belonging to the same class, the less does the value of (V) (V) BaCO3=45°8 crystals exhibit differences from those of SrCO, and PbCO,1. 2 Kopp has concluded that if D, the difference between what he calls the molecular volumes' of two isomorphous compounds, is represented as D=-(V) then the value of D may attain a maximum, equal to 0.328, without isomorphism being impossible. Determinations of (V) for anhydrous and hydrated salts promise to throw some light on various questions implied in the commonly used expressions 'water of crystallisation' and 'water of constitution.' Graham distinguished 'saline' water from 'basic' water in salts and acids; the replacement of the former by another salt, or by an oxide, produced a double—or in the case of acids a normal-salt; the replacement of the 'basic' water in an acid produced a basic salt. Thus, MgSO,H,O6H,O gave MgSO,K2SO46H2O ; saline basic N2O,H2O3H2O gave (N,O,CuOзH,O normal nitrate of copper. saline basic N2O,CuO3CuO basic Graham further distinguished basic water from water of constitution; e.g. Thorpe and Watts have determined (V) for the salts MSO,, when M = Mg, Zn, Cu, Mn, Fe, Co; and for the hydrated salts MSOH2O when M = Mg, Zn, &c. and x varies from 1 to 7. 1 For more details see Naumann's Handbuch der Allgemeinen und Physikalischen Chemie, 360–362. 2 Annalen 36. 1. Pogg. Ann. 52. 262; 53. 446; 56. 371. See also article "Isomorphie," in the Neues Handwörterbuch der Chemie. 3 C. S. Journal Trans. for 1880, 102. The value of (V)MSO, was found to be independent of the nature of M for the dehydrated salts. The difference (V)MSO ̧¤H2O−(V)MSO, gave the increase in (V) for xH2O added to the salts. The following results were obtained. [(V)S=(V) MSO4, (V) S.xH2O=(V) MSO.≈H2O.] Hence the value of (V)MSO,H,O is influenced in a different degree by each of the molecules of water which combines with the salt; or, it may be said, that the water molecules contribute in unequal degrees towards the total value of (V). Clarke' has compared the differences between (V) for hydrated and (V) for dehydrated salts, belonging to two classes of compounds. In the first class, where M = Ca, Sr, Ba, Mg, Cu, Fe, or Co, and x varies from 2 to 6, the mean value of (V) MCl2H2O − (V) MCl1⁄2 χ was found to be = 13.76 (with a maximum value of 15'0, and a minimum of 12.5). The second class comprised various hydrated oxides and hydroxides, viz. B2OззH2O, IO¿H2O, KOH2O, CuOH2O, SÃOH2O, BaOH,O, In this class the value of the difference (V) oxide xH2O - (V) oxide varied from 7'4 to 19'4. χ If S represent one of the chlorides belonging to the first class, or one of the oxides belonging to the second class, then, for class I, the formula (V)S xH2O = (V)S+(x. 13·76) gives 1 Amer. Journal of Sci. and Arts, (3). 8. 428. results which agree fairly well with the observed results; but no such simple relation between (V)S xH2O and (V)S can be traced among the results obtained for compounds belonging to class II. But the hydrates of class I belong to the group of compounds containing 'water of crystallisation,' whereas those of class II, or most of them at any rate, belong to the group containing 'water of constitution'; hence, although the results obtained by Thorpe and Watts (loc. cit.) lead to the conclusion that the value of (V)H2O in the salts MC1,H,O is probably different for each addition of H2O, nevertheless Clarke's numbers, taken as a whole, emphasise the difference between 'water of crystallisation' and 'water of constitution,' and shew that the chemical difference implied in these expressions is connected with the relative magnitudes of the spaces occupied by chemically comparable quantities of hydrated salts belonging to each group of compounds. 156. The quotient formula-weight has been treated as an specific gravity empirically determined quantity: incidentally it has been regarded as expressing the volume occupied by a quantity of the compound formulated proportional to the weight of the molecules which form the vapour of that compound. The question is often propounded in papers on 'Specific volumes', whether the volume of an element in the free state is, or is not, identical with the volume of the same element in combination. This question, it seems to me, may be better put in another form. What is the connection between the value of (V) for a given compound, and the nature and arrangement of the atoms which constitute the molecule of that compound? It has been shewn (pars. 152, 153) that the partial value to be assigned to each atom is not a constant quantity; in other words that (V) varies with variations in the arrangement, no less than in the nature of the atoms which form the molecule of the compound for which (V) has been determined. But is there any connection between the variations of (V), the valencies of the atoms on the one hand, and the distribution of the