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
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]).