CHAPTER XVIII

SYSTEMS OF FOUR COMPONENTS

In the systems which have so far been studied, we have met with cases where two or three components could enter into combination; but in no case did we find double decomposition occurring. The reason of this is that in the systems previously studied, in which double decomposition might have been possible, namely in those systems in which two salts acted as components, the restriction was imposed that either the basic or the acid constituent of these salts must be the same; a restriction imposed, indeed, for the very purpose of excluding double decomposition. Now, however, we shall allow this restriction to fall, thereby extending the range of study.

Hitherto, in connection with four-component systems, the attention has been directed solely to the study of aqueous solutions of salts, and more especially of the salts which occur in sea-water, _i.e._ chiefly, the sulphates and chlorides of magnesium, potassium, and sodium. The importance of these investigations will be recognized when one recollects that by the evaporation of sea-water there have been formed the enormous salt-beds at Stassfurt, which constitute at present the chief source of the sulphates and chlorides of magnesium and potassium. The investigations, therefore, are not only of great geological interest as tending to elucidate the conditions under which these salt-beds have been formed, but are of no less importance for the industrial working of the deposits.

It is, however, not the intention to enter here into any detailed description of the different systems which have so far been studied, and of the sometimes very complex relationships {312} met with, but merely to refer briefly to some points of more general import in connection with these systems.[382]

Reciprocal Salt-Pairs. Choice of Components.--When two salts undergo double decomposition, the interaction can be expressed by an equation such as

NH_{4}Cl + NaNO_{3} = NaCl + NH_{4}NO_{3}

Since one pair of salts--NaCl + NH_{4}NO_{3}--is formed from the other pair--NH_{4}Cl + NaNO_{3}--by double decomposition, the two pairs of salts are known as _reciprocal salt-pairs_.[383] It is with systems in which the component salts form reciprocal salt-pairs that we have to deal here.

It must be noted, however, that the four salts formed by two reciprocal salt-pairs do not constitute a system of four, but only of _three_ components. This will be understood if it is recalled that only so many constituents are taken as components as are necessary to _express_ the composition of all the phases present (p. 12). It will be seen, now, that the composition of each of the four salts which can be present together can be expressed in terms of three of them. Thus, for example, in the case of NH_{4}Cl, NaNO_{3}, NH_{4}NO_{3}, NaCl, we can express the composition of NH_{4}Cl by NH_{4}NO_{3} + NaCl - NaNO_{3}; or of NaNO_{3} by NH_{4}NO_{3} + NaCl - NH_{4}Cl. In all these cases it will be seen that negative quantities of one of the components must be employed; but that we have seen to be quite permissible (p. 12). The number of components is, therefore, three; but any three of the four salts can be chosen.

Since, then, two reciprocal salt-pairs constitute only three {313} components or independently variable constituents, another component is necessary in order to obtain a four-component system. As such, we shall choose water.

Transition Point.--In the case of the formation of double salts from two single salts, we saw that there was a point--the _quintuple point_--at which five phases could coexist. This point we also saw to be a transition point, on one side of which the double salt, on the other side the two single salts in contact with solution, were found to be the stable system. A similar behaviour is found in the case of reciprocal salt-pairs. The four-component system, two reciprocal salt-pairs and water, can give rise to an invariant system in which the six phases, four salts, solution, vapour, can coexist; the temperature at which this is possible constitutes a _sextuple point_. Now, this sextuple point is also a transition point, on the one side of which the one salt-pair, on the other side the reciprocal salt-pair, is stable in contact with solution.

The sextuple point is the point of intersection of the curves of six univariant systems, viz. four solubility curves with three solid phases each, a vapour-pressure curve for the system: two reciprocal salt-pairs--vapour; and a transition curve for the condensed system: two reciprocal salt-pairs--solution. If we omit the vapour phase and work under atmospheric pressure (in open vessels), we find that the transition point is the point of intersection of four solubility curves.

Just as in the case of three-component systems we saw that the presence of one of the single salts along with the double salt was necessary in order to give a univariant system, so in the four-component systems the presence of a third salt is necessary as solid phase along with one of the salt-pairs. In the case of the reciprocal salt-pairs mentioned above, the transition point would be the point of intersection of the solubility curves of the systems with the following groups of salts as solid phases: Below the transition point: NH_{4}Cl + NaNO_{3} + NaCl; NH_{4}Cl + NaNO_{3} + NH_{4}NO_{3}; above the transition point: NaCl + NH_{4}NO_{3} + NaNO_{3}; NaCl + NH_{4}NO_{3} + NH_{4}Cl. From this we see that the two salts NH_{4}Cl and NaNO_{3} would be able to exist together with solution below the transition point, but not above it. This transition point has not been determined. {314}

Formation of Double Salts.--In all cases of four-component systems so far studied, the transition points have not been points at which one salt-pair passed into its reciprocal, but at which a double salt was formed. Thus, at 4.4deg Glauber's salt and potassium chloride form glaserite and sodium chloride, according to the equation

2Na_{2}SO_{4},10H_{2}O + 3KCl = K_{3}Na(SO_{4})_{2} + 3NaCl + 20H_{2}O

Above the transition point, therefore, there would be K_{3}Na(SO_{4})_{2}, NaCl and KCl; and it may be considered that at a higher temperature the double salt would interact with the potassium chloride according to the equation

K_{3}Na(SO_{4})_{2} + KCl = 2K_{2}SO_{4} + NaCl

thus giving the reciprocal of the original salt-pair. This point has, however, not been experimentally realized.[384]

