it is clear that the value of A or c can be calculated approximately if one of these values is known. § 15. Exceptions.-In attempting to calculate the thermic equivalents of the elements by this method, we occasionally obtain values which cannot represent the true atomic weights. Regnault found for pure carbon in the form of diamond the specific heat c = 0.147, and for graphite, another modification of the same element, c = 0·198. The chemical equivalent of carbon is in § 11 stated to be 2·9925. The atomic weight must either be 2.9925 or a simple multiple of this number. If a = 2.9925, then A = n. a, where n is a whole number and c.Ac.n. a = 6·3 approximately. Let n 1.2.3, &c.; then we have for = The atomic weight of carbon, calculated from the specific heat of the diamond, would be 13.a 38.90; or 14. a = 41.89. But if it is deduced from the specific heat of graphite, then 10.a = 29·92; or 11. a = 32.92. Even if we disregard the want of agreement between these results, such atomic weights would lead to monstrous formulæ for the numerous compounds of carbon, and on this ground alone they could not be accepted. Carbon forms the most pronounced exception to the law. Boron, silicon, and beryllium also form exceptions, and the values for phosphorus and sulphur do not agree closely with the atomic heats of the other elements. INFLUENCE OF TEMPERATURE 25 It is a well-known fact that the specific heat, and therefore the atomic heat, is different at different temperatures. A careful comparison of all the determinations of specific heat led H. F. Weber to the conclusion that the influence of temperature on the specific heats of those elements which form exceptions to the law is so great that they would follow the law at temperatures above 100°. Weber proved by experiment this hypothesis to be correct in the case of carbon, silicon, and boron. Nilson, Pettersson, and Humpidge have recently proved the same for beryllium. The specific heats of these elements increase with the temperature, at first rapidly, afterwards more slowly, until they become almost constant at high temperatures. The values obtained at high temperatures agree fairly well with the law of Dulong and Petit. The smallest stachiometric quantities (equivalent to one part by weight of hydrogen) of these four elements are-carbon 2.99, boron 3.63, silicon 7.08, and beryllium, 4-55. The atomic weights must be simple multiples of these numbers. In the following table c gives the specific heats at high temperatures, A the atomic weights, which on multiplication by the specific heats yield the atomic heats A. c. These values of A obey the law of Dulong and Petit fairly well; but it is clear that this law would not have led to their adoption if they had not already been discovered by other methods. All the elements which exhibit deviations from the law, their atomic heats being too low, have small atomic weights, and are, as a rule, non-metals. The law always applies to elements with atomic weights thirty-six or forty times that of hydrogen. § 16. Specific Heat of Atoms in Compounds. The law of Dulong and Petit also holds good for elements in the state of combination. The specific heat of a compound in the solid 1 Calculated by interpolation from the observations. At 233°c = 0·366. state is approximately equal to the sum of the specific heats of its constituents. In the case of silver iodide, for example, we have The specific heat of silver iodide (AgI) is c = 0·061. If this value is multiplied by the sum of the atomic weights, then we obtain the capacity for heat of that quantity of the compound represented by the formula, AgI. c (Ag + I) = 0·061 × (107·66 +126·54) = 14·3. This is only a little larger than the sum of the specific heats of the constituents. In the same way, in the case of silver bromideAg.c 107.66 × 0·056 = 6.1 Br.c= 79.76 x 0.084 = 6.7 12.8 and (AgBr) = 187.42 × 0.074 = 13.9. The stœchiometric quantities of these substances composed of two thermic equivalents or atoms, AgI and AgBr, require about thirteen units of heat to raise their temperature by 1o C., i.e. double as much as a single atom. Compounds containing three thermic atoms have a capacity for heat three times as great, namely, 3 x 6.4, i.e. 19 or 20. In the case of lead bromide and iodide = 19.5 c. (Pb+2Br) = 0.0533 x (206-4+2 x 79-76) and the sum of the atomic heats of the elements are 6.4+2 × 6·7 = 19.8 6.4+2 × 6·8=20.0. This fact is made use of to determine the thermic equivalents of those elements of which the specific heat cannot be directly determined. If the specific heats of iodine and bromine were unknown they could be approximately calculated from the preceding data. 35-37 parts by weight of chlorine unite with the thermic atomic weight of silver, Ag=107·66, and form 143.03 parts by weight of silver chloride, 70-74 parts by weight of chlorine unite with one atom of lead, Pb = 206·4, to form 277.14 parts by weight of lead chloride. On multiplying these quantities by the corresponding values for the specific heats, the product is the capacity for heat of the stœchiometric quantity of the compounds; deduct from this the atomic heat of the metals, and the remainder is the capacity for heat of chlorine. c. 143.03 0.091 × 143.03 = 13.0 Capacity for heat of 35.37 parts by weight of chlorine 6.9 c. 2771 0.066 × 277·1 = 18.3 c. Pb = 0·031 × 206·4 = 6.4 Capacity for heat of 70-74 parts by weight of chlorine 11·9 Consequently the thermic equivalent of chlorine = 35.37, and the quantity which is attached to one atom of lead is twice this amount and represents two atoms, as the capacity for heat is nearly equal to twice 6 units. The thermic equivalent or atomic weight of an element can be deduced by means of the specific heat of its compounds, even when the atomic heats of the elements united with it are unknown, provided these elements form an analogous compound with an element of known atomic heat. For example : and 11.97 parts by weight of carbon unite with the thermic equivalent of lead= 206.4 to form 266.25 parts by weight of cerussite. This mineral has the specific heat c = 0.080 and the capacity 0.080 × 266·25=21.3. The following metals unite with the same quantities of carbon and oxygen: 136-9 parts of barium forming 196.75 parts by weight of witherite c=0.109; 87.3 parts of strontium forming 147.05 parts by weight of strontianite c=0·145; 39.9 parts of calcium forming 99.75 parts by weight of arragonite c=0.206. These quantities have, according to F. Neumann's discovery, the same capacity for heat as cerussite. From this we conclude that the amount of each metal contained in these compounds represents the thermic equivalents. Bunsen has proved by experiment that this is the case with regard to calcium. In this way the thermic equivalents of several elements have been arrived at, which could not be determined directly, and do not on this account appear in the table on pages 22 and 23, viz. Cl= 35.37 Ru= 85.2 But still the elements mentioned in § 15 remain exceptions, as the capacity for heat of their compounds is smaller than the value calculated from the number of their constituent atoms. This is also true of nitrogen, fluorine, oxygen, and hydrogen. §. 17. Relation between Atomic Weight and Vapour Density.As by chemical methods alone it was found impossible to fix the value of the atomic weights, other physical methods than the crystalline form and specific heat were soon employed. The most important of these is the law of combining volumes discovered by Gay Lussac and Alexander von Humboldt at the beginning of the present century. According to this law a simple relation exists between the volumes of the different gases (measured under similar conditions of temperature and pressure) entering into combination or mutually decomposing each other. The densities of the gaseous elements at the ordinary temperature compared with air or hydrogen are as follows: |