[1]Except when the volume of the liquid becomes exceedingly small, in which case the surface tension exerts an influence on the vapour pressure.[2]For reasons which will appear later (Chap. IV.), the volume of the vapour is supposed to be large in comparison with that of the solid and liquid.[3]Ramsay and Young,Phil. Trans., 1886, 177. 87.[4]See, more especially, Vogt,Die Silikatschmelzlösungen. (Christiania, 1903, 1904.)[5]Trans. Connecticut Acad., 1874-1878.[6]Lehre von der chemischen Verwandtschaft der Körper, 1777.[7]See Ostwald'sKlassiker, No. 74.[8]Etudes sur les affinités chimiques, 1867; Ostwald'sKlassiker, No. 104.[9]Died April, 1903.[10]For a mathematical treatment of the Phase Rule the reader is referred to the volume in this series on Thermodynamics, by F. G. Donnan.[11]Liebig'sAnnalen, 1873, 170, 192; Ostwald,Lehrbuch, II. 2. 111.[12]The action of gravity and other forces being excluded (see p.5).[13]It may seem as if this were a contradiction to what was said on p.4as to the effect of the addition of ammonia or hydrogen chloride to the system constituted by solid ammonium chloride in contact with its products of dissociation. There is, however, no contradiction, because in the case of ammonium chloride the gaseous phase consists of ammonia and hydrogen chloride in equal proportions, and in adding ammonia or hydrogen chloride alone we are not adding the gaseous phase, but only a constituent of it. Addition of ammonia and hydrogen chloride together in the proportions in which they are combined to form ammonium chloride would cause no change in the equilibrium.[14]The vapour pressure of water in small drops is greater than that of water in mass, and the solubility of a solid is greater when in a state of fine subdivision than when in large pieces (cf.Hulett,Zeitschr. physikal. Chem., 1901, 37. 385).[15]See Ostwald,Lehrbuch, II. 2. 476, 934; Roozeboom,Zeitschr. physikal. Chem., 1894, 15. 150;Heterogene Gleichgewichte, I. p. 16; Wegscheider,Zeitschr. physikal. Chem., 1903, 43. 89.[16]Ostwald,Lehrbuch, II. 2. 478.[17]See also Hoitsema,Zeitschr. physikal. Chem.1895,17. 651.[18]The term "degree of freedom" employed here must not be confused with the same term used to denote the various movements of a gas molecule according to the kinetic theory.[19]Trevor,Jour. Physical Chem., 1902,6. 136.[20]Ostwald,Principles of Inorganic Chemistry, translated by A. Findlay, 2nd edit., p. 7. (Macmillan, 1904.)[21]See the volume in this series onThermodynamicsby F. G. Donnan.[22]Pogg. Annalen, 1844,61.225.[23]Mémoires de l'Acad.,26.751.[24]Phil. Trans.1884,175.461; 1892, A,183.107.[25]Bihang Svenska Akad. Handl.1891,17.I. 1.[26]Abhandl. physikal.-tech. Reichsanstalt, 1900,3.71.[27]Ostwald-Luther,Physiko-chemische Messungen, 2nd edit., p. 156.[28]Annales chim. et phys., 1892 [6],26.425.[29]The vapour pressure of water at 0° has recently been very accurately determined by Thiesen and Scheel (loc. cit.), and found to be 4.579 ± 0.001 mm. of mercury (at 0°), or equal to 0.006025 atm.[30]Juhlin,Bihang Svenska Akad. Handl., 1891,17.I.58. See also Ramsay and Young,loc. cit.[31]Trans. Roy. Soc. Edin., 1849,16.575.[32]Proc. Roy. Soc. Edin., 1850,2, 267.[33]Annalen der Physik, 1899 [3], 68. 564; 1900 [4], 2. 1, 424. See also Dewar,Proc. Roy. Soc., 1880, 30. 533.[34]The pressure of 1 atmosphere is equal to 1.033 kilogm. per sq. cm.; or the pressure of 1 kilogm. per sq. cm. is equal to 0.968 atm.[35]Tammann,loc. cit., 1900, 2. 1, 424; cf. Goossens,Arch. néerland, 1886, 20. 449.[36]J. Thomson,Proc. Roy. Soc., 1874, 22. 28.[37]A field is "enclosed" by two curves when these cut at an angle less than two right angles. It may be useful to remember that an invariant system is represented by apoint, a univariant system by aline, and a bivariant system by anarea.[38]Phil. Trans., 1724, 39. 78.[39]Juhlin,loc. cit., p. 61; cf. Ramsay and Young,loc. cit.: Thiesen and Scheel,loc. cit.[40]This small difference is due to experimental errors in the determination of the vapour pressures; a differential method betrayed no difference between the vapour pressure of ice and of water at 0°.[41]Phil. Mag., 1874 [4],47.447;Proc. Roy. Soc., 1873,22.27.[42]Pogg. Annalen, 1858,103, 206.[43]SeePhil. Trans., 1884,175, 461.[44]This phenomenon of distillation from the supercooled liquid to the solid has been very clearly observed in the case of furfuraldoxime (V. Goldschmidt,Zeitschr. f. Krystallographie, 1897,28.169).[45]Annalen der Physik, 1900 [4],2.1, 424.[46]A similar triple point has been determined by Tammann in the case of phenol (Annalen der Physik, 1902 [4],9.249).[47]Annales chim. et phys., 1821,19.414.[48]Lehmann,Molekularphysik, I. 153.; Arzruni,Physikalische Chemie der Krystalle. (Graham-Otto,Lehrbuch der Chemie, I. 3.)[49]Brodie,Proc. Roy. Soc., 1855,7.24.[50]That solid sulphur does possess a certain vapour pressure has been shown by Hallock, who observed the formation at the ordinary temperature of copper sulphide in a tube containing copper and sulphur (Amer. Jour. Sci., 1889 [3],37.405). See also Zenghelis,Zeitschr. physikal. Chem., 1904,50.219.[51]Zeitschr. für Krystallographie, 1884,8.593.[52]Van't Hoff,Studies on Chemical Dynamics, p. 163.[53]Reicher,loc. cit.See also Tammann,Annalen der Physik, 1899 [3],68.663.[54]Tammann,Annalen der Physik, 1899 [3],68.633.[55]Rec. Trav.Chim. Pays-Bas, 1887,6.314.[56]Cf. van't Hoff,Lectures on Physical Chemistry, I., p. 27 (Arnold).[57]Annalen der Physik, 1899 [3],68.663.[58]Brauns,Jahrbuch für Mineralogie, 1899-1901, 13. Beilage, p. 39.[59]Fritsche,Ber., 1869, 2. 112, 540.[60]De mirabilibus Auscultationibus, Cap. 51 (v.Cohen,Zeitschr. physikal. Chem., 1901,36.513).[61]E. Cohen and C. van Eyk,Zeitschr. physikal. Chem., 1899,30.601; Cohen,ibid., 1900,33.59;35.588; 1901,36.513; Cohen and E. Goldschmidt,ibid., 1904,50.225.[62]Zeitschr. physikal. Chem., 1900, 33, 58.[63]Stortenbeker,Zeitschr. physikal. Chem., 1889,3.11;Rec. Trav. Chim. Pays-Bas, 1888,7.152.[64]Zincke,Ber., 1871,4.576.[65]Ostwald,Zeitschr. physikal. Chem., 1897,22.313.[66]Roozeboom,Das Heterogene Gleichgewicht, I. p. 177.[67]Roozeboom,ibid., p. 179.[68]Schrötter,Pogg. Annalen, 1850,81.276; Troost and Hautefeuille,Annales de Chim. et Phys.1874 [5],2.153;Ann. Scient. École Norm.1868 [2], II. 266.[69]Pedler,Trans. Chem. Soc., 1890,57.599.[70]Brodie,Trans. Chem. Soc., 1853,5,289.[71]This is a familiar fact in the case of the solubility in carbon disulphide.[72]Roozeboom,Das Heterogene Gleichgewicht, I. p. 170.[73]Trans. Chem. Soc., 1899,57.734.[74]Carnelley,Trans. Chem. Soc., 1876,29.489; 1878,33.275. V. Meyer and Riddle,Ber., 1893,26.2443.[75]Riecke,Zeitschr. physikal. Chem., 1890,6.411.[76]Annalen der Physik., 1898 [3],66.492.[77]Zeitschr. physikal. Chem., 1899,28.666.[78]See Naumann,Ber., 1872,4.646; Troost and Hautefeuille,Compt. rend., 1868,66.795; 1868,67.1345; Roozeboom,Das Heterogene Gleichgewicht, I. pp. 62, 171.[79]Mitscherlich,Lieb. Annalen, 1834,12.137; Deville and Troost,Compt. rend., 1863,56.891.[80]Beckmann,Zeitschr. physikal. Chem., 1890,5.79; Hertz,ibid.,6.358.[81]Ber., 1902,35.351.Cf.also, K. Schaum,Annalen der Chem., 1898,300.221; R. Wegscheider and Kaufler,Sitzungsber. kaiserl. Akad. Wissensch. in Wien, 1901,110, II. 606.