E. i. Heric University of Georgia
Athens
Tie Line Correlation and Plait Point
Determination
An experiment on phase equilibria in a heterogeneous ternary liquid system is frequently assigned in the laboratory in elementary physical chemistry, As presently constituted in the current laboratory texts, the experiment consists only of the determination of the binodal curve and several tic-lines. It is possible, however, using only the data taken for the above purpose, to make this a more informative experiment by utilizing tie-line behavior to determine the plait point. The method is one of those commonly followed in research, where a direct determination of the plait point appears to be a rarity. A number of approaches for tie-line correlation have been proposed {1-7). Of these, all but two, those of Bachman and Dryden, are of forms less desirable for work at the elementary level. The method selected for this experiment was that of Bachman. The Bachman equation may be expressed in the form m m (“‘/in) + k, where a\ is the per cent by weight of one of the lion-consolute liquids (A) in the phase richer in that component, t>2 is the per cent by weight of the other nonconsolute liquid {B) in the corresponding conjugate phase in which it is richer, and both m and k are empirical parameters. Frequently it is found that m and k are constant for an isothermal system; the equation is then obviously that of a straight line. This is generally found to be so when the two non-consolute liquids are markedly insoluble. The equation was first developed empirically, hut it has been shown (5) to bear a resemblance to the familiar Nernst distribution equa-
the students in this laboratory. They have been included to give an indication of how the accuracy in determining the plait point depends upon the accuracy in determining the solubility curve. The tie-lines determined by the students are not included here, since Acetic Acid
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tion. The basic experiment to which the work described in this paper was appended is described in a current laboratory text ((?). The system studied was acetic acidbenzene-water, although a number of other systems found in different texts would be equally suitable. Figure 1 illustrates the nature of the phase diagram of the system studied. The binodal curve and tie-lines represent the accepted values at 25 °C {2). The individual points on the diagram are those determined by Presented before the 15th Southwest Regional Meeting of the American Chemical Society, Baton Rouge, December, 1959.
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their accuracy is indicated in Figure 2 below. The experiment was performed at room temperature, which varied from about 23-7°C. The tie-line correlation plot used in estimating the plait point is given in Figure 2, where A represents water, and B benzene. The solid line is the relationship obtained by the use of the accepted values. Included in the figure, also, are the points obtained by the students, which indicate the spread in data to be expected. The laboratory text directs that four tie-lines be obtained. Several students had a single bad point, but in each instance their other three points gave a welldefined straight line.
point, for each of these points a ah and % a'/in “‘/a,, for the two conjugate phases become identical at the plait point. As the plait point must also lie on the extension of the line representing the Bachman equation, the intersection of the two lines defines the plait point. The dashed line used to illustrate this relationship in Figure 2 was drawn using the accepted values. From individual plots of student data the values of a at the plait point were found to be 7.0,7.2,7.5, 7.5, and S.5. The accepted value is 7.2, indicating a satisfactory agreement for the purpose intended. The reaction of the students toward this additional aspect of the experiment was favorable. They were interested to learn that there is a systematic relationship between the tielines which may be used both for interpolation purposes and for location of the plait point. It appears that the determination of an additional tie-line nearer the plait point might reduce the uncertainty in the required extrapolation of the Bachman plot. =
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Literature Cited Figure 2.
Bachman plot.
The plait point is determined by the intersection of the plot of the Bachman equation with the dashed line near the base in Figure 2. The latter line is established from the solubility curve and represents a locus of points upon which the plait point must lie. It is obtained by estimating possible locations of the plait point, which may be roughly fixed by the general trend of the tie-lines in the phase diagram. Values of a and b at the various estimated plait points are recorded. Since each point is tentatively assumed to be the plait
(1) “International Critical Tables,' McGraw-Hill Book Co., Inc., New York, 1926, Vol. Ill, p. 398. (2) Hand, D. B., J. Phys. Chem., 34, 1961 (1930). (3) Brancker, A. V., Hunter, T. G., and Nash, A. W., Ind. Eng. Chem., Anal. Ed., 12, 35 (1940). (4) Bachman, I., Ind. Eng. Chem., Anal. Ed.., 12, 38 (1940). (5) Othmer, D. F., and Tobias, P. E., Ind. Eng. Chem., 34, 693 ’
(1942),
(6) Dryden, C. E., Ind. Eng. Chem., 35,492 (1943). (7) Upchurch, ,J. C., and Van Winkle, M., Ind. Eng. Chem., 44, 618(1952). (8) Crockford, H. D., and Nowell, J. W., “Laboratory Manual of Physical Chemistry,” John Wiley and Sons, Inc., New York, 1956, pp. 105-9.
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