Part 28 The Phase Rule and Its Applications

Part 28

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.

[Ill.u.s.tration: FIG. 124.]

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--pota.s.sium chloride for the temperature 0 (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 const.i.tuent; viz. sodium chloride--sodium sulphate, sodium sulphate--pota.s.sium sulphate, pota.s.sium sulphate--pota.s.sium chloride, pota.s.sium chloride--sodium chloride. These four sets of curves are therefore similar to those discussed in the previous chapter. In the case of sodium and pota.s.sium 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 pota.s.sium sulphate respectively.

The lines which pa.s.s 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 pota.s.sium 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 pota.s.sium 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 pota.s.sium chloride, and the result is equal to twice the number of pota.s.sium sulphate molecules. Thus, in the above example, the total number of salt molecules is 64. The number of molecules of sodium and pota.s.sium chloride is 57; 64 - 57 = 7, and therefore the number of pota.s.sium 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 0:--[391]

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

Point.

Solid phases.

---------------------------------------- I.

NaCl

II.

KCl

III.

Na_{2}SO_{4},10H_{2}O

IV.

K_{2}SO_{4}

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}

{ 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

34.5

46.5

12.5

47.5

55.5

34.5

35.5

7.5

17.5

9.5

3.5

40.5

3.5

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 0 Glauber's salt and pota.s.sium 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 4.4, 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, pota.s.sium chloride, glaserite, and sodium chloride. But these four salts can coexist with solution only at the transition point; so that 4.4 is the transition temperature of the salt-pair: Glauber's salt--pota.s.sium 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 pota.s.sium chloride. This shows that at temperatures above the transition point the salt-pair Glauber's salt--pota.s.sium chloride cannot coexist in presence of solution.

[Ill.u.s.tration: FIG. 125.]

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 pa.s.sing 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 15, this temperature was the one chosen for the detailed investigation of the conditions of equilibrium. Since, further, it has been shown by Bodlander[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 const.i.tute 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).

[Ill.u.s.tration: FIG. 126.]

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 0 and 30 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 = 15) 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, 15):--

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

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.

[Ill.u.s.tration: FIG. 127.]

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.

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

HCO_{3}

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}

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._ pa.s.sage of carbon dioxide through a solution of sodium chloride saturated with ammonia, is not so good as the newer method of Schlosing, 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, const.i.tute 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.

[Ill.u.s.tration: FIG. 128.]

Barium Carbonate and Pota.s.sium 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 a.n.a.lytical method which allows of the detection of K_{2}CO_{3} in a mixture of the four solid salts. This a.n.a.lysis 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 pota.s.sium sulphate is very slightly soluble in the concentrated solution of pota.s.sium 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 quant.i.ty 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 25. 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 25.

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

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

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

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 100 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 25.

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