Transition Interval.--A double salt, we learned (p. 277), when brought in contact with water at the transition point undergoes partial decomposition with separation of one of the constituent salts; and only after a certain range of temperature (transition interval) has been passed, can a pure saturated solution be obtained. A similar behaviour is also found in the case of reciprocal salt-pairs. If one of the salt-pairs is brought in contact with water at the transition point, interaction will occur and one of the salts of the reciprocal salt-pair will be deposited; and this will be the case throughout a certain range of temperature, after which it will be possible to prepare a solution saturated only for the one salt-pair. In the case of ammonium chloride and sodium nitrate the lower limit of the transition interval is 5.5deg, so that above this temperature and up to that of the transition point (unknown), ammonium chloride and sodium nitrate in contact with water would give rise to a third salt by double decomposition, in this case to sodium chloride.[385]

{315}

Graphic Representation.--For the graphic representation of systems of four components, four axes may be chosen intersecting at a point like the edges of a regular octahedron (Fig. 122).[386] Along these different axes the equivalent molecular amounts of the different salts are measured.

To represent a given system consisting of _x_B, _y_C, and _z_D in a given amount of water (where B, C, and D represent equivalent molecular amounts of the salts), measure off on OB and OC lengths equal to _x_ and _y_ respectively. The point of intersection _a_ (Fig. 122) represents a solution containing _x_B and _y_C (_ab_ = _x_; _ac_ = _y_). From _a_ a line _a_P is drawn parallel to OD and equal to _z_. P then represents the solution of the above composition.

It is usual, however, not to employ the three-dimensional figure, but its horizontal and vertical projections. Fig. 122, if projected on the base of the octahedron, would yield a diagram such as is shown in Fig. 123. The projection of the edges of the octahedron form two axes at right angles and give rise to four quadrants similar to those employed for the representation of ternary solutions (p. 273). Here, the point _a_ represents a ternary solution saturated with respect to B and C; and _a_P, quaternary solutions in equilibrium with the same two salts as solid phases. Such a diagram represents the conditions of equilibrium only for one definite temperature, and corresponds, therefore, to the isothermal diagrams for ternary systems (p. 273). In such a diagram, since the temperature and {316} pressure are constant (vessels open to the air), a surface will represent a solution in equilibrium with only one solid phase; a line, a solution with two solid phases, and a point, one in equilibrium with three solid phases.

Example.--As an example of the complete isothermal diagram, there may be given one representing the equilibria in the system composed of water and the reciprocal salt-pair sodium sulphate--potassium chloride for the temperature 0deg (Fig. 124).[387] The amounts of the different salts are measured along the four axes, and the composition of the solution is {317} expressed in equivalent gram-molecules per 1000 gram-molecules of water.[388]

The outline of this figure represents four ternary solutions in which the component salts have a common acid or basic constituent; viz. sodium chloride--sodium sulphate, sodium sulphate--potassium sulphate, potassium sulphate--potassium chloride, potassium chloride--sodium chloride. These four sets of curves are therefore similar to those discussed in the previous chapter. In the case of sodium and potassium sulphate, a double salt, _glaserite_ [K_{3}Na(SO_{4})_{2}] is formed. Whether glaserite is really a definite compound or not is still a matter of doubt, since isomorphic mixtures of Na_{2}SO_{4} and K_{2}SO_{4} have been obtained. According to van't Hoff and Barscholl,[389] glaserite is an isomorphous mixture; but Gossner[390] considers it to be a definite compound having the formula K_{3}Na(SO_{4})_{2}. Points VIII. and IX. represent solutions saturated with respect to glaserite and sodium sulphate, and glaserite and potassium sulphate respectively.

The lines which pass inwards from these boundary curves represent solutions containing three salts, but in contact with only two solid phases; and the points where three lines meet, or where three fields meet, represent solutions in equilibrium with three solid phases; with the phases, namely, belonging to the three concurrent fields.

If it is desired to represent a solution containing the salts say in the proportions, 51Na_{2}Cl_{2}, 9.5K_{2}Cl_{2}, 3.5K_{2}SO_{4}, the difficulty is met with that two of the salts, sodium chloride and potassium sulphate, lie on opposite axes. To overcome this difficulty the difference 51 - 3.5 = 47.5 is taken and measured off along the sodium chloride axis; and the solution is therefore represented by the point 47.5Na_{2}Cl_{2}, 9.5K_{2}Cl_{2}. In order, therefore, to find the amount of potassium sulphate present {318} from such a diagram, it is necessary to know the total number of salt molecules in the solution. When this is known, it is only necessary to subtract from it the sum of the molecules of sodium and potassium chloride, and the result is equal to twice the number of potassium sulphate molecules. Thus, in the above example, the total number of salt molecules is 64. The number of molecules of sodium and potassium chloride is 57; 64 - 57 = 7, and therefore the number of potassium sulphate molecules is 3.5.

Another method of representation employed is to indicate the amounts of only two of the salts in a plane diagram, and to measure off the total number of molecules along a vertical axis. In this way a solid model is obtained.

