Chapter XXVI: Appendix: Experimental Determination of the Transition Point (2)

[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] _Vide_ Loewel, _Annales chim. phys._, 1857 [3], 49. 32. Cf. Loewenherz, _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. Etard, _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 the _quadruple point_ anhydrous 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 32.6deg 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 20deg to 78deg, 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 in _Wissenschaftliche Abhandl. der physikalisch-technischen Reichsanstalt_, Vol. III., or in the _Berichte_, 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._, 2^{te} Abteil, 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 is _completely undissociated_, even in the vapour phase, the two branches of the curve will _intersect_, (_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, I [wavy] Cl_{_x_} represents a solution containing _x_ atoms 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 30deg 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, the _partial pressure_ of the iodine in the vapour will be lowered by addition of chlorine, but the _total pressure_ is 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 point _b_ the 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 (_vide_ van Bemmelen, _Zeitschr. anorg. Chem._, 1897-1900. Cf. Zacharias, _Zeitschr. physikal. Chem._, 1902, 39. 480).

[263] _Zeitschr. physikal. Chem._, 1890, 5. 322.

[264] Kuester, _Zeitschr. physikal. Chem._, 1895, 17. 367. Bodlaender, _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 Loesungen_" (Ahrens'sche Sammlung), and to Bodlaender, _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] Kuester, _Zeitschr. physikal. Chem._, 1895, 17. 360.

[270] Kuester, _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 line _dc_ in Fig. 50, but only at a lower temperature.

[272] Adriani, _Zeitschr. physikal. Chem._, 1900, 33. 469.

[273] Reinders, _Zeitschr. physikal. Chem._, 1900, 32. 494.

[274] Hissink, _Zeitschr. physikal. Chem._, 1900, 32. 542.

[275] Van Eyk, _Zeitschr. physikal. Chem._, 1899, 30. 430.

[276] Cady, _Journ. Physical. Chem._, 1899, 3. 127.

[277] See Roberts-Austen and Stansfield, _Rapports du congres international de physique_, 1900, I. 363.

[278] Heycock and Neville, _Proc. Roy. Soc._, 1903, 71. 409. For the partial liquefaction of mixed crystals on cooling, see also A. C. de Kock (_Zeitschr. physikal. Chem._, 1904, 48. 129).

[279] Armstrong, _Watt's Dictionary of Chemistry_ (Morley and Muir), III., p. 88. See also Lowry, _Jour. Chem. Soc._, 1899, 75. 211.

[280] See Bancroft, _Journ. Physical Chem._, 1898, 2. 143; Roozeboom, _Zeitschr. physikal. Chem._, 1899, 28. 288.

[281] Hylotropic substances are such as can undergo transformation into other substances of the same composition (Ostwald, _Lehrbuch_, II. 2. 298).

[282] Also called Equilibrium Point (Lowry).

[283] For a discussion of these systems, see Roozeboom, _Zeitschr. physikal. Chem._, _loc. cit_.

[284] See Bancroft, _loc. cit._, p. 147; Wegscheider, _Sitzungsber. Wiener Akad._, 1902, 110. 908.

[285] Reference may be made here to the term "stability limit," introduced by Knorr (_Annalen_, 1896, 293. 88) to indicate that temperature above which liquefaction and isomeric change takes place. As employed by Knorr and others, the term does not appear to have a very precise meaning, since it is used to denote, not the temperature at which these changes can occur, but the temperature at which the change is rapid (vide _Annalen_, 1896, 293. 91; 1899, 306. 334); and the introduction of an indefinite velocity of change renders the temperature of the stability limit also somewhat indefinite. The definiteness of the term is also not a little diminished by the fact that the "limit" can be altered by means of catalytic agents. Since, as we have seen, the stable modification can always undergo isomeric change and liquefy at temperatures above the natural freezing point, but not below that point; and, further, the less stable modification can undergo isomeric transformation and liquefy at temperatures above the eutectic point, but will not liquefy at temperatures below that; it seems to the author that it would be more precise to identify these two points--the natural freezing point and the eutectic point--which are not altered by catalytic agents, with the "stability limits" of the stable and unstable modification respectively. A perfectly definite meaning would thereby be given to the term. In the case of those substances which do not undergo appreciable isomeric change at the temperature of the melting point, the stability limits would be the points G and H, Fig. 60.

