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This is a worked example problem using the 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.