# Law of Reciprocal Proportion: Definition & Examples

Instructor: Laura Foist

Laura has a Masters of Science in Food Science and Human Nutrition and has taught college Science.

Jeremias Richter discovered the Law of Reciprocal Proportion in the late 18th century. In this lesson we will learn what this law is and how it is used by looking at some examples.

## Law of Reciprocal Proportion

Do you like chocolate? Do you also like hot drinks? If you said yes to both questions, then you will probably like hot chocolate. We make comparisons such as this all the time throughout our lives. In the late 18th century Jeremias Richter, a German chemist, came up with an easy way to compare compounds and to see how two elements will combine to form another compound.

The law of reciprocal proportions says that if we know the proportion of elements in compound AB and the proportion of elements in compounds BC, we can determine the proportion of elements in compound AC. This law helped us to understand stoichiometry, or how we figure out the quantities of reactants and products in relation to their reactions.

Let's look at a few examples to make this law easier to understand.

## Methane and Water

Okay, so let's take a look at methane, CH4. Let's figure out the proportion of elements. The molecule weight of carbon is 12 g/mol, and the molecule weight of hydrogen is 1 g/mol. Since we have 4 atoms of hydrogen for every atom of carbon, the proportion is 12:4, which can be simplified down to 3:1.

Now, let's look at water, H2 O. The proportion of elements is 16:2, or 8:1 (oxygen has a molecular weight of 16).

So, methane and water both contain a hydrogen and one other element. According to this law if we combine carbon and oxygen (the other element in both compounds) it should be in a ratio of 3:8, or a simple multiple of that ratio.

We get 3:8 because, in methane, carbon is a ratio of 3, and in water, oxygen is a ratio of 8. Let's see if this is true, when carbon and oxygen combine they form carbon dioxide, CO2, which has a proportion of 12:32. This is equal to 3:8, exactly as we predicted!

## Sodium Chloride and Hydrochloric Acid

Let's take a look at another example, starting with sodium chloride, NaCl. Sodium has a molecular weight of 23 g/mol, and chloride has a molecular weight of 35 g/mol. So the ratio is 23:35.

Now let's look at hydrochloric acid, HCl, where the ratio is 35:1. If we combine sodium and hydrogen, we would expect to see a ratio of 23:1. Yep - when these combine we form sodium hydride, NaH, with the ratio of 23:1.

## Copper Oxide and Copper Sulfide

Now, let's look at an example where the 3 compounds are a simple multiple of the expected ratio. Copper oxide, CuO, has a ratio of 63.5:16. Copper sulfide, CuS, has a ratio of 63.5:32. We would expect sulfur and oxygen to combine to form a ratio of 32:16 or 2:1.

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