[82]See also Roozeboom,Das Heterogene Gleichgewicht, I. p. 177.[83]Annales de Chim. et Phys., 1874 [5],2.154.[84]Compt. rend., 1887,104.1505.[85]Compt. rend., 1868,66.795.[86]Phil. Mag., 1884 [5],18.210. See also Roozeboom,Das Heterogene Gleichgewicht, I. p. 177.[87]Brauns,Neues Jahrbuch für Mineralogie, 1900,13.Beilage-Band, p. 39; Roozeboom,Das Heterogene Gleichgewicht, I. p. 181.[88]Monatshefte, 1888,9.435.[89]Gattermann,Ber., 1890,53.1738.[90]Zeitschr. physikal. Chem., 1889,4.468;Annalen der Physik, 1900 [4],2.649.[91]Quincke,Annalen der Physik, 1894 [3],53.613; Tammann,Annalen der Physik, 1901 [4],4.524; 1902,8.103; Rotarski,ibid.,4.528.[92]Annalen der Physik, 1900 [4],2.649.[93]Annalen der Physik, 1902 [4],8.911.[94]See, more especially, O. Lehmann,Annalen der Physik, 1900 [4],2.649; Reinitzer,Sitzungsber. kaiserl. Akad. zu Wien., 1888,94.(2), 719;97.(1), 167; Gattermann,loc. cit.; Schenck,Zeitschr. physikal. Chem., 1897,23.703; 1898,25.337;27.170; 1899,28.280; Schenck and Schneider,ibid., 1899,29.546; Abegg and Seitz,ibid., 1899,29.491; Hulett,ibid., 1899,28.629; Coehn,Zeitschr. Elektrochem., 1904,10.856: Bredig and Schukowsky,ibid., 3419. For a full account of the subject, the reader is referred to the work by Lehmann,Flüssige Kristalle(Engelmann, 1904), or the smaller monograph by Schenck,Kristallinische Flüssigkeiten und flüssige Kristalle(Engelmann, 1905).[95]A. C. de Kock,Zeitschr. physikal. Chem., 1904,48.129.[96]On account of the fact that all grades of rigidity have been realized between the ordinary solid and the liquid state, in the case both of crystalline and amorphous substances, it has been proposed to abandon the terms "solid" and "liquid," and to class bodies as "crystalline" or "amorphous," the passage from the one condition to the other being discontinuous; crystalline bodies possess a certain regular orientation of their molecules and a directive force, while in amorphous bodies these are wanting (see Lehmann,Annalen der Physik, 1900 [4],2.696).[97]Hulett,loc. cit.[98]Roozeboom,Das Heterogene Gleichgewicht, I. p. 144. See also Schenck,Kristallinische Flüssigkeiten und flüssige Kristalle, p. 8 (Engelmann, 1904).[99]The possible number of triple points in a one-component system is given by the expressionn(n- 1)(n- 2),1.2.3wherenis the number of phases (Riecke,Zeitschr. physikal. Chem., 1890,6, 411). The number of triple points, therefore, increases very rapidly as the number of possible phases increases.[100]Duhem,Zeitschr. physikal. Chem., 1891,8. 371.Cf.Roozeboom,Das Heterogene Gleichgewicht, p. 94 ff.[101]Roozeboom,Das Heterogene Gleichgewicht, I. p. 99.[102]Roozeboom,Zeitschr. physikal. Chem., 1888,2. 474.[103]These changes can be predicted quantitatively by means of the thermodynamic equation,dp=Q,dtT(v2-v1)provided the specific volumes of the phases are known, and the heat effect which accompanies the transformation of one phase into the other.[104]Studies on Chemical Dynamics, translated by Ewan, p. 218.[105]Le Chatelier,Compt. rend., 1884,99. 786.[106]SeePrinciples of Inorganic Chemistry, translated by Findlay, 2nd edit., p. 133. (Macmillan, 1904.)[107]Roozeboom,Zeitschr. physikal. Chem., 1888,2. 474.[108]Roozeboom,Das Heterogene Gleichgewicht, I. p. 189.[109]Roozeboom,Das Heterogene Gleichgewicht, I. p. 125. See also Zawidski,Zeitschr. physikal. Chem., 1904,47.727; van Eyk,ibid., 1905,51.720.[110]Roberts-Austen,Proc. Roy. Soc.,63.454; Spring,Zeitschr. physikal. Chem., 1894,15.65. See also p.35.[111]Ramsay and Young,Phil. Trans., 1884,175.461; Allen,Trans. Chem. Soc., 1900,77.413.[112]Ramsay and Young,Phil. Trans.1886,177.87.[113]This is exemplified in the well-known experiment with the cryophorus.[114]Tammann has, however, found that the fusion curve (solid in contact with liquid) of phosphonium chloride can be followed up to temperatures above the critical point (Arch. néer., 1901 [2],6.244).[115]Phil. Mag., 1886,21.33. See also S. A. Moss,Physical Review, 1903,16.356.[116]This is found also in the case of bismuth. See Tammann,Zeitschr. anorgan. Chem., 1904,40.54.[117]See p. 57,footnote.[118]Pogg. Annalen, 1850,81.562.[119]Barus,Amer. Jour. Sci., 1892,42.125; Mack,Compt. rend., 1898,127.361; Hulett,Zeitschr. physikal. Chem., 1899,38.629.[120]Annalen der Physik, 1899 [3],68.553, 629; 1900 [4],1.275;2.1;3.161. See also Tammann,Kristallisieren und Schmelzen(Leipzig, 1903).[121]Ostwald,Lehrbuch, II.2. 373; Poynting,Phil. Mag., 1881 [5],12. 2; Planck,Wied. Annalen, 1882,15. 446.[122]Bakhuis Roozeboom,Das Heterogene Gleichgewicht, I. p. 91.[123]Lussana,Il nuovo Cimento, 1895 [4],1. 105.[124]Tammann,Zeitschr. physikal. Chem., 1903,46. 818.[125]Foote,Zeitschr. physikal. Chem., 1900,33. 740.[126]Ostwald,Zeitschr. physikal. Chem., 1897,22. 289.[127]Van't Hoff,Arch, néer., 1901,6. 471.[128]See, for example, the determinations of the solubility of rhombic and monoclinic sulphur, by J. Meyer,Zeitschr. anorg. Chem., 1902,33. 140.[129]Zeitschr. physikal. Chem., 1899,32. 506.[130]Kastle and Reed,Amer. Chem. Jour., 1902,27. 209.[131]Zeitschr. physikal. Chem., 1900,35. 581.[132]Compt. rend., 1882,95. 1278; 1884,97. 1298, 1366, 1433.[133]Zeitschr. physikal. Chem., 1893,12. 545.[134]Sitzungsber. Wiener Akad., 1894,103. IIa. 226.[135]Zeitschr. physikal. Chem.,23-29. See also Küster,ibid.,25-28.[136]Zeitschr. physikal. Chem., 1897,24. 152.[137]Ibid., 1898,27. 585.[138]See W. Guertler,Zeitschr. anorgan. Chem., 1904,40. 268; Tammann,Zeitschr. Elektrochem., 1904,10. 532.[139]E. von Pickardt,Zeitschr. physikal. Chem., 1902,42. 17.[140]Zeitschr. physikal. Chem., 1904,48. 467.[141]M. Padoa,Accad. Lincei, Atti, 1904,13. 329.[142]Deville,Compt. rend., 1852,34. 561; Payen,ibid., 1852,34. 508; Debray,ibid., 1858,46. 576. It has also been found by Jaffé (Zeitschr. physikal. Chem., 1903,43. 465) that when spontaneous crystallization from solution occurs, the less stable form always separates first when purification has been carried sufficiently far.[143]Brauns,Neues Jahrbuch für Mineralogie, 1899,13. (Beilage Band) 84.[144]Lehrbuch, II.2. 445. See alsoPrinciples of Inorganic Chemistry, 2nd edit., p. 210 ff.[145]Schaum and Schönbeck,Annalen der Physik, 1902 [4],8. 652. See also Chr. Füchtbauer,Zeitschr. physikal. Chem., 1904,48. 549.[146]Ramsay and Young,Phil. Trans., 1886,177. 87.[147]See volume in this series onChemical Dynamics, by Dr. J. W. Mellor.[148]Isambert,Compt. rend., 1881,92. 919; 1882,94. 958; 1883,96. 643. Walker and Lumsden,Jour. Chem. Soc., 1897,71. 428.[149]Compt. rend., 1867,64. 603.[150]Compt. rend., 1883,102. 1243.[151]Compt. rend., 1868,66, 1259.[152]Horstmann,Ber., 1876,9. 749.[153]Loc. cit.[154]For the reasons for choosing anhydrous salt and water instead of salt hydrate and water as components, see p.14.[155]See Ostwald,Lehrbuch, II.2.527.[156]Ostwald,Lehrbuch, II.2.538.[157]Zeitschr. physikal. Chem., 1889,4. 43.[158]Ber., 1876,9. 749.[159]See, for example, van't Hoff,Lectures on Theoretical and Physical Chemistry, I. p. 62 (Arnold).[160]Jour. Chem. Soc., 1877,32. 395.[161]Hoitsema,Zeitschr. physikal. Chem., 1895,17. 1.[162]Zeitschr. physikal. Chem., 1887,1. 5; 1895,17. 52.[163]It is important to powder the salt, since otherwise the dehydration of the hydrate and the production of equilibrium occurs with comparatively great tardiness.