The numerical data from which Fig. 124 was constructed are contained in the following table, which gives the composition of the different solutions at 0deg:--[391]

---------------------------------------- | | | | Point. | Solid phases. | | | ---------------------------------------- I. | NaCl | | | II. | KCl | | | III. | Na_{2}SO_{4},10H_{2}O | | | IV. | K_{2}SO_{4} | | | V. | NaCl; KCl | | | VI. | NaCl; Na_{2}SO_{4},10H_{2}O | | | VII. | KCl; K_{2}SO_{4} | | | VIII. |{ Glaserite; }| |{ Na_{2}SO_{4},10H_{2}O }| | | IX. | Glaserite; K_{2}SO_{4} | | | X. |{ Na_{2}SO_{4},10H_{2}O; KCl; }| |{ NaCl }| | | XI. |{ Na_{2}SO_{4},10H_{2}O; KCl; }| |{ glaserite }| | | XII. | K_{2}SO_{4}; KCl; glaserite | ---------------------------------------- [Transcriber's note: table continued below...] ------------------------------------------------------------------------- Composition of solution in gram-mols. | Total per 1000 gram-mols. water. | number -------------------------------------------------------------| of salt Na_{2}Cl_{2}. | K_{2}Cl_{2}. | Na_{2}SO_{4}. | K_{2}SO_{4}. | molecules. ------------------------------------------------------------------------- 55 | -- | -- | -- | 55 | | | | -- | 34.5 | -- | -- | 34.5 | | | | -- | -- | 6 | -- | 6 | | | | -- | -- | -- | 9 | 9 | | | | 46.5 | 12.5 | -- | -- | 59 | | | | 47.5 | -- | 8 | -- | 55.5 | | | | -- | 34.5 | -- | 1 | 35.5 | | | | -- | -- | 10 | 10 | 20 | | | | | | | | -- | -- | 7.5 | 10 | 17.5 | | | | 51 | 9.5 | -- | 3.5 | 64 | | | | | | | | 40.5 | 13 | -- | 3.5 | 57 | | | | | | | | 18 | 23 | -- | 3 | 44 -------------------------------------------------------------------------

From the aspect of these diagrams the conditions under which the salts can coexist can be read at a glance. Thus, {319} for example, Fig. 124 shows that at 0deg Glauber's salt and potassium chloride can exist together with solution; namely, in contact with solutions having the composition X--XI. This temperature must therefore be below the transition point of this salt-pair (p. 314). On raising the temperature to 4.4deg, it is found that the curve VIII.--XI. moves so that the point XI. coincides with point X. At this point, therefore, there will be _four_ concurrent fields, viz. Glauber's salt, potassium chloride, glaserite, and sodium chloride. But these four salts can coexist with solution only at the transition point; so that 4.4deg is the transition temperature of the salt-pair: Glauber's salt--potassium chloride. At higher temperatures the line VIII.--XI. moves still further to the left, so that the field for Glauber's salt becomes entirely separated from the field for potassium chloride. This shows that at temperatures above the transition point the salt-pair Glauber's salt--potassium chloride cannot coexist in presence of solution.

If it is only desired to indicate the mutual relationships of the different components and the conditions for their coexistence (_paragenesis_), a simpler diagram than Fig. 124 can be employed. Thus if the boundary curves of Fig. 124 are so drawn that they cut one another at right angles, a figure such as Fig. 125 is obtained, the Roman numerals here corresponding with those in Fig. 124.

Ammonia-Soda Process.--One of the most important applications of the Phase Rule to systems of four components with reciprocal salt-pairs has recently been made by Fedotieff[392] in his investigations of the conditions for the formation of sodium carbonate by the so-called ammonia-soda (Solvay) {320} process.[393] This process consists, as is well known, in passing carbon dioxide through a solution of common salt saturated with ammonia.

Whatever differences of detail there may be in the process as carried out in different manufactories, the reaction which forms the basis of the process is that represented by the equation

NaCl + NH_{4}HCO_{3} = NaHCO_{3} + NH_{4}Cl

We are dealing here, therefore, with reciprocal salt-pairs, the behaviour of which has just been discussed in the preceding pages. The present case is, however, simpler than that of the salt-pair Na_{2}SO_{4}.10H_{2}O + KCl, inasmuch as under the conditions of experiment neither hydrates nor double salts are formed. Since the study of the reaction is rendered more difficult on account of the fact that ammonium bicarbonate in solution, when under atmospheric pressure, undergoes decomposition at temperatures above 15deg, this temperature was the one chosen for the detailed investigation of the conditions of equilibrium. Since, further, it has been shown by Bodlaender[394] that the bicarbonates possess a definite solubility only when the pressure of carbon dioxide in the solution has a definite value, the measurements were carried out in solutions saturated with this gas. This, however, does not constitute another component, because we have made the restriction that the sum of the partial pressures of carbon dioxide and water vapour is equal to 1 atmosphere. The concentration of the carbon dioxide is, therefore, not independently variable (p. 10).

In order to obtain the data necessary for a discussion of the conditions of soda formation by the ammonia-soda process, solubility determinations with the four salts, NaCl, NH_{4}Cl, NH_{4}HCO_{3}, and NaHCO_{3} were made, first with the single salts and then {321} with the salts in pairs. The results obtained are represented graphically in Fig. 126, which is an isothermal diagram similar to that given by Fig. 124. The points I., II., III., IV., represent the composition of solutions in equilibrium with two solid salts. We have, however, seen (p. 314) that the transition point, when the experiment is carried out under constant pressure (atmospheric pressure), is the point of intersection of four solubility curves, each of which represents the composition of solutions in equilibrium with three salts, viz. one of the reciprocal salt-pairs along with a third salt. Since, now, it was found that the stable salt-pair at temperatures between 0deg and 30deg is sodium bicarbonate and ammonium chloride, determinations were made of the composition of solutions in equilibrium with NaHCO_{3} + NH_{4}Cl + NH_{4}HCO_{3} and with NaHCO_{3} + NH_{4}Cl + NaCl as solid phases. Under the {322} conditions of experiment (temperature = 15deg) sodium chloride and ammonium bicarbonate cannot coexist in contact with solution. These determinations gave the data necessary for the construction of the complete isothermal diagram (Fig. 127). The most important of these data are given in the following table (temperature, 15deg):--

