The Representation of-Ternary Liquid Composition Diagrams B. W. Clare, G. T. Hefter, and P. E. Kloeden School of Mathematical and Physical Sciences. Murdoch University, Murdoch, W.A. 6150, Australia MacCarthyl advocated the use Recently in THISJOURNAL of right isosceles triangles (RIT) instead of the conventional equilateral triangles (ET) for the representation of ternary composition diagrams. He cited the pedagogical advantages of being able to use familiar Cartesian coordinates and analytical geometry in an RIT diagram. The ability to store, manipulate, and display large amounts of data make computers and computer graphics systems valuable aids in a modern teaching or research laboratory. At Murdoch University we have been using computers to systematize the storaee and nresentation of ternarv . liouid . solubiiity data. In fitting It!nst-squares polynomial curves (using o H1'85 desktoo cornouter) lo such data we havr found thnt the E T coordinates 'have a clear advantage over the RIT coordinates favored by MacCarthy. Typical of the data analyzed to date is the pyridine-water-benzene system2 (which is a type I system in the terminology of Sorenson et aL3 and thus representative of about 75% of all ternnaryliquid systems, or about 97% if similar variants are included). Figures 1and.
2 clearly show that the experimental data can be fitted with simple polynomial curves to a much greater precision (typically R2 > 0.99) in E T coordinates? Similar precision may he obtained with RIT coordinates using higher order polynomials, but the resulting curves are physically unrealistic and would be misleading for interpolation or display. This phenomenon is a consequence of the greater symmetry of typical hinodal curves in an E T diagram. Such curves in an RIT coordinate system are almost asymptotic in one region of the composition diagram, making them difficult to fit to high precision with low-order least-squares polynomials. Of course, physically meaningful fits could be obtained with a much larger quantity of data. Alternatively, more sophisticated fitting routines or functions could he used, but these would probably be outside the experience of most chemistry students. In summary, E T coordinates are more convenient for the simple mathematical representation of ternary liquid compoiition diagrams than the RIT coordinates advocated by MacCarthy.
' MacCarthy, P., J. CHEM.EDUC.,60, 922 (1983).
Vriens, G. N., and Medcalf, E. C., Ind. Eng. Chern., 45,
1098
(1953).
Sorensen, J. M.. Magnussen. T., Rasmussen, P.. and Fredenslund. Fluid Phase Equilibria, 2, 297 (1979). 'This is in spite of having to fit the curve relative to Cartesian coordinates superimposed on the plane of the equilateral triangle.
A,,
0 Figure 2 composition diagram for the pyridine-water-benzene(PWB) system using right isosceles triangular coordinates.
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Figure I.Composition diagram for the pyridinewater-benzene (PWB) system using equilateral triangular cmrdinates. x = Experimenlai points curve: y = 4.534 X 1 0 - l 9 0.999: where x = B
680
- 2.774 X 10-29 + 2 . 3 7 0 ~- 5.914; R2 =
+ (P12). y = & Pl2.
Journal of Chemical Education
0 = Experimenlal points Curve 3: y = 5.940 X 10-'9 - 9.070 X 10-2X2 3.424 x 22.65: ?f = 0.891 Curve 4: y = -2.22 X 1 0 F # + 3.95 X 1 0 - 3 9 - 0.242.?+ 5.51x+ 18.2: R2 = 0.960 Curve 7: y = 3.29 X 10-9x7- 8.28 X lo-',$ 8.24 X 10-SXS - 4.18 X 10-3P 0.1169 - 1.779 14.2x+ 7.7; R2 = 0.998
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Curve numbers refer to lhe order of Me polynominai.
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