[164]A chemical individual is a substance which persists as a phase of constant composition when the conditions of temperature, pressure, and composition of the other phases present, undergo continuous alteration within certain limits—the limits of existence of the substance (Wald,Zeitschr. physikal. Chem., 1897,24. 648).[165]Van't Hoff,Zeitschr. physikal. Chem., 1890,5. 323; Ostwald,Lehrbuch, I. 606.[166]That mercury does dissolve in water can be argued from analogy, say, with mercury and bromonaphthalene. At the ordinary temperature these two liquids appear to be quite insoluble in one another, but at a temperature of 280° the mercury dissolves in appreciable quantity; for on heating a tube containing bromonaphthalene over mercury the latter sublimesthroughthe liquid bromonaphthalene and condenses on the upper surface of the tube.[167]Phil. Mag., 1884, [5],18. 22; 495.[168]Wied. Annalen, 1886,28. 305.[169]Zeitschr. physikal. Chem., 1898,26. 433.[170]Rothmund,loc. cit.[171]Rothmund,loc. cit.[172]A similar behaviour is found in the case of diethylamine and water (R. T. Lattey,Phil. Mag., 1905, [6],10, 397).[173]C. S. Hudson,Zeitschr. physikal. Chem., 1904,47. 113.[174]Konowaloff,Wied. Annalen, 1881,14. 219. Ostwald,Lehrbuch, II.2. 687. Bancroft,Phase Rule, p. 96.[175]Konowaloff,loc. cit.[176]Roozeboom,Zeitschr. physikal. Chem., 1891,8. 526;Rec. Trav. Chim. Pays-Bas, 1884,3. 38.[177]Konowaloff,loc. cit.Cf. Bancroft,Phase Rule, p. 100.[178]Phil. Mag., 1884 [5],18. 503.[179]See, for example, Walker,Introduction to Physical Chemistry, 3rd edit., p. 86 (Macmillan, 1903). Consult also Young,Fractional Distillation(Macmillan, 1903), or Kuenen,Verdampfung und Verflüssigung von Gemischen(Barth, 1906), where the subject is fully treated.[180]Since this is the only phase of variable composition present.[181]E. von Stackelberg,Zeitschr. physikal. Chem., 1896,20. 337. If the change of volume which accompanies solution, and the heat effect are known, the quantitative change of the solubility with the pressure can be calculated (Braun,Zeitschr. physikal. Chem., 1887,1. 259).[182]Van't Hoff,Arch. néerland.1901 [2],6. 471.[183]Tilden and Shenstone,Phil. Trans.1884,175. 23; Hulett and Allen,Jour. Amer. Chem. Soc.1902,24. 667; Andreä,Jour. prak. Chem.137. 474; Lumsden,Jour. Chem. Soc., 1902,81. 350; Mylius and v. Wrochem,Ber.1900,33. 3689.[184]E. von Stackelberg,Zeitschr. physikal. Chem.1896,20. 159; 1898,26. 533; Lumsden,Jour. Chem. Soc., 1902,81. 350; Holsboer,Zeitschr. physikal. Chem., 1902,39. 691.[185]Reicher and van Deventer,Zeitschr. physikal. Chem.1890,5. 559; cf. Ostwald,Lehrbuch, II.2. 803.[186]It has been shown that the formula of Ramsay and Young (p.66) can be applied (with certain restrictions) to the interpolation and extrapolation of the solubility curve of a substance provided two (or three) points on the curve are known. In this case T, T1, etc., refer to the temperatures at which the two substances—one the solubility curve of which is known, the other the solubility curve of which is to be calculated—have equal solubilities, instead of, as in the previous case, equal vapour pressures. (Findlay,Proc. Roy. Soc., 1902,69. 471;Zeitschr. physikal. Chem., 1903,42. 110.)[187]W. Müller and P. Kaufmann,Zeitschr. physikal. Chem.1903,42. 497.[188]W. O. Rabe,Zeitschr. physikal. Chem., 1901,38. 175.[189]With regard to the limits of supersaturation and the spontaneous crystallization of the solute from supersaturated solutions, see Jaffé,Zeitschr. physikal. Chem., 1903,43. 565, and the very interesting paper by Miers and Isaac,Trans. Chem. Soc., 1906,89. 413.[190]Annales chim. phys., 1894 [7],2. 524.[191]Phil. Trans., 1884,175. 23.[192]Hissink,Zeitschr. physikal. Chem., 1900,32. 543.[193]Zeitschr. physikal. Chem., 1903,43. 313.[194]Guthrie,Phil. Mag., 1875, [4],49. 1; 1884, [5],17. 462.[195]See Roloff,Zeitschr. physikal. Chem., 1895,17. 325; Guthrie,loc. cit.[196]Guthrie,Phil. Mag.,loc. cit.Cf. Ostwald,Lehrbuch, II.2. 843.[197]Guthrie,Phil. Mag., 1875 [4],49. 269.[198]Ber., 1877,20. 2223.[199]Silz-Ber. Wien. Akad., 1880,81. II. 1058.[200]Guthrie,Phil. Mag., 1875 [4],49. 206.[201]If in the neighbourhood of the cryohydric point solution should be accompanied by an evolution of heat, then as the solubility would in that case increase with fall of temperature, salt would pass into solution.[202]Walker,Zeitschr. physikal. Chem., 1890,5. 193.[203]Zeitschr. physikal. Chem., 1897,23. 418.[204]Provided the solid nitrile is not present in too great excess.[205]Wied. Annalen, 1886,28. 328. Cf. Ostwald,Lehrbuch, II.2. 872.[206]Walker,Zeitschr. physikal. Chem., 1890,5. 193. Schreinemakers,ibid., 1897,23. 417. Roozeboom,Rec. trav. chim. Pays-Bays, 1889,8. 257. Bruner,Zeitschr. physikal. Chem., 1897,23. 542.[207]Van't Hoff,Lectures on Theoretical Chemistry, I. p. 42. Ostwald,Lehrbuch, II.2. 824.[208]Ostwald,Principles of Inorganic Chemistry, translated by A. Findlay, 2nd edit., p. 453 (Macmillan, 1904); Skirrow and Calvert,Zeitschr. physikal. Chem., 1901,37. 217.[209]VideLoewel,Annales chim. phys., 1857 [3],49. 32. Cf. Löwenherz,Zeitschr. physikal. Chem., 1895,18. 82.[210]Loewel,loc. cit.Gay-Lussac,Annales chim. phys., 1819,11. 296. For the solubility at higher temperatures, see Tilden and Shenstone,Phil. Trans., 1884,175. 23. Étard,Annales chim. phys., 1894 [7],2. 548.[211]Richards,Zeitschr. physikal. Chem., 1898,26. 690; Richards and Wells,ibid., 1903,43. 465. This temperature is not quite the same as that of thequadruple pointanhydrous salt—hydrated salt—solution—vapour, because the latter is the temperature at which the system is under the pressure of its own vapour. Since, however, the influence of pressure on the solubility is very slight (p.107), the position of the two points will not be greatly different. The quadruple point was found by Cohen (Zeitschr. physikal. Chem., 1894,14. 90) to be 32.6° and 30.8 mm. of mercury.[212]Van't Hoff and van Deventer,Zeitschr. physikal. Chem., 1887,1. 185. Cf. Cohen,ibid., 1894,14. 88.[213]Debray,Compt. rend., 1868,66. 194.[214]Richards,Zeitschr. physikal. Chem., 1898,26. 690. A number of other salt hydrates, having transition-points ranging from 20° to 78°, which might be used for the same purpose, have been given by Richards and Churchill,ibid., 1899,28. 313.[215]Zeitschr. physikal. Chem., 1903,46. 818.[216]Van't Hoff,Lectures on Physical Chemistry,I. p. 67.[217]Cohen,Zeitschr. physikal. Chem., 1894,14. 90.[218]Ziz,Schweigger's Journal, 1815,15. 166. See Ostwald,Lehrbuch, II.2. 717.[219]See, for example, the solubility determinations published inWissenschaftliche Abhandl. der physikalisch-technischen Reichsanstalt, Vol. III., or in theBerichte, for the years 1897-1901.[220]Meusser,Ber., 1901,34. 2440.[221]Mylius and von Wrochem,Ber., 1900,33. 3693.[222]Walker and Fyffe,Jour. Chem. Soc., 1903,83. 180.[223]Monatshefte, 1887,8. 601.[224]The equilibria between calcium chloride and water have been most completely studied by Roozeboom (Zeitschr. physikal. Chem., 1889,4. 31).[225]Hammerl,Sitzungsber. Wien. Akad., 2teAbteil, 1878,78. 59. Roozeboom,Zeitschr. physikal. Chem., 1889,4. 31.[226]Lidbury,Zeitschr. physikal. Chem., 1902,39. 