Appendix
Experimental Determination of the Transition Point
For the purpose of determining the transition temperature, a number of methods have been employed, and the most important of these will be briefly described here. In any given case it is sometimes possible to employ more than one method, but all are not equally suitable, and the values of the transition point obtained by the different methods are not always identical. Indeed, a difference of several degrees in the value found may quite well occur.398 In each case, therefore, some care must be taken to select the method most suitable for the purpose.
I. The Dilatometric Method.—Since, in the majority of cases, transformation at the transition point is accompanied by an appreciable change of volume, it is only necessary to ascertain the temperature at which this change of volume occurs, in order to determine the transition point. For this purpose the dilatometer is employed, an apparatus which consists of a bulb with capillary tube attached, and which constitutes a sort of large thermometer (Fig. 129). Some of the substance to be examined is passed into the bulb A through the tube B, which is then sealed off. The rest of the bulb and a small portion of the capillary tube is then filled with some liquid, which, of course, must be without chemical action on the substance under investigation. A liquid, however, may be employed which dissolves the substance, for, as we have seen (p. 70), the transformation at the transition point is, as a rule, accelerated by the presence of a solvent. On the other hand, the liquid must not dissolve in the substance under examination, for the temperature of transformation would be thereby altered.
In using the dilatometer, two methods of procedure may be followed. According to the first method, the dilatometer containing the form stable at lower temperatures is placed in a thermostat, maintained at a constant temperature, until it has taken the temperature of the bath. The height of the meniscus is then read on a millimetre scale attached to the capillary. The temperature of the thermostat is then raised degree by degree, and the height of the meniscus at each point ascertained. If, now, no change takes place in the solid, the expansion will be practically uniform, or the rise in the level of the meniscus per degree of temperature will be practically the same at the different temperatures, as represented diagrammatically by the line AB in Fig. 130. On passing through the transition point, however, there will be a more or less sudden increase in the rise of the meniscus per degree (line BC) if the specific volume of the form stable at higher temperatures is greater than that of the original modification; thereafter, the expansion will again be uniform (line CD). Similarly, on cooling, contraction will at first be uniform and then at the transition point there will be a relatively large diminution of volume.
If, now, transformation occurred immediately the transition point was reached, the sudden expansion and contraction would take place at the same temperature. It is, however, generally found that there is a lag, and that with rising temperature the relatively large expansion does not take place until a temperature somewhat higher than the transition point; and with falling temperature the contraction occurs at a temperature somewhat below the transition point. This is represented in Fig. 130 by the lines BC and EF. The amount of lag will vary from case to case, and will also depend on the length of time during which the dilatometer is maintained at constant temperature.
As an example, there may be given the results obtained in the determination of the transition point at which sodium sulphate and magnesium sulphate form astracanite (p. 268).399 The dilatometer was charged with a mixture of the two sulphates.
| Temperature. | Level of oil in capillary. | Rise per 1°. |
| 15.6° 16.6° 17.6° 18.6° 19.6° 20.6° 21.6° 22.6° 23.6° 24.6° | 134 141 148 154 161 168 241 243 251 259 | 7 7 6 7 7 73 2 8 8 |
The transition point, therefore, lies about 21.6° (p. 268).
The second method of manipulation depends on the fact that, while above or below the transition point transformation of one form into the other can take place, at the transition point the two forms undergo no change. The bulb of the dilatometer is, therefore, charged with a mixture of the stable and metastable forms and a suitable liquid, and is then immersed in a bath at constant temperature. After the temperature of the bath has been acquired, readings of the height of the meniscus are made from time to time to ascertain whether expansion or contraction occurs. If expansion is found, the temperature of the thermostat is altered until a temperature is obtained at which a gradual contraction takes place. The transition point must then lie between these two temperatures; and by repeating the determinations it will be possible to reduce the difference between the temperatures at which expansion and contraction take place to, say, 1°, and to fix the temperature of the transition point, therefore, to within half a degree. By this method the transition point, for example, of sulphur was found to be 95.6° under a pressure of 4 atm.400 The following are the figures obtained by Reicher, who used a mixture of 1 part of carbon disulphide (solvent for sulphur) and 5 parts of turpentine as the measuring liquid.
| Temperature 95.1°. | |
| Time in minutes. | Level of liquid. |
| 5 | 343.5 |
| 30 | 340.5 |
| 55 | 335.75 |
| 65 | 333 |
| Temperature 96.1°. | |
| Time in minutes. | Level of liquid. |
| 5 | 342.75 |
| 30 | 354.75 |
| 55 | 360.5 |
| 60 | 361.5 |
| Temperature 95.6°. | |
| Time in minutes. | Level of liquid. |
| 5 | 368.75 |
| 100 | 368 |
| 110 | 368.75 |
At a temperature of 95.1° there is a contraction, i.e. monoclinic sulphur passes into the rhombic, the specific volume of the former being greater than that of the latter. At 96.1°, however, there is expansion, showing that at this temperature rhombic sulphur passes into monoclinic; while at 95.6° there is neither expansion nor contraction. This is, therefore, the transition temperature; and since the dilatometer was sealed up to prevent evaporation of the liquid, the pressure within it was 4 atm.
II. Measurement of the Vapour Pressure.—In the preceding pages it has been seen repeatedly that the vapour pressures of the two systems undergoing reciprocal transformation become identical at the transition point (more strictly, at the triple or multiple point), and the latter can therefore be determined by ascertaining the temperature at which this identity of vapour pressure is established. The apparatus usually employed for this purpose is the Bremer-Frowein tensimeter (p. 91).
Although this method has not as yet been applied to systems of one component, it has been used to a considerable extent in the case of systems containing water or other volatile component. An example of this has already been given in Glauber’s salt (p. 139).
III. Solubility Measurements.—The temperature of the transition point can also be fixed by means of solubility measurements, for at that point the solubility of the two systems becomes identical. Reference has already been made to several cases in which this method was employed, e.g. ammonium nitrate (p. 112), Glauber’s salt (p. 134), astracanite and sodium and magnesium sulphates (p. 268).
The determinations of the solubility can be carried out in various ways. One of the simplest methods, which also gives sufficiently accurate results when the temperature is not high or when the solvent is not very volatile, can be carried out in the following manner. The solid substance is finely powdered (in order to accelerate the process of solution), and placed in sufficient quantity along with the solvent in a tube carefully closed by a glass stopper; the latter is protected by a rubber cap, such as a rubber finger-stall. The tube is then rotated in a thermostat, the temperature of which does not vary more than one or two tenths of a degree, until saturation is produced. The solution is withdrawn by means of a pipette to which a small glass tube, filled with cotton wool to act as a filter, is attached. The solution is then run into a weighing bottle, and weighed; after which the amount of solid in solution is determined in a suitable manner.
For more accurate determinations of the solubility, especially when the solvent is appreciably volatile at the temperature of experiment, other methods are preferable. In Fig. 131 is shown the apparatus employed by H. Goldschmidt,401 and used to a considerable extent in the laboratory of van’t Hoff. This consists essentially of three parts: a, a tube in which the solvent and salt are placed; this is closed at the foot by an india-rubber stopper. Through this stopper there passes the bent tube cb, which connects the tube a with the weighing-tube d. At c there is a plug of cotton wool. Tube e is open to the air. The wider portion of the tube cb, which passes through the rubber stopper in a, can be closed by a plug attached to a glass rod ff, which passes up through a hollow Witt stirrer, g. After being fitted together, the whole apparatus is immersed in the thermostat. After the solution has become saturated, the stopper of the bent tube is raised by means of the rod ff and a suction-pump attached to the end of e. The solution is thereby drawn into the weighing-tube d, the undissolved salt being retained by the plug at c. The apparatus is then removed from the thermostat, tube d detached and immediately closed by a ground stopper. It is then carefully dried and weighed.
