Stephen W. Tobey' West Virginia Wesleyan College Buckhannon
Ideal Solution Laws Apparatus and experiment
The usual physical chemistry laboratory experiment illustrating binary solution behavior entails the construction of a boiling point versus composition diagram at constant pressure for a non-ideal liquid pair.2 An equally interesting and undoubtedly more fundamental experiment involves verification of the ideal binary solution laws governing vapor-liquid equilibria at constant temperature. The apparatus and experiment described below fulfill the need for a simple experiment of this type. Equafions
The equationsa which give the total pressure (PT) exerted by a binary ideal solution a t temperature T containing the components A and B, and the partial pressures (PAand Pe) of A and B in the vapor are P* = P*O X X* (1) PB = PB' x XB (a PT = P.,O X X* PB*X XB (3)
+
where XAand XBare the mole fractions of A and B in the liquid, and PAoand PBoare the equilibrium vapor pressures of pure A and B at the temperature T. The mole fractions (YAand Y e ) of A and B in the equilibrium vapor in terms of the above parameters are given by the equations P*' X x* Y* = (4) PA' X X A (1 - X d X Pe"
+
For the purposes of the experiment described below it is convenient to rearrange (4) and (5) to their linear forms4:
Apparatus
The critical dimensions and construction details of an appararbus suitable for testing the ideal solution laws are given in Figure 1. There are two special features of this particular equipment that deserve mention. One is that no pump is required to produce the above-atmospheric pressures required within the apparatus during operation. This pressure is automatically generated by compressing the air normally contained in the flask into the condenser and ballast bulb. The other is the form of the reflux sampler. It is simply a leaky cup. During operation a constant stream of recondensed equilibrium vapor flows through the cup, and a steady-state condition is rapidly achieved in which the composition of the liquid in the sampler cup is identical to the composition of the vapor. The remainder of the apparatus is quite conventional. Teflon stopcocks are used to eliminate contamination of the liquid samples with stopcock grease. The asbestos-covered aluminum foil heat shield prevents condensation and fractionation of vapor on the walls of the flask. The thermometer wick is of asbestos, since this fiber is resistant to chemical degradation and in addition provides many efficient nucleating centers which effectively prevent bumping. The wick may be cut from an asbestos finger-clamp sleeve, but should be washed with water and acetone before use to remove the soluble filler. The semiball joints should be lubricated lightly with silicone grease and clamped securely with thumbscrew-lock collars. The 0-360° thermometer may be replaced with a shorter range type if temperature determinations more accurate than +0.2'C are desired. The apparatus was constructed in part by the Scientific Glass Apparatus Company according to specifications. Liquids
The validity of equations (I), (Z), (3), (6), and (7) may he directly established by the experiment outlined below in which experimental data on the behavior of an ideal binary solution are compared with the theoretical predictions of these laws. 1 Present address: Chemistry Department, University of Wisconsin, Madison. J. W., A N D CAOPPIN,A. R., J. CAEM. ROGERS, J. W., KNIGRT, Ennc., 24,491 (1947). T o r the derivations of equations (1) through (5) see, for F., and ALBERTY, R. A,, "Physical Chemexample, DANIELS, istry," 2nd ed., John Wiley & Sons, Inc., New York, 1961, pp. 147-50. 4 Equations (6) and (7) become indeterminate at X = 0, and are most useful when 1.0 > X > 0.3.
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Journal of Chemical Mucafion
Since the factor which ultimately l i i t s the success of the experiment is the ideality of the liquid pair used, the two liquids chosen for study should be closely related in physical and chemical properties. In addition, to work well in the apparatus described, the two liquids should both boil above 10O0, have a boilmg point diierence of no more than 25', and have a didference in refractive indexes of more .than 0.0150. Table 1 lists several readily available benzene derivatives which fulfill these requirements and which have been found to give good results. Purified grades of the liquids listed may be used as received. Procedure
The compositions of the various solutions obtained
Binary Solution Pairs of Benzene Derivatives
Table 1.
TJDC
1. 2. 3. 4.
Bromobenzene Ethylbenzene Chlorobenaene Methvlbenzene
156 136 132 111
1.5598 1.4983 1.5248 1.4969
13 2-1 3-2 4-3
24 20 4 21
0.0350 0.0615 0.0265 0.0279
during the experiment are most easily determined with a refractometer. Mixtures containing the two liquids under study are prepared by weight in the mole ratios 1 : 3, 1 : 1 and 3 : 1. The refractive indexes of these solutions and of the two pure liquids are determined to 10.0001 on a refractometer held to a constant temperature zt0.1" and plotted versus the calculated mole fraction^.^ The operation of the liquid-vapor equilibrium apparatus is very simple and no difficulty should be encountered in obtaining excellent results. To start the measurements, the sample drains and capillary
PRESSURE TUBING
THUMBSCREW
COPRR SUSPENSIO
5 0 r r LIEBIG CONDENSER
-CAPILLARY 0-360' THERMOMETER WITH FUSED MARKINGS
LOCK CLAMP
CAPILLARY BORE
PRESSURE STOPCOCK
FLASK HEATER
Figure 1.
