the number of particles in a given mass of mat-
ter eould of course never be actually counted.
The following considerations, however, will show
at once the real significance of Avogadro's rule.
An immediate consequence of the rule is, that
comparing equal volumes of substances in the
gaseous state, as to weight, composition, etc.,
is the same as comparing single molecules. Fol-
lowing the rule, chemists have therefore adopted
as the standard quantity for investigation, not
a unit of weight, but a unit of volume, and have
for many years now been comparing, not equal
weights of substances, but equal volumes. Now,
this practice has led to the acquirement of a
stupendous amount of purely empirical informa-
tion that forms a solid part of the science of
chemistry, the original rule merely explaining
iihy comparing equal volumes should lead to so
many excellent results. If, therefore, the atomic
hypothesis should sometime be discarded as no
longer necessary, the hypothetical form of Avo-
gadro's rule would of course go with it; but its
corollary, the expediency of comparing equal
volumes of substances, would still remain a
great guiding rule in the science of chemistry.
The rule was originally jjroposed as an addi- tion to the atomic theory, the purpose being to account for a remarkable general fact then re- cently discovered by Gay Lussac; viz., that when two gases react with each other eliemically, their reacting volumes bear to each other a ratio that can be expres.sed by small integral numbers. Thus, when lij'drogen and chlorine unite to form liydro- chloric acid, the volumes of the reacting gases are equal, i.e. their ratio is 1 -^ 1. Similarly, equal volumes of hydrochloric acid gas and annnonia combine to fonn sal-ammoniac : i.e. the ratio is again 1 -r- 1. In the formation of water from hydrogen and oxygen, these two gases unite in the simple ratio of 2-^1. Gay Lussac's law holds eijualh' good in the case of gaseous products of chemical decomiiosition and with regard to the ratios of the volume of a gaseous compound to the volumes of its gaseous chemical components. Thus, 3 volumes of hydrogen and 1 volume of nitrogen are produced by the decomposition of 2 volumes of ammonia. This law, examined from the standpoint of the atomic hypothesis, indi- cates that some very simple relation must exist between the numbers of particles contained in the reacting volumes of gases. For according to that hypothesis all chemical reactions of sub- stances take place really between their jiarticles. The simplest relation that suggests itself to the mind is expressed by Avogadro's rule ; viz., that equal volumes of gases contain equal numbers of molecules. If, then, the reacting volumes of hydrogen and chlorine are equal, it is because every single molecule of chlorine reacts with one single molecule of hydrogen. Although it thus formed a plausible explanation of Gay Lussac's law, the idea, when first advanced by Avogadro in 1811 and resuggested by Amp&re in 1814, was not accepted by the scientific world. The scanty stock of experimental knowledge of the time did not warrant the incorporation in science of a general theoretical principle of this nature.
The practical importance of the rule is mainly in the fact that it permits of ascertaining the relative weights of molecules ('molecular weights'), these weights being represented, ac- cording to the rule, by the relative weights of equal volumes of substance in the gaseous state. The substance with which all other substances are usuallj' compared is hydrogen, to which chemists assign the molecular weight 2, since its molecule is supposed to consist of two atoms of unit atomic weight (the unit is of course arbitrary and is chosen merely for convenience sake ) . Comparing equal volumes of hydrogen and oxygen, the latter is found to weigh 16 times as much as the former. The molecular weiglit of oxygen is, therefore, in accordance w'ith Avo- gadro's Rule, said to be 32. In a similar man- ner the molecular weight of any other substance in the gaseous state may be ascertained by nuil- tiplying the density (i.e. its relative weight with respect to hydrogen) bj' 2. Thus, the densitj' of ammonia gas being about 8. .5, its molecular weight is 17; the density of hydrochloric acid gas being about 18.25, its molecular weight is 30.5, etc.
Now, equal volumes of ammonia gas and hydro- chloric acid combine to form anunonium chloride (sal-ammoniac, NH,C1) and nothing else. Both the chlorine of hydrochloric acid and the nitro- gen of ammonia represent the smallest relative weights of those elements found in any compound ; or, in the language of the atomic theory, hydro- chloric acid contains only one atom of chlorine, and ammf)nia only one atom of nitrogen. Hence, one entire molecule of hydrochloric acid (molecu- lar weight = 30.5) and one entire molecule of M ammonia (molecular weight = 17) must be com- fl bined in one molecule of ammonium chloride; for otherwise the latter compound could not, as it does, contain both chlorine and nitrogen. Con- sequently, the molecular weight of ammonium chloride could not possibly be less than 17 -j- 36.5 ==: 53.5, and hence its density could not, according to Avogadro's rule, be less than 53.5 -^ 2 = 26.75. When, however, ammonium chloride is heated and its vapor studied experi- mentally, the density is found to be only about one-half as great. This fact was for a long time regarded as proving that Avogadro's rule is incapable of general apjilication, although in most other cases the molecvilar weights obtained with the aid of the rule were found to agree thoroughly with the chemical behavior of the compounds. But even in the case of anmioniuan chloride, the exception was finally shown to be only apparent. Pebal and Than, namely, demon- strated that when anunonium chloride is evapo- rated, it breaks up into its constituents, am- monia gas and hydrochloric acid, the dissocia- tion naturally causing an increase of volume, and hence a decrease of density. As long as the products remain mixed in a vessel, or are al- lowed to escape together, it is impossible to prove directly that the vapor is a mixture of ammonia and acid, the reaction with litmus paper being of course neutral. But Pebal and Than proceeded as follows: They divided a glass tube into tw'o parts by a porous partition and heated a lump of ammonium cliloride in one part of the tube ; the ammonia gas produced, diffusing through the partition more rapidly than the hydrochloric acid, soon filled the other part of the tube and showed the ordinary alkaline re- action with red litmus paper (i.e. turned it blue). The case of ammonium chloride thus changed from an exception into an additional indication of the correctness of Avogadro's rule.
