T H E QUATERNARY SYSTEM ACETIC ACID-CHLOROFORMACETONE-WATER AT 25OC. A. V. BRANCKER, T. G. H U N T E R ,
AND
A. W. NASH
Department of Oil Engineering and Refining, The University of Birmingham, Birmingham, England Received July 18, 1989
Equilibrium in liquid mixtures has been studied for a large number of ternary systems, but no detailed study of a quaternary system such as will be considered in this paper has, so far as we are aware, been reported. The choice of liquids to be used was based on the ease of purification and analysis, the particular system studied being composed of acetone, acetic acid, chloroform, and water a t a temperature of 25OC. PURIFICATION OF THE FOUR COMPONENTS
Pure glacial acetic acid crystals were prepared by equilibrium melting, and the resultant acid was freed from water by distillation with the addition of ethylene dichloride. The ethylene dichloride was found to be stable in boiling acetic acid solution, no chlorine derivatives being formed. Analar acetone was dried over calcium chloride, filtered, and fractionated. The fraction distilling a t 56.0°C. a t 760 mm. was employed. Distilled water was treated with solid barium hydroxide, filtered, and redistilled. Analar chloroform was fractionated and the fraction boiling at 61.1"C. a t 760 mm. was employed. All solutions were stored in clean dry Winchester bottles, fitted with soda lime tubes and hand pumps for transfer of reagents. Air in the storage bottles was previously displaced by nitrogen. METHODS OF ANALYSIS
I , Chloroform A method was developed for the estimation of chloroform, based upon the formation of potassium chloride by treatment with alcoholic potassium hydroxide, the potassium chloride formed being titrated with silver nitrate. About 5 ml. of chloride-free normal alcoholic potassium hydroxide was weighed in a small stoppered glass tube. A few drops of chloroform were 683
6%
A. V. BRANCKER, T. G . HUNTER AND A. W. NASH
added and the reweighed tube dropped into a flask containing 40 to 50 ml. of normal alcoholic potassium hydroxide. The solution was then refluxed under two double-surface condensers in series, down which trickled alcoholic potassium hydroxide. The reaction was found to be complete within 15 min. The solution was then cooled to O"C., filtered, and washed with alcohol previously saturated with potassium chlorate a t room temperature. The potassium chloride was dissolved in chloride-free water, the solution made up to 100 ml., and aliquot parts taken for titration with silver nitrate. 8. Acetone
For the estimation of this component a modification of Messingers' ( 1 ) method was used. It is based on the formation of iodoform by the addition of iodine to an alkaline solution of acetone. The excess iodine is liberated by acid, and titrated with sodium thiosulfate. About 10 ml. of water was weighed in a glass-stoppered bottle, ten drops of acetone were added, and the mixture was reweighed and made up to 200 ml. A 25-ml. portion of this acetone solution was then pipetted into a conical flask containing 25 ml. of normal caustic soda. Twenty-five milliliters of decinormal iodine was run in slowly, the liquid in the flask being gently agitated. The flask was stoppered and allowed to stand a t room temperature until the yellow iodoform settled out, and the supernatant liquid was perfectly clear. The clear solution was then neutralized with 2 N sulfuric acid. T o avoid using excess acid, this was run in until the solution was just brown due to liberated iodine. The brown color was then discharged with decinormal sodium thiosulfate. A few more drops of acid were added, which again darkened the solution, and the titration was continued. Proceeding in this way it was possible to restrict the excess acid to not more than one drop. Towards the end of the titration starch indicator waa added, the end point being sharp. Inconsistent results were obtained only when insufficient time had been allowed for the complete formation of the iodoform. By waiting until the iodoform settled, leaving the supernatant liquid perfectly clear, complete iodoform formation was assured. 3. Acetic acid
