RITCHTER-WENZEL'S LAW: STORIES, STATEMENTS AND EXAMPLES - CHEMISTRY - 2025

The Ritchter-Wenzel law or reciprocal proportions is one that states that the mass proportions between two compounds allow us to determine that of a third compound. It is one of the laws of stoichiometry, together with Lavoisier's law (law of conservation of mass); Proust's law (law of definite proportions); and Dalton's law (law of multiple proportions).

Ritcher stated his law in 1792 in a book that defined the fundamentals of stoichiometry, based on the research works of Carl F Wenzel, who in 1777 published the first equivalence table for acids and bases.

Triangle of reciprocity. Source: Gabriel Bolívar

A simple way to visualize it is through a “triangle of reciprocity” (image above). By knowing the masses of A, C, and B that mix to form compounds AC and AB, it can be determined how much of C and B mix or react to form compound CB.

In compounds AC and AB, element A is present in both, so dividing their mass proportions will find out how much C reacts with B.

History and generalities of the law of reciprocal proportions

Richter found that the weight ratio of compounds consumed in a chemical reaction is always the same.

In this regard, Ritcher found that 615 parts by weight of magnesia (MgO) are required, for example, to neutralize 1000 parts by weight of sulfuric acid.

Between 1792 and 1794, Ritcher published a three-volume summary containing his work on the law of definite proportions. The abstract dealt with stoichiometry, defining it as the art of chemical measurements.

Noting, furthermore, that stoichiometry deals with the laws according to which substances unite to form compounds. However, Richter's research papers were criticized for the mathematical treatment he used, even pointing out that he adjusted his results.

In 1802, Ernst Gottfried Fischer published the first table of chemical equivalents, which used sulfuric acid with the figure of 1000; similar to the value found by Richter, for the neutralization of sulfuric acid by magnesia.

However, it has been noted that Richter constructed a table of combination weights that indicated the rate at which a number of compounds reacted. For example, it is stated that 859 parts of NaOH neutralize 712 parts of HNO ₃.

Statements and consequences

The statement of the Richter-Wenzel Law is as follows: the masses of two different elements that combine with the same quantity of a third element, have the same relationship as the masses of those elements when they are combined with each other.

This law made it possible to establish the equivalent weight, or weight-equivalent-gram, as the amount of an element or compound that will react with a fixed amount of a reference substance.

Richter called combination weights relative to the weights of the elements that combined with each gram of hydrogen. Richter's relative combination weights correspond to what is currently known as the equivalent weight of the elements or compounds.

In accordance with the previous approach, the Richter-Wenzel law can be stated as follows:

The combination weights of different elements that are combined with a given weight of a given element are the relative combination weights of those elements when combined with each other, or multiples or submultiples of these quantity relationships.

Examples

Calcium chloride

In calcium oxide (CaO), 40 g of calcium combine with 16 g of oxygen (O). Meanwhile, in hypochlorous oxide (Cl ₂ O), 71 g of chlorine are combined with 16 g of oxygen. What compound would calcium make if combined with chlorine?

Using the triangle of reciprocity, oxygen is the common element for the two compounds. The mass proportions of the two oxygenates are first determined:

40g Ca / 16 gO = 5g Ca / 2g O

71g Cl / 16g O

And now dividing the two mass proportions of CaO and Cl ₂ O we will have:

(5g Ca / 2g O) / (71g Cl / 16g O) = 80g Ca / 142g Cl = 40g Ca / 71g Cl

Note that the law of mass proportions is fulfilled: 40 g of calcium react with 71 g of chlorine.

Sulfur oxides

Oxygen and sulfur react with copper to give copper oxide (CuO) and copper sulfide (CuS), respectively. How much sulfur would react with oxygen?

In copper oxide, 63.5 g of copper are combined with 16 g of oxygen. In copper sulfide, 63.5 g of copper binds to 32 g of sulfur. Dividing the mass proportions we have:

(63.5g Cu / 16g O) / (63.5g Cu / 32g S) = 2032g S / 1016g O = 2g S / 1g O

The 2: 1 mass ratio is a multiple of 4 (63.5 / 16), which shows that Richter's law is true. With this proportion, SO is obtained, sulfur monoxide (32 g of sulfur react with 16 g of oxygen).

If you divide this ratio by two, you will get 1: 1. Again, it is now a multiple of 4 or 2, and therefore it is SO ₂, sulfur dioxide (32g of sulfur reacts with 32g of oxygen).

Iron sulfide and oxide

Iron sulfide (FeS), in which 32 g of sulfur is combined with 56 g of iron, is reacted with ferrous oxide (FeO), in which 16 g of oxygen are combined with 56 g of iron. This item serves as a reference.

In the reacting compounds FeS and FeO, sulfur (S) and oxygen (O) relative to iron (Fe) are found in the ratio 2: 1. In sulfur oxide (SO), 32 g of sulfur are combined with 16 g of oxygen, so that sulfur and oxygen are in a 2: 1 ratio.

This indicates that the law of reciprocal proportions or Richter's law is fulfilled.

The ratio found between sulfur and oxygen in sulfur oxide (2: 1), could be used, for example, to calculate how much oxygen reacts with 15 g of sulfur.

g of oxygen = (15g of S) ∙ (1g of O / 2g of S) = 7.5g

References

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