Law of Multiple Proportion

This law was established by Dalton, in 1803. According to this law, when two elements A and B combine to form more than one compound, the masses of A which separately combine with a fixed mass of B (or vice versa) are in the ratio of small whole numbers. For example, copper and oxygen combine to form two oxides, namely, cuprous oxide and cupric oxide. If the copper and oxygen contents of these two compounds are determined, it is found that the masses are in the ratio of 7:94:1 and 3:97:1, respectively. Hence, the mass of copper in cuprous oxide is just double of that in cupric oxide.

Problem
Nitrogen combines with oxygen to form five oxides of nitrogen, namely, N2O, NO, N2O3, N2O4 and N2O5. Show that the law of multiple proportions is applicable to both atoms.

Solution
For nitrogen, we find the masses of nitrogen that combine with a fixed mass of oxygen (say, 16g). We will have
Mass of nitrogen in N2O    =   28g
Mass of nitrogen in NO      =  14g
Mass of nitrogen N2O3
Mass of nitrogen in N2O4
Mass of nitrogen in N2O5

Thus, we find that the ratio of the masses of nitrogen is
28:14: 7:
i.e. 4::2:1:
or   60:30:20:15:12

For oxygen, we find the masses of oxygen that combine with a fixed mass of nitrogen (say, 14g):
Mass of oxygen in N2O    =
Mass of oxygen in NO     =
Mass of oxygen in N2O3   =
Mass of oxygen in N2O4   =
Mass of oxygen in N2O5   =
Hence, the ratio of the masses of oxygen is
8:16:24:32:40 or 1:2:3:4:5

Since both the ratios involve only whole numbers, the law of multiple proportions is applicable to both nitrogen and oxygen.