453. The curvature at the melting point is all the greater the more the compound is dissociated into its components in the liquid state. If the compound iscompletely undissociated, even in the vapour phase, the two branches of the curve willintersect, (e.g.pyridine and methyl iodide; Aten,Versl. Konink. Akad. Wetensch. Amsterdam, 1905,13. 462). The smaller the degree of dissociation, therefore, the sharper will be the bend. (See Stortenbeker,Zeitschr. physikal. Chem., 1892,10. 194.) From the extent of flattening of the curve, it is also possible, with some degree of approximation, to calculate the degree of dissociation of the substance in the fused state. (See Roozeboom and Aten,Zeitschr. physikal. Chem., 1905,53. 463; Kremann,Zeitschr. Elektrochem., 1906,12. 259.)[227]See Roozeboom,Zeitschr. physikal. Chem., 1889,4. 31.[228]Tammann,Wied. Annalen, 1899,68. 577.[229]Duhem,Journ. Physical Chem., 1898,2. 31.[230]Gibbs,Trans. Conn. Acad.,3. 155; Saurel,Journ. Phys. Chem., 1901,5. 35.[231]In the case of the fusion of a compound of two components with formation of a liquid phase of the same composition, the temperature is a maximum; in the case of liquid mixtures of constant boiling-point, the temperature may be a minimum (p.105).[232]Roozeboom,Zeitschr. physikal. Chem., 1892,10. 477. The formula of ferric chloride has been doubled, in order to avoid fractions in the expression of the water of crystallization.[233]Roozeboom,Zeitschr. physikal. Chem., 1892,10. 477.[234]A similar series of hydrates is formed by zinc chloride and water (Dietz and Mylius,Zeitschr. anorg. Chem., 1905,44. 209).[235]Meyerhoffer,Ber., 1897,30. 1810.[236]Walden,Ber., 1899,32. 2863.[237]Zeitschr. physikal. Chem., 1903,42. 432.[238]This composition was also confirmed by measurements of the vapour pressure (cf. p.90).[239]Since all substances are no doubt volatile to a certain extent at some temperature, it is to be understood here that the substances are appreciably volatile at the temperature of the experiment.[240]For a general discussion of the partial pressures in a system of two components, see Bancroft,Journ. Physical Chem., 1899,3. 1.[241]Zeitschr. physikal. Chem., 1889,3. 11;Rec. trav. chim. Pays-Bas, 1888,7. 152.[242]The composition of a solution is represented symbolically by placing a double wavy line between the symbols of the components, and indicating the number of atoms present in the ordinary manner: thus, IwavyClxrepresents a solution containingxatoms of chlorine to one atom of iodine (Roozeboom,Zeitschr. physikal. Chem., 1888,2. 450).[243]Since iodine monochloride in the liquid state is only very slightly dissociated, the bend at C is very sharp (see p.147, footnote). See also the investigation of the system pyridine and methyl iodide (Aten,Versl. Konink. Akad. Wetensch. Amsterdam, 1905,13. 462).[244]This upper branch of the curve is not shown in the figure, as the ordinate corresponding to 30° would be very great.[245]Stortenbeker,Zeitschr. physikal. Chem., 1889,3. 22.[246]Ramsay and Young,Journ. Chem. Soc., 1886,49. 458.[247]Van't Hoff,Lectures on Physical Chemistry, I. p. 77 (Arnold).[248]This is different from what we found in the case of non-volatile solutes (p.126). In the present case, thepartial pressureof the iodine in the vapour will be lowered by addition of chlorine, but thetotal pressureis increased.[249]The diminution of volume is supposed to be carried out at constant temperature. The pressure and the composition of the phases must, therefore, remain unchanged, and only the relative amounts of these can undergo alteration.[250]At pointbthe ratio of chlorine to iodine in the solution is less than in the monochloride, so that by the separation of this the excess of chlorine yielded by the condensation of the vapour is removed.[251]Roozeboom,Rec. trav. chim. Pays-Bas, 1884,3. 29; 1885,4. 65;Zeitschr. physikal. Chem., 1888,2. 450.[252]Two curves "enclose" a field when they form with one another an angle less than two right angles.[253]Roozeboom,Zeitschr. physikal. Chem.,loc. cit.[254]Van't Hoff,Zeitschr. physikal. Chem., 1890,5. 323.[255]Bancroft has proposed to restrict the term "occlusion" to the formation of solid solutions, and to apply "adsorption" only to effects which are primarily due to surface tension. Such a distinction, however, would probably be very difficult to carry through, for although adsorption may, in large measure, be due to surface tension, the behaviour of adsorbed substances is similar to that of substances existing in solid solutions.[256]Tammann,Wied. Annalen, 1897,63. 16;Zeitschr. physikal. Chem., 1898,27. 323.[257]See, for example, Chappuis,Wied. Annalen, 1881,12. 161; Joulin,Annal. chim. phys., 1881, [5],22. 398; Kayser,Wied. Annalen, 1881,12. 526.[258]Hoitsema,Zeitschr. physikal. Chem., 1895,17. 1.[259]Annales chim. phys., 1874, [5],2. 279.[260]Hoitsema,Zeitschr. physikal. Chem., 1895,17. 1; Dewar,Phil. Mag., 1874, [4],47, 324, 342; Mond, Ramsay and Shields,Proc. Royal Soc., 1897,62. 290.[261]Loc. cit.[262]It is noteworthy that the form of curve obtained for hydrogen and palladium bears a striking resemblance to that for the dehydration of colloids containing absorbed water,e.g.silicic acid (videvan Bemmelen,Zeitschr. anorg. Chem., 1897-1900. Cf. Zacharias,Zeitschr. physikal. Chem., 1902,39. 480).[263]Zeitschr. physikal. Chem., 1890,5. 322.[264]Küster,Zeitschr. physikal. Chem., 1895,17. 367. Bodländer,Neues Jahrbuch f. Mineralogie, 1898-99, Beilage Band,12. 92.[265]Bruni and Padoa,Atti Accad. Lincei, 1902 [5],11. 1; 565.[266]Roozeboom,Zeitschr. physikal. Chem., 1899,30. 385; Bruni,Rend. Accad. Lincei, 1898,2. 138, 347. For a general account of "solid solutions" the reader is referred to Bruni, "Ueber feste Lösungen" (Ahrens'sche Sammlung), and to Bodländer,loc. cit.For the formation and transformation of liquid mixed crystals, see A. C. de Kock,Zeitschr. physikal. Chem., 1904,48. 129.[267]In discussing the various systems which may be obtained here, Roozeboom (loc. cit.) made use of the variation of the thermodynamic potential (p.29) with the concentration. In spite of the advantages which such a treatment affords, the temperature-concentration diagram has been adopted as being more readily understood and as more suitable for an elementary discussion of the subject.[268]These curves are also called the "liquidus" and the "solidus" curve respectively.[269]Küster,Zeitschr. physikal. Chem., 1895,17. 360.[270]Küster,ibid., 1891,8. 589.[271]It should be remarked that the behaviour described here will hold strictly only when the solid mixed crystals undergo change sufficiently rapidly to be always in equilibrium with the liquid. This, however, is not always the case (see Reinders,Zeitschr. physikal. Chem., 1900,32. 494; van Wyk,Zeitschr. anorg. Chem., 1905,48. 25), and complete solidification will not in this case take place at the temperature corresponding with the linedcin Fig. 50, but only at a lower temperature.
[1]Except when the volume of the liquid becomes exceedingly small, in which case the surface tension exerts an influence on the vapour pressure.
[2]For reasons which will appear later (Chap. IV.), the volume of the vapour is supposed to be large in comparison with that of the solid and liquid.
[3]Ramsay and Young,Phil. Trans., 1886, 177. 87.
