T E R N A R Y MIXTURES, I11
BY WILDER D. BANCROFT
Some twenty years ago Duclaux’ found that a clear solution composed of amyl alcohol, ethyl alcohol and water in certain definite proportions could be made to cloud and separate into two layers by the addition of a drop of amyl alcohol or of water. This result has been confirmed by all who have since then studied the behavior of two liquid phases containing three compotients and it may be stated as a general proposition that, with two partially miscible liquids and a third consolute with the other two, it is always possible to prepare a series of solutions any one of which will cloud on addition of .a drop of either of the two partially miscible liquids. This means that if we construct an isotherm for such a system using a triangular diagram, there must be a portion of the curve from any point of which lines drawn to the corners for the two partially miscible liquids will pass at once into the field for two solution phases. It is the object of this paper to show that one can deduce from the triangular diagram certain phenomena which have already been found experimentally but which have seemed hitherto to be lacking in theoretical justification. In Fig. I is given the general form of the isotherm for a system composed of two partially miscible liquids, A and C, and a third liquid, E, miscible in all proportions with the other two. The points x arid x, give the compositions of the two liquid phases when only A and C are present. On adding the third liquid the phases vary in composition, the change in one being represented by the line xyz and the change in the other by the line x l y l z . At the point z the two solution phases become identical. T h e field for unsaturated ‘Ann. Chim. Phys. ( 5 ) 7 , 264 (1876).
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solutions lies above and outside the isotherm while the field enclosed by the curves represents mixtures which separate into two liquid phases having compositions given by two points on the isotherm. From any point on the curve to the right of y and to the left of y , a straight line drawn either to the corner at A or to the corner at C passes into the field for two solutions immediately on leaving the
isotherm. Addition of either A or C will therefore produce clouding and the isotherm as,$Jawn is in accordance with the experimental data recorded by Dnclaux. With the diagram before us it is possible to draw another conclusion not reached by Duclaux. At the point x7 it is clear that addition of C will cause clouding but that addition of A will not. There must therefore be some point between x and z beyond which addition of A will cause clouding. This will occur at the point at which a straight line through the corner at A becomes tangent to the curve. I n the diagram this point is marked y and the intersection of the tangent with the side BC is represented
by H. If we start with a mixture of B and C containing less of B than the mixture denoted by H, addition of the liquid A will eventually cause clouding a i d formation of two liquid phases. If, however, we start with a mixture of B and C containing more of B than the solution denoted by H, addition of the liquid A will not cause clouding.' This phenomenon was first realized experimentally by Pfeiffer,' working in Ostwald's laboratory. Starting always with three cubic centimeters of a given ester he added varying quantities of alcohol and then saturated with water. On passing a given ratio of alcohol to ester-the value of the ratio being a function of the nature of the ester-he found that it was impossible to produce turbidity by addition of water. If we call water A , ester C and alcohol B, the critical concentration is evidently that of the point H. T h e same reasoning shows us that somewhere on the curve X,Z there must be a point at which a line through the corner at C is tangent to the isotherm. This point is represented in the diagram by y1 and the intersection of the tangent with the side AB is denoted by K. I t is clear that K and y1correspond to H and y. T h e isotherni is thus divided into four parts by the three points y,z and yl. Along xy addition of C produces cloudiness ; addition of. A does not. T h e precipitate formed by adding C will contain more of C than the original solution. Along yz addition of either A or C willproduce cloudiness. T h e new liquid phase will contain more of A than the original solution. Along zy,addition of either A or C will cause precipitation. T h e second phase contains more of A than the first. Along ylxl addition of C has no effect while addition of A causes clouding. The precipitate is chiefly A. Since these four portions of the isotherm are so distinct in their properties' T h e s e peculiarities of the isotherm have already been pointed out by Schreinemakers, Zeit. phys. Chem. a3, 652 (1897). I n his paper he was considering qualitative equilibrium whereas I wish to bring out the bearing of these points upon the quantitative equilibrium. 'Zeit. phys. Chem. 9 , 469 (1892). 3Roozeboom and Schreinemakers have shown that when the part of the isotherm for a ternary compound, solution and vapor consists of a closed curve, it may be considered as divided into six portions, Zeit. phys. Chem. 15, 611 (1894). They do not conclude from this that there are any points of discontinuity in the curve.