[286] Cameron, _Journ. Physical Chem._, 1898, 2. 409.

[287] Carveth, _Journ. Phys. Chem._, 1898, 2. 159. See also Dutoit and Fath, _Journ. chim. phys_., 1903, 1. 358; Findlay, _Trans. Chem. Soc._, 1904, 85. 403.

[288] Hollmann, _Zeitschr. physikal. Chem._, 1903, 43. 129.

[289] For other examples of the application of the Phase Rule to isomeric substances, see _Journ. Physical Chem._, vols. 2. _et seq._; Findlay, _Trans. Chem. Soc._, 1904, 85. 403.

[290] See Roozeboom, _Zeitschr. physikal. Chem._, 1899, 30. 410.

[291] See also Saposchnikoff, _Zeitschr. physikal. Chem._, 49. 688; Kremann, _Monatshefte_, 1904, 25. 1215, 1271, 1311.

[292] J. C. Philip, _Journ. Chem. Soc._, 1903, 83. 821.

[293] _Cf._ also Paterno and Ampolla, _Gazzetta chim. ital._, 1897, 27. 481.

[294] Philip, _loc. cit._, p. 826.

[295] Philip, _loc. cit._, p. 829. Compare curves for iodine monochloride, Fig. 42, p. 162.

[296] Kuriloff, _Zeitschr. physikal. Chem._, 1897, 23. 676.

[297] Ladenburg, _Ber._, 1895, 28. 163; 1991.

[298] Roozeboom, _Zeitschr. physikal. Chem._, 1899, 28. 494; Adriani, _ibid._, 1900, 33. 453.

[299] Adriani, _Zeitschr. physikal. Chem._, 1900, 33. 453.

[300] A. Findlay and Miss E. Hickmans.

[301] Kipping and Pope, _Journ. Chem. Soc._, 1897, 71. 993.

[302] See Roozeboom, _Zeitschr. physikal. Chem._, 1899, 28. 512; Adriani, _ibid._, 1900, 33. 473; 1901, 36. 168.

[303] In this connection reference should be made more especially to the paper by Roberts-Austen and Stansfield, "Sur la constitution des alliages metalliques," in the _Rapports du congres international de physique_, 1900, I. 363; J. A. Mathews, _Journ. of the Franklin Inst._, 1902; Gautier, _Compt. rend._, 1896, 123. 109; Roberts-Austen, "Reports of the Alloys Research Committee," in _Journ. Inst. Mechan. Engineers_, from 1891 to 1904; and the papers by Heycock and Neville, published in the _Journ. Chem. Soc._, and the _Trans. Roy. Soc._ since 1897; also Neville, _Reports of the British Association_, 1900, p. 131. Reference must also be made to the important metallographic investigations by Tammann and his pupils, and of Kurnakoff (_Zeitschr. anorgan. Chem._, vol. 40 and onwards), and also to those of Shepherd, _Journ. Physical Chem._, 8. A bibliography of the alloys is given in _Zeitschr. anorgan. Chem._, 1903, 35. 249.

[304] Kurnakoff and Puschin, _Zeitschr. anorgan. Chem._, 1902, 30. 104.

[305] Gautier, _Bull. Soc. d'Encouragement_, 1896 [5], 1. 1312.

[306] Heycock and Neville, _Phil. Trans._, 1900, 194. 201.

[307] Gautier, _loc. cit._ See also Roberts-Austen and Rose, _Proc. Roy. Soc._, 1903, 71. 161.

[308] Heycock and Neville, _Journ. Chem. Soc._, 1897, 71. 414.

[309] See Roberts-Austen, _Introduction to Metallurgy_, 5th edit., p. 102; Bakhuis Roozeboom, _Journ. Iron and Steel Inst._, 1900, II. 311; _Zeitschr. physikal. Chem._, 1900, 34. 437; von Jueptner, _Siderology_, p. 223 (translation by C. Salter); van't Hoff, _Zinn, Gips, und Stahl_, p. 24, or _Acht Vortraege ueber physikalische Chemie_, p. 37. Further, Roozeboom, _Zeitschr. Elektrochem._, 1904, 10. 489; E. Heyn, _ibid._, p. 491; Carpenter and Keeling, _Journ. Iron and Steel Inst._, 1904, 65. 224.

