Past exam of the medicine course of the University of Oxford / 1867 / First examination / Chemistry / 5 / Solution

Atomic theory explains fixed composition by fixed numbers of chemical atoms, and multiple proportions by different small whole-number combinations of the same chemical atoms. The two laws are empirical regularities which the theory explains; they are not themselves direct observations of individual chemical atoms.

For the law of definite proportions, suppose a pure chemical compound has composition ${\mathrm{A}}_x{\mathrm{B}}_y$. If the atomic masses are $m_A$ and $m_B$, every formula unit contains masses $x{m}_A$ and $y{m}_B$. Enlarging the sample multiplies both by the same number, soThe mass ratio is therefore independent of sample size or preparation route, provided the same pure stoichiometric chemical compound is obtained. Ordinary water supplies an example: its hydrogen-to-oxygen mass ratio is approximately $1:8$.

For the law of multiple proportions, compare ${\mathrm{A}}_x{\mathrm{B}}_y$ and ${\mathrm{A}}_u{\mathrm{B}}_v$. At a fixed mass of A, the masses of B are in the ratioThis is a ratio of integers, and is often a ratio of small integers for simple chemical compounds. With carbon monoxide and carbon dioxide, about $12$ mass units of carbon combine with about $16$ and $32$ of oxygen: the oxygen masses are in the ratio $1:2$. The chemical formulas explain why adding a second oxygen chemical atom doubles the oxygen contribution without changing the carbon contribution.

The laws alone do not uniquely determine the correct chemical formulas or the atomic weights; independent information is needed to distinguish, for example, one formula unit from a multiple of it. Modern qualifications include variations in isotopic composition and non-stoichiometric compounds. These refine the simple nineteenth-century formulation without removing its usefulness for pure compounds of fixed composition.