The acetic acid was estimated by titration with barium hydroxide free from carbon dioxide. In view of the low concentration of acetic acid encountered in certain parts of the work it was found essential to employ an indicator, the p H range of which included the pH of the reaction, found by calculation and electrometric titration to be about 7.5 for the concentrations used. From a comparison of determined and calculated titration
THE SYSTEM ACETIC ACID-CHLOROFORM-ACETONE-WATER
685
curves it was clear that a suitable indicator should have a pH range from 6 to 8. Titrations were then made using different indicators of this range. The indicator under test was added to 10 ml. of a buffer solution of pH = 7.5 and titration made to this color standard. By this method bromothymol blue was found to be the most suitable indicator for the titration. DETERMINATION OF TERNARY CURVES AND TIE LINES
Known weights of chloroform and acetone were run into a small glass bottle which was then attached to a buret containing water and immersed TABLE 1 Ternaru isotherm &to for the .system acetone-chloroform-water at 86°C. ACETONE
CHLOBOlORM
WATBB
weight pu e a t
wmcht pcr e a 1
w&ht pa cdnt
0.2
18.8 28.5 42.3 52.0 57.3 60.5 60.0 59.2 58.5 56.6 55.6 54.0 53.2 51.6 49.0 42.6 35.5 26.0 15.5
99.2 80.0 70.0 55.2 43.4 35.4 28.5 22.0 17.8 14.5 11.0 10.0 8.6 8.0 7.0 5.6 3.2 2.3 1.5 1.0 0.6
1.2 1.5 2.5 4.6 7.3 11.0 18.0 23.0 27.0 32.4 34.4 37.4 38.8 41.4 45.4 54.2 62.2 72.5 83.5 99.4
in a thermostat a t 25'C. Water was run into the bottle until the solution became slightly opalescent. The solution was then allowed to attain the temperature of the thermostat, and the addition of water was continued until turbid. The volume of water added waa recorded, the buret temperature read, and the titer in milliliters converted into grams. In this manner one half of the isotherm was obtained. Known weights of acetone and water were then run into a dry bottle and the solution titrated in the same way with chloroform to give the remainder of the isotherm.
686
A. V. BRANCKER, T. Q. HUNTER AND A. W. NASH
TABLE 2 Ternary isotherm dati 'or the system acetic acid-chloroform-water at 9PC. ACBTIC ACID
CHLOROFORM
weight psr cm:
w&A:
WATER
psr cent
weight per em:
99.2 90.0 80.0 70.0 65.0 60.0 55.0 45.0 40.0 35.0 25.0 20.0 15.0 10.0 6.4 3.5 1.9 1.6 1.2 0.8 0.6
8.7 17.8 26.0 29.0 32.1 35.0 41.1 43.5 46.0 49.7 50.6 50.0 47.6 43.6 36.5 34.6 24..9 18.8 9.2
0.8 1.3 2.2 4.0 6.0 7.9 10.0 14.0 16.5 19.0 25.3 29.4 35.0 42.4 50.0 60.0 63.5 73.5 80.0 90.0 99.4
TABLE 3 Ternary tie line data for the system acetic acid-chloroform-water at 96°C.
I
COMPONENTS
INITIAL UIXTURD
Water. . . . . , . , . . . . . . . , , . . . . . . . , . .
40 .O
Acetic acid, , . , , . , . . , , , , . . , . , . . . . Chloroform, , , . . . . . . . , , , . . . . . . . . .
23.5 40.0
TOP LAYER
BOTTOU LAYER
weight per cent
weight per cml
17.4 1.1 81.5
4.1 95.0 0.9
34.1 2.6 63.3
1.4
Acetic acid, , , , . , , , , , . . , , , , . , , , , I Chloroform. . . , , . , , , , , , , . . . . . . . . Water. , . . . . . . . . , . . . . . . . . . . , . . . , , I
I
34.0 35.0 31.0
44.5 7.0 48.5
80.0
i
37.0 41 .O 22.0
49.5 12.4 38.1
22.6 74.4 3.0
,
Acetic acid. . . , , . . . . . . . . . . . . , . . . . Chloroform, , , , , . . . . . . . . . . . . , . . , . Water, , . , , . . , , , , . , , , . . . . . . . . , . . .
* See table 9.