[310] The melting point of pure iron is given by Carpenter and Keeling (_Journ. Iron and Steel Inst._, 1904, 65. 224) as 1505deg.

[311] _Zeitschr. fuer Elektrochem._, 1904, 10. 491.

[312] See also Hiorns, _Journ. Soc. Chem. Ind._, 1906, 25. 50.

[313] Bancroft, _Jour. Physical Chem._, 1902, 6. 178; Bell and Taber, _ibid._, 1906, 10. 120.

[314] The method to be followed when the third component enters into the solid phase will be explained later.

[315] Tammann, _Zeitschr. anorg. Chem._, 1903, 37. 303; 1905, 45. 24. Reference may be made here to the registering pyrometer of Kurnakoff, _Zeitschr. anorg. Chem._, 1904, 42. 184.

[316] In this connection, see Doelter, _Physikalisch-chemisch Mineralogie_ (Barth, 1901); Meyerhoffer, _Zeitschr. f. Kristallographie_, 1902, 36. 593; Guthrie, _Phil. Mag._, 1884 [5], 17. 479; Le Chatelier, _Compt. rend._, 1900, 130. 85; and especially E. Baur, _Zeitschr. physikal. Chem._, 1903, 42. 567; J. H. L. Vogt, _Zeitschr. Elektrochem._, 1903, 9. 852, and _Die Silikatschmelzloesungen_, Parts I. and II. (Christiania, 1903, 1904). See also N. V. Kultascheff, _Zeitschr. anorg. Chem._, 1903, 35. 187.

[317] G. G. Stokes, _Proc. Roy. Soc._, 1891, 49. 174; Gibbs, _Trans. Conn. Acad._, 1876, 3. 176; Roozeboom, _Zeitschr. physikal. Chem._, 1894, 15. 147.

[318] This figure has been taken from Ostwald's _Lehrbuch_, II. 2. 984.

[319] Roozeboom, _Zeitschr. physikal. Chem._, 1893, 12. 369.

[320] C. R. A. Wright, _Proc. Roy. Soc._, 1891, 49. 174; 1892, 50. 375.

[321] The distribution coefficient will not remain constant because, apart from other reasons, the mutual solubility of chloroform and water is altered by the addition of the acid.

[322] Bancroft, _Physical Review_, 1895, 3. 21; Schreinemakers, _Zeitschr. physikal. Chem._, 1897, 23. 652, and subsequent volumes.

[323] C. R. A. Wright, _Proc. Roy. Soc._, 1889-1893.

[324] C. R. A. Wright, _Proc. Roy. Soc._, 1892, 50. 390.

[325] Bodlaender, _Berg- und Huettenmaenn. Ztg._, 1897, 56. 331.

[326] C. R. A. Wright, _Proc. Roy. Soc._, _loc. cit._

[327] Schreinemakers, _Zeitschr. physikal. Chem._, 1900, 33. 78.

[328] Schreinemakers, _Zeitschr. physikal. Chem._, 1898, 27. 95.

[329] Schreinemakers, _Zeitschr. physikal. Chem._, 1899, 29. 577.

[330] Schreinemakers, _Zeitschr. physikal. Chem._, 1898, 25. 543.

[331] Charpy, _Compt. rend._, 1898, 126. 1569. Compare the curves for the system KNO_{3}--NaNO_{3}--LiNO_{3} (H. R. Carveth, _Journ. Physical Chem._, 1898, 2. 209). Also alloys of Pb--Sn--Bi (E. S. Shepherd, _Journ. Physical Chem._, 1902, 6. 527).

[332] It should be remembered that in the triangular diagram a _line_ parallel to one of the sides indicates, at a given temperature, a constant amount of the component represented by the opposite corner of the triangle; and, hence, points in a _plane_, parallel to one face of a right prism, will indicate for different temperatures, variation in the amounts of two components, but constancy in the amount of the third.

[333] _Gazzetta chim. ital._, 1898, 28. II. 520.

[334] Bruni, _Gazzetta chim. ital._, 1898, 28. II. 508; 1900, 30. I. 35.

[335] _Zeitschr. physikal. Chem._, 1900, 36. 168.

[336] For a discussion of these systems, see van't Hoff, _Bildung und Spaltung von Doppelsalzen_ (Leipzig, 1897).

