molecules have combined to produce the molecules of the compounds formed in the reactions. If we now tabulate the data for the reverse chemical changes, and translate these data into the language of Avogadro's hypothesis, we have the following statements :— volumes of hydrogen chloride produce 1 volume of hydrogen and 1 volume of chlorine. 2x molecules of hydrogen chloride produce x molecules of hydrogen and x molecules of chlorine. volumes of hydrogen bromide produce 1 volume of hydrogen and 1 volume of bromine. 2x molecules of hydrogen bromide produce x molecules of hydrogen and x molecules of bromine. As we concluded from the former data that a single molecule of hydrogen reacting with a single molecule of chlorine (or bromine) produces 2 molecules of hydrogen chloride (or bromide), so now we conclude that 2 molecules of hydrogen chloride (or bromide), when decomposed produce 1 molecule of hydrogen and 1 molecule of chlorine (or bromine). The outcome of Avogadro's conception of the structure of 286 matter is given in the statement already enunciated; equal volumes of gases contain equal numbers of molecules. The application of this generalisation to the interactions between hydrogen and chlorine, and hydrogen and bromine, has led to the conclusion that the molecules of these elementary gases are composed each of at least two parts, and that these parts part company when the gases interact to form hydrogen chloride and bromide, respectively. Since the time of Avogadro the physical conception of the 287 molecule, as a minute portion of matter, has been much advanced. Every attempt to gain a consistent notion of the mechanism of physical changes has led to the recognition of the grained structure of matter. The hypothesis which asserts that a mass of apparently homogeneous matter is really homogeneous, that however small are the parts into which the body is divided each part exhibits all the properties of the body, has failed to explain any large class of physical facts. Physicists have fully adopted the view that a quantity of any kind of matter consists of a vast number of very minute particles in constant motion. These minute portions of matter they call molecules. The molecules of a gas are supposed to be continually moving about, frequently colliding against each other and rebounding again, but yet remaining intact during 288 289 290 these collisions. The physical definition of the molecule of a gas is given in the following words of Clerk Maxwell. "A gaseous molecule is that minute portion of a substance which moves about as a whole, so that its parts, if it has any, do not part company during the motion of agitation of the gas.' The theory that every portion of a body we can see or handle is composed of a great number of very minute particles, in constant motion, each of which is possessed of the properties which characterise the body in question, does not assert or deny the infinite divisibility of matter. What this theory asserts, to use the words of Clerk Maxwell, is "that after we have divided a body into a certain finite number of constituent parts called molecules, then any further division of these molecules will deprive them of the properties which give rise to the phenomena observed in the substance." The relations between the motions and the space occupied by a number of molecules which are mutually independent have been investigated by mathematical analysis. The equations arrived at, after making a justifiable assumption as to the dynamical meaning of temperature, express with considerable accuracy the observed relations between the volume, temperature, and pressure, of gases considerably removed from their liquefaction-points; that is to say the equations agree well with the laws of Boyle and Charles. The properties of a system of molecules moving about freely, and acting on each other only when they come into contact, have been investigated mathematically. One of the deductions arrived at is the generalisation which was stated by Avogadro in 1811; Equal volumes of gases contain equal numbers of molecules.' This generalisation is thus raised from a merely empirical statement to the rank of a deduction, made by dynamical reasoning, from a simple hypothesis regarding the structure of matter, which is itself justified by many classes of experimentally established facts. The generalisation of Avogadro is of fundamental importance in chemistry. It is essential that the student should understand that this statement rests on physical evidence and dynamical reasoning; and also that he should understand that the statement presupposes the physical definition of the molecule of a gas (s. par. 287). When this generalisation is applied to many chemical changes taking place between gaseous elements, it leads to the necessary conclusion that the molecules of most gaseous elements are composed of parts, and that these do part company when the molecules chemically interact. Hence in chemistry we must recognise two orders of small particles; molecules, and the parts of molecules or atoms. Avogadro's generalisation, or Avogadro's law as it is 291 usually called, furnishes a means for determining the relative weights of gaseous molecules. For, if the number of molecules in equal volumes of two gases (at the same temperature and pressure) is the same, it follows that the ratio of the densities of the gases is also the ratio of the masses of the two kinds of molecules. Now a specified volume of oxygen is 16 times heavier than an equal volume of hydrogen; therefore a molecule of oxygen weighs 16 times as much as a molecule of hydrogen. Therefore if the weight of the molecule of hydrogen is taken as unity, the molecular weight of oxygen must be 16. But ought the molecular weight of hydrogen to be taken 292 as unity? We have already found that the application of Avogadro's law to the interactions which occur between hydrogen and chlorine, and hydrogen and bromine, requires us to assert that each molecule of hydrogen