17.9 2.1
687
THE SYSTEM ACETIC ACID-CHLOROFORM-ACETONE-WATER
The equilibrium data for the acetone-chloroform-water system are given in table 1. The data so found agreed closely with those given by Hand (2) for this system . TABLE 4 Ternary tie line data for the system acslone-chloroform-water at Ib0C .
i
B O l T O Y LATER
weioht per cent
weight per cent
weight pa cent
6.0 44.0 50.0
3.0 1 .0 96.0
9.0 90.0 1.0
Acetone . . . . . . . . . . . . . . . . . . . . . . . . . . Chloroform . . . . . . . . . . . . . . . . . . . . . . Water. . . . . . . . . . . . . . . . . . . . . . . . . .
17.0 43.0 40.0
8.3 1.2 90.5
23.7 75.0 1.3
Acetone . . . . . . . . . . . . . . . . . . . . . . . . . . Chloroform . . . . . . . . . . . . . . . . . . . . . . Water. . . . . . . . . . . . . . . . . . . . . . . . . . .
24.0 38.0 38.0
13.5 1.5 85.0
1.6
29.0 33.0 38.0
17.4 1.6 81.0
38.0 60.0 2.0
34.0 33.0 33.0
22.1 1.8 76.1
42.5 55.0 2.5
Acetone . . . . . . . . . . . . . . . . . . . . . . . . . . Chloroform . . . . . . . . . . . . . . . . . . . . . . i Water . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.0 31.0 34.0
25.5 1.5 73.0
42.6 55.0 2.4
Acetone. . . . . . . . . . . . . . . . . . . . . . . . . . . Chloroform . . . . . . . . . . . . . . . . . . . . . . 1 Water. . . . . . . . . . . . . . . . . . . . . . . . . . .
44.0 30.0 26.0
31.9 2.1 66.0
50.5 45.0 4.5
Acetone . . . . . . . . . . . . . . . . . . . . . . . . . . Chloroform . . . . . . . . . . . . . . . . . . . . . . Water . . . . . . . . . . . . . . . . . . . . . . . . . .
50.0 20.0 30.0
44.5 4.5 51.0
57.0 35.0 8.0
Acetone . . . . . . . . . . . . . . . . . . . . . . . . . . Chloroform. . . . . . . . . . . . . . . . . . . . . . Water . . . . . . . . . . . . . . . . . . . . . . . . . . .
IXITIALXIXTURE
1
TOPLAYER
COMPONENTS
1 I
Acetone . . . . . . . . . . . . . . . . . . . . . . . . . . Chloroform. . . . . . . . . . . . . . . . . . . . . . Water. . . . . . . . . . . . . . . . . . . . . . . . . . . ~
I
Acetone . . . . . . . . . . . . . . . . . . . . . . . . . . Chloroform . . . . . . . . . . . . . . . . . . . . . . Water . . . . . . . . . . . . . . . . . . . . . . . . . . .
i
1 ~
.
* See table 8. The equilibrium data for the system acetic acid-water-chloroform were determined in an exactly similar way and are given in table 2. This system hm been previously studied by Wright (3) and Hand (2). whose results arc closely coincident with the present data . For the determination of tie lines. known quantities of the three liquids acetone-chloroform-water or acetic acid-chloroform-water such BS would
688
A. V. BRANCKER, T. G. HUNTER AND A. W. NASH
form two layers were placed in asmall glass-stoppered bottle. This bottle was immersed in the thermostat a t 25°C. for about 30 min., removed, dried, and placed in an insulated tube a t 25OC. The tube was fitted to a shaking machine and agitated for 2 hr. The glass bottle was then reimmersed in.the thermostat until both layers when viewed in a cone of light were clear. Samples for analysis were withdrawn from each layer by meansof a glass tube drawn into a very fine capillary and fitted with a rubber teat. The top-layer sample, usually about 0.5 g., was weighed in a small glassstoppered tube and the whole dropped into water. The resultant soluACETONE A
,D ACETIC ACID
WATER
FIG.1. Schematic representation of the quaternary system by a regular tetrahedron
tion was made up to a convenient volume, and aliquot parts taken for analysis of acetone and acetic acid. For chloroform determination in both top and bottom layers the small tube was dropped into alcoholic potash. As samples from the bottom layers contained most of the chloroform, it was necessary to dissolve the bottom layer in acetic acid when analyzing for acetone, and in neutral alcohol when analyzing for acetic acid. The total weights of the two layen were ascertained, and from these values, together with the concentrations of the three components in each layer as determined by analysis, the total weight of each component in the two-layer system was calculated. If these calculated weights differed by
