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Law of Multiple Proportions by Dalton

04th Jun 2019 @ 4 min read

Physical Chemistry

The law of multiple proportions is one of the basic laws studied in chemistry. It along with the law of definite proportions has contributed to the understanding of stoichiometry in early days. The law was proposed by English chemist John Dalton in 1803, who is also known for his law of partial pressures. Dalton published the law in his book New System of Chemical Philosophy (Vol 1).

The law of multiple proportions came after Proust’s law of definite proportions. The law was supportive of Proust’s work, and later, helped Dalton in his atomic theory.


The law states if two elements can react to form more than one compound, the ratio of the masses of one element that combine with a fixed mass of the other element are in the ratio of small whole numbers.

Explanations with Examples

Daltons Findings

Dalton was aware of carbon can form two compounds with oxygen. Today, they are known as carbon monoxide, CO and carbon dioxide, CO2. For 12 g of carbon, 16 g of oxygen is needed to form carbon monoxide. To form carbon dioxide, 12 g carbon is reacted with 32 g of oxygen. In each case, the amounts of carbon is fixed to 12 g. The ratio of mass of carbon monoxide to carbon dioxide is 16 : 32 = 1 : 2. Thus, it is a ratio in small whole numbers. Dalton carefully studied the numerical ratio of many reactions and confirmed that the law.

\text{C} &+& \text{O} &\longrightarrow & \text{CO} \\ 12\,\text{g}&&16\,\text{g}&& 28 \,\text{g} \text{C} &+& 2\text{O} &\longrightarrow & \text{CO}_2 \\ 12\,\text{g}&&32\,\text{g}&& 44 \,\text{g}


Example 1

Hydrogen (H) and oxygen (O) can react to form water (H2O) and hydrogen peroxide (H2O2). For 2 g of hydrogen, we need 16 g of oxygen to form water and 32 g of oxygen to form hydrogen peroxide. The ratio of masses of oxygen is 16 : 32 = 1 : 2.

2\text{H} &+& \text{O} &\longrightarrow & \text{H}_2\text{O} \\ 2\,\text{g}&&16\,\text{g}&& 18 \,\text{g} 2\text{H} &+& 2\text{O} &\longrightarrow & \text{H}_2\text{O}_2 \\ 2\,\text{g}&&32\,\text{g}&& 34 \,\text{g}

Example 2

In the above examples, only two compounds are formed. Let us consider a more complex example. Nitrogen can react with oxygen to form numerous nitrogen oxides under different reaction conditions. Some of them are nitrogen monoxide (NO), dinitrogen oxide (N2O), nitrogen dioxide (NO2), dinitrogen trioxide (N2O3), and dinitrogen pentoxide (N2O5). We will fix the amount of nitrogen to 28 g. The reactions are as follows.

2\text{N} &+& 2\text{O} &\longrightarrow & 2\text{N}\text{O} \\ 28\,\text{g}&&32\,\text{g}&& 34 \,\text{g} 2\text{N} &+& \text{O} &\longrightarrow & \text{N}_2\text{O} \\ 28\,\text{g}&&16\,\text{g}&& 44 \,\text{g} 2\text{N} &+& 4\text{O} &\longrightarrow & 2\text{N}\text{O}_2 \\ 28\,\text{g}&&64\,\text{g}&& 92 \,\text{g} 2\text{N} &+& 3\text{O} &\longrightarrow & \text{N}_2\text{O}_3 \\ 28\,\text{g}&&48\,\text{g}&& 76 \,\text{g} 2\text{N} &+& 5\text{O} &\longrightarrow & \text{N}_2\text{O}_5 \\ 28\,\text{g}&&80\,\text{g}&& 108 \,\text{g}

If we take the ratio of the amounts of oxygen required in each reaction, we get 32 : 16 : 64 : 48 : 80 or 2 : 1 : 4 : 3 : 5. Thus, the ratio is in small whole numbers and the law is valid for more than two reactions.

Limitations of Law

The law of multiple proportions is not universally true. There are some limitations, which are described below.

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