Liquid-vopor equilibrium oppardul.
vent are closed, the top condenser joint is opened, and 100 ml of the liquid component which has the higher atmospheric pressure boiling point is poured into the apparatus. The top condenser joint is then closed and clamped securely. The flask heater is turned on and a steady flow of water started through the reflux condenser. When the liquid in the flask reaches a temperature at which it begins to exert an appreciable vapor pressure, the pressure in the system will begin to rise and the capillary vent should be opened occasionally to prevent excessive pressure buildup. The heater is adjusted until liquid is refluxing in the condenser at a level on the thermometer about 5°C above the normal boiling point of the liquid and a steady stream of recondensed vapor is falling into the reflux sampling cup. The system pressure is then decreased by steps using the capillary vent until a small residual positive pressure remains in the system and the thermometer reading has fallen to a convenient reference temperature, usually an even degree. If the avvaratus is free of leaks, the system and temperature will remain constant indefinitely. Approximately 0.2 ml of liquid is withdrawn by drops through the flask sampledrain into a waste beaker to rinse the drain line, and another 0.2-ml sample is immediately drawn off by drops into a small vial which should be stoppered immediately. The mercury levels in the arms of the system manometer and the temperature of the boiling liquid are recorded, and a 0.2-ml sample of recondensed equilibrium vapor is removed from the reflux sampling cup observing the precautions listed above. The barometric pressure and heater setting are also recorded. When the above data have been obtained, the heater is turned off and the system vented slowly until the internal pressure falls back to atmospheric. The capillary vent is left open and the apparatus is allowed to cool for about five minutes during which time the refractive indexes of the solutions just withdrawn may conveniently be determined. To prepare the apparatus for obtaining the next set of data points, the top condenser joint is opened and a portion of the lowerboiling liquid is added. Following the procedure outlined above, the system is returned to the reference temperature and samples are withdrawn for analysis. No difficultyshould be encountered in reproducing the reference temperature to within 0.1'. It is very important that the system be vented cautiously, since the only practical method of re-obtaining the desired temperature (if the thermometer reading should fall below the desired reference point), is to turn off the heater, vent the system, and start over after the apparatus has cooled. By successively draining portions of liquid from the flask and adding the lower-boiling component, a series of sixor seven data points spread across the mole fraction scale can Volume
39, Number 5, May 1962
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259
Figure 3. Comparimn d experimental dota on +Br-&I mixtures with equations I61 and (71. P ~ + B J P ~ + C I = 0.548, PD+c~/Po4m = 1.82.6
Figure 2.
Comparison of experimental dota on @I-QCI mixtures with PO ot
(I), (2). and 13). T = 155.0 2~ O.lO. Experimental +Br-736 mm Hg, &I-1343 mm Hg. Accepted Po voluer 481-735.5 mm Hg, &I-1 343 mm Hg.'
equations
valuea
155.0':
easily be obtained. The maximum volume of liquid which can be contained in the flask without immersing the reflux sampler cup is about 150 ml. When it becomes necessary to remove an appreciable portion of the solution from the apparatus, the heater may be turned off and the flask drain opened while the system pressure is still above atmospheric. A positive internal pressure greatly accelerates the rate at which liquid can be drained from the system. To obtain the vapor pressure of the pure lowerboiling component at the reference temperature, the apparatus is disassembled, emptied, and rinsed with several portions of chloroform, acetone, or other volatile solvent; it is then dried and reassembled with a dry wick on the thermometer and 100 ml of the pure lowerboiling component in the flask. The pure lower-boiling component may be left in the apparatus after its vapor pressure has been determined and used in a subsequent experiment provided the second component in this 6 HODGUN, C. D., Editor, "Handbook of Chemistry and Physics," 41st ed., Chemical Rubber Publishing Co., Cleveland, 1959, p. 2415.
latter experiment has a still lower boiling point. Using this technique approximately 200 ml of each liquid will be used in each experiment. It should be noted that positive pressures approaching one atmosphere are generated in the apparatus during the course of a typical experiment. Since the possibility of mechanical failure of the apparatus does exist, a fire extinguisher should be kept handy and safety goggles should be worn during the experiment. No difficulty of this kind has ever been experienced with the apparatus described. Results
Figure 2 shows a graphical comparison of some typical experimental results on mixtures of bromobenzene and chlorobenzene with the theoretical predictions of equations (I), (2), and (3). A graphical presentation of these same results in a form suitable for comparison with the theoretical predictions of equations (6) and (7) is shown in Figure 3. As may be seen from the graphs, the agreement between the experimental results and the predictions of the ideal binary solution laws is very satisfactory, in accord with the results of Young on bromobenzene-chlorobenzene mixtures near 140°.6 The results presented are typical of those which can be obtained by two students working together during a normal four-hour laboratory period. YOUNO,J., J. Chem. Soc. (London), 81,768 (1902).
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Journal of Chemical Education