689
THE SYSTEM ACETIC ACID-CHLOROFORM-ACETONE-WATER
more than =k 4.0 per cent from the weights of the three liquids originally taken, the results were discarded. The average experimental error in the data obtained w&s f 0.9 per cent. Tie line data for the two systems are given in tables 3 and 4. TABLE 5 Quaternary isotherm data for the system acetone-acetic acid-chloroform-water at 86°C. ACETONE
weight p a unf
40.0 49.2 54.4 54.2 53.0
51.0 45.7 41.0 32.9 22.7 13.5
C€ILOBOFO~
IIXTUBE: AND
30 PEB CENT ACETIC ACID
70 PEE CENT
WATER
weight per cent
weigh1 p a cenl
98.5 56.4 43.8 32.0 26.8 23.5 21.0 16.1 13.0 8.1 4.2 2.5 1.9
1.5 3.6 7.0 13.6 19.0 23.5 28.0
38.2 46.0 59.0 73.1 84.0 98.1
TABLE 6 Qualermry isotherm data f o r the system acetone-acelic acid-chloroform-water at 86°C. IIXTUBE: AND
40 PER CENT ACETIC ACID
ACETONE
CHLOBOFOBY
weigh1 p a cent
weight per cent
weight p a cenl
14.1 39.7 46.3 47.7 47.4 45.7 42.8 38.0 31.1 18.7 10.2
98.6 83.4 54.3 43.1 36.6 31.6 27.0 22.8 18.6 13.9 7.7 6.3 4.4
1.4 2.5 6.0 10.6 15.7 21 .o 27.3 34.4 43.4 55.0 73.6 83.5 95.6
P I E CENT WATER
QUATERNARY EQUILIBRIUM CURVES
In figure 1 a schematic representation of the quaternary system is given in the usual manner by a regular tetrahedron. In all figures in this paper where solid models are illustrated schematic representation has been used,
690
A. V.. BRANCKER, T. G. HUNTER AND A. W. NABH
TABLE 7 Quaternary isotherm data for the system acetone-acetic acid-chloroform-water at 86%'. m m : M.7 ACID AND 3a.a
PER CENT ACETIC
ACETONE
CHLOBOEOBY
weight pa cent
weight p a cml
weioht pa cant
97.4 91.9 79.8 66.4 54.7 47.9 42.5 38.4 34.2 27.9 26.5
2.6 3.4 4.0 7.6 13.5 20.6 28.5 38.6 51.3 66.0 73.5
4.7 16.2 28.0
31.8 31.5 29.0 23.0 14.5 6.1
PEE CBNT WATER
Fxo. 2. The tetrahedron sectioned through the perpendicular plane A T D
THE SYSTEM ACETIC ACID-CHLOROFORM
ACETONE-WATER
691
that is, such figures are not exactly quantitative. All the remaining figures, however, are quantitative. The two ternary equilibrium curves for acetone-chloroform-water and acetic acid-chloroform-water lie on two triangular faces of the tetrahedron. By joining the two ternary isotherms a hollow figure or frustum is obtained inside the tetrahedron, as shown in figure 1 ; this frustum should define the heterogeneous region. From the chloroform apex C of the tetrahedron in figure 1 a line is drawn on the base of the figure to a point M on the side of the triangular base opposite the chloroform apex. This point M represents a mixture of acetic acid and water in a known ratio. From M a line M A is drawn to CHLOROFORM
ACETIC ACID
ACETONE
FIO.3. The tetrahedron projected orthogonally on to the acetic acid-acetone
.
chloroform base
the acetone apex. This construction gives an isoscles triangle C M A , where CM = M A . The intersection of the plane C M A with the quaternary equilibrium surface gives a quaternary equilibrium curve q z , shown in figure I, where x and z are the points of intersection of CM with the acetic acid-chloroform-water isotherm. A number of acetic acid-water mixtures were prepared whose composition could be represented by points M , MI and MZ, etc. The quaternary equilibrium curve in each triangular plane CM,A waa then determined by titrating known acetone-chloroform mixtures with the prepared acetic acid-water mixtures M , MI and Mz. Equilibrium data obtained in this way for three quaternary isotherms are given in tables 5, 6, and 7.
