0.2 Atomic masses and molecular formulas  (Page 7/10)

It is clear to see the Law of Multiple Proportions here since Oxide B has exactly twice the mass of Oxide A for the same mass of carbon. Now we would like to observe the Law of Combining Volumes and apply Avogadro’s Law, but carbon is not a gas. But we can at least look at the ratios of the volume of oxygen and the volume of the oxides produced. For Oxide A, 1 L of oxygen will produce 2 L of Oxide A. For Oxide B, 1 L of oxygen will produce 1 L of Oxide B. From these data, we can see that an Oxide A molecule contains one oxygen atom, since a single O ₂ molecule makes two Oxide A molecules. We can also see that an Oxide B molecule contains two oxygen atoms, since a single O ₂ molecule produces a single Oxide B molecule.

Now we know part of the molecular formulas each of the oxides, but we don’t know the number of carbon atoms in each. Oxide A could be CO, C ₂ O, C ₃ O, etc., and Oxide B could be CO ₂ , C ₂ O ₂ , etc. Our only way to proceed is with Avogadro’s Law. We can use this to determine the relative mass of each oxide molecule, even if we can’t determine the relative mass of the carbon atoms. The mass of 1 L of Oxide A is less than the mass of 1 L of oxygen. This is because, even though equal volumes contain the same number of particles, the particles themselves have different masses. In fact, since 1 L of each gas contains the same number of particles, then the mass ratio of 1 L of Oxide A to oxygen is exactly the same as the mass ratio of one Oxide A molecule to one oxygen molecule. An experimental measurement shows that the mass of 1 L of Oxide A is 87.5% of the mass of 1 L of oxygen. So the mass of one particle of Oxide A must be 87.5% of the mass of an O ₂ molecule. On the relative scale found in the previous section, the mass of one oxygen molecule is 15.86*2 = 31.72. So a particle of Oxide A must have relative mass 0.875*31.72 = 27.76. Remember though that an Oxide A contains just one oxygen atom. So, of this relative mass, 15.86 belongs to the oxygen atom, leaving 11.90 for the carbon.

Is this the relative mass of a carbon atom? We don’t know because we don’t know whether a molecule of Oxide A contains 1, 2, or 3 atoms of carbon (or for that matter, any number). What we can say is that the mass of a carbon atom is either 11.9, one-half of that, one-third of that, or some integer fraction of that depending on how many carbon atoms are in Oxide A.

How can we determine the right number? The answer is found from persistence. We can repeat this same measurement and calculation for Oxide B. The mass of 1 L of Oxide B is 1.375 times greater than the mass of 1 L of oxygen. Therefore, one particle of Oxide B has relative mass 43.59. But Oxide B molecules contain two oxygen atoms, so the part of this mass which is carbon is 43.59 minus the relative mass of the two oxygen atoms. This gives the mass of carbon in Oxide B as 11.9. This is the same mass of carbon that we found in Oxide A. Therefore, Oxide A and Oxide B have exactly the same number of carbon atoms. Perhaps, the number of carbon atoms in each is just one, but we can’t be sure from this data.