Law of Multiple Proportions Law of Multiple Proportions the law of multiple proportions is one of the basic laws of stoichiometry used to establish the atomic theory, alongside the law of conservation of mass and the law of definite proportions. It is sometimes called Dalton's Law after its discoverer, the English chemist John Dalton, who published it in the first part of the first volume of his "New System of Chemical Philosophy" (1808).The statement of the law is: If two elements form more than one compound between them, then the ratios of the masses of the second element which combine with a fixed mass of the first element will be ratios of small whole numbers. 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).
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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. Question 1: What is the ratio of copper and oxygen in cuprous oxide? Solution :- Copper forms two oxides namely Cuprous oxide (Cu2O) and Cupric oxide (CuO). Atomic mass of copper is 63. In terms of oxygen 1 atom of oxygen combines with 2 atoms or 2 X 63 parts by mass of Copper in cuprous oxide and 1 atom of oxygen combines with 1 atom or 1X 63 parts by mass of copper in cupric oxide. Thus the ratio is 2:1 which is a simple ratio. Question 2: A metal forms two oxides with first oxide having 1 and second having 3 oxygen atoms and their masses are 74g and 164 g respectively. If the g.at.mass of oxygen is 16g, what is the atomic mass of the metal. prove that the two compounds follow the law of multiple proportions. Solution: First Oxide contains 16 g of oxygen and 74-16 g = 58 g of metal. Since 1 atom of oxygen has to combine with minimum of 1 atom of metal to form its stable oxide, the atomic mass of metal should be 58. Second Oxide has 3 X 16 = 48 g of oxygen and 164-48 = 116 g of metal.(since the formula shows two atoms of metal we can directly take 2 X 58=116 g) and has a formula M2O3
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To prove the law of multiple proportions, in case of oxide M2O3, 16 g of oxygen combine with 116/3 g of metal = 38.66 g of metal. Thus the metal ratios will be 38.66 : 58 or 1 : 1.5 (aprox) or 2: 3 which is a simple ratio. Question 3: Hydrogen and oxygen forms two compounds. The hydrogen content in these compounds is 42.9% and 27.3%. Prove these compounds agree with the law of multiple proportions. Solution: In the first compound, the mass of hydrogen is 42.9 g. and the mass of oxygen will be 100 - 42.9 = 57.1g. Therefore the mass of hydrogen that combines with 1 g of oxygen = 42.9 / 57.1 = 0.75g In the second compound the mass of hydrogen is 27.3g and the mass of oxygen will be 100 27.3 = 72.7g Therefore the mass of hydrogen that combines with 1 g of oxygen = 27.3 / 72.7 = 0.375g Thus the ratio of hydrogen combining with a fixed mass of oxygen is 0.75 : 0.375 or 2:1 which proves the law of multiple proportions.
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