------------------------------------------------------------------------- | | Composition of the solution in gram-molecules | | to 1000 gram-molecules Point. | Solid phases. | of water. | |---------------------------------------------- | | NaHCO_{3} | NaCl | NH_{4}HCO_{3} | NH_{4}Cl ------------------------------------------------------------------------- -- | NaHCO_{3} | 1.08 | -- | -- | -- -- | NaCl | -- | 6.12 | -- | -- -- | NH_{4}HCO_{3} | -- | -- | 2.36 | -- -- | NH_{4}Cl | -- | -- | -- | 6.64 I. | NaHCO_{3}; NaCl | 0.12 | 6.06 | -- | -- II. | NaCl; NH_{4}Cl | -- | 4.55 | -- | 3.72 III. | NH_{4}Cl; | -- | -- | 0.81 | 6.40 | NH_{4}HCO_{3} | | | | IV. | NaHCO_{3}; | 0.71 | -- | 2.16 | -- | NH_{4}HCO_{3} | | | | P_{1} | NaHCO_{3}; | 0.93 | 0.51 | -- | 6.28 | NH_{4}HCO_{3}; | | | | | NH_{4}Cl | | | | P_{2} | NaHCO_{3}; | 0.18 | 4.44 | -- | 3.73 | NaCl; NH_{4}Cl | | | | -------------------------------------------------------------------------

With reference to the solution represented by the point P_{1}, it may be remarked that it is an incongruently saturated solution (p. 279). If sodium chloride is added to this solution, the composition of the latter undergoes change; and if a sufficient amount of the salt is added, the solution P_{2} is obtained.

Turning now to the practical application of the data so obtained, consider first what is the influence of concentration on the yield of soda. Since the reaction consists essentially in a double decomposition between sodium chloride and ammonium bicarbonate, then, after the deposition of the sodium bicarbonate, we obtain a solution containing sodium chloride, ammonium chloride, and sodium bicarbonate. In order to ascertain to what extent the sodium chloride has been converted into solid sodium bicarbonate, it is necessary to examine the composition of the solution which is obtained {323} with definite amounts of sodium chloride and ammonium bicarbonate.

Consider, in the first place, the solutions represented by the curve P_{2}P_{1}. With the help of this curve we can state the conditions under which a solution, saturated for ammonium chloride, is obtained, after deposition of sodium bicarbonate. In the following table the composition of the solutions is given which are obtained with different initial amounts of sodium chloride and ammonium bicarbonate. The last two columns give the percentage amount of the sodium used, which is deposited as solid sodium bicarbonate (U_{Na}); and likewise the percentage amount of ammonium bicarbonate which is usefully converted into sodium bicarbonate, that is to say, the amount of the radical HCO_{3} deposited (U_{NH_{4}}):-- {324}

------+---------------------+ |Initial composition | |of the solutions: | |grams of salt to 1000| Point.|grams of water. | +------+--------------+ | NaCl | NH_{4}HCO_{3}| ------+------+--------------+ P_{2} | 479 | 295 | -- | 448 | 360 | -- | 417 | 431 | P_{1} | 397 | 496 | ------+------+--------------+ [Transcriber's note: table continued below...] +----------------------------------+---------+---------- | | | |Composition of solutions obtained:| | |gram-equivalents per 1000 grams |U_{Na} |U_{NH_{4}} |of water. |per cent.|per cent. +----------+------+------+---------+ | | HCO_{3} | Cl | Na | NH_{4} | | +----------+------+------+---------+---------+---------- | 0.18 | 8.17 | 4.62 | 3.73 | 43.4 | 95.1 | 0.31 | 7.65 | 3.39 | 4.56 | 55.7 | 93.4 | 0.51 | 7.13 | 2.19 | 5.45 | 69.2 | 90.5 | 0.92 | 6.79 | 1.44 | 6.28 | 78.8 | 85.1 +----------+------+------+---------+---------+----------

This table shows that the greater the excess of sodium chloride, the greater is the percentage utilization of ammonia (Point P_{2}); and the more the amount of sodium chloride decreases, the greater is the percentage amount of sodium chloride converted into bicarbonate. In the latter case, however, the percentage utilization of the ammonium bicarbonate decreases; that is to say, less sodium bicarbonate is deposited, or more of it remains in solution.

Consider, in the same manner, the relations for solutions represented by the curve P_{2}IV, which gives the composition of solutions saturated with respect to sodium bicarbonate and ammonium bicarbonate. In this case we obtain the following results:--

------+---------------------+ |Initial composition | |of the solutions: | |grams of salt to 1000| Point.|grams of water. | +------+--------------+ | NaCl | NH_{4}HCO_{3}| ------+------+--------------+ P_{1} | 397 | 496 | -- | 351 | 446 | -- | 316 | 412 | -- | 294 | 389 | -- | 234 | 327 | ------+------+--------------+ [Transcriber's note: table continued below...] +----------------------------------+------+---------- | | | |Composition of solutions obtained:| | |in gram-equivalents per 1000 grams|U_{Na}|U_{NH_{4}} |of water. | | +----------+------+------+---------+ | | HCO_{3} | Cl | Na | NH_{4} | | +----------+------+------+---------+------+---------- | 0.92 | 6.79 | 1.44 | 6.28 | 78.8 | 85.1 | 0.99 | 6.00 | 1.34 | 5.65 | 77.7 | 82.5 | 1.07 | 5.41 | 1.27 | 5.21 | 76.4 | 79.5 | 1.12 | 5.03 | 1.23 | 4.92 | 75.5 | 75.1 | 1.30 | 4.00 | 1.16 | 4.14 | 71.0 | 68.6 +----------+------+------+---------+------+----------