[337] Van Leeuwen, _Zeitschr. physikal. Chem._, 1897, 23. 35.

[338] Meyerhoffer, _Zeitschr. physikal. Chem._, 1889, 3. 336; 1890, 5. 97.

[339] Reicher, _Zeitschr. physikal. Chem._, 1887, 1. 220.

[340] For other examples of the formation and decomposition of double salts at a transition point, the reader is referred to the work by van't Hoff, already cited, on the _Bildung und Spaltung von Doppelsalzen_; or to Bancroft, _Phase Rule_, p. 180.

[341] Bancroft, _Phase Rule_, p. 183.

[342] Roozeboom, _Zeitschr. physikal. Chem._, 1888, 2. 514.

[343] The influence of pressure on the transition point in the case of tachydrite has been determined by van't Hoff, Kenrick, and Dawson (_Zeitschr. physikal. Chem._, 1901, 39. 27, 34; van't Hoff, _Zur Bildung der ozeanischen Salzablagerungen_, I. p. 66--Brunswick, 1905). This salt is formed from magnesium chloride and calcium chloride at 22deg, in accordance with the equation--

2MgCl_{2}.6H_{2}O + CaCl_{2}.6H_{2}O = Mg_{2}CaCl_{6}.12H_{2}O + 6H_{2}O

Increase of pressure raises the transition point, because the formation of tachydrite is accompanied by increase of volume; the elevation being 0.016deg for an increase of pressure of 1 atm. The number calculated from the theoretical formula (p. 57) is 0.013deg for 1 atm.

If one calculates the influence of the pressure of sea-water on the temperature of formation of tachydrite (which is of interest on account of the natural occurrence of this salt), it is found that a depth of water of 1500 metres, exerting a pressure of 180 atm., would alter the temperature of formation of tachydrite by only 3deg. The effect is, therefore, comparatively unimportant.

[344] Roozeboom, _Zeitschr. physical. Chem._, 1887, 1. 227.

[345] _Zeitschr. physical. Chem._, 1887, 1. 227.

[346] Van't Hoff and Mueller, _Ber._, 1898, 31. 2206.

[347] Van't Hoff and van Deventer, _Zeitschr. physikal. Chem._, 1887, 1. 165.

[348] For a full discussion of the solubility relations of sodium ammonium racemate, see van't Hoff, _Bildung und Spaltung von Doppelsalzen_, p. 81.

[349] _Annales chim. phys._, 1848 [3], 24. 442.

[350] See Van't Hoff and van Deventer, _Zeitschr. phys. Chem._, 1887, 1. 165.

[351] Meyerhoffer, _Zeitschr. physikal. Chem._, 1890, 5. 121.

[352] Roozeboom, _Zeitschr. physikal. Chem._, 1888, 2. 518.

[353] Meyerhoffer, _Zeitschr. physikal. Chem._, 1890, 5. 109. On the importance of the transition interval in the case of optically active substances, see Meyerhoffer, _Ber._, 1904, 37. 2604.

[354] In connection with this chapter, see, more especially, van't Hoff, _Bildung und Spaltung von Doppelsalzen_, p. 3, _ff._; Roozeboom, _Zeitschr. physikal Chem._, 1892, 10. 158; Bancroft, _Phase Rule_, p. 201; 209.

[355] The same restriction must be made here as was imposed in the preceding chapter, namely, that the two salts in solution give a common ion.

[356] For example, addition of ammonium chloride to solutions of ferric chloride (Roozeboom, _Zeitschr. physikal. Chem._, 1892, 10. 149).

[357] It must, of course, be understood that the temperature is on that side of the transition point on which the double salt is stable.

[358] Excess of the double salt must be taken, because otherwise an unsaturated solution might be formed, and this would, of course, not deposit any salt.

[359] Meyerhoffer, _Ber._, 1904, 37. 2605.

[360] Meyerhoffer, _Ber._, 1897, 30. 1809.

[361] Meyerhoffer, _Ber._, 1904, 37. 2604.

[362] Bancroft, _Phase Rule_, p. 203; Roozeboom, _Zeitschr. physikal. Chem._, 1891, 8. 504, 531; Stortenbeker, _ibid._, 1895, 17. 643; 1897, 22. 60; 1900, 34. 108.

