Chapter XXV: Appendix: Experimental Determination of the Transition Point (1)

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.

{331}

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 {332} 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 1deg.
--------------------------------------------------------
15.6deg | 134 |
16.6deg | 141 | 7
17.6deg | 148 | 7
18.6deg | 154 | 6
19.6deg | 161 | 7
20.6deg | 168 | 7
21.6deg | 241 | 73
22.6deg | 243 | 2
23.6deg | 251 | 8
24.6deg | 259 | 8
--------------------------------------------------------

The transition point, therefore, lies about 21.6deg (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, 1deg, 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 95.6deg under a pressure of 4 atm.[400] The following are the figures obtained by Reicher, who used a mixture {333} of 1 part of carbon disulphide (solvent for sulphur) and 5 parts of turpentine as the measuring liquid.

TEMPERATURE 95.1deg.

-----------------------------------
Time in minutes. | Level of liquid.
-----------------------------------
5 | 343.5
30 | 340.5
55 | 335.75
65 | 333
-----------------------------------

TEMPERATURE 96.1deg.

-----------------------------------
Time in minutes. | Level of liquid.
-----------------------------------
5 | 342.75
30 | 354.75
55 | 360.5
60 | 361.5
-----------------------------------

TEMPERATURE 95.6deg.

-----------------------------------
Time in minutes. | Level of liquid.
-----------------------------------
5 | 368.75
100 | 368
110 | 368.75
-----------------------------------

At a temperature of 95.1deg 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 96.1deg, however, there is expansion, showing that at this temperature rhombic sulphur passes into monoclinic; while at 95.6deg 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 {334} 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 {335} 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 {336} 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:--

CuK_{2}Cl_{4},2H_{2}O <--> CuKCl_{3} + KCl + 2H_{2}O

the temperature being noted from minute to minute: 95deg, 93deg, 91.8deg, 91.7deg, 92deg, 92.3deg, 92.4deg, 92.2deg, 92.2deg, 92deg, 90.5deg, 89deg, and then a rapid fall in the temperature. From this we see that the transition point is about 92.2deg. It is also evident that a slight supercooling took place (91.7deg), 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.

{337}

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 {338} 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 {339} 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).

* * * * *

{340}

NAME INDEX

A
Abegg, 52
Adriani, 186, 217, 220
Alexejeff, 97, 125
Allan, 298
Allen, L. E., 109
Allen, R. W., 63
Ampolla, 213
Andreae, 109
Aristotle, 41
Armstrong, E. F., 313
Armstrong, H. E., 196
Arzruni, 33
Aten, 147, 163
Auerbach, 326

B
Babo, 126
Bancroft, 102, 104, 161, 176, 196, 202, 229, 246, 260, 261, 272, 281, 302
Barnes, 331, 339
Barschall, 318
Barus, 67
Battelli, 23
Baur, 233, 307
Beckmann, 49
Bell, 229
Berthollet, 7
Bodlaender, 181, 247, 311, 321
Bogojawlenski, 72
Boudouard, 309, 311
Braun, 107
Brauns, 40, 51, 74
Bredig, 52
Bremer, 91
Brodie, 34, 47
Bruner, 126
Bruni, 181, 182, 256, 257
Bunsen, 67

C
Cady, 192
Calvert, 130
Cameron, 203
Carnelley, 47
Carpenter, 225
Carveth, 204, 255
Centnerszwer, 158
Chapman, 47
Chappuis, 51, 176
Charpy, 255
Churchill, 140
Coehn, 52
Cohen, 41, 72, 136, 139, 140
Cooke, 331, 339
Cox, 301

D
Dawson, 263
Debray, 74, 81, 139
Deville, 49, 74
Dewar, 26, 51, 178
Dietz, 157
{341}
Doelter, 233
Donnan, 8, 18
Dreyer, 73
Duhem, 56, 151
Dutoit, 204

E
Etard, 115, 135

F
Fahrenheit, 30
Faraday, 82, 89
Fath, 204
Fedotieff, 315, 320
Findlay, 111, 204, 206, 219
Foote, 69
Friedlaender, 72
Fritsche, 41
Frowein, 91
Fuechtbauer, 75
Fyffe, 143

