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When only a few compounds of a specified element have 299 been gasified and analysed, the value thence deduced for the atomic weight of that element may be, and very possibly is, too large; it cannot be too small. Thus only three compounds of aluminium have been gasified &c.; a molecule of each is composed of 54:04 parts by weight of aluminium, combined with 212.22 parts by weight of chlorine, 478.5 of bromine, and 759.18 of iodine, respectively. Hence the atomic weight of aluminium is not greater, but may be less, than 54:04. From other data we know that the atomic weight of this metal is 54:04
= 27.02. (s. par. 305.) 2
Determinations of the specific gravities of gases are subject 300 to several sources of error. But the mass of an element which combines with one part by weight of hydrogen, or eight parts by weight of oxygen, or 35.5 parts by weight of chlorine, or 16 parts by weight of sulphur, i.e. the smallest value of the combining weight of the element (v. ante, Chap. v. pars. 73 to 75), can be determined with great accuracy. It is evident that the molecular weight of an element must be either equal to, or a whole multiple of, the combining weight of the element; and that the molecular weight of a compound must be either equal to, or a whole multiple of, the sum of the combining weights of the constituent elements. Hence the data required for an accurate determination of the molecular weight of an element are (1) an accurate determination of the combining weight of the element, and (2) a fairly accurate determination of the specific gravity of the element in the gaseous state.
Similarly, the data required for an accurate determination of the molecular weight of a compound are (1) accurate determinations of the combining weights of the elements which form the compound, and (2) a fairly accurate determination of the specific gravity of the compound in the gaseous state.
Thus 35.37 parts by weight of chlorine combine with 1 part by weight of hydrogen; therefore the molecular weight of chlorine is n35-37, where n is a whole number. A determination of the specific gravity of chlorine shews that this gas is approximately 351 times heavier than hydrogen ; therefore the molecular weight of chlorine is approximately 35.5 x 2 = 71. But 35•37 2 = 70.74; therefore the molecular weight of chlorine is 70-74. Again, 10:32 parts by weight of phosphorus combine with 1 part by weight of hydrogen to produce M. E. C.
phosphorus hydride; therefore the molecular weight of this compound is n 11:32 (n=a whole number). Gaseous phosphorus hydride is found to be about 17 times heavier than hydrogen; therefore the molecular weight of this gas is about 17 x 2 = 34. But 11:32 x 3 = 33.96 ; therefore the molecular weight of gaseous phosphorus hydride is 33.96.
The meaning of the heading of col. III. in the tables in pars. 297 and 298,-Sp. Gr. (air = 1) ~ 28.87 corrected, i.e. molecular weight'—will now be apparent.
By applying Avogadro's law, values have been obtained for the atomic weights of rather more than half the elements; gaseous compounds of the remaining elements have not yet been obtained, and hence the atomic weights of these elements have not been determined by the method based on the law of Avogadro.
The following table gives the results of the application of Avogadro's law to determining the atomic weights of elements.
Maximum Atomic Weights of Elements. (Avogadro's law.)
126.53 Carbon 11.97 Germanium 72:3 [Copper*
126.8] Nitrogen 14.01 Arsenic
78.8 Tantalum 182 orir
19.1 Bromine 79.75 Tungsten 183.6 Silicon 28 Zirconium 90 Osmium
193 (?) Phosphorus 30.96 Niobium
94 Mercury 199.8 Sulphur 31.98 Molybdenum 95.9 Thallium 203.6 Chlorine 35.37 [Iron*
206.4 Potassium 39.04 Cadmium 112 Bismuth
208 Titanium 48 Indium
113.4 Thorium 232 Vanadium 51.2 Tin
117.8 Uranium 240
Avogadro's law—equal volumes of gases contain equal numbers of molecules—furnishes chemists with a method whereby they may determine the relative weights of the molecules of all gaseous compounds and elements, and the maximum values to be given to the relative weights of the atoms of all elements which form gaseous compounds. But at present only 14 or 15 elements have been gasified, and gaseous compounds of only 42 elements have been prepared and analysed. Hence the application of the method based on the law of Avogadro is limited. This method is at present the only general method for determining the relative weights of the gaseous molecules of elements and compounds. But there is another general method whereby values may be found for the atomic weights of elements. This method is contained in the statement;
* The atomic weights of these four elements are almost certainly 27.02, 55.9, 63.4, and 69, respectively (8. par. 305).
The products of the specific heats of solid elements, determined in each case at the temperature-interval for which specific heat is nearly constant, into the atomic weights of these elements, approach a constant, the mean value of which is 6.4.
This statement is a modification of the so-called law of Dulong and Petit. From their study of the specific heats of 13 solid elements in the year 1819, these naturalists announced that “the atoms of all simple bodies have exactly the same capacity for heat.” Investigation has shewn that this statement was too absolute. The specific heats of some solid elements, e.g. carbon, boron, silicon, beryllium, vary much with variations of temperature, and become approximately constant only at high temperatures. The specific heat of a solid also varies to some extent with variations in the greater or less compactness of the specimen.