[4]See, more especially, Vogt,Die Silikatschmelzlösungen. (Christiania, 1903, 1904.)
[5]Trans. Connecticut Acad., 1874-1878.
[6]Lehre von der chemischen Verwandtschaft der Körper, 1777.
[7]See Ostwald'sKlassiker, No. 74.
[8]Etudes sur les affinités chimiques, 1867; Ostwald'sKlassiker, No. 104.
[9]Died April, 1903.
[10]For a mathematical treatment of the Phase Rule the reader is referred to the volume in this series on Thermodynamics, by F. G. Donnan.
[11]Liebig'sAnnalen, 1873, 170, 192; Ostwald,Lehrbuch, II. 2. 111.
[12]The action of gravity and other forces being excluded (see p.5).
[13]It may seem as if this were a contradiction to what was said on p.4as to the effect of the addition of ammonia or hydrogen chloride to the system constituted by solid ammonium chloride in contact with its products of dissociation. There is, however, no contradiction, because in the case of ammonium chloride the gaseous phase consists of ammonia and hydrogen chloride in equal proportions, and in adding ammonia or hydrogen chloride alone we are not adding the gaseous phase, but only a constituent of it. Addition of ammonia and hydrogen chloride together in the proportions in which they are combined to form ammonium chloride would cause no change in the equilibrium.
[14]The vapour pressure of water in small drops is greater than that of water in mass, and the solubility of a solid is greater when in a state of fine subdivision than when in large pieces (cf.Hulett,Zeitschr. physikal. Chem., 1901, 37. 385).
[15]See Ostwald,Lehrbuch, II. 2. 476, 934; Roozeboom,Zeitschr. physikal. Chem., 1894, 15. 150;Heterogene Gleichgewichte, I. p. 16; Wegscheider,Zeitschr. physikal. Chem., 1903, 43. 89.
[16]Ostwald,Lehrbuch, II. 2. 478.
[17]See also Hoitsema,Zeitschr. physikal. Chem.1895,17. 651.
[18]The term "degree of freedom" employed here must not be confused with the same term used to denote the various movements of a gas molecule according to the kinetic theory.
[19]Trevor,Jour. Physical Chem., 1902,6. 136.
[20]Ostwald,Principles of Inorganic Chemistry, translated by A. Findlay, 2nd edit., p. 7. (Macmillan, 1904.)
[21]See the volume in this series onThermodynamicsby F. G. Donnan.
[22]Pogg. Annalen, 1844,61.225.
[23]Mémoires de l'Acad.,26.751.
[24]Phil. Trans.1884,175.461; 1892, A,183.107.
[25]Bihang Svenska Akad. Handl.1891,17.I. 1.
[26]Abhandl. physikal.-tech. Reichsanstalt, 1900,3.71.
[27]Ostwald-Luther,Physiko-chemische Messungen, 2nd edit., p. 156.
[28]Annales chim. et phys., 1892 [6],26.425.
[29]The vapour pressure of water at 0° has recently been very accurately determined by Thiesen and Scheel (loc. cit.), and found to be 4.579 ± 0.001 mm. of mercury (at 0°), or equal to 0.006025 atm.
[30]Juhlin,Bihang Svenska Akad. Handl., 1891,17.I.58. See also Ramsay and Young,loc. cit.
[31]Trans. Roy. Soc. Edin., 1849,16.575.
[32]Proc. Roy. Soc. Edin., 1850,2, 267.
[33]Annalen der Physik, 1899 [3], 68. 564; 1900 [4], 2. 1, 424. See also Dewar,Proc. Roy. Soc., 1880, 30. 533.
[34]The pressure of 1 atmosphere is equal to 1.033 kilogm. per sq. cm.; or the pressure of 1 kilogm. per sq. cm. is equal to 0.968 atm.
[35]Tammann,loc. cit., 1900, 2. 1, 424; cf. Goossens,Arch. néerland, 1886, 20. 449.
[36]J. Thomson,Proc. Roy. Soc., 1874, 22. 28.
[37]A field is "enclosed" by two curves when these cut at an angle less than two right angles. It may be useful to remember that an invariant system is represented by apoint, a univariant system by aline, and a bivariant system by anarea.
[38]Phil. Trans., 1724, 39. 78.
[39]Juhlin,loc. cit., p. 61; cf. Ramsay and Young,loc. cit.: Thiesen and Scheel,loc. cit.
[40]This small difference is due to experimental errors in the determination of the vapour pressures; a differential method betrayed no difference between the vapour pressure of ice and of water at 0°.
[41]Phil. Mag., 1874 [4],47.447;Proc. Roy. Soc., 1873,22.27.
[42]Pogg. Annalen, 1858,103, 206.
[43]SeePhil. Trans., 1884,175, 461.
[44]This phenomenon of distillation from the supercooled liquid to the solid has been very clearly observed in the case of furfuraldoxime (V. Goldschmidt,Zeitschr. f. Krystallographie, 1897,28.169).
[45]Annalen der Physik, 1900 [4],2.1, 424.
[46]A similar triple point has been determined by Tammann in the case of phenol (Annalen der Physik, 1902 [4],9.249).
[47]Annales chim. et phys., 1821,19.414.
[48]Lehmann,Molekularphysik, I. 153.; Arzruni,Physikalische Chemie der Krystalle. (Graham-Otto,Lehrbuch der Chemie, I. 3.)
[49]Brodie,Proc. Roy. Soc., 1855,7.24.
[50]That solid sulphur does possess a certain vapour pressure has been shown by Hallock, who observed the formation at the ordinary temperature of copper sulphide in a tube containing copper and sulphur (Amer. Jour. Sci., 1889 [3],37.405). See also Zenghelis,Zeitschr. physikal. Chem., 1904,50.219.
[51]Zeitschr. für Krystallographie, 1884,8.593.
[52]Van't Hoff,Studies on Chemical Dynamics, p. 163.
[53]Reicher,loc. cit.See also Tammann,Annalen der Physik, 1899 [3],68.663.
[54]Tammann,Annalen der Physik, 1899 [3],68.633.
[55]Rec. Trav.Chim. Pays-Bas, 1887,6.314.
[56]Cf. van't Hoff,Lectures on Physical Chemistry, I., p. 27 (Arnold).
[57]Annalen der Physik, 1899 [3],68.663.
[58]Brauns,Jahrbuch für Mineralogie, 1899-1901, 13. Beilage, p. 39.
[59]Fritsche,Ber., 1869, 2. 112, 540.
[60]De mirabilibus Auscultationibus, Cap. 51 (v.Cohen,Zeitschr. physikal. Chem., 1901,36.513).
[61]E. Cohen and C. van Eyk,Zeitschr. physikal. Chem., 1899,30.601; Cohen,ibid., 1900,33.59;35.588; 1901,36.513; Cohen and E. Goldschmidt,ibid., 1904,50.225.
[62]Zeitschr. physikal. Chem., 1900, 33, 58.
[63]Stortenbeker,Zeitschr. physikal. Chem., 1889,3.11;Rec. Trav. Chim. Pays-Bas, 1888,7.152.
[64]Zincke,Ber., 1871,4.576.
[65]Ostwald,Zeitschr. physikal. Chem., 1897,22.313.
[66]Roozeboom,Das Heterogene Gleichgewicht, I. p. 177.
[67]Roozeboom,ibid., p. 179.
[68]Schrötter,Pogg. Annalen, 1850,81.276; Troost and Hautefeuille,Annales de Chim. et Phys.1874 [5],2.153;Ann. Scient. École Norm.1868 [2], II. 266.
[69]Pedler,Trans. Chem. Soc., 1890,57.599.
[70]Brodie,Trans. Chem. Soc., 1853,5,289.
[71]This is a familiar fact in the case of the solubility in carbon disulphide.
[72]Roozeboom,Das Heterogene Gleichgewicht, I. p. 170.
[73]Trans. Chem. Soc., 1899,57.734.
[74]Carnelley,Trans. Chem. Soc., 1876,29.489; 1878,33.275. V. Meyer and Riddle,Ber., 1893,26.2443.
[75]Riecke,Zeitschr. physikal. Chem., 1890,6.411.
[76]Annalen der Physik., 1898 [3],66.492.
[77]Zeitschr. physikal. Chem., 1899,28.666.
[78]See Naumann,Ber., 1872,4.646; Troost and Hautefeuille,Compt. rend., 1868,66.795; 1868,67.1345; Roozeboom,Das Heterogene Gleichgewicht, I. pp. 62, 171.
[79]Mitscherlich,Lieb. Annalen, 1834,12.137; Deville and Troost,Compt. rend., 1863,56.891.
[80]Beckmann,Zeitschr. physikal. Chem., 1890,5.79; Hertz,ibid.,6.358.