G
Gattermann, 51, 52
Gautier, 222, 223
Gay-Lussac, 135
Gernez, 72
Gibbs, 7, 8, 151, 236
Glaessner, 307
Goldschmidt, E., 41
Goldschmidt, H., 335
Goldschmidt, V., 32
Goossens, 26
Gossner, 318
Graham, 178
Guertler, 73
Guldberg, 7
Guthrie, 97, 104, 117, 118, 119, 233

H
Haber, 311
Hahn, 309, 311
Hallock, 35
Hammerl, 145
Hautefeuille, 46, 49, 50, 51, 178
Heller, 311
Henry, 94
Herold, 321
Hertz, 49
Heycock, 194, 221, 223
Heyn, 225, 228
Hickmans, 219
Hiorns, 228
Hissink, 115, 190
Hoitsema, 14, 90, 177, 178, 298
Hollmann, 204
Holsboer, 110
Horstmann, 8, 83, 89
Hudson, 102
Hulett, 10, 48, 52, 54, 67, 109

I
Isaac, 114
Isambert, 80, 82, 84

J
Jaffe, 74, 114
Joulin, 176
Juhlin, 23, 24, 30
von Jueptner, 225

K
Kastle, 71
Kaufler, 49
Kaufmann, 112
Kayser, 176
Keeling, 225
Kelvin, 25
Kenrick, 263, 297
Kipping, 219
Kirchhoff, 32
Knorr, 203
de Kock, 53, 182, 194
Konowaloff, 102, 103, 104
Krasnicki, 144
Kremann, 147, 212
Kuenen, 105
Kultascheff, 233
{342}
Kuriloff, 216
Kurnakoff, 221, 222, 230
Kuester, 72, 181, 183

L
Laar, 195
Labenburg, 216
Lattey, 101
Le Chatelier, 58, 81, 233
Lehfeldt, 338, 340
Lehmann, 33, 52, 53
Lidbury, 147
Loewel, 134, 135
Loewenherz, 134, 316
Lowry, 196, 198
Ludwig, 327
Lumsden, 80, 109, 110
Lussana, 68
Luther, 22

M
Mack, 67
Magnus, 22
Mathews, 221
Mellor, 80
Meusser, 142
Meyer, J., 71
Meyer, V., 47
Meyerhoffer, 158, 233, 259, 268, 271, 278, 279, 280, 284, 313, 315, 317,
319, 327, 328, 336, 337
Middelberg, 116
Miers, 114
Miller, 297
Mitscherlich, 33, 49
Mond, 178
Moore, 72
Moss, 66
Mueller, 112, 265
Mylius, 109, 142, 157

N
Naumann, 49
Neville, 194, 221, 223

O
Offer, 119
Ostwald, 8, 10, 13, 16, 22, 44, 58, 68, 70, 74, 85, 88, 92, 102, 110,
117, 125, 127, 130, 141, 198

P
Padoa, 73, 181
Parsons, 298
Pasteur, 266
Paterno, 213
Payen, 74
Pedler, 47
Pfaundler, 119
Philip, 213, 214
von Pickardt, 73
Planck, 68
Pope, 219
Poynting, 68
Preuner, 311
Puschin, 222

Q
Quincke, 52

R
Rabe, 113
Ramsay, 3, 22, 23, 24, 30, 32, 63, 64, 66, 79, 90, 165, 178
Raoult, 180
Reed, 71
Regnault, 22
Reicher, 36, 37, 110, 260, 333
Reinders, 71, 185, 188
Reinitzer, 51, 52
Richards, 136, 140
Riddle, 47
Riecke, 48, 55
Roberts-Austen, 63, 194, 221, 223, 225
Roloff, 117
Roozeboom, 10, 38, 45, 47, 49, 50, 51, 54, 56, 57, 62, 63, 68, 88, 103,
126, 145, 147, 150, 151, 157, 162, 170, 174, 178, 182, 196, 201, 211,
217, 220, 225, 236, 238, 262, 264, 269, 272, 273, 281, 282, 290, 331
{343}
Rose, 223
Rotarski, 52
Rothmund, 97, 98, 100
Rutten, 298

