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element unites with another. For example, in the two oxides of nitrogen the ratios of the two elements by weight are

Nitrous oxide . . Nitrogen : oxygen = 28:16.

Nitric oxide . . Nitrogen : oxygen = 28 :(16: X 2), while the volumetric relation in which the two constituents are present is

Nitrous oxide . . Nitrogen : oxygen = 2:1.
Nitric oxide . . Nitrogen : oxygen = 2:(1 X 2).

In other words, there is twice as much oxygen by weight in the one compound as in the other, and there is twice as much oxygen by volume in the one as compared to the other. Moreover, if 14 and 16 respectively represent the relative weights of atoms of nitrogen and oxygen, then the numbers representing the relative volumes in which these elements unite will also express the number of atoms of each in the molecule.

The connection existing between the proportions in which elements unite by weight, and by volume, was first explained by the Italian physicist and chemist Avogadro, who in the year 1811 advanced the theory now recognised as a fundamental principle, and known as Avogadro's hypothesis. This theory may be thus stated : Equal volumes of all gases or vapours, under the same conditions of temperature and pressure, contain an equal number of molecules. If this be true, if there are the same number of molecules in equal volumes of all gases, it must follow that the ratio between the weights of equal volumes of any two gases will be the same as that between the single molecules of the particular gases. If a litre of oxygen be found to weigh sixteen times as much as a litre of hydrogen (under like conditions of temperature and pressure), inasmuch as there are the same number of molecules in each, the oxygen molecule must be sixteen times heavier than that of hydrogen ; and therefore by the comparatively simple method of weighing equal volumes of different gases, it becomes possible to arrive at the relative weights of their molecules.

The relative weights of equal volumes of gases and vapours, in terms of a given unit, are known as their densities or specific gravities. Sometimes densities are referred to air as the unit, but more often hydrogen, as being the lightest gas, is taken as the standard. Taking hydrogen as the unit, the density or specific gravity of a gas is the weight of a given volume of it, as compared

with the weight of the same volume of hydrogen--or in other words, the ratio between the weight of a molecule of that gas and a molecule of hydrogen. The ratio that exists between the weight of a gaseous molecule and half the weight of a molecule of hydrogen, chemists term the molecular weight of that gas ; hence it will be obvious that the number which represents the molecular weight of a gas is double that of its density or specific gravity.

If i litre of hydrogen and 1 litre of chlorine be caused to combine, 2 litres of gaseous hydrochloric acid are formed. As equal volumes of all gases (under like conditions) contain the same number of molecules, in the 2 litres of hydrochloric acid there must be twice as many molecules of that compound as there were of hydrogen molecules in the 1 litre, or of chlorine molecules in the other. But each molecule of hydrochloric acid is composed of chlorine and hydrogen (from other considerations one atom of each element), therefore there must have been at least twice as many atoms of hydrogen in the litre of that gas as there were molecules ; and by the same reasoning, twice as many chlorine atoms in the litre of chlorine as there were molecules : in other words, both hydrogen and chlorine molecules consist of two atoms. The molecular weight of hydrogen therefore is 2 ; that is, its molecule is twice as heavy as its atom. The atom of hydrogen is the unit to which molecular weights are referred, while the weight of the molecule of hydrogen is taken as the standard of densities or specific gravities.

In order, therefore, to find the molecular weight of any gas or vapour, it is necessary to learn its density-that is, to ascertain how many times a given volume of it is heavier than the same volume of hydrogen,* and to double the number so obtained.t

The following table gives the densities or specific gravities of all the elements whose vapour densities have been determined. The list includes all those elements which are gases at the ordinary temperature, and those that can be vaporised under conditions

* Certain exceptions to this rule are discussed under the subject of Dissociation, chap. x. p. 88.

+ The specific gravity of hydrogen, as compared with air taken as unity, is 0.0693, or air is 14.43 times heavier than hydrogen. If, therefore, it be desired to find the molecular weight of a given gas, whose density as compared with air is known, it is only necessary to multiply its density (air=1) by the number 14.43, which gives its density as compared with hydrogen, and then to double the number so obtained.

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Mercury :

which render such determinations experimentally possible. (Hydrogen being taken as unity, the other numbers are the approximate values, which for purposes of discussion are more suitable than figures that run to two or three decimal places.) Hydrogen . .

Selenium . . : 79 Helium . . . 2 Bromine. . 80 Neon . .

Iodine . Nitrogen

Sodium .

11.5 Oxygen

Potassium.

19.5 Fluorine :

Zinc . .

32.5 Argon .

Cadmium. Sulphur . . : 32

. . 100 Chlorine . . . 35.5

Phosphorus . . 62 Krypton . . . 41 Arsenic .

. 150 Xenon , . 64.0

Let us now consider how the knowledge of the relative weights of gaseous molecules is utilised in assigning a particular number as the atomic weight of an element.

The molecular weight of chlorine is 71. It has been shown that the molecule certainly contains more than i atom, and probably 2, in which case 35.5 would represent the relative weight of the atom.

