0.2 Atomic masses and molecular formulas  (Page 6/10)

This is a good start, but now we need more elements. To bring in hydrogen, we can analyze the data from [link] in the first Concept Development Study which gives the mass ratio of oxygen and hydrogen in water. That data shows that the mass ratio of oxygen to hydrogen is 7.93 to 1.00. But we found in the previous section that the molecular formula of water is H ₂ O. This means that in a sample of water there are twice as many hydrogen atoms as there are oxygen atoms. Therefore, the ratio of the mass of one oxygen atom to one hydrogen atom must be 7.93 to 0.50, or 15.86 to 1.00.

These atomic mass ratios need to be consistent with each other, since the masses of the atoms of an element are always the same. So if the ratio of one hydrogen to one oxygen is 1.00 to 15.86, and the ratio of one nitrogen to one oxygen is 1.00 to 1.14, then the ratio of one hydrogen to one nitrogen must be 1.00 to 13.91. We should be able to check this by looking at the hydrogen-nitrogen compound ammonia, also listed in [link] of the previous Concept Development Study. There we find that the mass ratio of nitrogen to hydrogen is 4.65 to 1.00. Clearly, ammonia is not NH. To find the molecular formula of ammonia, we need data from the Law of Combining Volumes. Experimental data reveal that 1 L of N ₂ reacts with 3 L of H ₂ to produce 2 L of ammonia. From this, we should be able to conclude that an ammonia molecule has the molecular formula NH ₃ . Therefore, in a sample of ammonia, there are three times as many hydrogen atoms as there are nitrogen atoms. This means that the ratio of the mass of a nitrogen atom to a hydrogen atom is 3*4.65 to 1.00, or 13.95 to 1.00. We now have enough data to say that hydrogen, nitrogen, and oxygen atoms have mass ratio of 1.00:13.95:15.86.

Observation 3: atomic masses for non-gaseous elements

The next element we would certainly like to have an atomic mass for would be carbon, and we would certainly like to be able to determine molecular formulas for carbon containing compounds. We have data from [link] in the previous CDS on compounds of hydrogen and carbon. But our analysis is not going to work this time. The Law of Combining Volumes and Avogadro’s Law in combination allow us to count atoms and find molecular formulas, but only for elements and compounds which are gases. Carbon is not a gas. It exists in several different elemental forms, but all are solid at normal temperatures and even at very high temperatures.

This means that we need to work harder and add some additional observations to our work. Let’s start with the two most common oxides of carbon, which for now we will give the names Oxide A and Oxide B. (Their real names, carbon monoxide and carbon dioxide, are based on assuming that we already know their molecular formulas. But we don’t know these, so we’ll stick with these code names for now.) Here are the data for the mass relationships from the Law of Multiple Proportions: