[Ill.u.s.tration: FIG. 118.]

Bi_{2}O_{3}--N_{2}O_{5}--H_{2}O.--Although various systems have been studied in which there is formation of basic salts,[373] we shall content ourselves here with the description of some of the conditions for the formation of basic salts of bis.m.u.th nitrate, and for their equilibrium in contact with solutions.[374]

Three normal salts of bis.m.u.th oxide and nitric acid are known, viz.

Bi_{2}O_{3},3N_{2}O_{5},10H_{2}O(S_{10}); Bi_{2}O_{3},3N_{2}O_{5},4H_{2}O(S_{4}); and Bi_{2}O_{3},3N_{2}O_{5},3H_{2}O(S_{3}). Besides these normal salts, there are the following basic salts:--

{299}

Bi_{2}O_{3},N_{2}O_{5},2H_{2}O (represented by B_{1-1-2}) Bi_{2}O_{3},N_{2}O_{5},H_{2}O ( " " B_{1-1-1}) 6Bi_{2}O_{3},5N_{2}O_{5},9H_{2}O ( " " B_{6-5-9}) 2Bi_{2}O_{3},N_{2}O_{5},H_{2}O ( " " B_{2-1-1})

Probably some others also exist. The problem now is to find the conditions under which these different normal and basic salts can be in equilibrium with solutions of varying concentration of the three components. Having determined the equilibrium conditions for the different salts, it is then possible to construct a model similar to that for MgCl_{2}--KCl--H_{2}O or for FeCl_{3}--HCl--H_{2}O, from which it will be possible to determine the limits of stability of the different salts, and to predict what will occur when we bring the salts in contact with solutions of nitric acid of different concentrations and at different temperatures.

For our present purpose it is sufficient to pick out only some of the equilibria which have been studied, and which are represented in the model (Fig. 119). In this case use has been made of the triangular method of representation, so that the surface of the model lies within the prism.

[Ill.u.s.tration: FIG. 119.]

This model shows the three surfaces, A, B, and C, which represent the conditions for the stable existence of the salts B_{1-1-1}, S_{10}, and S_{3} in contact with solution at different {300} temperatures. The front surface of the model represents the temperature 9, and the farther end the temperature 75.5. The dotted curve represents the isotherm for 20. The prominences between the surfaces represent, of course, solutions which are saturated in respect of two solid phases. Thus, for example, _pabc_ represents solutions in equilibrium with B_{1-1-1} and S_{10}; and the ridge _qdc_, solutions in equilibrium with S_{10} and S_{3}. The point _b_, which lies at 75.5, is the point of maximum temperature for S_{10}. If the temperature is raised above this point, S_{10} decomposes into the basic salt B_{1-1-1} and solution. This point is therefore a.n.a.logous to the point M in the carnallite model, at which this salt decomposes into pota.s.sium chloride and solution (p. 284); or to the point at which the salt 2FeCl_{3},2HCl,12H_{2}O decomposes into 2FeCl_{3},12H_{2}O and solution (p. 294). The curve _pab_ has been followed to the temperature of 72 (point _c_). The end of the model is incomplete, but it is probable that in the neighbourhood of the point _c_ there exists a quintuple point at which the basic salt B_{1-2-2} appears. In the neighbourhood of _e_ also there probably exists another quintuple point at which S_{4} is formed. These systems have, however, not been studied.

The following tables give some of the numerical data:--

ISOTHERM FOR 20.

----------------------------------------------------------------------

Composition of the solution. Gram-mols.

in 1000 gm.-mols. of water.

Solid phase.

----------------------------------------

Bi_{2}O_{3}

N_{2}O_{5} -----------------------------

-----------------

---------------------- B_{1-1-1}

10.50

38.65 --

27.20

83.84 B_{1-1-1}; S_{10}

30.15

97.97 S_{10}

29.70

96.57 --

19.65

98.76 --

10.51

162.58 --

33.51

355.87 S_{10}; S_{3}

51.00

403.0 S_{3}

14.35

492.0 --

7.45

592.9 ----------------------------------------------------------------------

SYSTEMS IN EQUILIBRIUM WITH B_{1-1-1} AND S_{10} (CURVE _pabc_).

------------------------------------------------------------

Composition of the solution. Gram-mols.

in 1000 gm.-mols. of water.

Temperature.

----------------------------------------

Bi_{2}O_{3}

N_{2}O_{5} -------------------

---------------

------------------------ 9

26.7

88.2 20 (point _a_)

30.15

97.97 30

33.6

112.3 50

41.8

148.4 65

57.21

190.8 75.5 (point _b_)

87.9

288.4 72 (point _c_)

96.0

327.0 ------------------------------------------------------------

SYSTEMS IN EQUILIBRIUM WITH S_{10} AND S_{3} (CURVE _qde_).

--------------------------------------------------------

Composition of the solution. Gram-mols.

in 1000 gm.-mols. of water.

Temperature.

-----------------------------------------

Bi_{2}O_{3}

N_{2}O_{5} --------------

---------------

------------------------- 11.5

44.5

396 20

51.0

405.4 50

66.5

444.2 65

80.0

454.4 --------------------------------------------------------

Basic Mercury Salts.--The Phase Rule has also been applied by A. J.

c.o.x[375] in an investigation of the basic salts of mercury, the result of which has been to show that, of the salts mentioned in text-books, quite a number are incorrectly stated to be chemical compounds or chemical individuals (p. 92). The investigation, which was carried out essentially in the manner described above, included the salts mentioned in the following table; and of the basic salts said to be derived from them, only those mentioned really exist. In the following table, the numbers in the second column give the minimum values of the concentration of the acid, expressed in equivalent normality, necessary for the existence of the {301} corresponding salts in contact with solution at the temperature given in the third column:--

------------------------------------------------------------- Salt.

