INDUSTRIAL AND ENGINEERING CHEMISTRY
February, 1945
185
LITERATURE CITED
chlorine and then rises rapidly for chlorine contents above 35%. This rise is undoubtedly associated with the higher viscosities obtained above 35% chlorine contents. The present paper represents a portion Of a comparative investigation on the preparation and study of the physical and chemical properties of halogenated petroleum fractions. This work has been interrupted by conditions. However, when _ present _ opportunity permits, we plan to resume our investigations and to present comparative data on other types of petroleum fractions.
(1) Hartman, Be?., 24, 1019 (1891)* (2) Rice, H. T., and Lieber, E., IND.ENG.CHEM.,ANAL. ED., 16, 107 (1944). (3) Ruh, E. L., Walker, R. W., and Dean, E. W., Ibid., 13,346 (1941). (4) Sohrauth, German Patent 327,048(1914): Chem. Abs.. 15. 2009 (1921). ( 5 ) Thomas, . , . " a \ c. - 4 . 3 and O h J. F.. U. S. Patent 2,065,323(Dec. 22, lY50).
PRESENTED before the Division of Petroleum Chemistry a t the 108th MeetCHEMICAL SOCIETYin New York, N. Y. ing of the AMERICAN
Analvsis of Ternarv Mixtures Containing Nonconsolute Components J
J
ALLEN S . SMITH' Blaw-Knox Company, Pittsburgh, Pa. A n indirect method of analysis for liquid mixtures of three components is described. It is applicable to ternary systems having a miscibility gap. The method requires determination of two saturation points on a solubility iso-
therm of the ternary by addition of two of the components to the unknown mixture. The original composition of the mixture is then obtained by graphical or algebraic calculation.
L
nonconsolute component to the point of immiscibility. If the mixture is heterogeneous, it is titrated with the consolute component to the point of miscibility. These points lie on the solubility curve. The original composition of the binary mixture is calculated from the weights of the sample and component, and the ternary composition is read from the curve. If no point of immiscibility or miscibility is reached in titration, the composition of the original unknown mixture must be altered by adding one of the pure components of the mixture to bring the composition within the range of the immiscible portion of the solubility diagram. It is also necessary to do this if the end point is difficult to detect because of critical opalescence. No preliminary trials are necessary after experience is gained in use of ternary diagrams, as any one of the three components can be added to the unknown mixture a t will to obtain a good end point.
IQUID-liquid and vapor-liquid equilibria in ternary systems have, in many instances, been studied because of the ease of analysis rather than because the systems were industrially important. I n fundamental investigation it is desirable to have direct methods of analysis for homogeneous ternary mixtures, from specific analytical procedures or from adequate data for two independent physical properties. Many valuable data of industrial importance, however, have been reported for which the methods of analysis were indirect. These methods were used because they were necessary or convenient, but they are also capable of good precision and sensitivity. The analysis of *ter in alcohol with the aid of dicyclohexyl (8) is an example of a sensitive indirect method. Aniline points have been used in a similar manner for more than twenty years ( I ) t o analyze hydrocarbon mixtures. The more recent furfural method (7) extends the usefulness of the method to include highly aromatic solutions. The temperature of complete miscibility or the critical solution temperature is employed, and the measurements age referred t o those of known compounds or mixtures. Indirect methods at constant temperature facilitate the analysis of binary mixtures and the location of tie lines in ternary equilibria. This paper extends these methods to the analysis of ternary mixtures with one pair of nonconsolute components. I n these applications i t is necessary to have only solubility data at a convenient temperature and measurements of weight. BINARY MIXTURES
A binary mixture is analyzed with the aid of a third component chosen so that one pair of nonconsolute components will be present. Alcohol and water or benzene and hexane, for example, can be analyzed by use of benzene and dipropylene glycol, respectively. The ternary solubility diagram is *first obtained. If the mixture to be analyzed is homogeneous. it is titrated with a '
1
Present addreas, P. 0. Box 48, Ann Arbor, Mioh.
'
TIE LINE DETERMINATION
~
Indirect methods are conveniently used to determine the composition of phases at equilibrium when the over-all composition of the heterogeneous ternary is known. The phases, which lie on the solubility curve, are located by use of the familiar lever arm relation in one method. The weight ratio of the two conjugate phases is in inverse relation to their distances from the ternary point, in the solubility diagram, t o the solubility curve (6).
Bancroft and Hubard ( 2 ) described a graphical method for determining dineric distribution between phases at equilibrium. The phases separated at equilibrium are titrated through the region of immiscibility t o saturation on the opposite side of the solubility isotherm with two of the components. The original composition of the given phases is determined by trial-and-error calculation to be that composition which required the addition of the particular amounts of the two components to depart from the isotherm and then return to it. This method serves to de-
INDUSTRIAL AND ENGINEERING CHEMISTRY
186
I 40 9.0
9.5
0
0.5
1.0
1.5
2.0
LOG B I W
Figure 1.