S
Saposchnikoff, 212
Saunders, 313, 317, 319, 336, 337
Saurel, 151
Schaum, 49, 75
Scheel, 22, 23, 30
Schenck, 49, 52, 54, 311
Schneider, 52
Schoenbeck, 75
Schreinemakers, 122, 126, 246, 248, 250, 252, 290, 302
Schroetter, 46
Schukowsky, 52
Schwarz, 331
Seitz, 52
Shenstone, 109, 115, 135
Shepherd, 221, 255
Shields, 178
Skirrow, 130
Spring, 63
von Stackelberg, 107, 110
Staedel, 267
Stansfield, 194, 221
Stokes, 236
Stortenbeker, 44, 147, 161, 164, 281

T
Taber, 229
Tammann, 26, 32, 33, 37, 38, 39, 48, 52, 65, 67, 68, 72, 73, 140, 151,
176, 221, 230
Thiesen, 22, 23, 30
Thomson, J., 25, 28, 32
Thomson, W., 25
Tilden, 109, 115, 135
Trevor, 16
Troost, 46, 49, 50, 51
Tumlirz, 72

V
Van Bemmelen, 180
Van Deventer, 110, 139, 266, 267, 333
Van Eyk, 41, 63, 192, 338
Van't Hoff, 36, 38, 58, 70, 90, 92, 108, 127, 139, 140, 165, 175, 225,
258, 260, 263, 265, 266, 267, 272, 284, 290, 313, 318, 333, 340
Van Leeuwen, 259
Van Wyk, 185
Vogt, 5, 233

W
Waage, 7
Wald, 92
Walden, 158
Walker, 80, 105, 122, 126, 143
Wegscheider, 10, 49, 202
Wells, 136
Wenzel, 7
Wiebe, 22
Witt, 327
Wright, 241, 246, 247
von Wrochem, 109, 142

Y
Young, 3, 22, 23, 24, 30, 32, 63, 64, 66, 79, 105, 165

Z
Zacharias, 180
Zawidski, 63
Zenghelis, 35
Zimmermann, 311
Zincke, 44
Ziz, 141

* * * * *

{344}

SUBJECT INDEX

A
Acetaldehyde and paraldehyde, 204
Acetic acid, chloroform, water, 241
Acetone, phenol, water, 248
Adsorption, 176
Alcohol, chloroform, water, 246
----, ether, water, 246
Alloys, equilibrium curves of, 221
---- of copper and tin, liquefaction of, by cooling, 194
---- of iron and carbon, 223
---- of thallium and mercury, 222
----, ternary, 246
Ammonia compounds of metal chlorides, 82
Ammonia silver chlorides, 82
---- ---- ----, dissociation pressures of, 84
Ammonia-soda process, 320
Ammonium chloride, dissociation of, 3, 79
---- cyanide, dissociation of, 80
---- hydrosulphide, dissociation of, 80
---- nitrate, solubility of, 113
Aniline, phenol, water, 250
Astracanite, 260, 261, 268, 274

B
Babo, law of, 126
Barium acetate, solubility of, 143
Barium carbonate and potassium sulphate, 328
---- nitrite, preparation of, 327
Basic salts, 296
Benzaldoximes, 203
Benzene and picric acid, 216
Bismuth, effect of pressure on the melting point of, 67
----, lead, tin, 255
---- nitrates, basic, 298
Bivariant systems, 16
Bromocinnamic aldehyde and chlorocinnamic aldehyde, 183