As is evident from this table, diminution in the relative amount of sodium chloride exercises only a slight influence {325} on the utilization of this salt, but is accompanied by a rapid diminution of the effective transformation of the ammonium bicarbonate. So far as the efficient conversion of the sodium is concerned, we see that it reaches its maximum at the point P_{1}, and that it decreases both with increase and with decrease of the relative amount of sodium chloride employed; and faster, indeed, in the former than in the latter case. On the other hand, the effective transformation of the ammonium bicarbonate reaches its maximum at the point P_{2}, and diminishes with increase in the relative amount of ammonium bicarbonate employed. Since sodium chloride is, in comparison with ammonia--even when this is regenerated--a cheap material, it is evidently more advantageous to work with solutions which are relatively rich in sodium chloride (solutions represented by the curve P_{1}P_{2}). This fact has also been established empirically.

When, as is the case in industrial practice, we are dealing with solutions which are saturated not for two salts but only for sodium bicarbonate, it is evident that we have then to do with solutions the composition of which is represented by points in the area P_{1}P_{2}I,IV. Since in the commercial manufacture, the aim must be to obtain as complete a utilization of the materials as possible, the solutions employed industrially must lie in the neighbourhood of the curves P_{2}P_{1}IV, as is indicated by the shaded portion in Fig. 127. The best results, from the manufacturer's standpoint, will be obtained, as already stated, when the composition of the solutions approaches that given by a point on the curve P_{2}P_{1}. Considered from the chemical standpoint, the results of the experiments lead to the conclusion that the Solvay process, _i.e._ passage of carbon dioxide through a solution of sodium chloride saturated with ammonia, is not so good as the newer method of Schloesing, which consists in bringing together sodium chloride and ammonium bicarbonate with water.[395]

{326}

Preparation of Barium Nitrite.--Mention may also be made here of the preparation of barium nitrite by double decomposition of barium chloride and sodium nitrite.[396]

The reaction with which we are dealing here is represented by the equation

BaCl_{2} + 2NaNO_{2} = 2NaCl + Ba(NO_{2})_{2}

It was found that at the ordinary temperature NaCl and Ba(NO_{2})_{2} form the stable salt-pair. If, therefore, barium chloride and sodium nitrite are brought together with an amount of water insufficient for complete solution, transformation to the stable salt-pair occurs, and sodium chloride and barium nitrite are deposited. When, however, a stable salt-pair is in its transition interval (p. 315), a third salt--in this case barium chloride--will be deposited, as we have already learned. On bringing barium chloride and sodium nitrite together with water, therefore, three solid phases are obtained, viz. BaCl_{2}, NaCl, Ba(NO_{2})_{2}. These three phases, together with solution and vapour, constitute a univariant system, so that at each temperature the composition of the solution must be constant.

Witt and Ludwig found that the presence of solid barium chloride can be prevented by adding an excess of sodium nitrite, as can be readily foreseen from what has been said. Since the solution in presence of the three solid phases must have a definite composition at a definite temperature, the addition of sodium nitrite to the solution must have, as its consequence, the solution of an equivalent amount of barium chloride, and the deposition of an equivalent amount of sodium chloride and barium nitrite. By sufficient addition of sodium nitrite, the complete disappearance of the solid barium chloride can be effected, and there will remain only the stable salt-pair sodium chloride and barium nitrite. As was pointed out by Meyerhoffer, however, the disappearance of the barium chloride is effected, not by a change in the {327} composition of the solution, but by the necessity for the composition of the solution remaining constant.

Barium Carbonate and Potassium Sulphate.--As has been found by Meyerhoffer,[397] these two salts form the stable pair, not only at the ordinary temperature, but also at the melting point. For the ordinary temperatures this was proved in the following manner: A solution with the solid phases K_{2}SO_{4} and K_{2}CO_{3}.2H_{2}O in excess can only coexist in contact either with BaCO_{3} or with BaSO_{4}, since, evidently, in one of the two groups the stable system must be present. Two solutions were prepared, each with excess of K_{2}SO_{4} + K_{2}CO_{3}.2H_{2}O, {328} and to one was added BaCO_{3} and to the other BaSO_{4}. After stirring for a few days, the barium sulphate was completely transformed to BaCO_{3}, whereas the barium carbonate remained unchanged. Consequently, BaCO_{3} + K_{2}SO_{4} + K_{2}CO_{3}.2H_{2}O is stable, and, therefore, so also is BaCO_{3} + K_{2}SO_{4}. That BaCO_{3} + K_{2}SO_{4} is the stable pair also at the melting point was proved by a special analytical method which allows of the detection of K_{2}CO_{3} in a mixture of the four solid salts. This analysis showed that a mixture of BaCO_{3} + K_{2}SO_{4}, after being fused and allowed to solidify, contains only small amounts of K_{2}CO_{3}; and this is due entirely to the fact that BaCO_{3} + K_{2}SO_{4} on fusion deposits a little BaSO_{4}, thereby giving rise at the same time to the separation of an equivalent amount of K_{2}CO_{3}.