Another form of solubility vessel, due to Meyerhoffer and Saunders, is shown in Fig. 132.402 This consists of a single tube, and the stirring is effected by means of a glass screw.
The progress of the solution towards saturation can be very well tested by determining the density of the solution from time to time. This is most conveniently carried out by means of the pipette shown in Fig. 133.403 With this pipette the solution can not only be removed for weighing, but the volume can be determined at the same time. It consists of the wide tube a, to which the graduated capillary b, furnished with a cap c, is attached. To the lower end of the pipette the tube e, with plug of cotton wool, can be fixed. After the pipette has been filled by sucking at the end of b, the stop-cock d is closed and the cap c placed on the capillary. The apparatus can then be weighed, and the volume of the solution be ascertained by means of the graduations.
As has already been insisted, particular care must be paid to the characterization of the solid in contact with the solution.
IV. Thermometric Method.—If a substance is heated, its temperature will gradually rise until the melting point is reached, and the temperature will then remain constant until all the solid has passed into liquid. Similarly, if a substance which can undergo transformation is heated, the temperature will rise until the transition point is reached, and will then remain constant until complete transformation has taken place.
This method, it will be remembered, was employed by Richards for the determination of the transition point of sodium sulphate decahydrate (p. 136). The following figures give the results obtained by Meyerhoffer in the case of the transformation:—
CuK2Cl4,2H2O reversible arrow CuKCl3 + KCl + 2H2O the temperature being noted from minute to minute: 95°, 93°, 91.8°, 91.7°, 92°, 92.3°, 92.4°, 92.2°, 92.2°, 92°, 90.5°, 89°, and then a rapid fall in the temperature. From this we see that the transition point is about 92.2°. It is also evident that a slight supercooling took place (91.7°), owing to a delay in the transformation, but that then the temperature rose to the transition point. This is analogous to the supercooling of a liquid.
A similar halt in the temperature would be observed on passing from lower to higher temperatures; but owing to a lag in the transformation, the same temperature is not always obtained.
V. Optical Method.—The transition point can sometimes be determined by noting the temperature at which some alteration in the appearance of the substance occurs, such as a change of colour or of the crystalline form. Thus mercuric iodide changes colour from red to yellow, and the blue quadratic crystals of copper calcium acetate change, on passing the transition point, into green rhombs of copper acetate and white needles of calcium acetate (p. 260). Or again, changes in the double refraction of the crystals may be also employed to ascertain the temperature of the transition point. These changes are best observed by means of a microscope.
For the purpose of regulating the temperature of the substance a small copper air-bath is employed.404
VI. Electrical Methods.—Electrical methods for the determination of the transition point are of two kinds, based on measurements of conductivity or of electromotive force. Both methods are restricted in their application, but where applicable give very exact results.
The former method, which has been employed in several cases, need not be described here. The second method, however, is of considerable interest and importance, and calls for special reference.405
If two pieces, say, of zinc, connected together by a conducting wire, are placed in a solution of a zinc salt, e.g. zinc sulphate, the potential of the two electrodes will be the same, and no current will be produced in the connecting wire. If, however, the zinc electrodes are immersed in two solutions of different concentration contained in separate vessels, but placed in connection with one another by means of a bent tube filled with a conducting solution, the potentials at the electrodes will no longer be the same, and a current will now flow through the connecting wire. The direction of this current in the cell will be from the weaker to the more concentrated solution.
The greater the difference in the concentration of the solutions with respect to zinc, the greater will be the difference of the potential at the two electrodes, or the greater will be the E.M.F. of the cell. When the concentration of the two solutions becomes the same, the E.M.F. will become zero, and no current will pass.