The compound hydrochloric acid has the molecular weight 36.5. It has been already proved that this compound contains i atom of hydrogen, therefore 36.5-1 = 35.5.

The compound carbon tetrachloride gives a molecular weight 154. Analysis shows that this compound contains 12 parts of carbon in 154 parts, therefore 154 – 12 = 142=35.5 X 4.

In these three molecules the weights of chlorine relative to the weight of i atom of hydrogen are 142, 35.5, and 71, the greatest common divisor of which is 35.5. This number, therefore, is selected as the atomic weight of chlorine.

Again, it has been shown that by the action of metals upon water, the hydrogen contained in the water could be expelled in two separate portions, thus proving that there must be 2 atoms of hydrogen in the molecule of that compound.

The molecular weight of wateris found to be 18 ; deducting from this the weight of the two hydrogen atoms we get 18 -2 = 16.

The molecular weight of carbon monoxide is 28 ; 28 parts of this compound contain 12 parts of carbon, therefore 28 – 12 = 16.

The molecular weight of carbon dioxide is 44 ; 44 parts of this compound also contain 12 parts of carbon, therefore 44 – 12 = 32.

When i litre of oxygen combines with two litres of hydrogen, 2 litres of water vapour are formed ; there are therefore twice the number of water molecules produced as there are oxygen molecules (since by Avogadro's hypothesis 2 litres contain twice as many molecules as i litre). But each water molecule contains certainly i atom of oxygen, therefore the original oxygen molecules must have consisted of not less than 2 atoms. When the density of oxygen is determined it is found to be 16, its molecular weight therefore is 32.

In these four various molecules the weights of oxygen relative to the weight of i atom of hydrogen are 16, 16, 32, 32, the greatest common divisor of which is 16. This number, therefore, is selected as the atomic weight of oxygen.

Again, it has already been shown that in the compound ammonia, the hydrogen can be removed in three separate moieties, proving that there must be three atoms of that element in the molecule. The molecular weight of ammonia is found to be 17, therefore 17-3 = 14, which is the weight of the nitrogen.

The molecular weight of nitrous oxide is 44 ; 44 parts of this compound are found to contain 16 parts of oxygen and 28 parts of nitrogen.

The molecular weight of nitric oxide is 30 ; 30 parts of this compound contain 16 parts of oxygen and 14 parts of nitrogen.

The molecular weight of nitrogen is found to be 28.

In these four different molecules the weights of nitrogen relative to the weight of i atom of hydrogen are 14, 28, 14, 28, the greatest common divisor of which is 14. The atomic weight of nitrogen, therefore, is regarded as 14.

These three examples, namely, chlorine, oxygen, and nitrogen are instances of elements which are gaseous at ordinary temperatures ; but the same methods are applicable in the case of the nonvolatile elements, such as carbon, provided they furnish a number of compounds that are readily volatile.

On comparing the numbers in the foregoing table (p. 42), representing the densities of various elements, with the atomic weights of those elements as given on p. 22, it will be seen that in several cases the numbers given are approximately the same. This agreement is merely because the molecules of these elements consist of two atoms. The molecules of helium, neon, argon, krypton, xenon, sodium, potassium, zinc, cadmium, and mercury consist of only one atom; their atomic weights, therefore, will be the same as their molecular weights, that is, twice their densities. The elements arsenic and phosphorus, on the other hand, contain in their molecules four atoms-that is to say, the number which represents the smallest weight of phosphorus and of arsenic, capable of taking part in a chemical change, is only half the density, and therefore a fourth of the molecular weight.

The definition of atomic weight that is furnished by the consideration of volumetric relations may be thus stated. The atomic weight is the smallest weight of an element that is ever found in a volume of any gas or vapour equal to the volume occupied by one molecule of hydrogen at the same temperature and pressure.

The volume occupied by one molecule of hydrogen is regarded as the standard molecular volume, while that occupied by an atom of hydrogen-or, in other words, the atomic volume of hydrogen-is called the unit volume. The standard molecular volume, therefore, is said to be two unit volumes; and as, from Avogadro's law, all gaseous molecules have the same volume, it follows that the molecules of all gases and vapours occupy two unit volumes. Atomic weight may therefore be defined as the smallest weight of an element ever found in two unit volumes of any gas or vapour.

The molecular volume of a gas is its molecular weight divided by its relative density, a ratio which in all cases will obviously equal 2, that is, two unit volumes.

The atomic volume of an element in the state of vapour is its atomic weight divided by its relative density. In the case of such elements as chlorine, nitrogen, oxygen, &c., whose molecules are diatomic, the quotient will be 1-that is to say, the atomic volume of these elements is equal to I unit volume. In the case of mer

atomic weight=200 , cury vapour, however, we have

density=100 The atomic volume of mercury vapour, therefore, is equal to 2 unit volumes, and is identical with its molecular volume. On the other hand, with the element phosphorus the atomic

atomic weight = 31 volume is a 13 density=62

=-5, or one-half the unit volume, and therefore one-fourth the molecular volume ; consequently, four atoms exist in this molecule.

The method of determining atomic weights based upon volumetric relations, when taken by itself, is not an absolutely certain

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