# What is a formula that demonstrates the law of multiple proportions?

Apr 21, 2014

You need two formulas to illustrate the Law of Multiple Proportions, for example, $\text{CO}$ and ${\text{CO}}_{2}$.

#### Explanation:

The Law of Multiple Proportions deals with elements that form more than one compound.

It states that the masses of one element that combine with a fixed mass of the second element are in a small whole number ratio.

For example, carbon and oxygen react to form two compounds. In the first compound (A), 42.9 g of $\text{C}$ react with 57.1 g of $\text{O}$.

In the second compound (B), 27.3 g of $\text{C}$ react with 72.7 g of $\text{O}$.

Let's calculate the mass of $\text{O}$ in each compound that reacts with 1 g ("a fixed mass") of $\text{C}$.

In Compound A, $\text{mass of O" = 1 color(red)(cancel(color(black)("g C"))) × ("57.1 g O")/(42.9 color(red)(cancel(color(black)( "g C")))) = "1.33 g O}$

In Compound B, $\text{mass of O" = 1 color(red)(cancel(color(black)("g C"))) × ("72.7 g O")/(27.3 color(red)(cancel(color(black)("g C")))) = "2.66 g O}$

"Ratio" = ("Mass of O in B")/("Mass of O in A") = (2.66 color(red)(cancel(color(black)("g"))))/(1.33 color(red)(cancel(color(black)("g")))) = 2.00 ≈ 2

The masses of oxygen that combine with a fixed mass of carbon are in a 2:1 ratio.

The whole-number ratio is consistent with the Law of Multiple Proportions.

The simplest formulas that fit are $\text{CO}$ and ${\text{CO}}_{2}$.