C
Calcium carbonate, dissociation of, 3, 11, 81
---- chloride hexahydrate, solubility of, 146
---- ----, solubility of hydrates of, 148
---- ----, vapour-pressure of hydrates of, 88
Camphor oximes, 219, 257
Carnallite, 284
Carvoximes, 186, 219
Cementite, 224
Chlorine and iodine, 161
Chlorocinnamic aldehyde and bromocinnamic aldehyde, 183
Chloroform, acetic acid, water, 241
----, alcohol, water, 246
{345}
Classification of systems, 17
Component, 8, 10, 12
----, systems of one, 21, 55
Components, choice of, 12, 13, 14, 76, 313
----, determination of number of, 13
----, systems of four, 312
----, ---- of three, 234
----, ---- of two, 76, 207
----, variation in number of, 11, 14
Composition, determination of, without analysis, 228, 302
Concentration-temperature curve for two liquids, 101
Condensed systems, 36
Constituent, 10
Cooling curve, 230
Copper calcium acetate, 260
---- chloride, heat of solution of, 110
---- dipotassium chloride, 259
---- sulphate, 85
Critical concentration, 98, 242
---- pressure of water, 23
---- solution temperature, 98
---- temperature of water, 23
Cryohydrates, 117, 118
Cryohydric point, 117
---- ----, changes at the, 119
---- ---- for silver nitrate and ice, 116
Crystals, liquid, 51
----, ----, equilibria of, 53
----, ----, list of, 54
----, ----, nature of, 52
----, mixed, 180
Crystallization, velocity of, 72, 74
----, spontaneous, 114

D
Deliquescence, 130
Devitrification, 73
Diethylamine and water, solubility of, 101
Dilatometer, determination of transition points by, 331
Dineric surface, 247
Dissociation equilibrium, effect of addition of dissociation products on,
4
---- of ammonia compounds of metal chlorides, 82, 84
---- of ammonium chloride, 3, 79
---- ---- cyanide, 80
---- ---- hydrosulphide, 80
---- of calcium carbonate, 3, 81
---- of compounds, degree of, 147
---- of phosphonium bromide, 80
---- of salt hydrates, 85
----, phenomena of, 79
Dissociation pressure, 81
Distillation of supercooled liquid to solid, 32, 50
Double salt interval, 278
---- salts, crystallization from solution, 280
---- ----, decomposition by water, 267
---- ----, formation of, 258, 273, 315

E
Efflorescence, 86
Electrical methods of determining transition points, 338
Enantiotropy, 44, 51
Equilibria, Gibbs's theory of, 8
----, metastable, 69
Equilibrium apparent (false), 5, 6
---- between ice and solution, 116
---- between ice and water, 25
---- between ice, water, vapour, 27
---- between water and vapour, 21
----, chemical, 3, 16
----, heterogeneous, 5
----, homogeneous, 5
----, independence of, on amounts of phases, 9
----, law of movable, 58
{346}
----, physical, 3, 16
---- real (true), 5, 6
Ether, alcohol, water, 246
----, succinic nitrile, water, 252
Ethylene bromide, picric acid, [beta]-naphthol, 256
Eutectic mixtures, 117, 191, 209, 255, 257
---- point, 117, 209, 213, 253

F
Ferric chloride, evaporation of solutions of, 155
---- ----, hydrates of, 151, 153
---- ----, hydrogen chloride and water, systems of, 290
Ferrite, modifications of, 224
Freedom, degree of, 14
Freezing mixtures, 120
---- point, natural, 198
Fusion curve, 66
---- ---- of ice, 25
---- of ice, influence of pressure on, 26
----, partial, 139

G
Glaserite, 315, 317
Glasses, 176
Glauber's salt, 13, 134
---- ----, transition curve of, 68, 140
Graphic representation in space, 77, 284

H
Hydrates, range of existence of, 89
---- chloride and water, 174
Hydrogen bromide and water, 174
Hylotropic substances, 198

I
Ice I., 32
---- II., 32
---- III., 32
----, equilibrium between water and, 25
----, influence of pressure on melting point of, 25, 26
----, sublimation curve of, 24
----, vapour pressure of, 25, 31
Indifferent point, 150
Individual, chemical, 92
Inversion temperature, 36
Iodine and chlorine, 161
Iron--carbon alloys, 223
----, carbon monoxide and carbon dioxide, 305
Isomerides, dynamic, 195, 196
----, ----, equilibrium between, 195, 196
----, ----, equilibrium point of, 198
----, transformation of unstable into stable, 201
Isomerism, dynamic, 196
Isothermal evaporation, 278
---- solubility curves, 272

L
Lead, bismuth, tin, 255
----, desilverization of, 247
----, silver, zinc, 246
Le Chatelier, theorem of, 57
Lime, burning of, 3
Liquidus curve, 182