Normality of

Temperature.

acid.

------------------------------------------------------------- HgCrO_{4}

1.41

50 3HgO.CrO_{3}

2.6 10^{-4}

50

Hg(NO_{3})_{2}.H_{2}O

18.72

25 3HgO.N_{2}O_{5}

0.159

25

HgSO_{4}

6.87

25 3HgO.SO_{3}

1.3 10^{-3}

25

HgF_{2}

1.14

25

HgNO_{3}.H_{2}O

2.95

25 5Hg_{2}O.3N_{2}O_{5}.2H_{2}O

ca. 0.293

25 2Hg_{2}O.N_{2}O_{5}(?)

0.110

25 3Hg_{2}O.N_{2}O_{5}.2H_{2}O(?)

1.7 10^{-3}

25

Hg_{2}SO_{4}

4.2 10^{-3}

25 2Hg_{2}O.SO_{3}.H_{2}O

5.6 10^{-4}

25 -------------------------------------------------------------

Mercuric fluoride does not form any basic salt.

Since two succeeding members of a series can coexist only in contact with a solution of definite concentration, we can prepare acid solutions of definite concentration by bringing an excess of two such salts in contact with water.

Indirect Determination of the Composition of the Solid Phase.--It has already been shown (p. 228) how the composition of the solid phase in a system of two components can be determined without a.n.a.lysis, and we shall now describe how this can be done in a system of three components.[376]

We shall a.s.sume that we are dealing with the aqueous solution of two salts which can give rise to a double salt, in which case we can represent the solubility relations in a system of rectangular co-ordinates. In this case we should obtain, as before (Fig. 120), the isotherm _adcb_, if we express the {302} composition of the solution in gram-molecules of A or of B to 100 gram-molecules of water.

[Ill.u.s.tration: FIG. 120.]

Let us suppose, now, that the double salt is in equilibrium with the solution at a definite temperature, and that the composition of the solution is represented by the point e. The greater part of the solution is now separated from the solid phase, and the latter, _together with the adhering mother liquor_, is a.n.a.lyzed. The composition (expressed, as before, in gram-molecules of A and B to 100 gram molecules of water) will be represented by a point (_e.g._ _f_) on the line _e_S, where S represents the composition of the double salt. That this is so will be evident when one considers that the composition of the whole ma.s.s must lie between the composition of the solution and that of the double salt, no matter what the relative amounts of the solid phase and the mother liquor.

If, in a similar manner, we a.n.a.lyze a solution of a different composition in equilibrium with the same double salt (not necessarily at the same temperature as before), and also the mixture of solid phase and solution, we shall obtain two other points, as, for example, _g_ and _h_, and the line joining these must likewise pa.s.s through S. The method of finding the {303} composition of an unknown double salt consists, therefore, in finding, in the manner just described, the position of two lines such as _ef_ and _gh_. The point of intersection of these lines then gives the composition of the double salt.

If the double salt is anhydrous, the point S lies at infinity, and the lines _ef_ and _gh_ are parallel to each other.

The same result is arrived at by means of the triangular method of representation.[377] If we start with the three components in known amounts, and represent the initial composition of the whole by a point in the triangle, and then ascertain the final composition of the solution in equilibrium with the solid phase at a definite temperature, the line joining the points representing the initial and end concentration pa.s.ses through the point representing the composition of the solid phase. If two determinations are made with solutions having different initial and final concentrations in equilibrium with the same solid phase, then the point of intersection of the two lines so obtained gives the composition of the solid phase.

{304}

CHAPTER XVII

ABSENCE OF A LIQUID PHASE

In the preceding chapters dealing with equilibria in three-component systems, our attention was directed only to those cases in which liquid solutions formed one or more phases. Mention must, however, be made of certain systems which contain no liquid phase, and in which only solids and gases are in equilibrium. Since, in all cases, there can be but one gas phase, four solid phases will be necessary in order to form an invariant system. When only three solid phases are present, the system is univariant; and when only two solid phases coexist with gas, it is bivariant. If, however, we make the restriction that the gas pressure is constant, we diminish the variability by one.

On account of their great industrial importance, we shall describe briefly some of the systems belonging to this cla.s.s.

Iron, Carbon Monoxide, Carbon Dioxide.--Some of the most important systems of three components in which equilibrium exists between solid and gas phases are those formed by the three components--iron, carbon monoxide, and carbon dioxide--and they are of importance especially for the study of the processes occurring in the blast furnace.

If carbon monoxide is pa.s.sed over reduced iron powder at a temperature of about 600, the iron is oxidized and the carbon monoxide reduced with separation of carbon in accordance with the equation

Fe + CO = FeO + C

This reaction is succeeded by the two reactions

FeO + CO = Fe + CO_{2} CO_{2} + C = 2CO

{305}

[Ill.u.s.tration: FIG. 121.]

The former of these reactions is not complete, but leads to a definite equilibrium. The result of the different reactions is therefore an equilibrium between the three solid phases, carbon, iron, and ferrous oxide, and the gas phase consisting of carbon monoxide and dioxide. We have here four phases; and if the total pressure is maintained constant, equilibrium can occur only at a definite temperature.

Since, under certain conditions, we can also have the reaction

Fe_{3}O_{4} + CO = 3FeO + CO_{2}

{306} a second series of equilibria can be obtained of a character similar to the former. These various equilibria have been investigated by Baur and Glaessner,[378] and the following is a short account of the results of their work.

Mixtures of the solid phases in equilibrium with carbon monoxide and dioxide were heated in a porcelain tube at a definite temperature until equilibrium was produced, and the gas was then pumped off and a.n.a.lyzed. The results which were obtained are given in the following tables, and represented graphically in Fig. 121.