MULTIPLE VALENCE.

119

(and it is), then iron is bivalent in ferrous chloride (FeCl2), but trivalent in ferric chloride (FeCl3). If oxygen is bivalent in the oxides, then carbon is bivalent in carbon monoxide (CO), and quadrivalent in the dioxide (CO2). So phosphorus is trivalent in the formulas PCl, and P2O3, but quinquivalent (pentavalent) in PCl5 and P2O5. Sulphur is bivalent in hydrogen sulphide (H2S) and all sulphides, quadrivalent in sulphur dioxide, and sexivalent (hexavalent) in sulphur trioxide. The element argon (cf. § 191), which forms no compounds, is of valence zero (0).

In general, the valence of an element is smaller at high temperatures than at low. Thus, sulphur trioxide breaks up when heated,

SO SO2+0.

Here the valence of sulphur falls from six to four. Phosphorus pentachloride, also, is dissociated when heated,

PCI, PC13+2 Cl.

An element may show a higher valence when combined with some elements than with others. This is shown in the reaction by which chlorine is prepared (cf. § 115):

MnO2+4 HCI

MnCl2+2 Cl↑ +2 H2O.

In manganese dioxide the valence of manganese is probably 4 (cf. §341). In a true double decom

position, valences do not change; hence we should expect manganese tetrachloride to be formed:

Instead, we obtain manganous chloride, MnCl2: the valence of the manganese falls from four to two.

139. Exercises.

1. If the valence of an element M is 1, write the formulas of its sulphate, carbonate, sulphide, nitrate, phosphate, and nitride. Write the formulas of the same compounds of an element, R, having a valence of 2.

2. Give the valence of each element in the following: Li,N, Fe2S3, ZnBr2, KI, SгO, As2O5, SbCl3, PH3. Name each of these substances.

3. Considering all but the first element in each of the following to be a radical, give the valences of the first elements and of the radicals: KClO3, NaNO3, BaCO3, SrSO4, AIPO4, Ag3PO4, Fe(OH)3, Bi(NO3)3. Name each of these compounds.

CHAPTER XII.

MOLECULAR WEIGHTS.

140. Combination by Volume; Gay-Lussac's Law. We have already studied two cases of combination which show that elements unite, not only in definite proportions by weight, but also, if they are gases, in definite proportions by volume. The two cases are, (1) the union of hydrogen and oxygen to give steam (cf. § 63), and (2) the combination of hydrogen with chlorine to produce hydrogen chloride (cf. § 128). The proportions by volume in these

The facts regarding combination by volume are summarized in Gay-Lussac's Law of Definite Proportions by Volume: The volumes of reacting gases have a definite (and simple) relation to one another and to the volumes of the products, if these are gases.

Just as elements may unite in more than one proportion by weight (cf. § 94), so gaseous elements may unite in more than one proportion by volume.

The case of hydrogen peroxide and water illustrates this: while two volumes of steam are formed from two volumes of hydrogen and one of oxygen, two volumes of gaseous hydrogen peroxide are composed of two volumes of hydrogen and two of oxygen.

CO +

2 vols. hydrogen peroxide. 2 vols. hydrogen.

2 vols. oxygen.

141. Avogadro's Hypothesis. -In §§ 98 and 99 we learned that molecules " occupy space." The hypothesis of Avogadro is that it takes equal numbers of molecules to occupy equal spaces, or, that equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules. Avogadro was an Italian physicist, and announced his hypothesis in 1811. Ampère reached the same conclusion in 1814.

142. The Molecules of Elements. Avogadro's hypothesis gives us a basis for important deductions regarding the numbers of atoms in the molecules of gaseous elements. Let us take the case of hydrogen chloride.

1 vol. hydrogen.

+

1 vol. chlorine. 2 vols. hydrogen chloride.

We have no idea how many molecules there actually are in any given volume, but let us assume that there are 1,000 molecules in one volume of hydrogen. Then one volume of chlorine will contain 1,000 molecules (Avogadro's hypothesis), and the two volumes of hydrogen chloride produced will contain 2,000

MOLECULAR WEIGHTS OF GASES.

123

molecules. But each molecule of hydrogen chloride must contain some hydrogen and some chlorine. It cannot contain a whole molecule of either, for there were only 1,000 molecules of each gas,

1,000 mols. H+1,000 mols. Cl

2,000 mols. HCl.

Hence, one molecule of hydrogen chloride must contain a molecule of hydrogen and a molecule of chlorine.

Similar reasoning leads to the conclusion that there must be a half-molecule of oxygen in the molecule of water (steam); for 2,000 mols. H+1,000 mols. O →→→→→ 2,000 mols. H2O;

therefore one molecule of steam must contain one molecule of hydrogen and a molecule of oxygen.

The facts regarding nitrogen are deduced from the equation for the union of nitrogen with hydrogen (cf. § 213), —

Hence, one molecule of ammonia must consist of a molecule of nitrogen and 14 molecules of hydrogen.

The half-molecules of these four elementary gases are assumed to be the atoms, hence we conclude that the molecules of hydrogen, nitrogen, oxygen, and chlorine consist of two atoms each.

Avogadro's

143. Molecular Weights of Gases. hypothesis is also the basis of molecular weights. We cannot get at the actual weights of molecules, but we can get at their relative weights, if we assume that there are equal numbers of molecules in equal