ON T E R N A R Y M I X T U R E S . SECOND P A P E R .
BIT W I L D E R D. BANCROFT.
I n a previous paper' I have shown that the general form.ula
describes the equilibria when two non-miscible liquids are dissolved in a consolute liquid. This same equation must still hold good if I substitute a solid for one of the non-miscible liquids, nothing being allowed to vary except the change of condition of one of the coniponents at the temperature of the experiment. As solids which are miscible in all proportions with a liquid are neither coninion nor easy to work with, I have thought it better to study the less simple case of two non-miscible substances, one a liquid and one a solid, dissolved in a liquid solvent in which the solid has a limited solubility, but with which the liquid is consolute. T h e only example of this for which I have been able to fitid data ready to niy hand is for the equilibria between alcohol, a salt and water. Of course, formula (I) will not hold in its present form and it must be niodified to give a limiting value for the salt when the concentration of the alcohol beconies zero. There are several ways of doing this ; but in this paper I shall consider only one, a change in the origin of the coordinates. Let .x represent the quantitj- of alcohol, _I' the quantity of salt i n a constant quantity of water, the whole to be expressed in any units or combination of units that ilia!. be preferred. T h e general equation will then take the form : (x
where
(4,
+A ) y =C'
(11.)
,5, A and C' are constants for constant temperature,
'Physical Review 3, P I (1895).
(1
and
Tcrita ~ ; r21fi.vfI ~ W S .
35
,5 depending on the nature of the coiiiponents only, .4 and C'
011
these and on the units in whicli the components are expressed. Since the ratio of and , j is all that interests us a t present, we may set it or its reciprocal equal to 11 as I have done in the first paper on this subject and we shall have, when , j i '/.=H, the expression : (.L+A)
J'"=c-.
(Ha.)
This equation is in a form i n which it can be tested. T h e best numerical data on the subject are those of Bodlander'. He deterniiiied the salt by evaporation of the solution and weighing the residue in the usual manner. T h e composition of the aqueous alcohol was obtained by distillation and examination of the distillate optically. This method can not be considered accurate, as it is necessary to distill off all the liquid without losing any, a thing very difficult to do. A slight error in the percentage coinposition of a mixture rich in alcohol makes a large absolute error when the concentration is expressed in grams of alcohol per hundred granis of water. I t is not clear from the author's description how he kept the temperature constant or that it was kept rigidly constant. In spite of the large experimental error in some of the data, I find that Bodlander's results are expressed with a very fair degree of accuracy by equation (IIa), or rather lq.two equations of that form. This last fact makes it necessary to consider what the significance of two equations is. I found that two equations were usually necessary practically, always theoreticall)., to express the results with two lion-miscible liquids and I showed that this was due to the fact that the precipitate changed as.one passed from one curve to the other. Following out this analog>, one would expect two curves also wheii one of the iion-miscible substances was a solid, and that along one curve we should have the solid separating out and along the other the liquid, forming two liquid phases. This is exactly what we find for acetone with iiiost salts and for alcohol with soiiie salts. Carrying the analog!. still further, we should expect that in the case of two noli-miscible solids we should have one curve when the solution was saturated in respect to one salt, and another when ~
~~~
~
~
'Zeit. phys. Chem. 7 , 308 ( 1x91 ).
it was saturated in respect to tlie other, a n d that the intersection of the two curves would come a t the concentration at which the two salts could crj,stallise side by side. 4 s I shall show in this paper, this is wliat happens. W e have identity of behavior as we change from two liquids to a liquid and a solid and then to two solids. This identit,. holds for alcohol with such substances a s nianganoiis sulfate, potassium carbonate, ferric chlorid, potassiuni hydroxide. It is very probable that it holds for all salts at suitahle temperatures. This siiiiplifies the case 1.ery much. \ITe find experimentally that there are two curves when salt is precipitated by alcohol and we are forced to conclude that along tlie second curve tlie precipitation of the salt is secondary, a s tlie primary reaction is the formation of a second liquid phase. Since there is no change in the nature of the precipitate, there must be a change iii the nature of tlie liquid phase and we coiiclude that along the first curve we have alcohol dissolved in water, along the second water dissolved i n alcohol. I n other words, the difference in the behavior of alcohol with salt solutions is not that in some cases there is formation of a second liquid phase and in otliers not ; but that in certain cases the first liquid phase can be i n equilibriutii with the second and in others not. For ternary mixtures we are able to answer Lotliar Meyer's question :
TABLE I. (.E+
KCl at 1 4 O . 5 15)-J)?.$ = c, Log c,=/.975,
. .~.~ ...
.~
.L
.
-J'calc.
J'found
rog
c.
0.0
3.26
5.93 13.4
2 0 . 'i
29: 3 34.7
80.5 120.0
441.4
3.080 3.104 2.945
Tt'/. n7y ,f ,If/.. \.f //I%.s.
37
(c\iVheii does a mixture of alcohol and water change from a solution of alcohol in water to a solution of water in alcohol ? I ) Before long I trust that we shall be able to answer the question when alcohol aiid water are the onlj. coniponents. In Tables 1-1'11 are the calculations of Bodlatider's results. I11 all cases .I' denotes t h e graiiis of alcohol, _I' the grams of salt i n one hundred grams of [vater. LJiitler the lieatling cccalc.)) are the granis of salt required to satisf!. the foriiiula espressiiig the relation between . t ' and y.
T A B L TI. E
.t-
-3 1- . 5
0.0
10.9
. I S .j 11.9
33.4 69.2 89.3 137.3 248.4 499.0
.l'
s.0
6.9 5.24 3.5 2.2
-1'
calc.
