Law Of Chemical Combination: Law Of Reciprocal Proportions

The Law of Reciprocal Proportions was put forth in 1792 by Jeremias Richter. It states that: 

The ratio of masses of 2 elements, A and B, which when mixed with a third element C of a fixed mass, is either the same or some multiple of the ratio of the masses in which A and B combine directly with each other.

Let us consider an example of the law of reciprocal proportions. When Carbon and oxygen are mixed with hydrogen separately, the third element that’s created is methane and water, respectively. However, they can combine directly to create carbon dioxide. In methane, 12 parts per mass of carbon mix in 4 parts mass hydrogen. In water, two portions by mass of hydrogen mix together with the oxygen equivalent of 16 parts per mass.

The proportion of carbon and oxygen that combine with the fixed weight of hydrogen is 12 and 32 parts, respectively. Thus, they are in the ratio of 12:32 = 3:8. Carbon dioxide has twelve parts of carbon mass, which are combined directly with 32 components of oxygen mass. They get directly merged in the ratio 12:32, or 3:18. It is exactly the same as the original ratio.

Law of Reciprocal Proportions: an example

Consider three grams C reacting with one gram of H to produce methane.

Also, 8 grams of O reacts with one gram of H to make water.

In this case, the mass ratio between carbon and oxygen is 3 to 8.

In the same way, 12 grams of C reacts with 32 grams of O to create CO2.

The mass ratio between carbon and oxygen is 12:32 = 3:8.

The mass ratio in the case where C and O mix together is similar to the ratio of mass in which they are paired with the fixed mass of H.

What is the Law of Reciprocal Proportions?

Weights of two or more distinct elements that are combined with the fixed weight of an element are identical to, or simply the multiplication of, the weights of the elements when they are combined.

For instance, let us consider a scenario that highlights this law. Look at the reaction of A and C in order to create D, while B can be added to C to create E. 

These reactions can be described below:

A + C = D

B + C = E

Let mA, MB and mC be the total mass consumed by B, A, and C during those reactions. C is kept at a constant level in both reactions. The ratio is the mass of B and A.

rAB = mA/mB

Another example we can consider is the reaction of A and B to create AB. 

A + B = AB

Let m’A and M’B be the combined mass of B and A in the reaction above. The proportion of these two masses is r’AB.

r’AB = m’A/m’B

As per the law, rAB is the same or multiple of r’AB.

r’AB = n x r’AB

rAB / r’AB = n

where n is a multiplier.

Dalton’s Atomic Theory to Explain the Law of Reciprocal Proportions

In Dalton’s theory of atomicity, all the atoms of the same element are said to be identical and the compounds are created through the blend of elements’ atoms in an easy ratio of whole numbers. Thus, the weights of elements when combined with the weights of a fixed element must have an easy proportion to the elements’ weights when they are combined with one other. 

History of Law of Reciprocal Proportions

The law on reciprocal proportions was formulated by Richter in his study of the ratios of neutralisation of metals in the presence of acid.

In the early years of the 19th century, it was studied by Berzelius who proposed it in the following way: 

When two different substances A and B, have affinities for two other substances, C and D, the proportion of C and D that can saturate the same amount A is the same as that of C and D that can saturate the same amount B.

Later, Jean Stas showed that within the range of experimental error, these stoichiometric rules were right.

Limitations of the Law of Reciprocal Proportions:

In elements that cause discrepancies, the existence of isotopes is similar to those observed in the laws of continuous proportions. Hence, it is recommended that the exact same element or mixture of isotopes must be used when preparing the various compounds.

Since there are only a handful of elements that can be combined to form the third element, and can also be combined with one another, this law can be applied to only a few elements that display the property.

Conclusion

The Law of Reciprocal Proportions was formulated by Jeremias Richter in 1792. It says that if the third element with the same weight is the combination of two different elements, you will find that the ratio of their masses is either the multiple or the same as the mass ratio in which the combination has happened.

In Dalton’s theory of atomicity, all the atoms in an element are the same, and the compounds are formed through the union of atoms of various elements in a proportion of whole numbers. So, the weights of elements that are combined with the weights of a fixed element should be in a simple ratio to the elements’ weights when they mix with each other.