It will be understood now how this method can be made use of for determining the transition point of a salt, when we bear in mind that at the transition point the solubility of the two forms becomes identical. Thus, for example, the transition point of zinc sulphate heptahydrate into hexahydrate could be determined in the following manner. Tube A (Fig. 134) contains, say, a saturated solution of the heptahydrate along with some of the solid salt; tube B, a saturated solution of the hexahydrate along with the solid salt. The tube C is a connecting tube bent downwards so as to prevent the mixing of the solutions by convection currents. ZZ are two zinc electrodes immersed in the solution; the cell is placed in a thermostat and the zinc electrodes connected with a galvanometer. Since, now, at temperatures below the transition point the solubility of the hexahydrate (the metastable form) is greater than that of the heptahydrate, a current will be produced, flowing in the cell from heptahydrate to hexahydrate. As the temperature is raised towards the transition point, the solubilities of the two hydrates also approach, and the current produced will therefore become weaker, because the E.M.F. of the cell becomes less; and when the transition point is attained, the E.M.F. becomes zero, and the current ceases. If the temperature is raised above this, the solubility of the heptahydrate becomes greater than that of the hexahydrate, and a current will again be produced, but in the opposite direction. By noting the temperature, therefore, at which the current ceases, or the E.M.F. becomes zero, the transition temperature can be ascertained.406
In the case just described, the electrodes consisted of the same metal as was contained in the salt. But in some cases, e.g. sodium sulphate, electrodes of the metal contained in the salt cannot be employed. Nevertheless, the above electrical method can be used even in those cases, if a suitable non-polarizable mercury electrode is employed.407
Although, as we saw, no current was produced when two pieces of zinc were immersed in the same solution of zinc salt, a current will be obtained if two different metals, or even two different modifications of the same metal, are employed. Thus an E.M.F. will be established when electrodes of grey and of white tin are immersed in the same solution of zinc salt, but at the transition point this E.M.F. will become zero. By this method Cohen determined the transition point of grey and white tin (p. 42).
Notes
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’s Klassiker, No. 74.
8 Etudes sur les affinités chimiques, 1867; Ostwald’s Klassiker, 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’s Annalen, 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. 4 as 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 on Thermodynamics by 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 a point, a univariant system by a line, and a bivariant system by an area.
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 See Phil. 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
| n(n - 1)(n - 2) | , |
| 1.2.3 |
where n is 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 | , |
| dt | T(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 See Principles 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.
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 also Principles 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 on Chemical 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 sublimes through the 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 Vide Loewel, 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 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 32.6° 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 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., 2te 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 Clx 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 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, 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 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 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 congrès 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 métalliques,” in the Rapports du congrès 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 Jüptner, Siderology, p. 223 (translation by C. Salter); van’t Hoff, Zinn, Gips, und Stahl, p. 24, or Acht Vorträge über 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 1505°.
311 Zeitschr. für 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 Silikatschmelzlösungen, 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 Bodländer, Berg-und Hüttenmänn. 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 KNO3—NaNO3—LiNO3 (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 22°, in accordance with the equation—
2MgCl2.6H2O + CaCl2.6H2O = Mg2CaCl6.12H2O + 6H2O
Increase of pressure raises the transition point, because the formation of tachydrite is accompanied by increase of volume; the elevation being 0.016° for an increase of pressure of 1 atm. The number calculated from the theoretical formula (p. 57) is 0.013° 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 3°. 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 Müller, 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 168° undergoes decomposition with separation of three-fourths of the potassium chloride (van’t Hoff, Acht Vorträge über 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—SO3—H2O; 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; Bodländer, 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—NH4HCO3 (p. 321). In this case the upper limit of the transition interval was found by extrapolation of the solubility curve for NaHCO3 + NH4Cl + NH4HCO3 and NaHCO3 + NH4Cl + NaCl to be 32° (Fedotieff, Zeitschr. phys. Chem., 1904, 49. 179).
386 Löwenherz, 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. für 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. Bodländer, Zeitschr. für 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. für 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, Beiträge zur Kenntnis der umkehrbaren Umwandlungen polymorpher Korper (Göttingen, 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. für 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.