple Proportions Example Problem

Worked Example Problem Using the Law of Multiple Proportions

This is the space-filling molecular structure for carbon dioxide.

Ben Mills
This is a worked example chemistry problem using the Law of Multiple Proportions.

Example Law of Multiple Proportions Problem

Two different compounds are formed by the elements carbon and oxygen. The first compound contains 42.9% by mass carbon and 57.1% by mass oxygen. The second compound contains 27.3% by mass carbon and 72.7% by mass oxygen. Show that the data are consistent with the Law of Multiple Proportions.

Solution

The Law of Multiple Proportions is the third postulate of Dalton's atomic theory. It states that the masses of one element which combine with a fixed mass of the second element are in a ratio of whole numbers.

Therefore, the masses of oxygen in the two compounds that combine with a fixed mass of carbon should be in a whole-number ratio. In 100 g of the first compound (100 is chosen to make calculations easier) there are 57.1 g O and 42.9 g C. The mass of O per gram C is:

57.1 g O / 42.9 g C = 1.33 g O per g C

In the 100 g of the second compound, there are 72.7 g O and 27.3 g C. The mass of oxygen per gram of carbon is:

72.7 g O / 27.3 g C = 2.66 g O per g C

Dividing the mass O per g C of the second (larger value) compound:

2.66 / 1.33 = 2

Which mean that the masses of oxygen that combine with carbon are in a 2:1 ratio. The whole-number ratio is consistent with the Law of Multiple Proportions.

Anne Marie Helmenstine, Ph.D.