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one would expect the conipositions of each series of solutions to vary in general in slightly different ways. While studying systems of this type during the winter of 1893-94 I found that the experimental data for the whole isotherm could be represented by the same general formula : ' ( x - S2Y>"(Y- S A = consfant, p+r
I n this formula x,y and z denoted the amounts of the liquids A , C and B respectively in a constant quantity of the three. I n the experiments as actually made these values were expressed in cubic centimeters; but it was shown at the time that any other units might have been taken without changing the general form of the equation. I n the formula s, denotes the solubility of liquid A in liquid C while s, denotes the solubility of liquid C in liquid A. While the same general formula described the equilibrium along the whole isotherm, it was found experimentally that four values of the exponential factor and of the integration constant must be assumed in order to describe the facts accurately. A t the time I pointed out that these four distinct sets of eqilibrium referred to the following four series of saturated solutions.' I . T h e solution is saturated with respect to C. Excess of A produces no prec'ipitate. 2. The solution is saturated with respect to C. Excess of A or C produces a precipitate of C. 3. T h e solution is saturated with respect to A. Excess of A or C produces a precipitate of A. 4. T h e solution is saturated with respect to A. Excess of C produces no precipitate.' It will be noticed that the conditions for the four sets of equilibria as deduced from the experimental data are identical with those which can be predicted from the knowledge of the single fact that 'Proc. Am. Acad. 3 0 , 340 (1894) ; Phys. Rev. 3, 120 (1895). ZIn the original B is used instead of C as I took A and B as the partially miscible liquids. I t was also statrd- there that ((precipitateof A ) ) was used as a condensed phrase meaning that the new phase contained more of A than the old one,
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there are some solutions which cloud on addition of either of the partially miscible liquids. We can see also from the diagram that the ratio of C to B passes through a minimum at y and the ratio of A to €3 passes through a minimum at yl. If therefore we work with a constant quantity of B and varying quantities of A and C we should expect to find the amount of C decreasing as we pass from z t o y and increasing as we pass along the curve from y to x . Similarly the amount of A in the saturated solution would decrease from z to y1and increase from y1to x,. This is exactly what I found in the experimental studies already referred to. If the liquids A and C are practically non-miscible the points x and x, will coincide very closely with the corners at A and C respectively. Other things being equal, the points y and y1will approach the corners A and C as the non-miscibility of the liquids increases and the curves xy and xlyl will decrease in length.' With practically non-miscible liquids such as benzene and water, chloroform and water, these two curves will not be realizable experimentally unless one works on a colossal scale and we should therefore expect to find but two sets of equilibria. Two conclusions which I drew from the experimental data which were tabulated in my first paper on ternary mixtures were :' I . For two partially miscible liquids and a consolute liquid there are four sets of equilibria corresponding to four different series of solutions. 2. If the two liquids are practically non-miscible, there are only two sets of equilibria. It is, of course, not necessary that there should be any points of discontinuity in the isotherm. I t is always conceivable that the same expression might describe the whole curve. With benzene, alcohol and water there seems to be no break at the point z. What can be stated definitely is that if there are points of discontinuity they can occur only at y, z and yl. T h e fact that breaks at y and y, have been found in all cases that have yet been studied and that T h e positions of y and yI will vary with the nature of the consolute liquid unless A and C are absolutely non-miscible. "Proc. Am. Acad. 30, 368 (1894) ; Phys. Rev. 3, 204 (1895).
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only one case is yet known in which there is not a break at z together with the fact that no breaks in the curve have been found at any other points is strong evidence that y,y, and z are theoretically points of discontinuity. This becomes the more probable when one retails that these points were determined experimentally long before their theoretical significance was perceived.
Cornell University