separates, in these reactions, into at least two parts. A similar examination of other reactions between hydrogen and various gaseous elements confirms this conclusion. A molecule of hydrogen then is composed of at least two parts, or atoms. But we agree to call the atomic weight of hydrogen one, and to make this the standard in terms of which the relative weights of the atoms of other elements are to be stated. Hence the smallest value which we can give to the molecular weight of hydrogen is two. Of course we may assume that when hydrogen and chlorine react, each molecule of either element separates into 4, 6, 8, 10, &c. parts or atoms; we must assert that each separates into at least two parts. Suppose the assumption is made that each molecule separates into 4 atoms; then, as there are twice as many molecules of hydrogen chloride formed as the number of molecules of hydrogen or chlorine taking part in the reaction, it follows that each molecule of hydrogen chloride is composed of 2 atoms of hydrogen and 2 atoms of chlorine. But no chemical reactions of hydrogen chloride are in keeping with this conclusion. When this compound is decomposed with separation of * The student should observe that the term law is used here in a sense different from that in which the same term is applied to the facts of chemical combination: s. note at end of Chap. xvI. 293 294 295 hydrogen or chlorine, the whole of the hydrogen or of the chlorine is removed. But the chemical reactions of a gaseous compound are regarded by the molecular theory as the reactions of the molecules of that compound; therefore, when a molecule of hydrogen chloride reacts chemically with other molecules, the whole of the hydrogen, or the whole of the chlorine, is removed. The conclusion is that, most probably, a molecule of hydrogen chloride is composed of one atom of hydrogen and one atom of chlorine. For reasons such as these, we conclude that the molecular weight of hydrogen is almost certainly two; that is, that the molecule of hydrogen is composed of two atoms, the weight of each of which we have agreed to call one. Now oxygen is 16 times heavier than hydrogen; but the molecular weight of hydrogen is 2; therefore the molecular weight of oxygen is 32. Similarly, chlorine gas is 35.5 times heavier than hydrogen; therefore the molecular weight of chlorine is 71. Mercury-gas is 100 times heavier than hydrogen; therefore the molecular weight of mercury-gas is 200: and so on, for all the elements which can be obtained as gases. Similarly with gaseous compounds. Water-gas is 9 times heavier than hydrogen; therefore the molecular weight of water-gas is 18. Ammonia is 8·5 times heavier than hydrogen; therefore the molecular weight of ammonia is 17. Alcohol-gas is 23 times heavier than hydrogen; therefore the molecular weight of alcohol-gas is 46; and so on, for all compounds which can be obtained as gases. We can now define the term molecular weight of a gas. The definition may be stated in various forms of words. The molecular weight of a gaseous element or compound is twice the specific gravity of the gas referred to hydrogen. Or; The molecular weight of a gaseous element or compound is a number which tells the weight of two volumes of the gas, that is, the weight of that volume of the gas which is equal to the volume occupied (under the same conditions of temperature and pressure) by two parts by weight of hydrogen. Or, inasmuch as air is 14-435 times heavier than hydrogen, we may say that; The molecular weight of a gaseous element or compound is the product obtained by multiplying the specific gravity of the gas referred to air, by 28.87. The application of Avogadro's law to chemical interactions leads to the recognition of the atom as a particle of matter means weighing less than the molecule; it also gives a The atom of an element is, by definition, the ultimate particle of the element of which cognisance is to be taken in chemistry; hence, it is evident that the molecule of a compound gas formed by the union of (say) two elements, A and B, must be formed by the union of at least one atom of A with at least one atom of B. Or, in general terms, a molecule of a compound gas must be composed of at least one atom of each of the elements which unite to produce the compound. This is equivalent to saying, the atom of an element is the smallest mass of that element which combines with other atoms to form a gaseous molecule. As we have agreed to call the mass of one atom of hydrogen unity, and to state the weights of all other atoms in terms of that of the atom of hydrogen, we arrive at a definition of the maximum value to be given to the atomic weight of an element. The smallest mass of an element, in terms of hydrogen as unity, which is found to combine with other elements to form a gaseous molecule represents the maximum value to be given to the atomic weight of the element in question. Or; The number which expresses how many times heavier than the smallest mass of hydrogen which combines with other elements to form gaseous molecules, is the smallest mass of a specified element which combines with other elements to form gaseous molecules, also expresses the maximum value which can be given to the atomic weight of the element in question. The greater the number of gaseous compounds of the 296 specified element which have been examined, the greater is the probability that the maximum value deduced for the atomic weight of the element represents the true value. Let it be required to determine the atomic weight of 297 oxygen. The definition of atomic weight tells; (1) that several gasifiable compounds of oxygen must be prepared; (2) that these compounds must be gasified and the specific gravity of each, and hence the molecular weight of each, determined; (3) that each compound must be analysed, and the results stated as parts of each element per molecule of the compound. Then the smallest mass of oxygen in any one of these molecules is taken as the atomic weight of oxygen. |