J. S. Shapiro, E. C. Watton, and J. M. Kilford Macquarie University North Ryde, New South Wales 21 13 Australia
II I
Relationship between Rate 01 haporotiom and Vapor Pressure of Binary Systems
In a prevLous article1 we described a simple method for determining the activation energy of evaporation of volatile liquids. We demonstrated the close relationship hetween rate of evaporation and vapor pressure, hence the dynamic nature of the liquid/vapor equilihrium. What follows here is a natural extension of this approach to hinary liquid systems in order to test the universality of the relationship in a more complex situation. With the present series of experiments the rate of evaporation of binary liquid mixtures was followed by weighing, isothermally. This procedure eliminated initial difficulties encountered with variable drop size when the simple method already described' was applied to the liquid mixture. Changes in the drop size were due to variation of surface tension and viscosity with composition. Experimental About 10 ml of liquid was placed in a porcelain crucible and allowed to evaporate while resting on the pan of a 4-figure analytical balance with the balance case windows closed. It was found important to use the same volume of liquid for each determination in order to reproduce the same surface area in the evaporation vessel. Weight loss by evaporation was determined four times for each composition for a period of 2 min, each determination heing followed by a 5-min interval to allow the vapors to leave the balance enclosure, and to allow the crucible to return to room temperature. Precision of this measurement was about +5%. Though the sample temperature was not thermostatically controlled it did not fluctuate by more than 1.5"C during a day's experiment in which an entire range of composition could he examined (about 10-15 mixtures). All reagents used were first purified by distillation then thoroughly dried by suitable reagents. Results Several binary systems were examined with this technique; these included ideal and non-ideal mixtures. Systems of liquids of similar structure produced the expected results, hut in cases of non-ideal systems we observed more than a single maximum or minimum in the evapnration rate/composition curves. These deviations are not entirely surprising since the present experiments are carried out a t around room temperature rather than at the boiling points of the mixtures. Secondly, the present experiments involve dynamic rather than equilibrium measurements. We have elected to report only three systems which hehave in a similar manner to vapor pressure/composition data found in the literature. The three examples are chosen for their similarity to vapor pressure/composition characteristics and this relationship may not be typical. Benzene-Toluene System This binary mixture was chosen as a representative of an "ideal" mixture and is illustrated graphically in Figure l(a). The observed relationship is in reasonable agreement with an analogous plot of vapor pressure versus mole fraction reported in the literature.2 In the present experiment the total pressure corresponds to the combined evapora-
Figure 1. Benzene-toluene system: evaporation rate versus composition.
tion rate of benzene and toluene. Somewhat more correct representation can he obtained if the evaporation rate is expressed in moles/min. However, allowance must he made for the greater volatility of one of the components. Using the following expression2 i t is possible to calculate the composition of the vapor in equilibrium with an ideal solution of any composition
where XA, xg = mole fractions in liquid phase, xAVa4 x e v a ~= mole fractions in vapor phase, and PAO, P B O = vapor pressures of pure components A, B, respectively. Using the expression we can derive an average molecular weight which takes into account the higher volatility of one of the components relative to the other. Average molecular weight
+ ab
= (*)-
1
( M .- M")+ M R
where a = x ~ / x g and , b = Pn0/P~O.We have applied this correction to the present system despite i t being a dynamic system. Corrected data, where average molecular weight was used in computing the molar evaporation rate, are plotted in Figure l ( b ) . 'Brennan, J. F., Shapiro, J. S., Watton, E. C., J. CHEM. EDUC.,51,276 (1974). 2Barrow, G. M., "Physical Chemistry," Chap. 14, MeGrawHill, New York, International Student Edition, 1961. Vohrme 52. Number 7. July 1975 / 439
Figure 2.
sition.
Benzene-cyclahexane system: evaporation rate versus compo-
Benzene-Cyclohexane System For this binary mixture a maximum in the vapor pressure plot is expected; hence i t provides a good example of positive deviation from Raoult's Law. In the literature3 a boiling point minimum is reported a t 77.8"C, with corresponding composition of 0.598 mole fraction of benzene. Present results illustrated in Figure 2(a) also show a maximum in evaporation rate a t a similar mole fraction of henzene. As in the case of henzeneJtoluene, data were plotted with the evaporation rate described in g/min (Za), average moleJmin (2b). Chloroform-Acetone System The chloroform-acetone mixture is often quoted as a classical example of negative deviation from Raoult's Law, due to hydrogen bonding. This trend is also indicated here in Figure 3(a) where a definite minimum in the evaporation rate/composition plot is observed, a t mole fraction of acetone of about 0.40. In the literature a boiling point maximum a t 64.7"C is reported with the corresponding wmposition of 0.214 mole fraction of a ~ e t o n e .Again, ~ data are plotted in two ways as discussed ahove. Molecular Weight Determination The evaporation technique by weighing described ahove can he used to estimate molecular weights since Raoult's Law is obeyed hy the systems examined. The system chosen to illustrate the point is the benzeneJnitrobenzene. Samples of pure solvent and dilute solutions were evaporated under identical conditions. For pure benzene, evaporation rate = 0.0175 g/min. For a mixture of 95 ml benzene and 5 ml nitrohenzene (density--0.874), evaporation rate = 0.0167 g/min. From Raoults' Law
a"Handbwk of Chemistry and Physics," The Chemical Rubber Co., Table Dl, 48th Ed., 1967-1968. 'Bechtold. M. F.. and Newton. R. F.. J. Arne?. Chem. Soc... 62.. 1390 (1940). Waniels, F.,Williams, J. W., Bender, P., Alberty, R. A,, Comwell, C. D., Hamman, J. E., "Experimental Physical Chemistry," 7th Ed., p. 490,1970.
Figure 3. tion.
Acetone-chloroformsystem: evaporation rate versus composi-
where A P = lowering of vapor pressure, Pso = vapor pressure of pure solvent, x = mole fraction of solute, and mol wt = molecular weight of solute. Due to the analogy of vapor pressure with evaporation rate, the expression becomes (Evaporation Rate) benzene -(Evaporation Rate)Solution
=
(Evaporation Rate) benzene wt
GTz For the above mixture the calculated molecular weight is 132. This compares favorably with the true molecular weight of 123.1. Similarly for a mixture of 90 ml benzene and 10 ml nitrobenzene the molecular weight calculated by the evaporation technique is 124. This procedure was applied successfully to other binary liquid systems, e.g., for the henzeneJtoluene a molecular weight 99 is calculated compared with the true value of 92. An entire determination including calculation can be completed in less than 1 hr. However, this method is not applicable to solutions with a solid solute, e.g. benzoic acid in benzene or ferrocene in benzene. In these cases there is evidence of an increase rather than a decrease in evaporation rate. The last effect appears to be caused by the increased surface area provided by a crust of solid formed around the edge of the evaporating dish. Discussion The experimental results confirm that the direct relationship between evaporation rate and vapor pressure is valid for binary mixtures as well as for pure liquids.1 The measurement of vapor pressure of binary mixtures by a dynamic method is relatively old and is known as the transpiration meth0d4.~and it is perhaps noteworthy that
this was apparently restricted to liquid solutes. However, the evaporation method described here is a much simpler, faster one and requires little instrumentation. Though absolute correspondence does not exist between vapor pressure data for binary liquid systems and the evaporation
results reported in this experiment, the salient features demonstrating Raoult's Law are clearly evident. Molecular weight determinations despite the limitation to liquids are highly successful considering the little effort involved.
Volume 52. