Flgure 1. Tournament bracket %ore card for Chemical Pursuit tournament. (One of two brackets is shown.)

The 1986-1987 competition a t Indian Hills did not result in just the advanced students winning. Its structure mimics the actual Trivial Pursuit game, which allows some means for the less knowledgeable student to win. You still have to roll (via the computer) and land on a Pie. After 30 matches the two teams that made i t to the finals were the number one seeded team (Derail the Express) made up of the best two Advanced Placement students in school, and an unseeded team (The Hosers), made up of two first-year students in a standard-level chemistry class.

The final match was played on the last day of school. Several students from other classes surrounded the players and cheered on their favorites. With the Silver Flask prizes@') on the shelf in the background each team moved from square to square. They had learned enough chemistry from class and on their own to answer about 80% of the questions correctly. All four students had been motivated by this competition to such an extent that their extra studying had also resulted in A's on their final chemistry exam. This made the competition a total success.

A Computer-SimulMed Experiment on Vapor- Liquid Phase Equilibrium

Norman C. Cralg, Brlan J. Brown, William S. Chamness, and Elalne B. Mulvey

Oberlin College Oberlin. OH 44074

A traditional experiment in the physical chemistry labora- tory is the study of two-component, vapor-liquid phase equilibria. The principal result is the construction of a tem- oerature-comoosition 1T-X) nhase diaeram for a nonideal solution syste&. The typical Gperimeniconsists of allowing mixtures to reach nhase eauilihrium a t atmospheric pres- sure in a small reflux system and withdrawing separate sam- ~ l e s of the ~ o t contents and of the condensate of the vapor phase for analysis (3).

Although such an experiment is of considerable value in helping students understand phase equilibria and distilla- tion processes, obtaining the necessary data in the lahorato- ry is a tedious process. Furthermore, a study of the equally interesting pressure-composition (P-X) diagram is too dif- ficult for a standard laboratory experiment because of the problems of working a t variable pressures. In a simulation it is feasible to include studies of T-X systems a t constant pressures other than atmospheric pressure as well as to in-

Table 1. Parameters for Components 01 Ideal Solutions'

AHovep ASo,, TBP compound callmol caI/K-mol O C

carbon tetrachloride 7628.8 21.53 76.5 cyclohexane 7830.9 21.88 80.7 hexane 7627.2 22.13 69.0 oentane 6595.1 21.09 36.1

clude studies of P-X systems over a range of constant tem- perature. The hazardous nature of many of the traditional liquids used in vapor-liquid equilibria studies is another reason to recommend a simulation.

The simulation includes some ideal liquid solution sys- tems and some nonideal ones. Throughout the simulation we treated the vapor phase as ideal. For ideal solution systems appropriate analytical functions can he written, from which the computer program can calculate equilibrium concentra- tions as requested in the liquid and vapor phases (4). Vapor pressures of the pure liquids, Pi*, are represented by the integral form of the Clausius-Clapeyron equation

P;*latm = exp (-AH~IRT + ASyIR) (1)

The parameters for this equation are shown in Tahle 1. Temperatures are in kelvins, and pressures are in atmos- pheres throughout the experiment. Raoult's Law,

p. = xlp.' , , , (2)

expresses the partial vapor pressure of each component in terms of its mole fraction in the liquid phase, xil, and the vapor pressure of the pure component. The total pressure, P, is the sum of partial pressures of species A and B,

and the concentration of species A in the vapor phase is

For the constant temperature P-X option the computation of the concentrations in the vapor phase in equilibrium with chosen liquid-phase compositions is a straightforward appli- cation of eqs 1 to 4. Available liquids for the ideal solution optionof the experiment and parameters for eq 1 are given in Table 1.

For T-X phase diagrams under the constraint of constant pressure for ideal solution systems, a different calculation path is followed. Equation 1 is inverted to give temperature as a function of pressure,

from which the boiling points of the two pure components are computed a t the designated total pressure. Then, for various temperatures between the two hoilingpoints, the Pi* values are computed from eq 1 and used to calculate the corresponding x ~ ' values from

z,' = ( P - P,*)I(PAa - PB*) (6)

and XA" values from eq 4. Including nonideal solution systems in this simulation was

a greater challenge. Analytic expressions for activity coeffi- cients for the components in solution were needed. Torepre- sent the activity coefficients we use the expression,

from simple solution theory. The b parameters for each

792 Journal of Chemical Education

Table 2. Parameters for Components of Non-Ideal Solutions

acetone(A) 7563.1 23.0 56.0 -4.370 0.010920 7454.2 22.3 61.0 -2.945 0.006923

285.5 chioraform(B)