[363] Roozeboom, _Zeitschr. phys. Chem._, 1899, 28. 494; _Ber._, 1899, 32. 537.

[364] As, for instance, strychnine racemate, a compound of racemic acid with the _optically active_ strychnine. This would be resolved into strychnine _d_-tartrate and strychnine _l_-tartrate, which are not enantiomorphous forms.

[365] Van't Hoff and Meyerhoffer, _Zeitschr. physikal Chem._, 1898, 27. 75; 1899, 30. 86. Fig. 113 is taken from the latter paper.

[366] Solid models constructed of plaster of Paris can be obtained from Max Kaehler and Martini, Berlin.

[367] Instead of the present method of obtaining potassium chloride by decomposing carnallite with water, advantage might be taken of the fact that carnallite when heated to 168deg undergoes decomposition with separation of three-fourths of the potassium chloride (van't Hoff, _Acht Vortraege ueber physikalische Chemie_, 1902, p. 32).

[368] Roozeboom and Schreinemakers, _Zeitschr. physikal. Chem._, 1894, 15. 588.

[369] These curves represent only portions of the isotherms, since the systems in which a ternary solution is in equilibrium with solid hydrogen chloride or a hydrate, have not been investigated.

[370] The numbers printed beside the points on the curves refer to the number of the experiment in the original paper.

[371] Lash, Miller and Kenrick, _Journ. Physical. Chem._, 1903, 7. 259; Allan, _Amer. Chem. Journ._, 1901, 25. 307.

[372] Allan, _Amer. Chem. Journ._, 1901, 25. 307.

[373] Hoitsema, _Zeitschr. physikal. Chem._, 1895, 17. 651; Allan, _loc. cit._

[374] Rutten, _Zeitschr. anorgan. Chem._, 1902, 30. 342. Compare the system BeO--SO_{3}--H_{2}O; Parsons, _Zeitschr. anorgan. Chem._, 1904, 42. 250.

[375] _Zeitschr. anorgan. Chem._, 1904, 40. 146.

[376] Schreinemakers, _Zeitschr. physikal. Chem._, 1893, 11. 76; Bancroft, _Journ. Physical Chem._, 1902, 6. 179.

[377] _Zeitschr. anorgan. Chem._, 1904, 40. 148.

[378] _Zeitschr. physikal. Chem._, 1903, 43. 354.

[379] These equilibria were obtained by Boudouard, _Annales chim. phys._, 1901 [7], 24. 5. See also Hahn, _Zeitschr. physikal. Chem._, 1903, 42. 705; 44. 513.

[380] G. Preuner, _Zeitschr. physikal. Chem._, 1903, 47. 385.

[381] See Hahn, _Zeitschr. physikal. Chem._, 1903, 42. 705; 44. 513; Boudouard, _Bull. Soc. chim._, [3], 25. 484; Bodlaender, _Zeitschr. f. Elektrochem._, 1902, 8. 833; R. Schenck and Zimmermann, _Ber._, 1903, 36. 1231, 3663; Schenck and Heller, _ibid._, 1905, 38. 2132; _Zeitschr. f. Elektrochem._, 1903, 9. 691; Haber, _Thermodynamik technischer Gasreaktionen_, p. 293 (Munich, 1903).

[382] A very useful summary of the investigations carried out by van't Hoff and his pupils on the formation of the Stassfurt salt-beds is given by E. F. Armstrong, in the _Reports of the British Association for 1901_, p. 262. See also van't Hoff, _Zur Bildung der ozeanischen Salzablagerungen_ (Brunswick, 1905).

[383] See especially Meyerhoffer, _Silzungsber. Wien. Akad._, 1895, 104. II. _b_, 840; Meyerhoffer and Saunders, _Zeitschr. physikal. Chem._, 1899, 28. 453; 31. 370. The investigation of the equilibria between reciprocal salt-pairs alone (three-component systems) is of great importance for the artificial preparations of minerals, as also in analytical chemistry for the proper understanding of the methods of conversion of insoluble systems into soluble by fusion (see Meyerhoffer, _Zeitschr. physikal. Chem._, 1901, 38. 307).

[384] See Meyerhoffer, _Zeitschr. physikal. Chem._, 1899, 28. 459.