The different solubilities are shown in Fig. 128. In this diagram the solubility of the two barium salts has been neglected. A is the solubility of K_{2}CO_{3}.2H_{2}O; addition of BaCO_{3} does not alter this. B is the solubility of K_{2}CO_{3}.2H_{2}O + K_{2}SO_{4} + BaCO_{3}. A and B almost coincide, since the potassium sulphate is very slightly soluble in the concentrated solution of potassium carbonate. D gives the concentration of the solution in equilibrium with K_{2}SO_{4} + BaSO_{4}. The most interesting point is C. This solution is obtained by adding a small quantity of water to BaCO_{3} + K_{2}SO_{4}, whereupon, being in the transition interval, BaSO_{4} separates out and an equivalent amount of K_{2}CO_{3} goes into solution. C is the end point of the curve CO, which is called the Guldberg-Waage curve, because these investigators determined several points on it.

In their experiments, Guldberg and Waage found the ratio K_{2}CO_{3} : K_{2}SO_{4} in solution to be constant and equal to 4. This result is, however, not exact, for the curve CO is not a straight line, as it should be if the above ratio were constant; but it is concave to the abscissa axis, and more so at lower than at higher temperatures.

The following table refers to the temperature of 25deg. The Roman numbers in the first column refer to the points in Fig. 128. The numbers in the column [Sigma]_k__{2} give the amount, {329} in gram-molecules, of K_{2}CO_{3} + K_{2}SO_{4} contained in 1000 gram-molecules of water:--

SOLUBILITY DETERMINATIONS AT 25deg.

-----+-------------------------------------+-----------------------+ | | 100 gms. of the | | | solution contain, | No. | Solid phases. | in grams, | | | | | | |K_{2}CO_{3}|K_{2}SO_{4}| -----+-------------------------------------+-----------+-----------+ I. | K_{2}CO_{3}.2H_{2}O + BaCO_{3} | 53.2 | -- | | | | | II. |{ K_{2}CO_{3}.2H_{2}O + K_{2}SO_{4} }| 53.0 | 0.023 | |{ + BaCO_{3} }| | | | | | | III.}| K_{2}SO_{4} + BaCO_{3} | { 28.5 | 0.886 | IV. }| | { 22.1 | 1.72 | | | | | V. | BaCO_{3} + K_{2}SO_{4} + BaSO_{4} | 17.81 | 2.485 | | | | | VI. }| K_{2}SO_{4} + BaSO_{4} | { 12.6 | 3.92 | VII.}| | { 5.85 | 6.76 | | | | | VIII.| K_{2}SO_{4} | -- | 10.76 | | | | | IX. }| BaCO_{3} + BaSO_{4} | { 7.35 | 0.602 | X. }| | { 2.85 | 0.173 | -----+-------------------------------------+-----------+-----------+ [Transcriber's note: table continued below...] -----+-----------------------+-----------------+----------- | 1000 moles | | | of water contain, | | K_{2}CO_{3} No. | in moles, |[Sigma]_k__{2} | ----------- | | | | K_{2}SO_{4} |K_{2}CO_{3}|K_{2}SO_{4}| | -----+-----------+-----------+-----------------+----------- I. | 147.9 | -- | -- | -- | | | | II. | 147.8 | 0.051 | -- | -- | | | | | | | | III.}| 52.58 | 1.296 | -- | -- IV. }| 37.79 | 2.333 | -- | -- | | | | V. | 29.11 | 3.220 | 32.32 | 9.03 | | | | VI. }| 19.66 | 4.853 | -- | -- VII.}| 8.724 | 7.995 | -- | -- | | | | VIII.| -- | 12.47 | -- | -- | | | | IX. }| 10.43 | 0.676 | 11.11 | 15.0 X. }| 3.828 | 0.184 | 4.0 | 21.0 -----+-----------+-----------+-----------------+-----------

The Guldberg-Waage curve at 100deg was also determined, and it was found that the ratio K_{2}CO_{3}: K_{2}SO_{4} is also not constant, although the variations are not so great as at 25deg.

GULDBERG-WAAGE CURVE AT 100deg.

----------------------+-----------------------+-----------------+------- |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 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.

[198] _Ber._, 1877, 20. 2223.

[199] _Silz-Ber. Wien. Akad._, 1880, 81. II. 1058.

[200] Guthrie, _Phil. Mag._, 1875 [4], 49. 206.

[201] If in the neighbourhood of the cryohydric point solution should be accompanied by an evolution of heat, then as the solubility would in that case increase with fall of temperature, salt would pass into solution.

[202] Walker, _Zeitschr. physikal. Chem._, 1890, 5. 193.

[203] _Zeitschr. physikal. Chem._, 1897, 23. 418.

[204] Provided the solid nitrile is not present in too great excess.

[205] _Wied. Annalen_, 1886, 28. 328. Cf. Ostwald, _Lehrbuch_, II. 2. 872.

[206] Walker, _Zeitschr. physikal. Chem._, 1890, 5. 193. Schreinemakers, _ibid._, 1897, 23. 417. Roozeboom, _Rec. trav. chim. Pays-Bays_, 1889, 8. 257. Bruner, _Zeitschr. physikal. Chem._, 1897, 23. 542.

[207] Van't Hoff, _Lectures on Theoretical Chemistry_, I. p. 42. Ostwald, _Lehrbuch_, II. 2. 824.

[208] Ostwald, _Principles of Inorganic Chemistry_, translated by A. Findlay, 2nd edit., p. 453 (Macmillan, 1904); Skirrow and Calvert, _Zeitschr. physikal. Chem._, 1901, 37. 217.

