0.2 Atomic masses and molecular formulas

Introduction

In this study, our goals are to determine the masses of the atoms of each element and to find the ratios of the atoms that combine to form the molecules of different compounds. We will find that we determine the atomic masses relative to one another. In other words, we will find that the atoms of one element may be 1.2 times as massive as the atoms of another element. We will not actually determine the mass of an atom relative to, say, a large sample of matter like a bar of metal or a glass of water. For almost all purposes in Chemistry, it turns out that we only need these relative masses. We will also find the formulas of individual molecules for different compounds. The “molecular formula” tells us how many atoms of each type there are in a molecule of a compound. For example, many people know that water is H ₂ O, meaning that a molecule of water contains two hydrogen atoms and one oxygen atom. Although we haven’t shown it yet, the molecular formula of water is H ₂ O.

The postulates of the Atomic Molecular Theory provide us a great deal of understanding of pure substances and chemical reactions. For example, the theory reveals the distinction between an element and a compound. In an element, all atoms are identical. In a compound, there are atoms of two or more elements combined into small identical molecules in small integer ratios. The theory also reveals to us what happens during a chemical reaction. When two elements react, their atoms combine to form molecules in fixed ratios, making a new compound. When two compounds react, the atoms in the molecules of these reactant compounds recombine into new molecules of new product compounds.

As good as this is, it is about as far as we can go without further observations and analysis. We don’t know the relative masses of the atoms, and we don’t know the molecular formula for any compound. It turns out that to know one of these things we need to know the other one.

To see this, let’s take another look at the data in the Concept Development Study on Atomic Molecular Theory . Here it is again as [link] :

We now know that a fixed mass of nitrogen means a fixed number of nitrogen atoms, since each atom has the same mass. And if we double the mass of oxygen, we have doubled the number of oxygen atoms. So, comparing Oxide A to Oxide B, for the same number of nitrogen atoms, Oxide A has twice as many oxygen atoms as Oxide B, which has twice as many oxygen atoms as Oxide C.

There are many possible molecular formulas which are consistent with these ratios. To see this, we can show that any one of the oxides A, B, or C could have the molecular formula NO. If Oxide C has the molecular formula NO, then Oxide B has the formula NO ₂ , and Oxide A has the formula NO ₄ . If Oxide B has molecular formula NO, then Oxide A has formula NO ₂ , and Oxide C has formula N ₂ O. It might not be clear that Oxide C would be N ₂ O. The mass data tell us that Oxide B has twice as many oxygen atoms per nitrogen atom as Oxide C. So if Oxide B and Oxide C have the same number of oxygen atoms, then Oxide C has twice as many nitrogen atoms as Oxide B. As a similar example, if Oxide A has formula NO, then Oxide B has formula N ₂ O and Oxide C has formula N ₄ O. These three possibilities are listed in [link] .