68.7 6

ethyl alcohol(A) 9830.1 27.9 79.1 3.829 -0.008310 280.0 25.0 22.3 82.0 3.928 -0.008264 acetonitriie(B) 7911.9

acetonitrile(A) 1.900 -0.001914 280.0 35.0 7 taluene(B) 8703.5 22.7 110.4 2.742 -0.004239

component in the three pairs shown in Table 2 were fitted separately to experimental data (6, 7). (This procedure is a departure from simple solution theory, which calls for the same b parameter to apply to the two components in a solution.) Then, the b parameters a t various temperatures were fitted to a linear function of temperature,

b = b, + b,T (8)

Table 2 gives these parameters for the three nonideal sys- tems. The acetone-chloroform system illustrates negative deviations from Raoult's law, whereas the other two systems display positive deviations.

For the constant temperature P-X option for nonideal solutions the program uses the same calculational path as for ideal solutions except that activity coefficients, y,, are in- cluded. Equation 3 becomes

P = yAxAIPA* + yg(l - ll*I)PB* (9)

and eq 4 becomes

zAY = yAzI\%*IP (10)

Thus, mole fractions in the equilibrium vapor, XA", are com- puted from designated mole fractions of the liquid phase, %A', and eqs 1,8, and 7.

An incremental search method was applied to the con- stant pressure T-X option for nonideal solutions. As part of the method, we use the boiling temperatures of the azeo- tropes. These temperatures are represented by linear func- tions of pressure, which were fitted to the observed values (6, 7). The parameters for the expression,

T,, = a, + a,P (11)

for each of the three nonideal systems are given in Table 2. For a given mole fraction in the liquid phase, XA', eq 9 is used to calculate a total pressure a t successively incremented temperatures between the minimum and maximum allowa- ble temperatures. These extrema must be the azeotrope temperature and the boiling point of either A or B, depend- ing on the system. This search continues until the computed total pressure is in acceptable agreement with the designat- ed total pressure. Finally, the mole fraction in the vapor phase, x ~ " , is found at this temperature by means of eq 10.

In our use of the simulation for the laboratory students have been asked to choose a nonideal system to study. They have constructed both T-X and P-X phase diagramsfor the selected system. They have used data fromP-X diagrams a t two temperatures to compute AG, AS, and AH of mixing as a function of liquid-phase composition and have then com- pared these results with those for formation of ideal solu- tions. They have also been asked to discuss the fractional distillation of a designated solution. A possible addition is an exploration of the dependence of the azeotropic composition on overall pressure.

The terminal-oriented, computer code is FORTRAN 77 and has been realized on a Dec VAX 11/780. Listings of the program are availahle upon request. Copies of this FOR- TRAN code on 5II4-in. floppy disks are available in IBM- compatible DOS format from Project SERAPHIM.

The van der Waals Equation and Vapor Pressure of Liquids

Herbert R. Elllson Wheaton College

Norton, MA 02766

Any discussion of real gases inevitably leads to a consider- ation of the van der Waals equation, even though i t is cer- tainly not the hest ana l~~t ica le~~~ress ion for the tFeatrnent of real gases. At low temperatures or at high gas densities this equation produces re&s that are not much better than those obtained from the ideal gas equation. However, the van der Waals equat,ion has a certain simplicity about i t that helps students readily grasp the significance of the two cor- rection terms (embodied in the constants a and b) that are part of it. Most textbooks of physical chemistry give ade- quate treatment to PV isotherms, and it is a relatively simple matter for students to write programs so that they can con- struct such plots. What rarely is pointed out, however, is the fact that it is possible to use the van der Waals equation to obtain estimates of vapor pressures of liquids (8,9). I t is the purpose of this communication to illustrate how this can be done.

Figure 2 shows an isotherm for COz a t 250 K with a hori- zontal line ae a t 31.79 atm drawn in such a way that the area abc (S2) equals the area cde (Sl). The significance of this line is best considered by starting a t point x to the right of a and then proceding to the left along the isotherm. Curve xa is approximately a Boyle's law isotherm. When point a is reached, liquid is observed to form by the appearance of a meniscus between vapor and liquid. Here the molar volume is 0.4690 L with a pressure of 31.79 atm. Further compres-

Figure 2. Van der V b l s PV isotherm for C02 at 250 K (a = 3.592 L2 atm m ~ l - ~ , b = 0.04267 L mol-') calculated with program VDWVAP showing the equilibrium Vapor pre65UrB of 31.79 am.

Volume 65 Number 9 S e ~ t e m b e r 1988 793