Solubility Data for Five Ternary Systems
System .I I Ethyl alcohol I1 2-Propanol I11 Diphenylhexane IV Acetone V Methyl ethyl ketone a Obtained by A. R. Jensen
B Benzene Nitromethane Docosane Chloroform Carbon disulfide in this laboratory.
W Water Water Furfural Water Water
Temp.,
' 6.
Reference
25 25 45 25 25
(8) (9) (3')
(t)
termine the composition of a ternary homogeneous mixture lying on a 6olubility isotherm. TERNARY MIXTURES
The need for an indirect method of analysis arose in the course of work on ternary vapor-liquid equilibria. The vapor and liquid samples, which were obtained in the equilibrium apparatus of Colburn, Schoenborn, and Schilling (4) for partially miscible components, consisted of both homogeneous and heterogeneous mixtures of three components whose over-all composition was unknown. The precision of the analytical method developed is good, but the accuracy depends upon the reliability of the isothermal solubility diagram, as is true in all the indirect methods mentioned. The method is based on the assumption that isothermal solubility in ternary heterogeneous systems follows a mass law equation of the type:
Vol. 37, No, 2
of the type ( a / b ) " / ( b / w ) = K . This form has been used although there is no theoretical justification for it. The points seem to give less dispersion from a straight line and the line is longer, n hich is convenient. Solubility data for five representative systems are plotted in Figure 1 according to the equation. The same data are plotted on triangular coordinates in Figure 2 . The curves in both figures extend over the same range. The application of the method is illustrated with reference to system I. The unknown mixtures are assumed to be those represented by Arabic numerals 2 and 6 in Figure 2. Sample 2 IS titrated with water to saturation a t point 3, additional water ia added to 4, and the mixture is titrated to miscibility a t 5 with alcohol. \T7hen the unknown sample lies on the water-rich side of the diagram, as a t 6, it is diluted with benzene, as to 7, titrated with alcohol to miscibility at 8, diluted with benzene to 9, and finally titrated again to miscibility a t 10. The location of the unknown sample in the solubility diagram can be approximated from the proportion of the phases in a heterogeneous mixture, as the slope of the tie lines can be estimated, or by trial addition of one or more components in the case of homogeneous mixtures. The addition of nonconsolute components and titration \ n t h consolute component can then be made so that two end points are obtained, lying on the portion of the isotherm which folloii > the mass law equation. The operations with the mixtures are represented in Figuie 3. The numerals correspond to those in Figure 2. I n each example the titration has been made with a constant amount of one of the nonconsolute components benzene or water. Each miscibility or saturation point, 3 and 5 or 8 and 10, lies on a line whose equation is: log A J B = log K m log B/W (1) As either B or W is the same for two pairs of points, the conipositions of the two points are related in the following manner Aa W = -m log 3A t constant B: log (2) A6 A B At constant W : log 2 = (1 m ) log -2 (3) A10 BlO The quantities rcpresented by A , B , and W in Equations 2 and 3 are made up of the unknown amounts of each plus the added amounts to obtain the two points on the isot,herm; thus A , =
+
-
+
w5
A
Figure 2.
Solubility Data
for Five Ternary System\
of Figure 1 Plotted uti Triangulxr C o o rdi 11 a Le 3
(a/b)m/(a/w) = K
where a consolute component b, w = nonconsolute components m, K = constants Lincoln (5) found that his data on the system benxene-alcoholwater followed this equation. Bancroft and Hubard (2) confirmed this. The latter found that the system acetone-chloroformwater did not give a straight line when plotted according to the equa tion. Thirty systems for which solubility data have been plotted by the mass law equation have been found to follow the equation over part of the isotherm. The deviations of the data from the logarithmic straight lines are small and, in view of the cloud point method used in most solubility determinations, could be due to experimental error. If points in some systems do represent sigmoidal curves, as in the acetone-chloroformwater system, the best straight line drawn through the points adequately represents the isotherm for thepurpose. Thesystemsalsofollowanequation 8 SO
80
70
69'
50
40
30
20
to
w
INDUSTRIAL AND ENGINEERING CHEMISTRY
February, 1945
182
Subtract quantities added to make 3 and compute composition : B
144.5 A = 95.0 W = 24.5
- 0 = 144.5 == 59.0% - 0 = 95.0 = 38.8 - 19.5 = 5.0 2.2
=
composition of unknown mixture 2
244.5
The procedure would be the same if the data for point 5 were used. If the unknown mixture had been 100 grams of 1 to which 144.5 grams of B had been added to obtain 2, the percentage composition would be obtained directly in the last step of the example. This is true whenever the sample is taken or calculated to the basis of 100. A check on the accuracy is obtained when the final composition totals 100%. This is shown by an analysis of a n unknown mixture of system V for which this method mas used in vapor-liquid equilibria measurements. EXAMPLE. Heterogeneous mixture of methyl ethyl ketone, carbon disulfide, and water:
BIW
Sample MEK added to saturation Ha0 added to immiscibility MER added to saturation
Operation of Mixtures Shown in Figure 2
Figure 3.