M
Mandelic acid, 217
Martensite, 224
Mass action, law of, 7
Melting point, influence of pressure on, 66
{347}
---- ----, congruent, 146
---- ----, incongruent, 139
---- under the solvent, 122
Menthyl mandelates, 219
Mercuric bromide and iodide, 188
Mercury salts, basic, 301
Metastable equilibria, 69
---- region, 30
---- state, 30
Methylethyl ketone and water, 100
Minerals, formation of, 232
Miscibility of liquids, complete, 95, 104, 114
---- ----, partial, 95, 96, 121
Mixed crystals, 180, 281
---- ----, changes in, with temperature, 192
---- ----, examples of, 183, 186, 187, 190, 192, 219, 223
---- ----, formation of, 181, 182
---- ----, fractional crystallization of, 188
---- ----, freezing points of, 182
---- ----, melting points of, 182, 184
---- ----, pseudoracemic, 219
Mixtures, isomorphous, 181
---- of constant boiling point, 105
---- of constant melting point, 117, 186, 187, 192, 209, 255, 257
Monotropy, 44, 51
Multivariant systems, 16

N
Naphthalene and monochloracetic acid, 192
---- and [beta]-naphthol, mixed crystals of, 183
[beta]-Naphthol, ethylene bromide, picric acid, 256
[alpha]-Naphthylamine and phenol, 213
Nickel iodate, solubility of, 142
_o_-Nitrophenol and _p_-toluidine, 213

O
Occlusion of gases, 176
Optical method of determining transition points, 338
Optically active substances, freezing-point curves of, 216
Order of a system, 13
Organic compounds, application of Phase Rule to, 212

P
Palladium and hydrogen, 90, 178
Paragenesis, 320
Paraldehyde and acetaldehyde, 204
Partial pressures of two components, 102
Pearlite, 224
Phase, 8
---- Rule, 8, 16
---- ----, deduction of, 18
---- ----, scope of, 1
Phases, formation of new, 69
----, number of, 9
Phenol, acetone, water, 248
----, aniline, water, 250
---- and [alpha]-naphthylamine, 213
---- and _p_-toluidine, 214
---- and water, solubility of, 97
Phosphonium bromide, dissociation of, 80
---- chloride, 65
Phosphorus, 46
----, distillation of white to red, 50
----, melting point of red, 47
----, ---- ---- of white, 48
----, solubility of white and red, 47
----, vapour pressure of white and red, 46
Picric acid and benzene, 216
---- ----, ethylene bromide, and [beta]-naphthol, 256
Polymorphic forms, solubility of, 112
{348}
---- substances, list of, 63
Polymorphism, 33
Potassium nitrate and thallium nitrate, 192
Potential, chemical, 19
Pressure-concentration diagram for two liquids, 102
Pressure-temperature diagram for solutions, 126
Pseudomonotropy, 45
Pseudo-racemic mixed crystals, 21
Pyridine and methyl iodide, 147
Pyrometer, registering, 230

Q
Quadruple point, 116
Quintuple point, 234, 261

R
Racemates, characterization of, 217, 282
Reactions, law of successive, 73
Reciprocal salt-pairs, 313
---- ----, transition point of, 314
Rubidium tartrates, 265

