GULDBERG-WAAGE CURVE AT 100.

----------------------+-----------------------+-----------------+-------

100 moles of water

K2CO3 Solid phases.

contain, in moles,

[Sigma]_k__{2}

-----

K2SO4

K_{2}CO_{3}

K_{2}SO_{4}

----------------------+-----------+-----------+-----------------+------- BaCO_{3} + K_{2}SO_{4}

23.9

12.65

35.65

1.82 + BaSO_{4}

BaCO_{3} + BaSO_{4}

6.28

2.02

8.3

3.1 " "

3.17

0.851

4.025

3.7 ----------------------+-----------+-----------+-----------------+-------

{330}

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 const.i.tutes a sort of large thermometer (Fig. 129). Some of the substance to be examined is pa.s.sed 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 pa.s.sing 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.

[Ill.u.s.tration: FIG. 129.]

[Ill.u.s.tration: FIG. 130.]

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 1.

-------------------------------------------------------- 15.6

134

16.6

141

7 17.6

148

7 18.6

154

6 19.6

161

7 20.6

168

7 21.6

241

73 22.6

243

2 23.6

251

8 24.6

259

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 {333} 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 pa.s.ses 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 pa.s.ses 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 {334} multiple point), and the latter can therefore be determined by ascertaining the temperature at which this ident.i.ty 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 quant.i.ty along with the solvent in a tube carefully closed by a gla.s.s 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 gla.s.s 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 pa.s.ses 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 pa.s.ses through the rubber stopper in _a_, can be closed by a plug {335} attached to a gla.s.s rod _ff_, which pa.s.ses 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.

[Ill.u.s.tration: FIG. 131.]

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 gla.s.s screw.

[Ill.u.s.tration: FIG. 132.]

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-c.o.c.k _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.

[Ill.u.s.tration: FIG. 133.]

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 pa.s.sed 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: 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 a.n.a.logous to the supercooling of a liquid.

A similar halt in the temperature would be observed on pa.s.sing 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 pa.s.sing 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.