[81]Ber., 1902,35.351.Cf.also, K. Schaum,Annalen der Chem., 1898,300.221; R. Wegscheider and Kaufler,Sitzungsber. kaiserl. Akad. Wissensch. in Wien, 1901,110, II. 606.
[82]See also Roozeboom,Das Heterogene Gleichgewicht, I. p. 177.
[83]Annales de Chim. et Phys., 1874 [5],2.154.
[84]Compt. rend., 1887,104.1505.
[85]Compt. rend., 1868,66.795.
[86]Phil. Mag., 1884 [5],18.210. See also Roozeboom,Das Heterogene Gleichgewicht, I. p. 177.
[87]Brauns,Neues Jahrbuch für Mineralogie, 1900,13.Beilage-Band, p. 39; Roozeboom,Das Heterogene Gleichgewicht, I. p. 181.
[88]Monatshefte, 1888,9.435.
[89]Gattermann,Ber., 1890,53.1738.
[90]Zeitschr. physikal. Chem., 1889,4.468;Annalen der Physik, 1900 [4],2.649.
[91]Quincke,Annalen der Physik, 1894 [3],53.613; Tammann,Annalen der Physik, 1901 [4],4.524; 1902,8.103; Rotarski,ibid.,4.528.
[92]Annalen der Physik, 1900 [4],2.649.
[93]Annalen der Physik, 1902 [4],8.911.
[94]See, more especially, O. Lehmann,Annalen der Physik, 1900 [4],2.649; Reinitzer,Sitzungsber. kaiserl. Akad. zu Wien., 1888,94.(2), 719;97.(1), 167; Gattermann,loc. cit.; Schenck,Zeitschr. physikal. Chem., 1897,23.703; 1898,25.337;27.170; 1899,28.280; Schenck and Schneider,ibid., 1899,29.546; Abegg and Seitz,ibid., 1899,29.491; Hulett,ibid., 1899,28.629; Coehn,Zeitschr. Elektrochem., 1904,10.856: Bredig and Schukowsky,ibid., 3419. For a full account of the subject, the reader is referred to the work by Lehmann,Flüssige Kristalle(Engelmann, 1904), or the smaller monograph by Schenck,Kristallinische Flüssigkeiten und flüssige Kristalle(Engelmann, 1905).
[95]A. C. de Kock,Zeitschr. physikal. Chem., 1904,48.129.
[96]On account of the fact that all grades of rigidity have been realized between the ordinary solid and the liquid state, in the case both of crystalline and amorphous substances, it has been proposed to abandon the terms "solid" and "liquid," and to class bodies as "crystalline" or "amorphous," the passage from the one condition to the other being discontinuous; crystalline bodies possess a certain regular orientation of their molecules and a directive force, while in amorphous bodies these are wanting (see Lehmann,Annalen der Physik, 1900 [4],2.696).
[97]Hulett,loc. cit.
[98]Roozeboom,Das Heterogene Gleichgewicht, I. p. 144. See also Schenck,Kristallinische Flüssigkeiten und flüssige Kristalle, p. 8 (Engelmann, 1904).
[99]The possible number of triple points in a one-component system is given by the expression
wherenis the number of phases (Riecke,Zeitschr. physikal. Chem., 1890,6, 411). The number of triple points, therefore, increases very rapidly as the number of possible phases increases.
[100]Duhem,Zeitschr. physikal. Chem., 1891,8. 371.Cf.Roozeboom,Das Heterogene Gleichgewicht, p. 94 ff.
[101]Roozeboom,Das Heterogene Gleichgewicht, I. p. 99.
[102]Roozeboom,Zeitschr. physikal. Chem., 1888,2. 474.
[103]These changes can be predicted quantitatively by means of the thermodynamic equation,
provided the specific volumes of the phases are known, and the heat effect which accompanies the transformation of one phase into the other.
[104]Studies on Chemical Dynamics, translated by Ewan, p. 218.
[105]Le Chatelier,Compt. rend., 1884,99. 786.
[106]SeePrinciples of Inorganic Chemistry, translated by Findlay, 2nd edit., p. 133. (Macmillan, 1904.)
[107]Roozeboom,Zeitschr. physikal. Chem., 1888,2. 474.
[108]Roozeboom,Das Heterogene Gleichgewicht, I. p. 189.
[109]Roozeboom,Das Heterogene Gleichgewicht, I. p. 125. See also Zawidski,Zeitschr. physikal. Chem., 1904,47.727; van Eyk,ibid., 1905,51.720.
[110]Roberts-Austen,Proc. Roy. Soc.,63.454; Spring,Zeitschr. physikal. Chem., 1894,15.65. See also p.35.
[111]Ramsay and Young,Phil. Trans., 1884,175.461; Allen,Trans. Chem. Soc., 1900,77.413.
[112]Ramsay and Young,Phil. Trans.1886,177.87.
[113]This is exemplified in the well-known experiment with the cryophorus.
[114]Tammann has, however, found that the fusion curve (solid in contact with liquid) of phosphonium chloride can be followed up to temperatures above the critical point (Arch. néer., 1901 [2],6.244).
[115]Phil. Mag., 1886,21.33. See also S. A. Moss,Physical Review, 1903,16.356.
[116]This is found also in the case of bismuth. See Tammann,Zeitschr. anorgan. Chem., 1904,40.54.
[117]See p. 57,footnote.
[118]Pogg. Annalen, 1850,81.562.
[119]Barus,Amer. Jour. Sci., 1892,42.125; Mack,Compt. rend., 1898,127.361; Hulett,Zeitschr. physikal. Chem., 1899,38.629.
[120]Annalen der Physik, 1899 [3],68.553, 629; 1900 [4],1.275;2.1;3.161. See also Tammann,Kristallisieren und Schmelzen(Leipzig, 1903).
[121]Ostwald,Lehrbuch, II.2. 373; Poynting,Phil. Mag., 1881 [5],12. 2; Planck,Wied. Annalen, 1882,15. 446.
[122]Bakhuis Roozeboom,Das Heterogene Gleichgewicht, I. p. 91.
[123]Lussana,Il nuovo Cimento, 1895 [4],1. 105.
[124]Tammann,Zeitschr. physikal. Chem., 1903,46. 818.
[125]Foote,Zeitschr. physikal. Chem., 1900,33. 740.
[126]Ostwald,Zeitschr. physikal. Chem., 1897,22. 289.
[127]Van't Hoff,Arch, néer., 1901,6. 471.
[128]See, for example, the determinations of the solubility of rhombic and monoclinic sulphur, by J. Meyer,Zeitschr. anorg. Chem., 1902,33. 140.
[129]Zeitschr. physikal. Chem., 1899,32. 506.
[130]Kastle and Reed,Amer. Chem. Jour., 1902,27. 209.
[131]Zeitschr. physikal. Chem., 1900,35. 581.
[132]Compt. rend., 1882,95. 1278; 1884,97. 1298, 1366, 1433.
[133]Zeitschr. physikal. Chem., 1893,12. 545.
[134]Sitzungsber. Wiener Akad., 1894,103. IIa. 226.
[135]Zeitschr. physikal. Chem.,23-29. See also Küster,ibid.,25-28.
[136]Zeitschr. physikal. Chem., 1897,24. 152.
[137]Ibid., 1898,27. 585.
[138]See W. Guertler,Zeitschr. anorgan. Chem., 1904,40. 268; Tammann,Zeitschr. Elektrochem., 1904,10. 532.
[139]E. von Pickardt,Zeitschr. physikal. Chem., 1902,42. 17.
[140]Zeitschr. physikal. Chem., 1904,48. 467.
[141]M. Padoa,Accad. Lincei, Atti, 1904,13. 329.
[142]Deville,Compt. rend., 1852,34. 561; Payen,ibid., 1852,34. 508; Debray,ibid., 1858,46. 576. It has also been found by Jaffé (Zeitschr. physikal. Chem., 1903,43. 465) that when spontaneous crystallization from solution occurs, the less stable form always separates first when purification has been carried sufficiently far.
[143]Brauns,Neues Jahrbuch für Mineralogie, 1899,13. (Beilage Band) 84.
[144]Lehrbuch, II.2. 445. See alsoPrinciples of Inorganic Chemistry, 2nd edit., p. 210 ff.
[145]Schaum and Schönbeck,Annalen der Physik, 1902 [4],8. 652. See also Chr. Füchtbauer,Zeitschr. physikal. Chem., 1904,48. 549.
[146]Ramsay and Young,Phil. Trans., 1886,177. 87.
[147]See volume in this series onChemical Dynamics, by Dr. J. W. Mellor.
[148]Isambert,Compt. rend., 1881,92. 919; 1882,94. 958; 1883,96. 643. Walker and Lumsden,Jour. Chem. Soc., 1897,71. 428.
