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criterion, for although the atomic weight of an element cannot be greater than the smallest mass that enters into the composition of the molecules of any of its known compounds, it might be less than this, as there is always the possibility of a new compound being discovered, in which the relative weight of an element is such as to make it necessary to halve the previously accepted atomic weight. 3. Determination of Atomic Weight from the Specific Heat of Elements in the Solid State.-When equal weights of different substances are heated through the same range of temperature, it is found that they absorb very different quantities of heat, and on again cooling to the original temperature, they consequently give out different amounts of heat. Thus, if I kilogramme of water, and 1 kilogramme of mercury be each heated to a temperature of 100°, and then each be poured into a separate kilogramme of water at o°, in the first case the resultant mixture will have a temperature of 50°, while in the second it will only reach the temperature of 3.2°; that is to say, while the water in cooling through 50° has raised the temperature of an equal weight of water from o° to 50°, the amount of heat in 1 kilogramme of mercury at 100° has only raised the temperature of an equal weight of water from o° to 3.2°, and in so doing has itself become lowered in temperature 100-3.2=96.8°. The amount of heat contained, therefore, in equal weights of water and of mercury at the same temperature, as shown by these figures, is as50 3.2

:

50 96.8

=1:30;

therefore it requires 30 times as much heat to raise a given weight of water through a given number of degrees as to raise an equal weight of mercury through the same interval of temperature, or the thermal capacity of mercury is th that of water.

The specific heat of a substance is the ratio of its thermal capacity to that of an equal weight of water; or, the ratio between the amount of heat necessary to raise a unit weight of the substance from o° to 1°, and that required to raise the same weight of water from o° to 1°; thus, the specific heat of mercury is 3, or 0.033. Water is chosen as the standard of comparison because it possesses the highest thermal capacity of all known substances; the numbers, therefore, which express the specific heats of other substances are all less than unity.

Dulong and Petit were the first to draw attention (1819) to a remarkable relation which exists between the specific heats and the atomic weights of various solid elements, whose specific heats

they themselves had determined. They found that the specific heats of the solid elements were inversely as their atomic weights; that is to say, the capacity for heat of masses of the elements proportional to their atomic weight was equal. This law, known as the law of Dulong and Petit, may be thus stated: The thermal capacities of atoms of all elements in the solid state are equal.

The thermal capacity of an atom is termed its atomic heat; hence the law may be more briefly stated, all elements in the solid state have the same atomic heat. This important constant is the product of the atomic weight into the specific heat. From the following table it will be seen that the number expressing the atomic heat is not perfectly constant: the departures from the mean 6.4 are, as a rule, only slight, and may be attributed to the fact that the determinations are not always made upon the elements under conditions that are strictly comparable. At the end of the table, however, there are certain elements which appear to present marked exceptions to the law.

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It will be seen that, relatively speaking, the four elements which show a considerable departure from the law of Dulong are elements with low atomic weights. Low atomic weight, however, is not always accompanied by such deviation, as is shown in the case of lithium and sodium.

When the different allotropes of carbon are experimented upon, it is found that the departure is not the same for each modification of the element, thus

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It has been observed that, as a general rule, the specific heat of an element is slightly higher at higher temperatures; but in the case of the four elements showing abnormal atomic heats, this increase rises rapidly with increased temperature, until a certain point is reached, when it remains practically constant, and represents an atomic heat which closely approximates to the normal value; thus in the case of diamond, the specific heat at increasing temperatures is—

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The same result is seen in the case of graphite, and it is also to be remarked, that while at low temperatures there exists a wide difference between the specific heats of these two modifications of carbon, this difference vanishes at a temperature of about 600°.

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Both the elements boron and silicon are found to follow the same rule, and ať moderate temperatures their atomic heats nearly approximate the normal constant.

The case of the somewhat rare element beryllium is of special interest from another point of view, which will be referred to when treating of the natural classification of the elements from the following numbers it will be seen that its atomic heat very rapidly rises with moderate increase of temperature.

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The relation between atomic weight and specific heat, established by Dulong and Petit, is of service in the determination of atomic weights, not as a method of ascertaining the exact value with any degree of refinement, but rather as a means of deciding between two numbers which are multiples of a common factor.

If specific heat × atomic weight = atomic heat, it will be obvious that, if we experimentally determine the specific heat, and divide that value into the constant atomic heat, 6.4, we obtain the approximate atomic weight.

The two following examples will serve to illustrate the application of the method.

The element indium combines with chlorine in the proportion—

Indium chlorine = 37.8 35.5.

If InCl is the formula, then 37.8 is the atomic weight of indium; but from the chemical similarity between indium and zinc (whose chloride has the formula ZnCl2), it was believed that the formula for indium chloride was InCl2, in which case, in order to preserve the ratio between the two elements, the atomic weight would have to be 37.8 x 2 €75.6.

=

When the specific heat of indium was determined,* it was found to be 0.057.

6.4
= 112.28
0.057

Therefore the atomic weight must be raised by one-half, from
75.6 to 113.4, and the formula for the chloride will be InCl.
The element thallium combines with chlorine in the proportion—
Thallium chlorine 203.6: 35.5.

In some of its compounds thallium exhibits a strong resemblance to potassium, the chloride of which has the formula KCl. If the formula for the thallium chloride is TICI, the atomic weight of the metal must be 203.6.

In many respects thallium exhibits a striking analogy with lead,

Bunsen, 1870.

the chloride of which has the formula, PbCl. If thallium chloride has a corresponding formula, TIC, then the atomic weight of thallium must be raised to 407.2.

When the specific heat of thallium was ascertained,* it was found to be 0.0335.

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This result shows that the number 203.6 and not 407.2 is the atomic weight of thallium, and that the chloride has the formula TICI.

Molecular Heat of Compounds.-The capacity for heat of an atom undergoes no alteration when the atom enters into combination with different atoms-in other words, the atomic heat of an element is the same in its compounds. The molecular heat of a compound (that is, the product of the molecular weight into the specific heat) will therefore be the sum of the atomic heats of its constituent elements. Hence it is possible to calculate what will be the atomic heat of an element which does not exist as a solid under ordinary conditions; and therefore the atomic weight of such an element, as deduced from other considerations, is capable of verification, by determinations of the molecular heat of various of its compounds: thus

The specific heat of silver chloride, AgCl, is 0.089 :—

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The atomic heat of silver

=

6.1, therefore, as deduced from this compound, the atomic heat of chlorine is 12.77 - 6.1 = 6.6.

Again, the specific heat of stannous chloride, SnCl2, is 0.1016:—

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The atomic heat of tin is 6.6, therefore the atomic heat of two atoms of chlorine, as deduced from this compound, is 19.2-6.6= 12.6, giving 6.3 as the atomic heat of chlorine.

The differences that appear in the value, as deduced from various compounds, are lessened, because the method are more equally distributed, if we divide heat by the number of atoms in the molecule.

* Regnault.

errors of the the molecular Thus, in the

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