THE BOILING POINTCOMPOSITION DIAGRAM OF IMMISCIBLE AND PARTIALLY MISCIBLE LIQUID SYSTEMS1
im
MERLE RANDALL
AND
WILLIAM AVILA
University of California, Berkeley, California
IT IS widely recognized that Raoult's law is obeyed for the solute in the solute-rich layer and for the solvent in the solvent-rich layer in partially miscible liquid systems. If one plots a fugacity2 or vapor pressure vs.
composition is enormous. On the left part of Figure 1 we have plotted the vapor pressures in atmospheres of water and of benzene, and their sum against the temperature. As is obvious from the construction, the temperature of the boiling point is that a t which the 110 total pressure is one atmosphere, and the composition of the vapor or the rnol fraction of a constituent is giveu by the ratio of its partial pressure to the total pressure, or since the total pressure is one, the rnol fractiou of benzene in the vapor is equal to its partial pressure. At temperatures above the eutectic boiling point, the rnol fraction of the benzene is also E 3 70 given by its vapor pressure, etc. We thus observe that e 60 8 the curve BC in the right-hand part of Figure 1is idenG tical with the vapor curve of benzene in the left-hand 50 o 0.2 a4 a6 0.8 l o 1.2 0 a 2 04. a6 a8 1.0 side of Figure 1, and that similarly the curve AC is vapor pressure, atmos N~ Nsthe vapor pressure curve of water from the left-hand side reversed. FIGURE1.-BENZENE-WATERSYSTEM We might have drawn the curve on the right-hand Left, Temperature us. Vapor Pressure side of Figure 1immediately by plotting the ratio of the Right. Temperature us. Mol Fraction vapor pressure of benzene to the boiling pressure against rnol fraction curve for such a system a t constant tem- the temperature, and the ratio of the vapor pressure perature, he finds that, notwithstanding the very great of the water to the boiling pressure from right to left divergence from Raoult's law for the solute in the sol- against the temperature. The boiling point and eutecvent-rich layer, and for thesolvent in thesolute-richlayer tic composition of the immiscible boiling liquids are (Henry's law regions) the departure from Raoult's thus giveu by the intersection of the two curves as is law a t the other end of the curve is never more than a indicated. This procedure is valid for any boiling few per cent, provided the mutual solubility of the pressure so long as the liquid phases are substantially liquids is reasonably small. Even in case the mutual mutually insoluble and so long as Dalton's law is solubility of the liquids is relatively great the following obeyed. method of plotting will yield a temperature as. rnol fraction diagram with only a small error. We will assume that the fugacity of a constituent is given by its partial pressure, and that Dalton's l a g of partial pressure is obeyed. If we designate by P the total pressure, by 91' the vapor pressure of the pure solvent, by p1 the partial pressure a t its rnol fraction NI in the solvent-rich layer, by N,' the rnol fraction in the vapor, and by A', A, NZ, and N*' the corresponding quantities in the solute-rich. 6 E layer, then the total pressure is given by the equation:
:
B =h
+ Pr =
+
N I ~ ~ L ' N&'
= P(NI'
+ N~')
(1)
In the case of mutually very slightly soluble pairs of substances such as benzene and water, the mutual solubility in the liquid phase is so slight tbat the limit of unsaturated solutions is practically identical with the margins of the diagram. The rate of change of the boiling points of the unsaturated solutions with the Clerical assistance by the Works Progress Administration is gratefully acknowledged. (O.P. 65-1-08-165). a See LEWISAND RANDALL.thermodynamic^ and the free energy of chemical substances," McGraw-Hill Book Co., New Yark City, 1923, p. 212.
G
- -.- ..
. . ... Vapor Pressure, atmos
10 -N~n
N-
40
FIGURE2.-ANILINE-WATER SYSTEM Left, Temperature us. Vapor Pressure Right. Temperature us. Mol Fraction
Assuming that the partial mutual solubility of aniline and water are as shown by curves D F and EG in the right part of Figure 2, we can easily construct approximate complete curves for the aniline-water system by a preliminary calculation on the basis of complete im-
miscibility. We then have an approximate location of the eutectic temperature along the line DE. Hence we draw the branches AD and BE. As we shall indicate later, slight errors in drawing these curves will cause relatively slight errors in the curves AC and BC. In the left side of Figure 1 we have plotted the vaporpressure curves of aniline and water against the temperature, using as the horizontal axis the ratio of the vapor pressure to the boiling pressure. We now transfer the vapor-pressure curve of water to the righthand diagram, multiplying the vapor pressure of water by the mol fraction of water along the line BE, thus
obtaining the curve BC. Similarly reversing the aniline curve and multiplying by the mol fraction of aniline along the line AD, we obtain the curve AC of the righthand part of Figure 2. The intersection gives the vapor composition of the eutectic and the temperature of the boiling partially miscible mixture. In drawing Figure 2, we assumed that the curve AD was a straight line. The cnrve is probably more nearly like the dotted curve AD, by the use of which we find the dotted curve AC which does not differ greatly from the cnrve obtained on the assumption of the straight line.
