In combining two volumes of carbon monoxide and one volume of oxygen contract to form two volumes of carbon dioxide; hence 1 volume of the mixed gases forms only

And to reduce these 22.6 volumes to one volume requires a pressure of 22.6 atmospheres, which therefore is the explosive force of the gaseous mixture.

It must be noticed, that, as the specific heat at constant volume differs from that under constant pressure, each gas has two calorific intensities according as it is burnt in a closed or open space.

There are so many assumptions, unwarranted as yet by experiment, in the majority of these calculations, that it is doubtful if the results are more than rough approximations to the truth.

(25) THE DETERMINATION OF EQUIVALENTS.

The equivalent of an element or compound is the proportion of it, which can do the same amount of chemical work in combining with or replacing other elements or compounds, as one part of hydrogen.

The equivalent of an element is determined either by analysing a compound of it with an element or radical the equivalent of which is known, or by causing a known mass of it to combine with or replace another element or radical the equivalent of which is known.

: The masses of the two substances which unite with or replace one another are in the same proportion as the equivalents or as multiples of the equivalents by small whole numbers. Hence knowing the two masses and one of the equivalents the other equivalent may be determined.

Thus to determine the equivalent of lead, that of oxygen being 8, Berzelius found that 21.9425 grams of lead oxide contain 20-3695 grams of lead, and hence 21.9425 - 20-3695 = 1.573 grams of oxygen.

Since 1.573 grams of oxygen unite with 20-3695 grams
8 × 20.3695
1.573

=

of lead, 8 grams of oxygen unite with 103.596 grams of lead. Hence 103-596 is the equivalent of lead.

Again when excess of cupric oxide was heated in hydrogen, the oxide lost 59.789 grams and 67·282 grams of water were formed.

cu o + h=ho + cu.

Since 67-282 grams of water contain 59.789 grams of oxygen, the residue or 7·493 grams is hydrogen.

Therefore 7.493 grams of hydrogen unite with 59.789

1 gram of hydrogen unites with

59.789 7.493

of oxygen, or grams grams of oxygen. Hence 7.979 is the equivalent of oxygen.

(26) THE DETERMINATION OF ATOMIC WEIGHTS.

The atomic weight of an element is the mass of the least portion of it, which can take part in a chemical change, compared with the mass of the least portion of hydrogen which can take part in a chemical change. If the atomic

theory be admitted, the atomic weight of an element is the number of times its atom is heavier than an atom of hydrogen.

Atomic weights are in all cases multiples of the equivalents of the elements by small (1-8) whole numbers. Which multiple is to be chosen is determined by a careful consideration of all the reactions into which the element is known to enter, with the object of detecting the smallest multiple of the equivalent which may be considered to take part in each case; special attention being paid to compounds with monovalent elements or groups.

Further assistance is rendered by the isometric law of Mitscherlich; that, "Bodies, which are composed of the same number of similar atoms arranged in the same manner, crystallize in similar forms." And also by the law of Dulong and Petit; that, "64 divided by the specific heat of an element in the solid condition gives a number which is approximately equal to the number expressing the atomic weight of the element."

There are however somewhat numerous exceptions to both these laws.

Thus to find the atomic weight of lead, the equivalent of which has been found to be 103-596.

The choice has to be made between the various multiples by 1, 2, 3, 4, &c. or 103.596, 207-192, 310-798, 414·384, &c. The specific heat of lead is found to be 0315, and

6.4 0315

=

203.1.

Hence 207.192 is the most probable atomic weight of

lead.

(27)

THE DETERMINATION OF MOLECULAR
WEIGHTS.

In considering the methods of finding the symbols of bodies, which represent their molecular weights, it is convenient to consider first the case of compounds and then that of elements.

The molecular weight of a body is the number of times which the mass of the smallest portion of it, which can exist by itself or in the free state, is heavier than the atom of hydrogen.

When a compound is analysed, the results are usually calculated into percentages or parts of each element present in 100 parts of the compound. If then the proportion of each element present be divided by the atomic weight of that element, the quotients express the relative number of atoms of each element present in the compound.

Thus hydrogen phosphide is found to contain:

[When water is present as water of crystallization, it is usual not to calculate the number of atoms of hydrogen and oxygen separately, but to reckon it as though it were an element, H2O = Aq = 18.]

To accord with the atomic theory the proportions expressed by these quotients must be expressible by whole

numbers usually small. If simple inspection affords no clue there are three methods of effecting this reduction:

(i) Divide each quotient by the smallest quotient, all then frequently become whole numbers or may be made so by multiplication in each case by the same number.

Thus in the case taken above:

(ii) Write instead of one quotient an easily divisible. number, such as 6, 12, 28, 60, 210, 360, and alter the other quotients in the same proportion. Division by the greatest common measure then frequently gives the small whole numbers required.

Thus crystallized ferrous sulphate is found to contain:

Hence the formula is FeSO. 7H,0.

*(iii) It occasionally happens, usually in the case of organic compounds, that the ratio between the quotients is too complicated to be conveniently reduced by either of the foregoing methods. The continued fraction (Sect. 6) expressing the ratio between two of the quotients must then be