Determination of Molecular Formulas

Before structures of molecules could be established, there had to be a means of establishing molecular formulas and for this purpose the key concept was Avogadro's hypothesis, which can be stated in the form "equal volumes of gases at the same temperature and pressure contain the same number of molecules." Avogadro's hypothesis allowed assignment of relative molecular weights from measurements of gas densities. Then, with analytical techniques that permit determination of the weight percentages of the various elements in a compound, it became possible to set up a self-consistent set of relative atomic weights.11 From these and the relative molecular weights, one can assign molecular formulas. For example, if one finds that a compound contains 22.0% carbon (atomic weight =12.00), 4.6% hydrogen (atomic weight =1.008=1.008), and 73.4% bromine (atomic weight =79.90), then the ratios of the numbers of atoms are (22.0/12.00):(4.6/1.008):(73.4/79.90)=1.83:4.56:0.92. Dividing each of the last set of numbers by the smallest (0.92) gives 1.99:4.96:1≅2:5:1, which suggests a molecular formula of C2H5Br or a multiple thereof. If we know that hydrogen gas is H2 and has a molecular weight of 2×1.008=2.016, we can compare the weight of a given volume of hydrogen with the weight of the same volume of our unknown in the gas phase at the same temperature and pressure. If the experimental ratio of these weights turns out to be 54, then the molecular weight of the unknown would be 2.016×54=109  and the formula C2H5Br  would be correct.