S
Salt hydrates, 85
---- ----, indefiniteness of vapour pressure of, 87
---- ---- with definite melting point, 145
Separation of salt on evaporation, 130
Silicates, hydrated, 176
Silver, lead, zinc, 246
Silver nitrate, solubility of, 114
---- ---- and sodium nitrate, 190
Single salt interval, 278
Sodium ammonium tartrates, 266
---- nitrate and silver nitrate, 190
---- sulphate and water, equilibria between, 134
Sodium sulphate and water, vapour pressures of, 138, 140
---- ----, anhydrous, dehydration by, 138
---- ----, solubility of, 135
---- ---- decahydrate, solubility of, 134
---- ---- ----, transition point of, 136, 139
---- ---- heptahydrate, solubility of, 136
---- ---- ----, transition point of, 137
Solidus curve, 182
Solubility curve at higher temperatures, 114
---- ----, form of, 108
---- ---- of anhydrous salts, 111
---- ----, retroflex, 146, 151, 162
---- curves, interpolation and extrapolation of, 111
---- ---- of three component systems, 264
----, determination of transition points by, 335
----, influence of pressure on, 107
----, ---- of subdivision on, 10
----, ---- of temperature on, 109
---- of metastable forms, 47, 112, 137
Solubility of polymorphic forms, 112
---- of salt hydrates, 133, 145
---- of supercooled liquids, 125
----, retrograde, 245
Solute, 93
Solution, definition of, 92
----, heat of, 109, 110
----, saturated, 106, 108
----, supersaturated, 108
---- temperature, critical, 98
----, unsaturated, 108
Solutions, bivariant systems, 129
----, congruently saturated, 279
---- conjugate, 97, 241
{349}
----, incongruently saturated, 279, 289
----, inevaporable, 157
---- of gases in liquids, 93
---- ---- in solids, 176
---- of liquids in liquids (binary), 95
---- ---- ---- (ternary), 240
---- ----, influence of temperature on, 247
---- of solids in liquids, 106
---- ---- in solids, 180
----, solid, 175, 180
----, univariant systems, 127
Space model for carnallite, 284
Stability limit, 202
Steel, formation of, 223
Sublimation curve, 63
---- ---- of ice, 24
---- without fusion, 65
Succinic nitrile and water, 122
---- ether, water, 252
Sulphur, 33, 34
---- dioxide and water, 169
---- ---- and potassium iodide, 158
----, transition point of rhombic and monoclinic, 36
Supersaturation, 113, 114, 124
----, limits of, 114
Systems, condensed, 36
---- of one component, 21
---- of two components, 76, 77, 207

T
Tachydrite, influence of pressure on the transition point of, 263
Tartrate, dimethyl, 217
----, sodium potassium, 259
Tautomeric substances, 195
Tensimeter, 91
Thallium nitrate and potassium nitrate, 192
Theorem of van't Hoff and Le Chatelier, 57
Thermometric determination of transition point, 337
Tin, 41
----, lead, bismuth, 255
---- plague, 43
----, transition point of white and grey, 41
_p_-Toluidine and _o_-nitrophenol, 213
---- and phenol, 214
Transformation of optically active substances, 220
----, suspended, 37, 69, 89, 113, 137, 155
----, velocity of, 70
Transition curve, 66
---- ---- of Glauber's salt, 68, 140
---- ---- of rhombic and monoclinic sulphur, 37
---- interval, 270, 277, 315
---- point, 34
---- ---- for double salts, 258
---- ----, influence of pressure on the, 68
---- points, as fixed points in thermometry, 140
---- ----, methods of determining, 331
---- ---- of polymorphic substances, 63
Triangle, graphic representation by, 235
Triethylamine and water, 101
Triple point, 27, 55
---- ----, arrangement of curves round, 56
---- ----, changes at, 58
---- ----, ice, water, vapour, 27
---- ----, ice II., ice III., and water, 33
---- ----, metastable, 38
---- ----, monoclinic sulphur, liquid, vapour, 38
---- ----, monoclinic and rhombic sulphur, liquid, 38
---- ----, monoclinic and rhombic sulphur, vapour, 34
{350}
---- ----, red phosphorus, liquid, vapour, 47
---- ----, rhombic sulphur, liquid, vapour, 38
---- ---- solid, solid, vapour, 62
---- ----, white phosphorus, liquid, vapour, 48

U
Univariant systems, 16

V
Van't Hoff, theorem of, 57
Vaporization curve, 63
---- ----, interpolation and extrapolation of, 66
---- ---- of water, 21, 23
Vapour pressure, constancy of, and formation of compounds, 90
---- ----, dependence of, on solid phase, 88
---- ----, influence of surface tension on, 2
---- ---- in three-component systems, 261
---- ----, measurement of, 91, 334
---- ---- of calcium chloride solutions, 150
---- ---- of ice, 25, 31
---- ---- of small drops, 10
---- ---- of sodium sulphate and water, 138
Vapour pressure of solid, solution, vapour, 126
---- ---- of water, 21, 31
Variability of a system, 14, 16
Variance of a system, 16
Volatile components, two, 161