4
692
A. V. BRANCKER, T. Q. HUNTER AND A. W. NASH
The quaternary equilibrium data were plotted on equilateral triangles, as for a ternary system acetone-chloroform-mixture M , . The actual equilibrium curves as zyz in figure 1, however, are situated on triangles which are not equilateral, but isosceles. It is a simple matter of geometrical manipulation to transfer the curves from the equilateral triangle to the isosceles triangle C M , P . The curves so obtained are then true quaternary equilibrium curves as they exist in the tetrahedron. In figure 2 the tetrahedron has been sectioned through the perpendicular plane ATD. The section through ATD cuts the acetone-chloroformwater and the acetic acid-chloroform-water isotherms a t the points S and W , respectively, and cuts the quaternary isotherm xyz for the acetonechloroform-mixture M system a t the point y. By drawing the triangular plane ATD separate from the tetrahedron and locating on it geometrically the points S, y, and W , the shape of the equilibrium surface can be obtained from the curve SyW. Four parallel sections through the tetrahedron were taken and the curves of section plotted. In each case the curve of section was found to be a straight line. In figure 3 the tetrahedron has been projected orthogonally on to the acetic acid-acetone-chloroform base. Both of the determined isothermal ternary curves are shown in the figure, together with two of the isothermal quaternary curves. A projection with the tetrahedron in this position gives the shape of the equilibrium surface, and it will be seen that the quaternary isotherms touch the straight line S'W', which is the projection profile of the equilibrium surface. The frustum inside the tetrahedron as illustrated in figure 1 therefore represents the heterogeneous region for the quaternary system a t 25'C. QUATERNARY TIE LINES
Any point inside the quaternary equilibrium surface is in the heterogeneous region and represents a mixture of composition such that it forms two layers. The composition of the two layers can be represented by two points on the equilibrium surface in positions such that a straight line can be drawn through them and through the point representing the composition of the original mixture separating into two layers. The line so obtained is a quaternary tie line. It was found that a quaternary tie line was situated on the line of intersection of two planes, each of which had for its base line a ternary tie line in the two different ternary systems. This is shown in figure 4, where DEF and AGH are the two planes, M N and K L are ternary tie lines, and OP is the quaternary tie line on the line of intersection IJ of the two planes. The quaternary tie line OP contained on ZJ terminates at the quaternary equilibrium surface.
THE SYSTEM ACETIC ACID-CHLOROFORM-ACETONE-WATER
ACETONE
A
ACETIC ACID
C CHLOROFOR
0 WATE I?
FIQ.4
WATER
FIQ.5
693
694
A. V . BHANCXER, T. G . HUNTER AND A. W. NABH
A number of such coplanar tie lines, or tie lines on the same plane, would by terminating a t the equilibrium surface form a curve, such as KQL or M R N in figure 4. These curves are also formed by the intersection of the tie line planes with the equilibrium surface as is clearly shown in figure 5, where the curve KQL is formed by the intersection of the tie line plane DEF with the equilibrium surface. Mixtures of the four components acetic acid, chloroform, acetone, and water were prepared of composition such that two phases were formed a t TABLE 8
Quuternury tie line data for the system acetone-acetic acid-chloroform-water at 36°C. Initial mixtures all lie in the plane of the ternary tie line marked
wdpht per cent
Acetone . . . . . . . . . . . . . . . . . . . . . . . . . . Acetic acid. . . . . . . . . . . . . . . . . . . . . . Chloroform . . . . . . . . . . . . . . . . . . . . . . Water. . .
* in
table 4
TOP LAYEB
BO'ITOY LAYEU
weiqht per c a t
weight per e a t
21.6 9.3 32.8 36.3
11.2 15.3 1.8 71.7
31.6 3.3 63.5 1.6
Acetone. . . . . . . . . . . . . . . . . . . . . . . . . . Acetic acid. , , . , , , , , , , , . , , . , Chloroform . . . . . . . . . . . . . . . . . . . . . . ...................
