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We shall begin by considering compounds of the element potassium with (1) chlorine, (2) iodine; and then (3) the compound of chlorine with iodine. The percentage compositions of these compounds are ;I.

II.

III. Potassium chloride. Potassium iodide. Iodine chloride. potassium = 52.4

potassium = 23.6 iodine 78.1 chlorine 47.6 iodine

76.4

chlorine = 21.9

100.0

100.0

100.0

Let us find the masses of chlorine and iodine which severally combine with the same mass of potassium : this may be done by finding, (1) the mass of iodine combined with 52-4 of potassium, or (2) the mass of chlorine combined with 23.6 of potassium;

(1) 23•6 : 52:4 = 76°4 : x.

(2) 52:4 : 23.6 = 47.6 : c'. We shall choose (2); x = 21.4.

That is, with 23.6 parts by weight of potassium there combine, (1) 76-4 parts of iodine to form potassium iodide, (2) 21:4 parts of chlorine to form potassium chloride.

Now let us turn to the compound of chlorine and iodine. Let us ask; what is the mass of chlorine which is combined with 76.4 parts of iodine?

78.1 : 76'4 = 21:9 : X.

= 21:4.
We have now this result

;-
23:6 parts by weight of potassium combine with

76·4 parts by weight of iodine.
21:4

chlorine. 76•4 parts by weight of iodine combine with

21•4 parts by weight of chlorine. Or, stated more generally, the masses of chlorine and iodine which severally combine with a constant mass of potassium are also the masses of chlorine and iodine which combine with each other.

If another element is used instead of potassium, will a similar result be obtained ? Chlorine combines with hydrogen to form hydrogen chloride; iodine also combines with hydrogen

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to form hydrogen iodide. If the compositions of these compounds are tabulated we have the following results ;Hydrogen iodide.

Hydrogen chloride. hydrogen = 0.79

hydrogen = 2.77 iodine 99.21

chlorine 97.23 100.00

100.00
Treating these results as before, we find that
·79 parts by weight of hydrogen combine with

99.21 parts by weight of iodine.
27.8

chlorine.
Then we inquire ; how much iodine combines with 27.8
chlorine? The answer to this is found from the composition
of iodine chloride; it is 99.21. So that we complete the fore-
going statement by adding
99.21 parts by weight of iodine combine with

27.8 parts by weight of chlorine. Or, stated more generally, the masses of chlorine and iodine which severally combine with a constant mass of hydrogen are also the masses of chlorine and iodine which combine with each other.

Hydrogen combines with oxygen to form water; hydrogen 68 also combines with sulphur to form hydrogen sulphide; oxygen combines with sulphur to form oxide of sulphur. examine the compositions of these compounds. We need not state the composition of each in parts per 100; let it suffice to state the results thus 1 part by weight of hydrogen combines with

8 parts by weight of oxygen. 16

sulphur. Then we inquire; how many parts by weight of sulphur combine with 8 of oxygen? Experiment tells that 8 parts by weight of sulphur combine with 8 parts by weight of oxygen. We have then this result 1 part by weight of hydrogen combines with

8 parts by weight of oxygen. 16

sulphur. 8 parts by weight of oxygen combine with

8 parts by weight of sulphur. Phosphorus combines with hydrogen to form phosphorus 69 M. E. C.

4

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hydride; we know that chlorine combines with hydrogen to form hydrogen chloride; phosphorus also combines with chlorine to form phosphorus chloride.

We know that phosphorus combines with hydrogen, and that oxygen combines with hydrogen ; phosphorus also combines with oxygen to form phosphorus oxide.

If we determine the compositions of these various compounds, and treat the results as before, always in the case of a hydrogen compound determining the mass of the other element combined with 1 part by weight of hydrogen, we have these results :1 part by weight of hydrogen combines with

10:3 parts by weight of phosphorus. 35.5

chlorine, 10.3 parts by weight of phosphorus combine with

355 parts by weight of chlorine. 1 part by weight of hydrogen combines with

10.3 parts by weight of phosphorus. 8

oxygen. 10:3 parts by weight of phosphorus combine with

8 parts by weight of oxygen. Stating these results generally, we find that the masses of phosphorus and chlorine, or the masses of phosphorus and oxygen, which severally combine with a constant mass of hydrogen, are also the masses of phosphorus and chlorine, or of phosphorus and oxygen, which combine with each other.