W
Water, 21
----, acetic acid, chloroform, 241
----, acetone, phenol, 248
----, alcohol, ether, 246
----, ----, chloroform, 246
----, aniline, phenol, 250
----, bivariant systems of, 29
----, critical pressure of, 23
----, critical temperature of, 23
----, equilibrium between ice and, 25
----, ---- between vapour and, 21
----, ether, succinic nitrile, 252
----, supercooled, 30
----, ----, vapour pressure of, 31
----, vaporization curve of, 21
----, vapour pressure of, 23

Z
Zeolites, 176
Zinc, lead, silver, 246
---- chloride in water, solubility of, 157

THE END

PRINTED BY WILLIAM CLOWES AND SONS, LIMITED, LONDON AND BECCLES.

* * * * *

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 Silikatschmelzloesungen_. (Christiania, 1903, 1904.)

[5] _Trans. Connecticut Acad._, 1874-1878.

[6] Lehre von der chemischen Verwandtschaft der Koerper, 1777.

[7] See Ostwald's _Klassiker_, No. 74.

[8] Etudes sur les affinites 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] _Memoires 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] Abh_andl. 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 0deg has recently been very accurately determined by Thiesen and Scheel (_loc. cit._), and found to be 4.579 +/- 0.001 mm. of mercury (at 0deg), 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. neerland_, 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 0deg.

[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. fuer 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 fuer 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] Schroetter, _Pogg. Annalen_, 1850, 81. 276; Troost and Hautefeuille, _Annales de Chim. et Phys._ 1874 [5], 2. 153; _Ann. Scient. Ecole 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 fuer 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, _Fluessige Kristalle_ (Engelmann, 1904), or the smaller monograph by Schenck, _Kristallinische Fluessigkeiten und fluessige 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 Fluessigkeiten und fluessige 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_/_dt_ = Q/(T(_v_{2}_ - _v_{1}_)), 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. neer._, 1901 [2], 6. 244).

[115] _Phil. Mag._, 1886, 21. 33. See also S. A. Moss, _Physical Review_, 1903, 16. 356.

[116] This is found also in the case of bismuth. See Tammann, _Zeitschr. anorgan. Chem._, 1904, 40. 54.

[117] See p. 57, footnote.

[118] _Pogg. Annalen_, 1850, 81. 562.

[119] Barus, _Amer. Jour. Sci._, 1892, 42. 125; Mack, _Compt. rend._, 1898, 127. 361; Hulett, _Zeitschr. physikal. Chem._, 1899, 38. 629.

[120] _Annalen der Physik_, 1899 [3], 68. 553, 629; 1900 [4], 1. 275; 2. 1; 3. 161. See also Tammann, _Kristallisieren und Schmelzen_ (Leipzig, 1903).

[121] Ostwald, _Lehrbuch_, II. 2. 373; Poynting, _Phil. Mag._, 1881 [5], 12. 2; Planck, _Wied. Annalen_, 1882, 15. 446.

[122] Bakhuis Roozeboom, _Das Heterogene Gleichgewicht_, I. p. 91.

[123] Lussana, _Il nuovo Cimento_, 1895 [4], 1. 105.

[124] Tammann, _Zeitschr. physikal. Chem._, 1903, 46. 818.

[125] Foote, _Zeitschr. physikal. Chem._, 1900, 33. 740.

[126] Ostwald, _Zeitschr. physikal. Chem._, 1897, 22. 289.

[127] Van't Hoff, _Arch, neer._, 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 Kuester, _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 Jaffe (_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 fuer 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 Schoenbeck, _Annalen der Physik_, 1902 [4], 8. 652. See also Chr. Fuechtbauer, _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 280deg 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 Verfluessigung 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. neerland._ 1901 [2], 6. 471.

[183] Tilden and Shenstone, _Phil. Trans._ 1884, 175. 23; Hulett and Allen, _Jour. Amer. Chem. Soc._ 1902, 24. 667; Andreae, _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, T_{1}, 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. Mueller 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 Jaffe, _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.