[149]Compt. rend., 1867,64. 603.
[150]Compt. rend., 1883,102. 1243.
[151]Compt. rend., 1868,66, 1259.
[152]Horstmann,Ber., 1876,9. 749.
[153]Loc. cit.
[154]For the reasons for choosing anhydrous salt and water instead of salt hydrate and water as components, see p.14.
[155]See Ostwald,Lehrbuch, II.2.527.
[156]Ostwald,Lehrbuch, II.2.538.
[157]Zeitschr. physikal. Chem., 1889,4. 43.
[158]Ber., 1876,9. 749.
[159]See, for example, van't Hoff,Lectures on Theoretical and Physical Chemistry, I. p. 62 (Arnold).
[160]Jour. Chem. Soc., 1877,32. 395.
[161]Hoitsema,Zeitschr. physikal. Chem., 1895,17. 1.
[162]Zeitschr. physikal. Chem., 1887,1. 5; 1895,17. 52.
[163]It is important to powder the salt, since otherwise the dehydration of the hydrate and the production of equilibrium occurs with comparatively great tardiness.
[164]A chemical individual is a substance which persists as a phase of constant composition when the conditions of temperature, pressure, and composition of the other phases present, undergo continuous alteration within certain limits—the limits of existence of the substance (Wald,Zeitschr. physikal. Chem., 1897,24. 648).
[165]Van't Hoff,Zeitschr. physikal. Chem., 1890,5. 323; Ostwald,Lehrbuch, I. 606.
[166]That mercury does dissolve in water can be argued from analogy, say, with mercury and bromonaphthalene. At the ordinary temperature these two liquids appear to be quite insoluble in one another, but at a temperature of 280° the mercury dissolves in appreciable quantity; for on heating a tube containing bromonaphthalene over mercury the latter sublimesthroughthe liquid bromonaphthalene and condenses on the upper surface of the tube.
[167]Phil. Mag., 1884, [5],18. 22; 495.
[168]Wied. Annalen, 1886,28. 305.
[169]Zeitschr. physikal. Chem., 1898,26. 433.
[170]Rothmund,loc. cit.
[171]Rothmund,loc. cit.
[172]A similar behaviour is found in the case of diethylamine and water (R. T. Lattey,Phil. Mag., 1905, [6],10, 397).
[173]C. S. Hudson,Zeitschr. physikal. Chem., 1904,47. 113.
[174]Konowaloff,Wied. Annalen, 1881,14. 219. Ostwald,Lehrbuch, II.2. 687. Bancroft,Phase Rule, p. 96.
[175]Konowaloff,loc. cit.
[176]Roozeboom,Zeitschr. physikal. Chem., 1891,8. 526;Rec. Trav. Chim. Pays-Bas, 1884,3. 38.
[177]Konowaloff,loc. cit.Cf. Bancroft,Phase Rule, p. 100.
[178]Phil. Mag., 1884 [5],18. 503.
[179]See, for example, Walker,Introduction to Physical Chemistry, 3rd edit., p. 86 (Macmillan, 1903). Consult also Young,Fractional Distillation(Macmillan, 1903), or Kuenen,Verdampfung und Verflüssigung von Gemischen(Barth, 1906), where the subject is fully treated.
[180]Since this is the only phase of variable composition present.
[181]E. von Stackelberg,Zeitschr. physikal. Chem., 1896,20. 337. If the change of volume which accompanies solution, and the heat effect are known, the quantitative change of the solubility with the pressure can be calculated (Braun,Zeitschr. physikal. Chem., 1887,1. 259).
[182]Van't Hoff,Arch. néerland.1901 [2],6. 471.
[183]Tilden and Shenstone,Phil. Trans.1884,175. 23; Hulett and Allen,Jour. Amer. Chem. Soc.1902,24. 667; Andreä,Jour. prak. Chem.137. 474; Lumsden,Jour. Chem. Soc., 1902,81. 350; Mylius and v. Wrochem,Ber.1900,33. 3689.
[184]E. von Stackelberg,Zeitschr. physikal. Chem.1896,20. 159; 1898,26. 533; Lumsden,Jour. Chem. Soc., 1902,81. 350; Holsboer,Zeitschr. physikal. Chem., 1902,39. 691.
[185]Reicher and van Deventer,Zeitschr. physikal. Chem.1890,5. 559; cf. Ostwald,Lehrbuch, II.2. 803.
[186]It has been shown that the formula of Ramsay and Young (p.66) can be applied (with certain restrictions) to the interpolation and extrapolation of the solubility curve of a substance provided two (or three) points on the curve are known. In this case T, T1, etc., refer to the temperatures at which the two substances—one the solubility curve of which is known, the other the solubility curve of which is to be calculated—have equal solubilities, instead of, as in the previous case, equal vapour pressures. (Findlay,Proc. Roy. Soc., 1902,69. 471;Zeitschr. physikal. Chem., 1903,42. 110.)
[187]W. Müller and P. Kaufmann,Zeitschr. physikal. Chem.1903,42. 497.
[188]W. O. Rabe,Zeitschr. physikal. Chem., 1901,38. 175.
[189]With regard to the limits of supersaturation and the spontaneous crystallization of the solute from supersaturated solutions, see Jaffé,Zeitschr. physikal. Chem., 1903,43. 565, and the very interesting paper by Miers and Isaac,Trans. Chem. Soc., 1906,89. 413.
[190]Annales chim. phys., 1894 [7],2. 524.
[191]Phil. Trans., 1884,175. 23.
[192]Hissink,Zeitschr. physikal. Chem., 1900,32. 543.
[193]Zeitschr. physikal. Chem., 1903,43. 313.
[194]Guthrie,Phil. Mag., 1875, [4],49. 1; 1884, [5],17. 462.
[195]See Roloff,Zeitschr. physikal. Chem., 1895,17. 325; Guthrie,loc. cit.
[196]Guthrie,Phil. Mag.,loc. cit.Cf. Ostwald,Lehrbuch, II.2. 843.
[197]Guthrie,Phil. Mag., 1875 [4],49. 269.
[198]Ber., 1877,20. 2223.
[199]Silz-Ber. Wien. Akad., 1880,81. II. 1058.
[200]Guthrie,Phil. Mag., 1875 [4],49. 206.
[201]If in the neighbourhood of the cryohydric point solution should be accompanied by an evolution of heat, then as the solubility would in that case increase with fall of temperature, salt would pass into solution.
[202]Walker,Zeitschr. physikal. Chem., 1890,5. 193.
[203]Zeitschr. physikal. Chem., 1897,23. 418.
[204]Provided the solid nitrile is not present in too great excess.
[205]Wied. Annalen, 1886,28. 328. Cf. Ostwald,Lehrbuch, II.2. 872.
[206]Walker,Zeitschr. physikal. Chem., 1890,5. 193. Schreinemakers,ibid., 1897,23. 417. Roozeboom,Rec. trav. chim. Pays-Bays, 1889,8. 257. Bruner,Zeitschr. physikal. Chem., 1897,23. 542.
[207]Van't Hoff,Lectures on Theoretical Chemistry, I. p. 42. Ostwald,Lehrbuch, II.2. 824.
[208]Ostwald,Principles of Inorganic Chemistry, translated by A. Findlay, 2nd edit., p. 453 (Macmillan, 1904); Skirrow and Calvert,Zeitschr. physikal. Chem., 1901,37. 217.
[209]VideLoewel,Annales chim. phys., 1857 [3],49. 32. Cf. Löwenherz,Zeitschr. physikal. Chem., 1895,18. 82.
[210]Loewel,loc. cit.Gay-Lussac,Annales chim. phys., 1819,11. 296. For the solubility at higher temperatures, see Tilden and Shenstone,Phil. Trans., 1884,175. 23. Étard,Annales chim. phys., 1894 [7],2. 548.
[211]Richards,Zeitschr. physikal. Chem., 1898,26. 690; Richards and Wells,ibid., 1903,43. 465. This temperature is not quite the same as that of thequadruple pointanhydrous salt—hydrated salt—solution—vapour, because the latter is the temperature at which the system is under the pressure of its own vapour. Since, however, the influence of pressure on the solubility is very slight (p.107), the position of the two points will not be greatly different. The quadruple point was found by Cohen (Zeitschr. physikal. Chem., 1894,14. 90) to be 32.6° and 30.8 mm. of mercury.
[212]Van't Hoff and van Deventer,Zeitschr. physikal. Chem., 1887,1. 185. Cf. Cohen,ibid., 1894,14. 88.
[213]Debray,Compt. rend., 1868,66. 194.
[214]Richards,Zeitschr. physikal. Chem., 1898,26. 690. A number of other salt hydrates, having transition-points ranging from 20° to 78°, which might be used for the same purpose, have been given by Richards and Churchill,ibid., 1899,28. 313.