+
A and As = A z. Trial values of one of the unknown quantities (W, for example) are substituted in Equation 2, and the value of the other quantity, A , is calculated. T h e value of B is obtained by difference, as the sum of A , B, and W equals the weight of sample taken for analysis. Three values are sufficient. They define a straight line represented by either OP or QS in Figure 3 and related by the following equation: A+x B
log -= log K’
+
B W+Y
VZ’ log
(4)
where A , B , W = calculated v+es x, y = added quantities of A and W
If x and y are taken as the quantities necessary to obtain the first point on the isotherm, then OP represents the equation. It intersects the isotherm a t point 3. The original composition of the unknown mixture is calculated from the point of intersection. A solution can also be obtained algebraically from Equation 1 for the isotherm and from Equation 4 for the line OP or QS. The value of the abscissa at the point of intersection is:
K’
log B / W = log -E / (m
- m’)
(5)
The graphical method is more simply illustrated by a n example with mixture 2 of system I:
-
Assume unknown mixture 2 244.5 g. (point 2) Add W to saturation = 19.5g. (point 3) Add W to produce two phases = 88.6 g. (point 4) Add A to miscibility = 164.5 g. (point 6) Slope of isotherm = - 0.6562 (in Equation 1 for system I) Apply Equation 2: IOg
A
W f 19.5 A = 0.6562 log W 19.5 f 88.5 164.5
+
+
Slope of isotherm = -0.659 (in Equation 1 for system Y). Apply Equation 2 : log A
A 3. 111.6
W
+ 111.6 + 181.5 = 0*659log w + 21.5
Assume values for W , calculate corresponding values for A and B, and obtain values of ( A x ) / B and B / ( W y) in Equation 4 for the second point of saturation:
+
W
A
9 10 11
35.39 48.9 62.5
100
B =
+
- (W + A )
+ 293.1.
A
B 6.89 8.32 13.41
55.7 41.1 26.5
B
+ 21.6
W
1.825 1.306 0.814
Coordinates of intersection for the straight lines of Equations
1 and 4 for system V determined graphically are: A / B B / W = 1.025. Therefore:
W
= 7.67
=
10.75,
350.2 A in final mixt. 32.6 g. B i n final mixt. 31.8 g. W in final mixt.
Subtract quantities added to obtain the second saturation point, and compute composition: 350.2 - 293.1 = 57,1% A in original sample 32.6 - 0 = 32.6% B in original sample 31.8 - 21.5 = 10.3% W i n original sample Total 100.0 ACKNOWLEDGMENT
The criticism of Julian C. qmith and his check of the calculations are appreciated.
Assume values for W , calculate corresponding values for A and B , and obtain the values of ( A x ) / B and B / ( W y) in Equation 4 for point 3 or for point 5:
+
13.49 g. = 100.0 g. 15.06 g. E 111.6 g. 2.9 g. 21.5 g. 24.5 g. 181.5 g. Total 414.6 g.
+
LlTERATURE CITED
Ball, J. S., U. S. Bur. Mines, Rept. Investigations 3721 (1943). Bancroft, W. D., and Hubard, S. S., J . Am. Chem.Soc., 64, 347 -Point -3 -Point &-----. B A + 164.5 B - (1942). B-. ~ Briggs, S. W., and Comings, E. W.. IND.ENQ.CHEM.,35, 411 W A 244.6 (A f W) A/B W 19.6 B W + 108 (1943). 0.837 7.34 1.58 1.435 2 84.7 1S7.8 Colburn. A. P., Schoenborn, E. M., and Shilling, D., Ibid., 35, 0.621 6.32 1.73 1.323 4 92.2 148.3 0.706 5.49 1.88 1.228 6 98.6 139.9 1250 (1943). Lincoln, A. T., J. Phys. Chem., 4,161 (IQW). Plot the values of A / B and B / ( W 19.5)for point 3,and draw Othmer, D. F., and Tobias, P. E., IND.ENQ.CEEM..34, 690 straight line OP. The coordinates of the intersection are A / B = (1942). Rice, H. T., and Lieber, E., IND.ENQ.CHEM., ANAL. ED.,16, IO? 0.659,B/W = 5.9. Therefore:
-
+
+
(1944).
B = 54.7%
W
=
9.3
144.5 grams B X 264 ( = total wt. of 3)
5
24.6 grams W
Robertson, G. R., Ibid., 15, 451 (1943). Schumacher, J. E., and Hunt, H., IND.ENG. CHEM.,34, 701. (1942).