[209] _Vide_ Loewel, _Annales chim. phys._, 1857 [3], 49. 32. Cf. Loewenherz, _Zeitschr. physikal. Chem._, 1895, 18. 82.

[210] Loewel, _loc. cit._ Gay-Lussac, _Annales chim. phys._, 1819, 11. 296. For the solubility at higher temperatures, see Tilden and Shenstone, _Phil. Trans._, 1884, 175. 23. Etard, _Annales chim. phys._, 1894 [7], 2. 548.

[211] Richards, _Zeitschr. physikal. Chem._, 1898, 26. 690; Richards and Wells, _ibid._, 1903, 43. 465. This temperature is not quite the same as that of the _quadruple point_ anhydrous salt--hydrated salt--solution--vapour, because the latter is the temperature at which the system is under the pressure of its own vapour. Since, however, the influence of pressure on the solubility is very slight (p. 107), the position of the two points will not be greatly different. The quadruple point was found by Cohen (_Zeitschr. physikal. Chem._, 1894, 14. 90) to be 32.6deg and 30.8 mm. of mercury.

[212] Van't Hoff and van Deventer, _Zeitschr. physikal. Chem._, 1887, 1. 185. Cf. Cohen, _ibid._, 1894, 14. 88.

[213] Debray, _Compt. rend._, 1868, 66. 194.

[214] Richards, _Zeitschr. physikal. Chem._, 1898, 26. 690. A number of other salt hydrates, having transition-points ranging from 20deg to 78deg, which might be used for the same purpose, have been given by Richards and Churchill, _ibid._, 1899, 28. 313.

[215] _Zeitschr. physikal. Chem._, 1903, 46. 818.

[216] Van't Hoff, _Lectures on Physical Chemistry_, I. p. 67.

[217] Cohen, _Zeitschr. physikal. Chem._, 1894, 14. 90.

[218] Ziz, _Schweigger's Journal_, 1815, 15. 166. See Ostwald, _Lehrbuch_, II. 2. 717.

[219] See, for example, the solubility determinations published in _Wissenschaftliche Abhandl. der physikalisch-technischen Reichsanstalt_, Vol. III., or in the _Berichte_, for the years 1897-1901.

[220] Meusser, _Ber._, 1901, 34. 2440.

[221] Mylius and von Wrochem, _Ber._, 1900, 33. 3693.

[222] Walker and Fyffe, _Jour. Chem. Soc._, 1903, 83. 180.

[223] _Monatshefte_, 1887, 8. 601.

[224] The equilibria between calcium chloride and water have been most completely studied by Roozeboom (_Zeitschr. physikal. Chem._, 1889, 4. 31).

[225] Hammerl, _Sitzungsber. Wien. Akad._, 2^{te} Abteil, 1878, 78. 59. Roozeboom, _Zeitschr. physikal. Chem._, 1889, 4. 31.

[226] Lidbury, _Zeitschr. physikal. Chem._, 1902, 39. 453. The curvature at the melting point is all the greater the more the compound is dissociated into its components in the liquid state. If the compound is _completely undissociated_, even in the vapour phase, the two branches of the curve will _intersect_, (_e.g._ pyridine and methyl iodide; Aten, _Versl. Konink. Akad. Wetensch. Amsterdam_, 1905, 13. 462). The smaller the degree of dissociation, therefore, the sharper will be the bend. (See Stortenbeker, _Zeitschr. physikal. Chem._, 1892, 10. 194.) From the extent of flattening of the curve, it is also possible, with some degree of approximation, to calculate the degree of dissociation of the substance in the fused state. (See Roozeboom and Aten, _Zeitschr. physikal. Chem._, 1905, 53. 463; Kremann, _Zeitschr. Elektrochem._, 1906, 12. 259.)

[227] See Roozeboom, _Zeitschr. physikal. Chem._, 1889, 4. 31.

[228] Tammann, _Wied. Annalen_, 1899, 68. 577.

[229] Duhem, _Journ. Physical Chem._, 1898, 2. 31.

[230] Gibbs, _Trans. Conn. Acad._, 3. 155; Saurel, _Journ. Phys. Chem._, 1901, 5. 35.

[231] In the case of the fusion of a compound of two components with formation of a liquid phase of the same composition, the temperature is a maximum; in the case of liquid mixtures of constant boiling-point, the temperature may be a minimum (p. 105).

[232] Roozeboom, _Zeitschr. physikal. Chem._, 1892, 10. 477. The formula of ferric chloride has been doubled, in order to avoid fractions in the expression of the water of crystallization.

[233] Roozeboom, _Zeitschr. physikal. Chem._, 1892, 10. 477.

[234] A similar series of hydrates is formed by zinc chloride and water (Dietz and Mylius, _Zeitschr. anorg. Chem._, 1905, 44. 209).

[235] Meyerhoffer, _Ber._, 1897, 30. 1810.

[236] Walden, _Ber._, 1899, 32. 2863.

[237] _Zeitschr. physikal. Chem._, 1903, 42. 432.

[238] This composition was also confirmed by measurements of the vapour pressure (cf. p. 90).

[239] Since all substances are no doubt volatile to a certain extent at some temperature, it is to be understood here that the substances are appreciably volatile at the temperature of the experiment.

[240] For a general discussion of the partial pressures in a system of two components, see Bancroft, _Journ. Physical Chem._, 1899, 3. 1.

[241] _Zeitschr. physikal. Chem._, 1889, 3. 11; _Rec. trav. chim. Pays-Bas_, 1888, 7. 152.