We also find that the masses of oxygen and sulphur which combine with each other bear a simple relation to the masses of these elements which severally combine with a constant mass of hydrogen. We have learned that

10:3 parts by weight of phosphorus. 1 part by weight of hydro- 8

» oxygen. gen combines with 16

sulphur. 35.5

chlorine. Also that 10.3 parts by weight of phosphorus combine with

8 parts by weight of oxygen. 35.5

chlorine. Phosphorus forms two compounds with sulphur; when the

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composition of that mass of each of these which is produced by combining 10.3 parts of phosphorus with sulphur is stated, we have

(1) 8x2=16) parts by weight of 10.3 parts by weight of phos- sulphur. phorus combine with (2) 8x3} (=26.6)

sulphur. Chlorine and oxygen form two compounds, the compositions of which are ;

(1) 8 parts by weight of 35.5 parts by weight of chlorine oxygen. combine with

(2) 8 x 4 (=32) parts by weight

of oxygen. Chlorine and sulphur form a compound the composition of which is; 35.5 parts by weight of chlorine combine with 8x4(=32) parts

by weight of sulphur. These results may be stated in more general terms thus :

The masses of phosphorus, oxygen, sulphur, and chlorine, which severally combine with a constant mass of hydrogen are also the masses of those elements which combine with each other, or they bear a simple relation to these masses.

This statement, or a statement equivalent to this, holds good 71 for all the elements. The statement is known as The law of reciprocal proportions.

This law may be expressed in various forms; thus

When two elements, A and B, severally combine with a third element, C, then the proportions in which masses of A and B severally combine with C are also the proportions in which A and B combine with each other, or they bear a simple relation to these proportions. Or, better, thus

The masses of different elements which severally combine with one and the same mass of another element are also the masses of those different elements which combine with each other, or they bear a simple relation to these masses.

The student should particularly observe that the laws of 72 multiple, and reciprocal, proportions, are generalised statements of facts. He should also familiarise himself with the method by which these laws are deduced from the composition of compounds. Statements of the percentage composition of a series of compounds do not suggest the laws in question, although

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they contain the data from which the laws are deduced. It is necessary to compare the compositions of compounds of each of two, or more, elements with one and the same element; it is also necessary to state these compositions so that the mass of the element with which the others combine is kept constant throughout all the compounds.

Any element may be chosen as the standard element; and any mass of the standard element may be chosen as the fixed mass with which other elements are to be combined. It is found that the relations between the masses of elements which mutually combine are very clearly and simply exhibited by choosing hydrogen as the standard element, and one part by weight (say 1 gram) of hydrogen as the fixed mass.

The following table illustrates this way of looking at the composition of several compounds. Column I. exhibits the composition of three compounds of hydrogen, stated, (a) as parts of each element per 100 parts of the compound, (6) so as to shew the weight of the second element combined with 1 part by weight of hydrogen. Columns II., III., and IV., exhibit the composition of compounds of two elements neither of which is hydrogen, stated, (a) as parts per 100, and (b) so as to shew the weights of those elements which severally combine with that weight of oxygen, sulphur, or chlorine, which has been shewn in I. to unite with 1 part by weight of hydrogen.

The masses of oxygen, sulphur, and chlorine, which severally combine with 1 part by weight-i.e. with unit mass

of hydrogen are 8, 16, and 35.5, respectively. The masses of copper, lead, and thallium, which severally combine with 8 parts by weight of oxygen are 31:7, 103-5, and 204, respectively; and these are also the masses of those elements which severally combine with 16 parts by weight of sulphur, and with 35.5 parts by weight of chlorine, respectively.

Let us call those masses of oxygen, sulphur, &c. the combining weights of oxygen, sulphur, &c. We have then :

Combining weights, deduced from composition of compounds with hydrogen.

Oxygen = 8; Sulphur = 16; Chlorine = 35.5. These numbers represent parts by weight of each element which combine with one part by weight of hydrogen.

Combining weights, deduced from composition of compounds with oxygen.

Copper = 31-7; Lead = 103-5; Thallium = 204.

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