Avogadro's hypothesis, that equal volumes of gases under the same conditions of temperature and pressure contain the same number of molecules, necessarily involves that the weights of equal volumes of gases are the relative weights of their molecules or that the ratio of densities of gases is the ratio of their molecular weights. The method of density is the fundamental method of determining molecular and atomic weights in chemistry, the atomic weight of an element being the smallest weight of it ever found in its molecular weight or in the molecular weight of any of its compounds. The method of gas or vapour density for deter mination of molecular weight is, however, inapplicable to the cases of elements and compounds that are not vaporizable under experimental conditions, and other methods have to be resorted to. Minimum values for molecular weight can be obtained for the majority of non-volatile compounds by the method of equiva lents. For example, fluorescein combines by replacement of hydrogen with alkalis to form salts in the proportion of 332 parts of fluorescein to one equivalent of an alkali metal. As a molecule cannot contain less than one atom of hydrogen, the least molec ular weight of fluorescein is 332. This method is in common use to determine the molecular weights of organic acids by the f or mation of silver salts. If the basicity of the acid is known, i.e., the number of hydrogen atoms that are replaceable, the true molecular weight is equal to the apparent molecular weight multi plied by the basicity. This method of equivalents may be used for all compounds, whether they contain hydrogen or not. All that is required is the percentage composition of any one con stituent of a compound, the minimum molecular weight being a hundred times the atomic weight of the constituent divided by the percentage of it in the compound.
Investigation of the properties of solutions has disclosed that an internal pressure called the osmotic pressure is set up in liquids by the presence of dissolved substances, such that this pressure is approximately equal to that exertable by the same weight of the substance if it existed as a gas and occupied the same volume as the solution. Comparison of osmotic pressures thus furnishes
a method of determining relative molecular weights, by reference to such properties as are dependent on osmotic pressures. These properties are lowering of the vapour pressure of the solvent, elevation of its boiling point, depression of its freezing point, and lowering of its solubility for other substances. Comparisons of molecular weights by these methods are seldom more than ap proximately correct, but they are invaluable in deciding which multiple of the equivalent weight is the molecular weight. A limi tation to this method is the fact that many substances are de composed or dissociate into smaller parts on solution. Substances that dissociate on solution form electrolytes, solutions that con duct electricity and give rise to abnormally high osmotic pres sures. S. A. Arrhenius in 1884 showed that the abnormality was due to ionization, each ion contributing to the osmotic pressure an amount equal to that of the non-ionized molecule, and the electrical conductivity being proportional to the number of ions. Measurements of conductivity thus supplement the osmotic pres sure method and enable determinations of molecular weight to be made even for substances which dissociate on solution.
Where only the equivalent weight of a compound is known, valuable indications as to the true molecular weight may often be obtained by analogy with other similar compounds. These analo gies are usually based on resemblances in composition, in valency of the constituent atoms, in constitution and the spatial distribu tion of the atoms or groups of atoms, and in crystalline form (isomorphism). (J. D. M. S.)