[242] The composition of a solution is represented symbolically by placing a double wavy line between the symbols of the components, and indicating the number of atoms present in the ordinary manner: thus, I [wavy] Cl_{_x_} represents a solution containing _x_ atoms of chlorine to one atom of iodine (Roozeboom, _Zeitschr. physikal. Chem._, 1888, 2. 450).

[243] Since iodine monochloride in the liquid state is only very slightly dissociated, the bend at C is very sharp (see p. 147, footnote). See also the investigation of the system pyridine and methyl iodide (Aten, _Versl. Konink. Akad. Wetensch. Amsterdam_, 1905, 13. 462).

[244] This upper branch of the curve is not shown in the figure, as the ordinate corresponding to 30deg would be very great.

[245] Stortenbeker, _Zeitschr. physikal. Chem._, 1889, 3. 22.

[246] Ramsay and Young, _Journ. Chem. Soc._, 1886, 49. 458.

[247] Van't Hoff, _Lectures on Physical Chemistry_, I. p. 77 (Arnold).

[248] This is different from what we found in the case of non-volatile solutes (p. 126). In the present case, the _partial pressure_ of the iodine in the vapour will be lowered by addition of chlorine, but the _total pressure_ is increased.

[249] The diminution of volume is supposed to be carried out at constant temperature. The pressure and the composition of the phases must, therefore, remain unchanged, and only the relative amounts of these can undergo alteration.

[250] At point _b_ the ratio of chlorine to iodine in the solution is less than in the monochloride, so that by the separation of this the excess of chlorine yielded by the condensation of the vapour is removed.

[251] Roozeboom, _Rec. trav. chim. Pays-Bas_, 1884, 3. 29; 1885, 4. 65; _Zeitschr. physikal. Chem._, 1888, 2. 450.

[252] Two curves "enclose" a field when they form with one another an angle less than two right angles.

[253] Roozeboom, _Zeitschr. physikal. Chem._, _loc. cit._

[254] Van't Hoff, _Zeitschr. physikal. Chem._, 1890, 5. 323.

[255] Bancroft has proposed to restrict the term "occlusion" to the formation of solid solutions, and to apply "adsorption" only to effects which are primarily due to surface tension. Such a distinction, however, would probably be very difficult to carry through, for although adsorption may, in large measure, be due to surface tension, the behaviour of adsorbed substances is similar to that of substances existing in solid solutions.

[256] Tammann, _Wied. Annalen_, 1897, 63. 16; _Zeitschr. physikal. Chem._, 1898, 27. 323.

[257] See, for example, Chappuis, _Wied. Annalen_, 1881, 12. 161; Joulin, _Annal. chim. phys._, 1881, [5], 22. 398; Kayser, _Wied. Annalen_, 1881, 12. 526.

[258] Hoitsema, _Zeitschr. physikal. Chem._, 1895, 17. 1.

[259] _Annales chim. phys._, 1874, [5], 2. 279.

[260] Hoitsema, _Zeitschr. physikal. Chem._, 1895, 17. 1; Dewar, _Phil. Mag._, 1874, [4], 47, 324, 342; Mond, Ramsay and Shields, _Proc. Royal Soc._, 1897, 62. 290.

[261] _Loc. cit._

[262] It is noteworthy that the form of curve obtained for hydrogen and palladium bears a striking resemblance to that for the dehydration of colloids containing absorbed water, _e.g._ silicic acid (_vide_ van Bemmelen, _Zeitschr. anorg. Chem._, 1897-1900. Cf. Zacharias, _Zeitschr. physikal. Chem._, 1902, 39. 480).

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

[264] Kuester, _Zeitschr. physikal. Chem._, 1895, 17. 367. Bodlaender, _Neues Jahrbuch f. Mineralogie_, 1898-99, Beilage Band, 12. 92.

[265] Bruni and Padoa, _Atti Accad. Lincei_, 1902 [5], 11. 1; 565.

[266] Roozeboom, _Zeitschr. physikal. Chem._, 1899, 30. 385; Bruni, _Rend. Accad. Lincei_, 1898, 2. 138, 347. For a general account of "solid solutions" the reader is referred to Bruni, "_Ueber feste Loesungen_" (Ahrens'sche Sammlung), and to Bodlaender, _loc. cit._ For the formation and transformation of liquid mixed crystals, see A. C. de Kock, _Zeitschr. physikal. Chem._, 1904, 48. 129.

[267] In discussing the various systems which may be obtained here, Roozeboom (_loc. cit._) made use of the variation of the thermodynamic potential (p. 29) with the concentration. In spite of the advantages which such a treatment affords, the temperature-concentration diagram has been adopted as being more readily understood and as more suitable for an elementary discussion of the subject.

[268] These curves are also called the "liquidus" and the "solidus" curve respectively.

[269] Kuester, _Zeitschr. physikal. Chem._, 1895, 17. 360.

[270] Kuester, _ibid._, 1891, 8. 589.

[271] It should be remarked that the behaviour described here will hold strictly only when the solid mixed crystals undergo change sufficiently rapidly to be always in equilibrium with the liquid. This, however, is not always the case (see Reinders, _Zeitschr. physikal. Chem._, 1900, 32. 494; van Wyk, _Zeitschr. anorg. Chem._, 1905, 48. 25), and complete solidification will not in this case take place at the temperature corresponding with the line _dc_ in Fig. 50, but only at a lower temperature.

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

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

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

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

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

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

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

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

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

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

[282] Also called Equilibrium Point (Lowry).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

* * * * *

Changes made to the printed original.

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

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

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

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

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

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

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

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

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

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