Proportions law of reciprocal

Partington, James Riddick. Jeremias Benjamin Richter and the Law of Reciprocal Proportions. Ann. Sci. 7, 173-198 (1951). 

The term stoichiometry was devised by German chemist Jeremias Richter in 1792 to describe the measnrement of the combining ratios of chemical elements by mass. The term has since been expanded to include the combining ratios of substances in any chemical reaction. Richter studied mathematics with philosopher Immanuel Kant and wrote a thesis on the nse of mathematics in chemistry. He was convinced that all chemical changes conld be described in terms of simple whole-number ratios. He put forward the Law of Reciprocal Proportions, stating that if two chemical elements unite separately with a third element, the proportion in which they unite with the third element will be the same or a multiple of the proportion in which they unite with each other. This law has disappeared from most chemistry textbooks, but a companion law, the Law of Multiple Proportions, has survived. 

The law of reciprocal proportions or the law of equivalents—Cavendish established in 1766 that identical weights of a given acid require different weights of different bases for neutralization, and he called these weights of the bases equivalents. It was Richter who in 1795 generalized these observations into the law of the reciprocal proportions thus ... 

The law of equivalent proportions states that if two elementsAand B each form a compound with a third element C, then a compound of A and B will contain A and B in the relative proportions in which they react with C. For example, sulphur and carbon both form compounds with hydrogen. In methane 12 g of carbon react with 4 g of hydrogen. In hydrogen sulphide, 32 g of sulphur react with 2 g of hydrogen (i.e. 64 g of S for 4 g of hydrogen). Sulphur and carbon form a compound in which the C S ratio is 1234 (i.e. CS2). The law is sometimes called the law of reciprocal proportions. 

Others, C and D, the ratio of the quantity of C which saturates A to the quantity of D which saturates A is also the ratio of the quantities of C and D which saturate B (a statement of the law of reciprocal proportions). He proved the law of multiple proportions (he does not use this name) for the three oxides of lead (PbO, Pb304, PbOg), the oxides of copper and iron, sulphurous and sulphuric acids, neutral and basic salts of copper and lead, sulphides of iron, and some salts and showed that the ratio of sulphur to metal in ferrous and lead sulphates is the same as in ferrous and lead sulphides (the latter is converted completely into sulphate by oxidation), which confirmed Richter s law, which he supposed held good generally. In lead sulphate the oxygen in the base is just one-third that in the acid [PbS04=Pb0 + S03]. All these results confirmed Dalton s theory. All the defects in Berzelius s analyses are clearly pointed out. 

The subject of stoichiometry (a name introduced by Richter (p. 680)) comprises the quantitative laws of chemical composition. These are stated in the law of constant composition (Proust), the law of multiple proportions (Higgins and Dalton), and the law of reciprocal proportions or equivalents (Richter). The first and third are dealt with in this chapter, the second in Chapts. XV and XVI. They are all consequences of Dalton s atomic theory, which forms the main topic of Chapt. XVII. 

This is a special case of the law of reciprocal proportions, which appears here for the first time. It was generalised in 179Z ... 

This is a clear statement of the law of reciprocal proportions as applied to a special case. 

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