The law of multiple proportions states that :
This is one of the basic laws of stoichiometry used to establish the atomic theory, alongside the law of conservation of mass (matter) and the law of definite proportions. It is sometimes called Dalton's Law after its discoverer, the British chemist John Dalton, who published it in the first part of the first volume of his "New System of Chemical Philosophy" (1808).
For example, Dalton knew that the element carbon forms two oxides by combining with oxygen in different proportions. A fixed mass of carbon, say 100 grams, may react with 133 grams of oxygen to produce one oxide, or with 266 grams of oxygen to produce the other. The ratio of the masses of oxygen that can react with 100 grams of carbon is 266:133 = 2:1, a ratio of small whole numbers. Dalton interpreted this result in his atomic theory by proposing (correctly in this case) that the two oxides have one and two oxygen atoms respectively for each carbon atom. In modern notation the first is CO (carbon monoxide) and the second is CO2 (carbon dioxide).
John Dalton first expressed this observation in 1804. A few years previously, the French chemist Joseph Proust had proposed the law of definite proportions, which expressed that the elements combined to form compounds in certain well-defined proportions, rather than mixing in just any proportion; and Antoine Lavoisier proved the law of conservation of mass, which helped out Dalton. Careful study of the actual numerical values of these proportions led Dalton to propose his law of multiple proportions. This was an important step toward the atomic theory that he would propose later that year, and it laid the basis for chemical formulas for compounds.
Another example of the law can be seen by comparing ethane (C2H6) with propane (C3H8). The weight of hydrogen which combines with 1 g carbon is 0.252 g in ethane and 0.224 g in propane. The ratio of those weights is 1.125, which can be expressed as the ratio of two small numbers 9:8.
The law of multiple proportions is best demonstrated using simple compounds. For example, if one tried to demonstrate it using the hydrocarbons decane (chemical formula C10H22) and undecane (C11H24), one would find that 100 grams of carbon could react with 18.46 grams of hydrogen to produce decane or with 18.31 grams of hydrogen to produce undecane, for a ratio of hydrogen masses of 121:120, which is hardly a ratio of "small" whole numbers.