In chemistry, the law of multiple proportions states that if two elements form more than one compound, then the ratios of the masses of the second element which combine with a fixed mass of the first element will always be ratios of small whole numbers. This law is also known as: ''Dalton's Law'', named after

John Dalton John Dalton (; 5 or 6 September 1766 – 27 July 1844) was an English chemist, physicist and meteorologist. He is best known for introducing the atomic theory into chemistry, and for his research into Color blindness, colour blindness, which ...

, the chemist who first expressed it. For example, Dalton knew that the element

carbon Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent—its atom making four electrons available to form covalent chemical bonds. It belongs to group 14 of the periodic table. Carbon ma ...

forms two

oxide An oxide () is a chemical compound that contains at least one oxygen atom and one other element in its chemical formula. "Oxide" itself is the dianion of oxygen, an O2– (molecular) ion. with oxygen in the oxidation state of −2. Most of the E ...

s by combining with

oxygen Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements ...

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 Carbon monoxide ( chemical formula CO) is a colorless, poisonous, odorless, tasteless, flammable gas that is slightly less dense than air. Carbon monoxide consists of one carbon atom and one oxygen atom connected by a triple bond. It is the simpl ...

) and the second is CO₂ (

carbon dioxide Carbon dioxide ( chemical formula ) is a chemical compound made up of molecules that each have one carbon atom covalently double bonded to two oxygen atoms. It is found in the gas state at room temperature. In the air, carbon dioxide is t ...

). John Dalton first expressed this observation in 1804. A few years previously, the

French French (french: français(e), link=no) may refer to: * Something of, from, or related to France ** French language, which originated in France, and its various dialects and accents ** French people, a nation and ethnic group identified with Franc ...

chemist Joseph Proust had proposed the ''

law of definite proportions In chemistry, the law of definite proportions, sometimes called Proust's law, or law of constant composition states that a given chemical compound always contains its component elements in fixed ratio (by mass) and does not depend on its source an ...

'', which expressed that the elements combined to form compounds in certain well-defined proportions, rather than mixing in just any proportion; and

Antoine Lavoisier Antoine-Laurent de Lavoisier ( , ; ; 26 August 17438 May 1794),
CNRS (

atomic theory Atomic theory is the scientific theory that matter is composed of particles called atoms. Atomic theory traces its origins to an ancient philosophical tradition known as atomism. According to this idea, if one were to take a lump of matter ...

that he would propose later that year, and it laid the basis for

chemical formula In chemistry, a chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule, using chemical element symbols, numbers, and sometimes also other symbols, ...

s 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.

Limitations

The law of multiple proportions is best demonstrated using simple compounds. For example, if one tried to demonstrate it using the

hydrocarbon In organic chemistry, a hydrocarbon is an organic compound consisting entirely of hydrogen and carbon. Hydrocarbons are examples of group 14 hydrides. Hydrocarbons are generally colourless and hydrophobic, and their odors are usually weak or ...

decane Decane is an alkane hydrocarbon with the chemical formula C10H22. Although 75 structural isomers are possible for decane, the term usually refers to the normal-decane ("''n''-decane"), with the formula CH3(CH2)8CH3. All isomers, however, exhib ...

(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. The law fails with

non-stoichiometric compound In chemistry, non-stoichiometric compounds are chemical compounds, almost always solid inorganic compounds, having elemental composition whose proportions cannot be represented by a ratio of small natural numbers (i.e. an empirical formula); m ...

s and also doesn't work well with

polymers A polymer (; Greek '' poly-'', "many" + '' -mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...

and

oligomers In chemistry and biochemistry, an oligomer () is a molecule that consists of a few repeating units which could be derived, actually or conceptually, from smaller molecules, monomers.Quote: ''Oligomer molecule: A molecule of intermediate relativ ...

History

The law of multiple proportions was a key proof of the atomic theory, but it is uncertain whether Dalton discovered the law of multiple proportions by accident and then used atomic theory to explain it, or whether his law was a hypothesis he proposed in order to investigate the validity of the atomic theory. In 1792,

Bertrand Pelletier Bertrand Pelletier (31 July 1761 – 21 July 1797) was an 18th-century French pharmacist and chemist. Biography Bertrand Pelletier was the son of the pharmacist Bertrand Pelletier, and his wife Marie Sabatier. After training with his father, ...

discovered that a certain amount of tin will combine with a certain amount of oxygen to form one tin oxide, or twice the amount of oxygen to form a different oxide. Joseph Proust confirmed Pelletier's discovery and provided measurements of the composition: one tin oxide is 87 parts tin and 13 parts oxygen, and the other is 78.4 parts tin and 21.6 parts oxygen. These were likely

tin(II) oxide Tin(II) oxide (stannous oxide) is a compound with the formula SnO. It is composed of tin and oxygen where tin has the oxidation state of +2. There are two forms, a stable blue-black form and a metastable red form. Preparation and reactions Blu ...

(SnO) and

tin dioxide Tin(IV) oxide, also known as stannic oxide, is the inorganic compound with the formula SnO2. The mineral form of SnO2 is called cassiterite, and this is the main ore of tin. With many other names, this oxide of tin is an important material in tin ...

(SnO₂), and their actual compositions are 88.1% tin—11.9% oxygen, and 78.7% tin—21.3% oxygen. Scholars who have reviewed the writings of Proust found that he had enough data to have discovered the law of multiple proportions himself, but somehow he did not. With regards to the aforementioned tin oxides, had Proust adjusted his figures for a tin content of 100 parts for both oxides, he would have noticed that 100 parts of tin will combine with either 14.9 or 27.6 parts of oxygen. 14.9 and 27.6 form a ratio of 1:1.85, which is 1:2 if one forgives experimental error. It seems this did not occur to Proust, but it occurred to Dalton. Henry (1854). ''Memoirs...'', p. 82

Footnotes

Bibliography

* * * *{{cite book , author1=Henry E. Roscoe , author2=Arthur Harden , year=1896 , title=A New View of the Origin of Dalton's Atomic Theory , publisher=Macmillan and Co. , url=https://archive.org/details/newviewoforigino00roscuoft/page/n10/mode/2up , ref=refRoscoeHarden1896 Physical chemistry Stoichiometry