0.1 Relative atomic masses and empirical formulae  (Page 2/5)

These simple integer ratios are striking, particularly when viewed in the light of our conclusions from theLaw of Multiple Proportions. Atoms combine in simple whole number ratios, and evidently, volumes of gases also combinein simple whole number ratios. Why would this be? One simple explanation of this similarity would be that the volume ratio andthe ratio of atoms and molecules in the reaction are the same. In the case of the hydrogen and oxygen, this would say that the ratioof volumes (1 liter of oxygen : 2 liters of hydrogen : 2 liters of water) is the same as the ratio of atoms and molecules (1 atom ofoxygen: 2 atoms of hydrogen: 2 molecules of water). For this to be true, equal volumes of gas would have to contain equal numbers ofgas particles (atoms or molecules), independent of the type of gas. If true, this means that the volume of a gas must be a directmeasure of the number of particles (atoms or molecules) in the gas. This would allow us to "count" the number of gasparticles and determine molecular formulae.

There seem to be big problems with this conclusion, however. Look back at the data for forming hydrogenchloride: 1 liter of hydrogen plus 1 liter of chlorine yields 2 liters of hydrogen chloride. If our thinking is true, then this isequivalent to saying that 1 hydrogen atom plus 1 chlorine atom makes 2 hydrogen chloride molecules. But how could that bepossible? How could we make 2 identical molecules from a single chlorine atom and a single hydrogen atom? This would require us todivide each hydrogen and chlorine atom, violating the postulates of the atomic-molecular theory.

Another problem appears when we weigh the gases: 1 liter of oxygen gas weighs more than 1 liter of watervapor. If we assume that these volumes contain equal numbers of particles, then we must conclude that 1 oxygen particle weighs morethan 1 water particle. But how could that be possible? It wouldseem that a water molecule, which contains at least one oxygen atom, should weigh more than a single oxygen particle.

These are serious objections to the idea that equal volumes of gas contain equal numbers of particles. Ourpostulate appears to have contradicted common sense and experimental observation. However, the simple ratios of theLaw of Combining Volumes are also equally compelling. Why should volumes react in simple whole number ratios if they donot represent equal numbers of particles? Consider the opposite viewpoint: if equal volumes of gas do not contain equal numbers ofparticles, then equal numbers of particles must be contained in unequal volumes not related by integers. Now when we combineparticles in simple whole number ratios to form molecules, the volumes of gases required would produce decidedly non-whole numberratios. The Law of Combining Volumes should not be contradictedlightly.

There is only one logical way out. We will accept our deduction from theLaw of Combining Volumes that equal volumesof gas contain equal numbers of particles , a conclusion known as Avogadro's Hypothesis . How do we account for the fact that 1 liter of hydrogen plus 1 liter of chlorine yields 2liters of hydrogen chloride? There is only one way for a single hydrogen particle to produce 2 identical hydrogen chloridemolecules: each hydrogen particle must contain more than one atom. In fact, each hydrogen particle (or molecule) must contain an evennumber of hydrogen atoms. Similarly, a chlorine molecule must contain an even number of chlorine atoms.