Activity Coefficients of Acetone-Chloroform Solutions An Undergraduate Experiment

J. Z. Ozog and J. A. Morrison McMaster University, Hamilton, Ontario, Canada

In the undergraduate laboratory for physical chemistry, the study of liquid-vapor equilihrium is normally restricted to the determination of a boiling point-composition phase diagram a t constant (atmospheric) pressure. The diaeram is used to

study of real solutions to include the determination of activity coefficients for a two component liquid-vanor svstem. Our motivation was the hope that activiG coeffkients would ac- quire more significance when the students obtained numerical values for them in the laboratory. Moreover, we wished to use a system for which the activity coefficients of both compo- nents were obtainable independently without the insertion of a model-as is necessary for the separation of the activity coefficients for a solution of an electrolyte.

The simple experimental system that we shall describe gives surprisingly good results for the acetone-chloroform system. The students in the introductory second year course in ther- modynamics, working in pairs, can easily perform the exper- iment with ten different solutions within the allotted 3-hr laboratory period. We have not investigated the use of solu- tions of other organic liquids, hut we have no reason to believe that the experiment would work less satisfactorily for them.

Background The experiment is performed at constant temperature.

Thus, we can write for the chemical potential of component i in the solution

where d ( 1 ) is the chemical potential of pure component i and the activity is given by

ai = PJP? (2)

The activity coefficient is defined by

yi = aJX; = PilPiuXi, (3)

where Xi is the mole fraction of component i in the liquid phase. By Dalton's Law,

where PT is the total pressure and Yi the mole fraction of i in the vapor phase. Thus,

yi = PTY~IP~OX~ (5)

which is the basis of the experiment. The quantities on the right-hand side of eqn. (5) are all determinable.

Strictly speaking, an account should be taken of deviations of the vapor phase from ideal behavior. But, since the cor- rections are very small fur P < 1 atm, the pedagogical value of including them is limited.

Experimental The experimental arrangement is illustrated in Figure 1.

The equilihrium still is of the recirculatory type based on the Cottrell pump principle. The solution is heated internally by

72 Journal of Chemical Education

Figure 1. Schematic drawing of the exper~mental apparatus.

Procedure for Preparing Solutions of Acetone and Chloroform

Sequence-a-Start with 100 ml CHCI, approximate

remove add C,H,O mole fraction run no. (ml) (ml) CHCI.

1 pure CHCI3 1.0 2 9 9 0 9 3 10 10 0.8 4 14 14 0.7 5 11 11 0.62

Sequence b-Start with 100 ml C3He0 approximate

remove add CHCI, mole fraction run no. (ml) (mi) CHCb

6 pure C,H,O 0 7 - 16 16 0.15 8 20 20 0.3 9 20 20 0.45

10 20 20 0.55

means of a coil of approximately 7 ohms resistance. This not only prevents superheating hut also allows the rate of heating to be controlled easily. As the liquid hoils, bubbles of vapor carry the liquid up and "pump" it over the bulb of the ther- mometer. The vapor is condensed and returns to the boiler through a U-tube. The thermometer is graduated in intervals of O.l°C.

To begin the series of experiments, the still is filled with approximately 100 ml of one of the pure components and the apparatus is assembled as is shown in Figure 1. Current is passed through the heating coil and the system is opened to the rotary pump until the liquid boils. The pressure is adjusted until boiling occurs at the desired temperature. (T = 35OC is a convenient temperature for the acetone-chloroform system.)

After equilibrium has been established and the pressure recorded, hoiling is stopped, the pressure is returned to at- mospheric and a simple procedure followed to investigate a

Figure 2. The total pressure as a function of mole fraction for the acetone- chloroform system at T = 35'C.

O-present results. V-Mueller and Kearns.

XCHCI,

Figure 3. The total and panial pressures of the acetone-chloroform system as a function of Xcm, at T = 35%

O-present results. v-Mueller and Kearns

series of compositions of solutions. The steps in the procedure should be ohvious from the Table. A prescribed volume of component 1 (for the first step) or of solution is replaced by the same volume of component 2, etc. Between sequences a and b, the still is emptied and dried. For the runs with solu- tions, samples of the liquid in the still and of the condensate in the U-tube (Fig. 11, which represent the equilibrium liq- uid-vapor system, are analyzed by refractometry to yield X i and Yj , respectively.

Results and Discussion

The remarkably good results obtained with the simple system are illustrated in Figures 2 to 4 where they are com- pared with data drawn from the literature.' Figure 2 shows the well-known azeotropic behavior of acetone-chloroform

012 0!4 0!6 d.8 i!O

X ~ ~ ~ ~ ,

Fioure 4. The activiw coefficients of acetone and chloroform as functions of mole - fraction at T = 35%

O-present results. v-Mueller and Kearns.

Figure 5. The excess Gibbs energy of the acetone-chloroform system as a function of mole fraction at T = 35%

O-present results. V-Mueller and Kearns

solutions. The deviations from Raoult's Law are displayed in a different way in Figure 3. The main object of the experi- ment-the determination of the activity coefficients-is satisfied by the plot of the results in Figure 4. One point for Y C ~ H ~ O a t XCHCL~ = 0.93 lies well off the smooth curve drawn through the other points. Such a result is not unusual in a student experiment and thus lends some authenticity to the data given here.

Some other quantities can be derived easily. For instance, the limiting slopes of the partial pressure curves in Figure 3 yield for the Henry's Law constants for acetone and chloro- form the values 150 and 140 torr, respectively. These may be compared with the values 151 and 141 torr calculated from data in Mueller and Kearns' and 155 and 142 torr from data in the "International Critical table^".^

' Mueller, C. R. and Kearns, E. R., J. Phys. Chem., 62, 1441 (1958).

International Critical Tables. McGraw-Hill, New York, 1928, Vol. 3, p. 286.

Volume 60 Number 1 January 1983 73

The excess Gibbs energies of mixing may be calculated from

again neglecting imperfection in the vapor phase. The result is illustrated in Figure 5.

Possible Refinements The exoerimental arrangement that we have develoned -

emphasizes simplicity. The mercury manometer is con- structed of 8-mm diameter tubine. and heiehts are determined -. with reference to a standard meter stick. No corrections are

made for temperature changes or for meniscus heights. The accuracy of pressure measurements could be improved with a more elaborate manometer, appropriate corrections and a cathetometer. Alternatively, any of several modern types of diaphragm gages could be used. However, in our case, the in- vestment required for the moderately large classes that we teach is more than the parlous state of the university's finances will accommodate.

The adjustment of the pressure through a two-way stopcock exposed to either the atmosphere or the rotary oil pump is definitely crude hut workable, as the results demonstrate. A pressure regulator or manostat arrangement would have ob- vious advantages for the manipulation of the apparatus.

74 Journal of Chemical Education