-1'
foulid 28.0
23.0 21.6
'9.4 IS.;. 16. I
'4.9 10.0
W. D . B a I I c y o f .
38
There are a few points which call for special notice. Bodlander makes sodiuni chloride more soluble at I 1'. j than at 13O.0, which must be due to experimental error. T h e foriiiulz used in calculating sodium nitrate solutions require that sodium nitrate should he less soluble at 16'. j than at 13O.0, which is absurd. T h e foriiiulz are therefore wrong, hut I ani unable to correct thein.
log
35.5 29.7 27.9 26.4 24.7
0.00
'5.07 21.35 27.14 37.93
c,+,
log -
'
c.
7.984 8.023 7 * 998 7.969 7.945
100
-
21.8
55.79 81.74 12 5.6' 197.2 295.4 642.9
18. j
5 ,I' 11.8 I
7.0 4.4
4,094 4.1'3 4.136 4.1313 3.926 3 * 909
TABLE V. NaCl at
I 1O.5
Lqp 0.00
3.32 6.45 9.73 13.38 14.2s
22.9j .
36. I 34.3 32.9 31.7 30.6 30.3 2s. j
35.8 34.4 33.1 32.0
c.
s.072
8. I O 1
8.106 S . 109
30.8
s. 104
30. I
S.07 I
2s. I
8.063
-
'There is a mistake
iii
Borlliinder's (lata. Cf the density.
I have also calculated the results of Gerardin' arid find that they can be expressed by the satlie general formula. His results are not I'ery accurate, but they cover quite a range of temperature, and are therefore interesting as throwing light on tlie variation of the constants in tlie formula with the temperature. His data are very unsdtisfactory in one sense because he made nieasurenients in a more or less haphazard way, with one concentration of aqueous alcohol at one set of temperatures and with another concentration at another set of temperatures, so that the series are not coinparable until reduced.
TABLE 1.1. NaNO, at 16O.5 (-1 + Z 5 ) -1'=c /Og C + . Z J O . ~
-18
calc.
________ 0.0
82. j
8.7 17.0 25.4 35.9 60.9 73.7
71.0
63.6 58. I 52.7 44 5 41.2
36.5 30.0 25.0
102.7
164.0 234.0 296. j
y found -
--
log c'.
~
82.7 77.2 67.6
5,233 5.303 5.283 5.277 5.224 5.225 5.222 5.119 5.216 4.929 4.280
61.3
52.3 44.2 40.9 32. I 29.5 18. I
7.7
23.0
.
TABLE \'II. NaNO, at 13'. log C = j . ~ j o x
1'
calc.
y found
84.4
0.0
4.2
20. j
24.9
81.8 78.0 74.3
._
66. I 63.0
65.5 63. I
59.7
,i6. j
5.204
73.0 69.6
8.4
c.
5,224 5.247 5.266 5.250 5.243 5.255
78.0
11.7 15.7
log -
._ .
~
'Ann. chiin. phys. (4) 5 , 129 (1S6ji.
69.6
T h e values given in the tables are obtained by interpolation from the experiniental data. N'liere the change of solubilitj. with the teiiiperature can be represented b ~ a. straight line, as iii tlie case of potassium chlorid aiid barium chlorid, interpolation is cas). and the results are fairly accurate. With potassiuiii nitrate and potassium chlorate, the chances for error are much greater. I n view of these facts, it will be well to regard these tables as approxiinations only, which serve to draw attention to the laws describing the phenomena, hut do not establish theiii definitely.' In Tables "111-XIV are the results of Ggrardin, while in Tables X\'-XVI are tlie calculations of soiiie of Schiff's' experiments. Some of his other data
TABLE VIII.
% water' calc. found /og C,calc. 'found log C,,I calc. found log C,, I
2S.5 28.5 4.591 137.3 31.4 22.3 23 2 4.631 2 5 . 3 25.9 18.7 19.9 4.65s 21.5 2 2 4 15.5 1 15.3 4.580 17.9 17.7 7 7 . 0 12.1 111.9 4.573 14.1 14.0 - 8 10.0 -9.9 _ _ 65.0 _ _8.5 1 8.5~_4 . 5 S 100.0
94.8 90.2 84.6
~
Yi5
4 784 34.4 34.3 4.9'7
4.So7 4.827 l4.768 4.769 4.770
28.1
24.0
28.6 4 9 3 9 25.0 4.966
20.1
20.1
1p+..g20
16.0 16.0 4.925 11.3 11.3 ~4.918
water ~
37.2 3 7 . 2 ij.073 40.3 94.8 31.0 3 1 . 3 15.080 33.7 90.2 26.7 27.5 15.105 29.3 S4.6 22.5 1 2 2 . 5 #5,070 24.8
100.0
~
~
~
~
40.1 5 . 1 8 4 ' 4 3 . 5 43.0 15.287 34.0 15.196 36.7 36.7 15.302 ~
130.1 ~ 5 . 2 2 1 31.9 32.6 15.324 24.9 ~5.193 2 7 . I 27.3 ~5.306
1
4.9 90.2
3.8 3.3
84.6
2.8
77.0
2.3
~
4.9 l3.927 7 . 2 4.0 14.053 5.5 3.3 3.962 4.S 2.8 13.g26 4 . 1 2 . 3 13,907 3.4
14.4 6.392 2 0 . 0 2 0 . 0 7.107 1 1 . 7 6 . 4 3 2 16.0 1 6 . 2 7 . 1 3 7 10.0 1 0 . 0 6.397 13.9 13.9 ~ 7 . 1 1 2 8.7 8.6 6.386 1 2 . 0 1 2 . 0 7.106 7.2 7.3 6,424 10.0 10.0 7.109
100.0
14.4
94.8
11.5
90.2 S4.6 77.0
TABLE X.
I
calc. found Io