interatomic reactions on the other? From the data concerning isomeric carbon compounds, firstly, containing only saturated polyvalent atoms, and secondly, containing also unsaturated polyvalent atoms, we may conclude, I think, that both connections exist. It seems probable that a decrease in the actual valency of an atom, other things remaining the same, is attended by an increase in the value of (V). But Stædel's investigation (par. 153) shews that the latter value is also modified by the nature of all the atoms in the molecule. If these connections can be made precise, and their nature ascertained by careful investigation, it may become possible to trace relations between the volumes occupied by molecules of defined structure and the energy-differences of these molecules, and perhaps to connect with these, the differences in the values of the refractive, and the rotatory powers, of the same molecules1. If the value of (V) for a compound is regarded from the point of view of the molecular theory, a connection may be traced between this value, and the partial value of (V) for each atom in the molecule of the compound. For it has been shewn by L. Meyer, and by Loschmidt, that the spaces occupied by gaseous molecules (calculated from data based on the transpiration-coefficients of the substances) are connected with the atomic structure of these molecules, in the same general way as has been shewn by Kopp and others to hold in the case of liquid compounds. The Clausian sphere-of-action (wirkungssphäre) of a molecule is the smallest space which the molecule can occupy under given conditions. Changes in these conditions (e.g. change of temperature), changes in the form of the molecule, or changes in the arrangement of the atoms in the molecule, will be accompanied by changes in the 1 We should thus gain clearer conceptions of the properties of atoms as these are exhibited in atomic interactions, and also be able to connect, in a more precise manner than is yet possible, these interactions with the properties of the systems thereby formed. If this view is accepted it is evident that the results obtained by the various physical methods discussed in this, and the preceding section, must have kinetical as well as statical aspects (see book II. chaps. III. and iv.). 2 Annalen, Supplbd. 5. 129. 3 Sitzberichte der K. Akad. zu Wien (math.-naturwiss. classe). 52. (2nd part) 395. See O. E. Meyer's Die Kinetische Theorie der Gase, 216–221. space occupied by the molecule. The relations between the values of these smallest spaces (spheres-of-action) occupied by the molecules of two gases can be calculated, by means of a formula deduced from the general principles of the molecular theory, from observations of the transpiration-coefficients of the gases. Putting the experimentally determined value of (V) as the value of the molecular sphere-of-action of one of the gases, the values of the molecular spheres-of-action of other gases can be found, and compared with those calculated from atomic weight specific gravity Kopp's, Meyer's, and Loschmidt's values for of nitrogen, oxygen, hydrogen1, &c., and from the partial values assigned, by different chemists, to various atoms in determining the total value of (V) for molecules containing these atoms. This is done by O. E. Meyer (loc. cit. pp. 219-221). The observed and calculated values of (V) agree as closely as could be expected, considering that regard has been paid in the calculations solely to volume, whereas the molecular spheresof-action must be conditioned by the form, the diameter, and the length of the molecular systems. Hence there is a wellestablished probability in favour of the conclusion that the partial values assigned to each atom, in determining the total value of (V) for a liquid compound, are proportional to the volumes occupied by these atoms in the gaseous state. But this is just the conclusion drawn from an empirical study of the values of (V) determined for series of liquid compounds. Much work must however be done before precise connections 1 For a description of the determination of this constant for oxygen and other gases from measurements of the transpiration-coefficients of these gases, see L. Meyer, Annalen, Supplbd. 5. 129. * Meyer (loc. cit. pp. 213-216) concludes that probably the atoms in the molecules H., Cl2, O2, N2, HCl, NO, H2O, and H„S are arranged rectilinearly in an open chain; the atoms in the molecules CO, NO, CN, and NH, are arranged in one plane but not rectilinearly; the atoms in the molecule CH, form a sphere; and those in the molecules CH,Cl, CH, C2HCl, and C2HO form oblate spheroids. Boltzmann [Wied. Ann. 18. 309 (also Ber. 16. 772)] has drawn conclusions as to the forms of various molecules, from determinations (chiefly those made by Strecker) of the ratio of specific heat at constant pressure to that at constant volume. |