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two examples quoted, silver chloride consists of two atoms, while the molecule of stannous chloride contains three; if, therefore, the molecular heats of these two compounds are divided respectively by 2 and by 3 we get

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as the value representing the atomic heat of chlorine.

The element calcium combines with chlorine in the proportionCalcium chlorine = 20: 35.5.

If the atomic weight of calcium is 20, the formula will be CaCl. whereas if 40 is the atomic weight of the metal, the compound must be represented by the formula CaCl.

The molecular weight of CaCl would be 55.5, that of CaCl, 111.0. When the specific heat of the compound was determined, it was found to be 0.1642. In order, therefore, to decide between the two values for the atomic weight of calcium, we calculate the molecular heat from both of the molecular weights, and divide the result by the number of atoms in the molecule in each case. On the supposition that Ca=20, and that CaCl represents the chloride :

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Or, if Ca=40, and CaCl, is the formula for the chloride, then

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The number 6.07, which nearly agrees with the constant 6.4, decides the value 40 as the atomic weight of calcium. The element calcium is one of those metals which it is very difficult to isolate and obtain in a state of purity, but when in recent years the specific heat of this metal was experimentally determined,* it was found to be 0.1704 :

0.1704 × 40=6.8.

Thus affording direct confirmation of the value 40 for the atomic weight of calcium, which had been deduced from the molecular heat of its compounds.

* Bunsen.

Deductions based upon molecular heats of compounds are only trustworthy in the case of the most simply constituted compounds. 4. Determination of Atomic Weight from Considerations based on Isomorphism.—It was early observed that certain relations existed between the crystalline forms of compounds and their chemical composition. Mitscherlich found that certain substances having an analogous chemical composition, as, for example, sodium phosphate and sodium arsenate, crystallised in the same geometric form. In the year 1821 he stated his law of isomorphism as follows: "The same number of atoms, combined in the same way, give rise to the same crystalline form, which is independent of the chemical nature of the atoms, being influenced only by their number and mode of arrangement." Subsequent investigations, however, have shown that this statement is too general.

In its broad sense as signifying the same crystalline form, isomorphism is found to exist

1. Between compounds containing the same number of atoms similarly combined, and which bear close chemical analogies to each other.

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Hydrogen disodium arsenate

Isomorphous {Hydrogen disodium phosphate. HN,PO,12H2O.

Rubidium alum.

Potassium chrome alum

Isomorphous

HNA,ASO4,12H2O.

Rb2SO4, Al2(SO4)3,24H,O.
K2SO4, Cr2(SO4)3,24H,O.

Potassium aluminium selenium K.,SO,,Al2(SO4)3,24H,O.

alum

2. Between compounds containing a different number of atoms, but which also bear close chemical analogies to one another.

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3. Between compounds containing either the same or a different number of atoms, and which exhibit little or no chemical analogies.

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Isomorphism of this order, where little or no chemical relations exist between the compounds, is sometimes distinguished as isogonism. It must not be supposed, that because two chemically analogous compounds contain the same number of atoms, they will necessarily crystallise in the same form: there are indeed a large number of similarly constituted analogous compounds that do not exhibit isomorphism.

No simple definition of isomorphism is possible, but the following test is generally accepted as a criterion, namely, the power to form either mixed crystals or layer crystals. Thus, when two substances are mixed in a state of liquidity, and allowed to crystallise, if the crystals are perfectly homogeneous, they are known as mixed crystals, and the substances are regarded as isomorphous.

Or when a crystal of one compound is placed in a solution of another compound, and the crystal continues to grow regularly in the liquid, the compounds are isomorphous. Thus, if a crystal of potassium alum (white) be placed in a solution of manganese alum, the crystal continues to grow without change of form, and a layer of amethyst-coloured manganese alum is deposited upon it. In making use of the law of isomorphism in the determination of atomic weights, it is assumed that the weights of different atoms that can mutually replace each other without altering the crystalline form are proportional to their atomic weights.*

Thus, if we suppose that, in the case of the sulphates of zinc and magnesium, the atomic weight of zinc is known, viz., 65, and that of magnesium is doubtful; from the fact of the isomorphism of the sulphates it may be premised that the elements are present in proportions relative to their atomic weights. Analysis shows that the proportion is 24 of magnesium to 65 of zinc, therefore 24 is presumably the atomic weight of magnesium.

In this way Berzelius corrected many of the atomic weights which in his day had been assigned to the elements.

*The group (NH) may be regarded as an atom, having the relative weight 18.

CHAPTER VII

QUANTITATIVE CHEMICAL NOTATION

THE use of chemical symbols and formulæ, as a convenient means of representing concisely the qualitative nature of chemical changes, has been explained in chapter iv. We are now in a position to read into these symbols a quantitative significance, which at that stage it would have been premature to explain.

The symbol of an element stands for an atom; but, as we have now learnt, the atoms of the various elements have different relative weights, hence these symbols represent relative weights of matter. The symbol Na signifies 23 relative parts by weight of sodium, O stands for 16 relative parts by weight of oxygen, H for 1 part of hydrogen; in other words, the weight of sodium represented by the symbol Na is 23 times as heavy as that which is conveyed by a symbol H. A chemical equation, therefore, is a strictly quantitative expression, in which certain definite weights of matter are present in the form of the reacting substances, and which reappear without loss or gain in the compounds resulting from the change. In this sense as chemical equation is a mathematical expression. Thus, the equation—

Na + Cl = NaCl,

not only means that an atom of sodium combines with an atom of chlorine and forms 1 molecule of sodium chloride, but it also means

2335.5 58.5
Na CI NaCl.

In other words, that sodium and chlorine unite in the relative proportion of 23 parts of the former and 35.5 parts of chlorine, and produce 58.5 parts of sodium chloride.

In the same way, into the equation which expresses the action of

sulphuric acid upon sodium carbonate, we read the quantitative meaning of the symbols

H2SO4 + Na2CO3 = Na„SO1 + CO2+ H2O.

2

32

64

98*

46
12

48

46

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+ 106 = 142 + 44 + 18

That is to say, 98 parts by weight of sulphuric acid act upon 106 parts of sodium carbonate, producing 142 parts of sodium sulphate, 44 parts of carbon dioxide, and 18 parts of water. It will be evident that it becomes a matter of the simplest arithmetic to calculate the weight of any product that can be obtained from a given weight of the reacting substances; or vice versa, to find the weight of any reacting substance which would be required to produce a given weight of the product of the action.

Not only is information respecting the quantitative relations by weight embodied in a chemical equation, but when gaseous substances are reacting, the equation also represents the volumetric relation between the gases. In order that the volumetric relations may be more manifest, the equations expressing the reactions are written in such a manner as to represent the molecules of the substances.

H+ Cl = HCI

is an atomic equation, but as the molecule is the smallest particle which can exist alone, a more exact statement of the chemical change is made, by representing the action as taking place between molecules, thus-

H2+ Cl2 = 2HC1.

I

From such an equation we see that I molecule of hydrogen, or 2 unit volumes, unites with 1 molecule or 2 unit volumes of chlorine, and forms 2 molecules or 4 unit volumes of hydrochloric acid : or again

O2 + 2H, = 2H2O.

One molecule, or 2 unit volumes of oxygen, unite with 2 molecules, or 4 unit volumes of hydrogen, and produce 2 molecules of

"

The number obtained by adding together the weights of the atoms in a formula is known as a formula weight," thus 98 is the formula weight of sulphuric acid.

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