[215]Zeitschr. physikal. Chem., 1903,46. 818.
[216]Van't Hoff,Lectures on Physical Chemistry,I. p. 67.
[217]Cohen,Zeitschr. physikal. Chem., 1894,14. 90.
[218]Ziz,Schweigger's Journal, 1815,15. 166. See Ostwald,Lehrbuch, II.2. 717.
[219]See, for example, the solubility determinations published inWissenschaftliche Abhandl. der physikalisch-technischen Reichsanstalt, Vol. III., or in theBerichte, for the years 1897-1901.
[220]Meusser,Ber., 1901,34. 2440.
[221]Mylius and von Wrochem,Ber., 1900,33. 3693.
[222]Walker and Fyffe,Jour. Chem. Soc., 1903,83. 180.
[223]Monatshefte, 1887,8. 601.
[224]The equilibria between calcium chloride and water have been most completely studied by Roozeboom (Zeitschr. physikal. Chem., 1889,4. 31).
[225]Hammerl,Sitzungsber. Wien. Akad., 2teAbteil, 1878,78. 59. Roozeboom,Zeitschr. physikal. Chem., 1889,4. 31.
[226]Lidbury,Zeitschr. physikal. Chem., 1902,39. 453. The curvature at the melting point is all the greater the more the compound is dissociated into its components in the liquid state. If the compound iscompletely undissociated, even in the vapour phase, the two branches of the curve willintersect, (e.g.pyridine and methyl iodide; Aten,Versl. Konink. Akad. Wetensch. Amsterdam, 1905,13. 462). The smaller the degree of dissociation, therefore, the sharper will be the bend. (See Stortenbeker,Zeitschr. physikal. Chem., 1892,10. 194.) From the extent of flattening of the curve, it is also possible, with some degree of approximation, to calculate the degree of dissociation of the substance in the fused state. (See Roozeboom and Aten,Zeitschr. physikal. Chem., 1905,53. 463; Kremann,Zeitschr. Elektrochem., 1906,12. 259.)
[227]See Roozeboom,Zeitschr. physikal. Chem., 1889,4. 31.
[228]Tammann,Wied. Annalen, 1899,68. 577.
[229]Duhem,Journ. Physical Chem., 1898,2. 31.
[230]Gibbs,Trans. Conn. Acad.,3. 155; Saurel,Journ. Phys. Chem., 1901,5. 35.
[231]In the case of the fusion of a compound of two components with formation of a liquid phase of the same composition, the temperature is a maximum; in the case of liquid mixtures of constant boiling-point, the temperature may be a minimum (p.105).
[232]Roozeboom,Zeitschr. physikal. Chem., 1892,10. 477. The formula of ferric chloride has been doubled, in order to avoid fractions in the expression of the water of crystallization.
[233]Roozeboom,Zeitschr. physikal. Chem., 1892,10. 477.
[234]A similar series of hydrates is formed by zinc chloride and water (Dietz and Mylius,Zeitschr. anorg. Chem., 1905,44. 209).
[235]Meyerhoffer,Ber., 1897,30. 1810.
[236]Walden,Ber., 1899,32. 2863.
[237]Zeitschr. physikal. Chem., 1903,42. 432.
[238]This composition was also confirmed by measurements of the vapour pressure (cf. p.90).
[239]Since all substances are no doubt volatile to a certain extent at some temperature, it is to be understood here that the substances are appreciably volatile at the temperature of the experiment.
[240]For a general discussion of the partial pressures in a system of two components, see Bancroft,Journ. Physical Chem., 1899,3. 1.
[241]Zeitschr. physikal. Chem., 1889,3. 11;Rec. trav. chim. Pays-Bas, 1888,7. 152.
[242]The composition of a solution is represented symbolically by placing a double wavy line between the symbols of the components, and indicating the number of atoms present in the ordinary manner: thus, IwavyClxrepresents a solution containingxatoms of chlorine to one atom of iodine (Roozeboom,Zeitschr. physikal. Chem., 1888,2. 450).
[243]Since iodine monochloride in the liquid state is only very slightly dissociated, the bend at C is very sharp (see p.147, footnote). See also the investigation of the system pyridine and methyl iodide (Aten,Versl. Konink. Akad. Wetensch. Amsterdam, 1905,13. 462).
[244]This upper branch of the curve is not shown in the figure, as the ordinate corresponding to 30° would be very great.
[245]Stortenbeker,Zeitschr. physikal. Chem., 1889,3. 22.
[246]Ramsay and Young,Journ. Chem. Soc., 1886,49. 458.
[247]Van't Hoff,Lectures on Physical Chemistry, I. p. 77 (Arnold).
[248]This is different from what we found in the case of non-volatile solutes (p.126). In the present case, thepartial pressureof the iodine in the vapour will be lowered by addition of chlorine, but thetotal pressureis increased.
[249]The diminution of volume is supposed to be carried out at constant temperature. The pressure and the composition of the phases must, therefore, remain unchanged, and only the relative amounts of these can undergo alteration.
[250]At pointbthe ratio of chlorine to iodine in the solution is less than in the monochloride, so that by the separation of this the excess of chlorine yielded by the condensation of the vapour is removed.
[251]Roozeboom,Rec. trav. chim. Pays-Bas, 1884,3. 29; 1885,4. 65;Zeitschr. physikal. Chem., 1888,2. 450.
[252]Two curves "enclose" a field when they form with one another an angle less than two right angles.
[253]Roozeboom,Zeitschr. physikal. Chem.,loc. cit.
[254]Van't Hoff,Zeitschr. physikal. Chem., 1890,5. 323.
[255]Bancroft has proposed to restrict the term "occlusion" to the formation of solid solutions, and to apply "adsorption" only to effects which are primarily due to surface tension. Such a distinction, however, would probably be very difficult to carry through, for although adsorption may, in large measure, be due to surface tension, the behaviour of adsorbed substances is similar to that of substances existing in solid solutions.
[256]Tammann,Wied. Annalen, 1897,63. 16;Zeitschr. physikal. Chem., 1898,27. 323.
[257]See, for example, Chappuis,Wied. Annalen, 1881,12. 161; Joulin,Annal. chim. phys., 1881, [5],22. 398; Kayser,Wied. Annalen, 1881,12. 526.
[258]Hoitsema,Zeitschr. physikal. Chem., 1895,17. 1.
[259]Annales chim. phys., 1874, [5],2. 279.
[260]Hoitsema,Zeitschr. physikal. Chem., 1895,17. 1; Dewar,Phil. Mag., 1874, [4],47, 324, 342; Mond, Ramsay and Shields,Proc. Royal Soc., 1897,62. 290.
[261]Loc. cit.
[262]It is noteworthy that the form of curve obtained for hydrogen and palladium bears a striking resemblance to that for the dehydration of colloids containing absorbed water,e.g.silicic acid (videvan Bemmelen,Zeitschr. anorg. Chem., 1897-1900. Cf. Zacharias,Zeitschr. physikal. Chem., 1902,39. 480).
[263]Zeitschr. physikal. Chem., 1890,5. 322.
[264]Küster,Zeitschr. physikal. Chem., 1895,17. 367. Bodländer,Neues Jahrbuch f. Mineralogie, 1898-99, Beilage Band,12. 92.
[265]Bruni and Padoa,Atti Accad. Lincei, 1902 [5],11. 1; 565.
[266]Roozeboom,Zeitschr. physikal. Chem., 1899,30. 385; Bruni,Rend. Accad. Lincei, 1898,2. 138, 347. For a general account of "solid solutions" the reader is referred to Bruni, "Ueber feste Lösungen" (Ahrens'sche Sammlung), and to Bodländer,loc. cit.For the formation and transformation of liquid mixed crystals, see A. C. de Kock,Zeitschr. physikal. Chem., 1904,48. 129.
[267]In discussing the various systems which may be obtained here, Roozeboom (loc. cit.) made use of the variation of the thermodynamic potential (p.29) with the concentration. In spite of the advantages which such a treatment affords, the temperature-concentration diagram has been adopted as being more readily understood and as more suitable for an elementary discussion of the subject.
[268]These curves are also called the "liquidus" and the "solidus" curve respectively.
[269]Küster,Zeitschr. physikal. Chem., 1895,17. 360.
[270]Küster,ibid., 1891,8. 589.
[271]It should be remarked that the behaviour described here will hold strictly only when the solid mixed crystals undergo change sufficiently rapidly to be always in equilibrium with the liquid. This, however, is not always the case (see Reinders,Zeitschr. physikal. Chem., 1900,32. 494; van Wyk,Zeitschr. anorg. Chem., 1905,48. 25), and complete solidification will not in this case take place at the temperature corresponding with the linedcin Fig. 50, but only at a lower temperature.