The product specific heat of solid element x atomic weight is usually called the atomic heat of the element.
The specific heats of a few elements have not yet been 303 determined. Values which may be approximately correct, have been indirectly obtained for some of these; but too great stress must not be laid on these values. The indirect method in question is based on the assumption, to some extent verified by facts, that the 'molecular heat' of a solid compound, i.e. the product of the specific heat into the mass of the compound expressed by its formula, is equal to the sum of the atomic heats of the elements in the compound; therefore if the molecular heat' (as thus defined) of a solid compound is known, and the atomic heats of all the elements in the compound except one are known, the atomic heat of the remaining one element can be calculated.
The following statements summarise the present state of 304 knowledge with regard to the atomic heats of the 42 elements maximum values for the atomic weights of which have been determined by applying the law of Avogadro (par. 301). Solid elements, 28 in number, the specific heats of which
have been directly determined, and the atomic heats of which are approximately equal to 6.4:—P, S, K, Ti, Cr, Al, Zn, As, Se, Br, Zr, Mo, Fe, Cd, In, Sn, Sb, Te, I, Cu, w, Os, Hg, TI, Pb, Bi, Th, U.
II. Solid elements, 6 in number, the specific heats of which have been directly determined, and the atomic heats of which are approximately equal to 5.5 :-Be, B, C, Si, Ga, Ge.
III. One solid element, the atomic heat of which has been indirectly determined and is probably equal to 6.4:-Vanadium.
IV. Five gaseous elements, the specific heats of which in solid form have only been determined indirectly and are extremely doubtful :-H, N, O, F, Cl.
V. Two solid elements the specific heats of which have not been determined directly or indirectly :-Nb, Ta.
These data establish a very fair probability in favour of the statement made in par. 302 regarding the constant value of the atomic heat of the solid elements. If this statement is granted, then an approximate value may be found for the atomic weight of an element by dividing 6.4 by the specific heat of that element in the solid form.
The maximum values found for the atomic weights of aluminium, iron, copper, and gallium, by the use of Avogadro's law were 54:04, 111:8, 126.8, and 138, respectively (8. Table, par. 301). Now the spec. heats of these elements are •225, *114, 097, and .08, respectively; dividing 6-4 by each of these numbers we get the quotients, 28.5, 56:1, 65.9, and 80. Therefore we conclude that the maximum values found for the atomic weights of these elements by applying Avogadro's law must be halved, and we adopt the numbers 27.02, 55-9, 63•4 and 69, as very probably the true atomic weights of aluminium, iron, copper, and gallium, respectively.
There is another physical method which has sometimes been found useful in determinations of atomic weights, but which can only be used as a guide to point the way to experimental inquiries. This method is founded on the generalisation, that similarity of chemical composition is usually associated with close similarity of crystalline form. In some cases marked similarity of composition is accompanied by identity of crystalline form ; e.g. the oxides of arsenic and antimony, Aso, and Sb., crystallise in identical forms; they are isomorphous.
The difficulties in applying this method-generally known as the method of isomorphism-lie in the vagueness of the ex
pressions (similarity of chemical composition and similarity of crystalline form.' The following example will indicate how the so-called law of isomorphism has been used as an aid in determining the atomic weight of gallium.
Gallium sulphate was found to form a double salt with ammonium sulphate; the crystalline form of this double sulphate was identical with that of ordinary ammonia-alum. Therefore the double sulphate in question doubtless belonged to the class of alums. Now the composition of the alums is expressed by the general formula M,380,.N,SO,. 24H,0 where M=A1, Fe, Cr, or Mn, and N=Na, K, Cs, Rb, or NÁ, In the case of common ammonia-alum M, = Al, = 2 27.02 parts by weight of aluminium ; in the double sulphate of gallium and ammonium M, was found to represent 138 parts by weight of gallium. Hence, as 2 atoms of aluminium have been replaced by 138 parts by weight of gallium without altering the crystalline form or the general chemical type of the compound, it was concluded that the atomic weight of gallium was 138 = 69. This number was afterwards verified by the application of the law of Avogadro, and also by the specific heat method *.
There are then two generally applicable methods whereby 307 values may be found for the atomic weights of the elements; the method founded on the law of Avogadro; and the method based on the specific heats of solid elements. Besides these, there is another method, arising out of the relations between the chemical composition and crystalline forms of similar compounds, which is useful as a guide in determinations of atomic weights. The first method is applicable to determinations of the atomic and molecular weights of elements, and the molecular weights of compounds, but it is restricted to bodies which are gasifiable without decomposition. The second and third methods can be strictly applied only to find values for the atomic weights of solid elements, and to some extent of elements which form solid compounds. All the methods are essentially physical; they are based on physical conceptions, and they are to a great extent developed by physical reasoning. Thus the image of the molecule which is called
in the mind by the statement “equal volumes of gases contain equal numbers of molecules” is that of a very small, definite,
* We do not propose to go more fully into the method of isomorphism here. The study of this subject is more suited to the advanced student of chemistry.