[385] Compare the reciprocal salt-pair NaCl--NH_{4}HCO_{3} (p. 321). In this case the upper limit of the transition interval was found by extrapolation of the solubility curve for NaHCO_{3} + NH_{4}Cl + NH_{4}HCO_{3} and NaHCO_{3} + NH_{4}Cl + NaCl to be 32deg (Fedotieff, _Zeitschr. phys. Chem._, 1904, 49. 179).

[386] Loewenherz, _Zeitschr. physikal. Chem._, 1894, 13. 464.

[387] Meyerhoffer and Saunders, _Zeitschr. physikal. Chem._, 1899, 28. 479.

[388] As the quantities of the salts are expressed in _equivalent_ gram-molecules, the molecule of sodium and potassium chloride must be doubled in order to be equivalent to sodium sulphate and potassium sulphate.

[389] _Sitz-Ber. der kgl. preuss. Akad. der Wiss._, 1903, p. 359. Van't Hoff, _Zur Bildung der ozeanischen Salzablagerungen_, I. p. 34 (Brunswick, 1905).

[390] _Zeitschr. fuer Kristallographie_, 1904, 39. 155.

[391] Meyerhoffer and Saunders, _Zeitschr. physikal. Chem._, 1899, 28. 479.

[392] _Zeitschr. physikal. Chem._, 1904, 49. 162.

[393] Another commercial process, in the study of which good service is done by the Phase Rule, is the caustification of the alkali salts (G. Bodlaender, _Zeitschr. fuer Elektrochem._, 1905, 11. 186; J. Herold, _ibid._, 418).

[394] _Zeitschr. physikal. Chem._, 1900, 35. 32.

[395] Mention may also be made here of the equilibria between magnesium carbonate and potassium carbonate, although these do not form a reciprocal salt-pair (Auerbach, _Zeitschr. fuer Elektrochem._, 1904, 10. 161).

[396] O. N. Witt and K. Ludwig, _Ber._, 1903, 36. 4384; Meyerhoffer, _ibid._, 1904, 37. 261, 1116.

[397] _Zeitschr. physikal. Chem._, 1905, 53. 513. Compare also, _ibid._, 1903, 38. 307.

[398] See Schwarz, _Beitraege zur Kenntnis der umkehrbaren Umwandlungen polymorpher Korper_ (Goettingen, 1892); or, Roozeboom, _Heterogen. Gleichgewicht_, I. p. 125. Also Barnes and Cooke, _Journ. Physical Chem._, 1902, 6. 172.

[399] Van't Hoff and van Deventer, _Zeitschr. physikal. Chem._, 1887, 1. 173.

[400] Reicher, _Zeitschr. fuer Krystallographie_, 1884, 8. 593.

[401] _Zeitschr. physikal. Chem._, 1895, 17. 153.

[402] _Zeitschr. physikal. Chem._, 1899, 28. 464.

[403] Meyerhoffer and Saunders, _ibid._, p. 466.

[404] See Van Eyk, _Zeitschr. physikal. Chem._, 1899, 30. 446.

[405] See in this connection the volume in this series on _Electro-chemistry_, by Dr. R. A. Lehfeldt.

[406] Barnes and Cooke, _Journ. Physical Chem._, 1902, 6. 172.

[407] For a description and explanation of these, the reader should consult the volume in this series by Dr. Lehfeldt on _Electro-chemistry_; and van't Hoff, _Bildung und Spaltung von Doppelsalzen_, p. 48 _ff._

* * * * *

Changes made to the printed original.

Pages 30-31. "Fig. 3, p. 27.": 'p. 25." in original. So also page 33, "Fig. 2, p. 27".

Page 57. "pp. 29 and 35": 'pp. 25 and 38" in original.

Page 65. "p. 57.": 'p. 60" in original (twice).

Page 166. "there is the point C_{1}": C' in original.

Page 225. "C is an eutectic point": 'eutetic' in original.

Page 228. "Although this view put forward by Heyn": 'Athough' in original.

Page 232. "the period of constant temperature for the eutectic point c": 'the eutectic point e' in original.

Page 249. "two liquid layers between 13deg and 31deg": 'betwen' in original.

Page 257. Tables entries 4 and 7. "naphthol": 'napthol' in original.

Page 287. "from which the model is constructed": 'he model' in original.

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