# Please explain the law of reciprocal proportion with an example?

Jul 3, 2017

Here's my explanation.

#### Explanation:

The law of reciprocal proportions states that, "If two different elements combine separately with a fixed mass of a third element, the ratio of the masses in which they do so are either the same as or a simple multiple of the ratio of the masses in which they combine with each other".

Although this law may seem complicated, it is fairly easy to understand with an example.

For example, 3 g of $\text{C}$ react with 1 g of $\text{H}$ to form methane.

Also, 8 g of $\text{O}$ react with 1 g of $\text{H}$ to form water.

The mass ratio of $\text{C:O} = 3 : 8$.

In the same way, 12 g of $\text{C}$ react with 32 g of $\text{O}$ to form ${\text{CO}}_{2}$.

The mass ratio of $\text{C:O = 12:32 = 3:8}$.

The mass ratio in which $\text{C}$ and $\text{O}$ combine with each other is the same as the mass ratio in which they separately combine with a fixed mass of $\text{H}$.

Similarly, 12 g of $\text{C}$ react with 16 g of $\text{O}$ to form $\text{CO}$.

Here, the mass ratio of $\text{C:O = 12:16 = 3:4}$.

The mass ratio in which they separately react with a fixed mass of $\text{H}$ is 3:8.

The ratio of the two ratios is $\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} / 4}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} / 8} = \frac{8}{4} = \frac{2}{1}$.

Here, the ratio in which $\text{C}$ and $\text{O}$ combine with each other is twice the ratio in which they separately combine with a fixed mass of $\text{H}$.