19.2 19.6 29.6 31.6
9.3 29.9 3.7 57.1
29.2 8.7 58.8 3.3
Acetone . . . . . . . . . . . . . . . . . . . . . . . . . . Acetic acid. . . . . . . . . . . . . . . . . . . . . . Chloroform. . . . . . . . . . . . . . . . . . . . . . Water. . . . . . . . . . . . . . . . . . . . . . . . . . .
19.2 26.6 30.6
10.8 38.2 9.8 41.2
25.8 16.2 51.8 6.2
13.6 39.0 19.1 28.3
22.8 24.1 42.5 10.6
,
,
, ,
~
Acetone . . . . . . . . . . . . . . . . . . . . . . . . . Acetic acid. . . . . . . . . . . . . . . . . . . . . . . Chloroform . . . . . . . . . . . . . . . . . . . . Water. . . . . . . . . . . . . . . . . . . . . . . . . . .
23.6 18.0 32.0 30.0
20.0
25°C. Further these mixtures were so chosen that their composition could be indicated by points on a triangular plane having for its base line a ternary tie line. From the predetermined ternary tie lines two tie lines were selected, one in the acetone-chloroform-water system and the other in the acetic acid-chloroform-water system. The composition of mixtures such as would fall on these two tie line planes and also in the heterogeneous region were then calculated, and these mixtures were used in the experimental determination of quaternary tie lines. In this way two series of coplanar quaternary tie lines were obtained. Experimental data for the two series of tie lines are given in tables 8 and 9.
THE SYSTEM ACETIC ACIU--CHLOHOFOnM--AC~TON~-WAT~n 695
As was done for the tcrnary tie lines, any experiment giving an error in the weight balance of any component greater than f 4.0 per cent wm rejected. The average experimental error was 1.0 per cent. In figure 6 DE’F’ and A’G’H’ are orthogonal projections of the tie line planes DEF and AGH. These two tie line planes intersect to give the line of intersection I J in figure 4. In figure 6 the points I’ and J’ give the TABLE 9 Quaternary tie line data at 86°C. Initial mixtures all lie in thc )lane of the tie line marked * in table 3 COMPONENT8
INITIAL MfXTUBE
TOP LAmB
weight per cent
w 4 h l pa cenl
BOTMY I A m B ~
weigh1 pa cenl
Acetic acid. . . . . . . . . . . . . , . . . . . . . . Acetone , . . . . . . . . . . . . . . . . . . . . . . . . , Chloroform. . . . . . . . , , , , , , . . . . . . . . Water. . . . . . . . . . . . . , . . . . . . . . . . . . .
19.6 8.5 43.5 28.4
32.8 4.6 3.1 59.5
9.6 11.8 76.8 1.8
Acetic acid. . , , . . . . . . . . . , , . . . . . . Acetone. . . . . . . . . . . . . , . . . . . . . . . . . . Chloroform . . . . . . . . , . , , . . . . , . . . . . Water, . . . . . . . . , . , . . . . . . . . . . . . . .
20.0 14.4 37.4 28.2
31.6 7.5 3.5 57.4
9.6 20.3 67.3 2.8
Acetic acid. . . . . . . . , . . . . , Acetone. . . . . . . . . . . . . , , , . . , . . . . , . Chloroform. . . . , , . , , . , . , . . . , . . . , Water . . . . . . . . . . . . , . . . . . . . . . . . . .
18.0 21.2 35.0 25.8
30.4 10.9 3.9
54.8
9.2 28.9 57.9 4.0
Acetic acid. . . . . . . . . . . . . . . . , . . . Acetone. . . . , . . . . . . . . . . . . . . , . . Chloroform . . . . . . . . . . . . . . . . . . Water. . . . . . . . . . . . . . . . . . . . . . . . . . .
17.6 27.2 28.1 27.1
28.8 15.4 4.4 51.4
9.6 36.8 47.3 6.3
.4cetic a c i d . , , .. . . . . .,. Acetone. . , . . . . . . . . . . . . . . . . . . Chloroform . . . . . . . . . . . . . . . . . Water. . , , , . . . . . . . . . . . . . . . . . . .
