Law of Definite Proportions or Proust's Law

02nd Jun 2019 @ 7 min read

The law of definite proportions is also known as the law of definite composition or the law of constant composition, or simply Proust’s law. It is one of the basic laws in chemistry and a part of the laws of chemical combinations. In 1794, French chemist Joseph Proust proposed this law. That time the knowledge of chemical compound was not fully evolved, and he was opposed by many well-known chemists of that time. But later they were proven wrong. The law of definite proportions was later extended by John Dalton when Dalton proposed the law of multiple proportions.

Statement

The law states a given chemical compound always contains its elements in the same proportions by mass.

Explanation with Examples

As per the law, the elements in a chemical compound are always in fixed composition by mass. This is true irrespective of source or method of preparation of that chemical compound. Consider a molecule of water H₂O. Now, water is a chemical compound since it is made up of more than one element. Any water molecule consists of 2 hydrogen atoms and one oxygen atom, and both the elements are always in the same proportions by mass. The mass percentage of hydrogen and oxygen in water is 11.11 % hydrogen and 88.89 % oxygen. These percentages are true for all the water molecules in the universe.

Figure 1: All water molecules have the same proportion by mass. In the above figure, river water, rainwater, and tap water have a fixed composition of hydrogen 11.11 % and oxygen 88.89 %.

rain water — Figure 1: All water molecules have the same proportion by mass. In the above figure, river water, rainwater, and tap water have a fixed composition of hydrogen 11.11 % and oxygen 88.89 %.

Proust’s Observation

The law of definite proportions was Proust’s largest achievement in his scientific career. Proust worked with two samples cupper carbonate CuCO₃. One was synthetic and the other was naturally occurring. He compared both the sample and found that both had the same composition of elements present in it. Thus, from this observation, he concluded that elements in a chemical compound are always combined in the same fixed proportions irrespective of the source of the chemical. He also studied the two-tin oxide and the two-iron oxide to prove this law.

Table 1: Elemental Composition of CuCO₃ by Mass
Sample Source	Cu %	C %	O %
Natural Sample	51.35	9.74	38.91
Synthetic Sample	51.35	9.74	38.91

More Examples

Consider carbon dioxide CO₂ which is a well-known gas. Carbon dioxide is an end product of cellular respiration in almost all living organisms on this planet. It is also released from anthropological activities, which is a cause of global warming. CO₂ from cellular respiration and from anthropological activities is the same. In each case, CO₂ has 27.27 % carbon and 72.73 % oxygen.

Let us consider one more example of ethyl alcohol (C₂H₆O). 1 molecule of ethyl alcohol contains 2 carbon atoms, 6 hydrogen atoms, and 1 oxygen atom, and their respective mass proportions are 52.18 %, 13.04 %, and 34.78 %. These percentages are universally true for all ethanol molecules.

Limitation of Proust’s Law

The law of definite proportions or Proust’s law is not universally valid. There are some exceptions, which are discussed below.

The law does not hold when there is the presence of an isotope in the compound. Isotopes are a variant of an element that has the same atomic number but different atomic mass due to the presence of extra neutrons. Consider an example of deuterium (aka heavy hydrogen). Deuterium is an isotope of hydrogen have atomic mass of 2 amu, and its oxide (deuterium oxide, D₂O) is called heavy water. The proportions of elements in normal water and heavy water are different. Thus, the law of definite proportions fails.
Non-stoichiometric compounds also do not obey Proust’s law. In non-stoichiometric compounds, the ratio of elements fluctuates within certain range. Classic example is ferrous oxide, whose ideal formula is FeO. But due to crystallographic vacancies, Fe atoms can vary from 0.83 to 0.95 for each O atom. Because of this variation, the proportions of elements (Fe, O) will vary, and Proust’s law fails again.
Many polymers (like protein, carbohydrates) do not have a fixed composition. These compounds also break the law.

Example

Consider two chemical samples. we do not know whether they consist of the same compound or different. But we do know both the sample have hydrogen and oxygen as their only elements. Sample 1 has 10 g of hydrogen and 80 g of oxygen. Sample 2 has 4 g of hydrogen and 64 g of oxygen. Determine whether the compound in both the samples is the same or not.

First, we need to calculate the mass percentage (or proportion) in both the samples. If the percentages match, it is the same compound.

For sample 1,

$\%\,\text{of}\,\text{H}=\frac{10}{10+80}=11.11\,\%$

$\%\,\text{of}\,\text{O}=\frac{80}{10+80}=88.89\,\%$

For sample 2,

$\%\,\text{of}\,\text{H}=\frac{4}{4+64}=5.88\,\%$

$\%\,\text{of}\,\text{O}=\frac{64}{4+64}=94.12\,\%$

As we can see the percentages differ, so, they are different compounds. Since the percentages of H and O matches with water molecule, sample 1 has water (H₂O) in it. Similarly, sample 2 has hydrogen peroxide (H₂O₂).

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Laws Of Chemical Combinations

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Thanks for your response!

Federiko
15th Mar 2022

Hello, is there an internationally accepted table where these proportions are stated for a large number of compounds? Thanks