STOICHEIOMETRY, in chemistry, is a term which, strictly, denotes the determination of the proportions in which elements or in clude react with one another, and may be extended to the determination of atomic and molecular weights (Gr.
arotxda, fundamental parts or elements; 12 rpov, measure). Actually, however, it is often used in the still broader sense cover ing the study of the physical properties of gases, liquids and solids; this aspect of the subject is dealt with in the article CHEMISTRY, Physical. The present article deals with the determination of molecular weights, the fundamental atomic weights being dealt with under that heading.
It is possible to determine with accuracy only the molecular weights of gases or vapours and of solids in solution. No method is known of determining the molecular weights of solids as such, although modern work on crystal structure (see CRYSTALLO GRAPHY) enables one to say how many simple molecules are packed together in one unit cell of the crystal. Similarly, no method is available for finding the molecular complexity of liquids with certainty, although several criteria are used for judging whether a liquid consists of simple or of complex molecules. Thus most of these criteria agree in assigning a complex struc ture, possibly (H20)2 or to liquid water, but none is capable of precisely fixing the degree of complexity; and most of them agree in giving the simple formula to liquid ben zene, i.e., it has the same molecular weight as its vapour. On the other hand, some recent views on this question regard water as having a considerable but variable degree of complexity, and benzene as having a similar but constant degree. (For fuller dis cussion of the molecular weights of liquids, see the article ASSOCIATION.) The two more precise cases are now dealt with, namely, (r) gases and (2) dissolved solids.
Gases.—The generalization due to Avogadro—that equal vol umes of gases under the same conditions of temperature and pressure contain equal numbers of molecules—may be stated in the form that the densities of gases are proportional to their molecular weights. If therefore the density of a gas relative to hydrogen or oxygen is determined, the molecular weight of the gas should follow by simple proportion, since that of oxygen is 32 (taken as standard) and that of hydrogen 2.0154. Avogadro's
law, however, is not rigorously true, except under extremely low pressures, and it is necessary to correct the observed densities to what they would be if the gases were ideal, i.e., if they showed no departure from Boyle's law. The principles underlying such corrections are briefly as follows.
P. A. Guye's Method.—According to Boyle's law, the product of the pressure and the volume of a gas is constant at any definite temperature, and, further, according to Gay Lussac's (or Charles's) law, this constant is directly proportional to the absolute temperature. Hence, pv=RT, where R is the so-called gas constant. J. D. van der Waals showed that, for representation of the actual behaviour of a gas, this ideal equation must be re placed by where a and b are constants for any one gas, but differ for different gases. Now a study of the behaviours of gases over a wide range of pressures has led to the assignment of appropriate values of a and b to each gas; hence, if v is the volume actually occupied by one gram-molecule of a gas at a pressure of 1 atmosphere and at a temperature T° (usually o° C is taken), and V is the volume which it would occupy under ideal conditions at the same tem perature and pressure, then we have a gas (except hydrogen) decreases slightly with increasing pressure until a pressure of several hundred atmospheres is reached. From a study of this decrease at low pressures it is possible to find what the relative densities of two gases would be at an infinitesi mally low pressure, If and are the volumes of a gas at pressures of about 1 atmos. and po respectively; if and if a' and v' are the corresponding values for the reference gas which has the same volume at Po; then, assuming that Avogadro's law holds rigidly for the very low pressure we have i.e., the ratio of the vapour densities at atmospheric pressure can be corrected to the ideal ratio.