16.0 36.7 21.7 25.6
24.2 24.4 6.9 44.5
11.2 44.3 30.8 13.7
,
projection of the line of intersection, and this line therefore contains in its length the projection of a quaternary tie line. In this manner it is possible to obtain a series of lines each containing in its length the projection of a quaternary tie line. These lines in themselves however give no indication of the position occupied in their length by the projerted tie lines. This position can only be defined by the projection of the curve K Q L of figures 4 and 5. I n figure 7 the projection of actual lines of intersection of a single acetone-chloroform-water tie line plane with a series of acetic acid-
696
A. V. BRANCKER, T. G . HUNTER A N D A. W. NABH
chloroform-water tie line planes are shown aa broken lines. Projections of the corresponding quaternary tie lines are shown aa full lines coincident ACLTIC ACID Ll
o
CHL &OFOR
M
WATER
FIG.6 ACLTIC ACID
D
CHLOROFORM
WATER
FIG.7 of course with the projected lines of intersection, but only occupying a portion of their length. The curve joining the terminal points of the projected tie lines is the projection of the quaternary tie line curve KQL of
THE SYSTEM ACETIC ACID-CHLOROFORM-ACETONE-WATER
097
figures 4 and 5. The projection of such quaternary tie line curves can be easily obtained by geometrical construction without actually knowing the quaternary tie lines. In figure 8 A T D is a triangular plane in the tetrahedron perpendicular to the base. S and W are points of intersection of this plane with the acetone-chloroform-water and acetic acid-chloroform-water i s o t h e m , respectively. C‘ is the intersection of plane A T D with the ternary tie line KL, and U D is the intersection of the plane A T D with the tie line plane EFD. S Q W is the intersection of the quaternary equilibrium surface with the plane A TD. In this particular case SQW is a straight line but &s a general ACETONE
A
WATER
FIG. 8
case its contour, curved or straight, would be known from the method of triangular section applied earlier (cf. figure 2). Point Q lies on the quaternary tie line curve and can be located from the intersection of UD and SW. Q’ is the orthogonal projection of Q on to the base of the tetrahedron. As A T D is a perpendicular plane, Q’ must be on TD. A series of planes similar to A T D would in this manner give a series of points similar to Q and a corresponding series of projected points similar to Q’, which would define the projection of such a quaternary tie line curve. It is possible to obtain such a curve in the EFD plane by titration where the three components are (1) acetic acid, (2) the acetone-chloroform mixture represented by point E (figure 8), and (3) the acetone-water mix-
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ture represented by point F (figure 8). This is unnecessary, however, as it is easily calculated by the above construction. It has been shown that in this quaternary system of mixed liquids a knowledge of the tie lines in the two heterogeneous ternary systems, together with a knowledge of the shape of the equilibrium surface, enables the quaternary tie lines to be located. THE COMPLETE QUATERNARY SYSTEM
The complete quaternary system acetic acid-chloroform-acetone-water a t 25OC. is illustrated in figure 9. The two ternary isotherms acetoncACETONE
WATER
FIG.9. The complete quaternary system acetic acid-chloroform-acetone-water at 25°C.
chloroform-water and acetic acid-chloroform-water define the heterogeneous region on two sides of the tetrahedron. The points of intersection of the ternary isotherms and triangular shaped planes perpendicular to both the acetone-chloroform-water and the acetic acid-chloroformwater triangles when joined by straight lines outline a frustum which defines the heterogeneous region. One tie line in each of the two heterogeneous ternary systems is shown in figure 9. The planes passing through each of these tie lines and the opposite apex of the tetrahedron intersect to give a quaternary tie line whose two terminal points lie on the quaternary equilibrium surface. REFERENCES (1) GOODWIN, L. F.:J. Am. Chem. Sac. 42, 39 (1920). (2) HAND,D.B.: J . Phys. Chem. 34, 1961 (1930). (3) WRIGHT,C.R. A , : Proc. Roy. Sac. (London) 48, 183 (1891);60,375 (1892)
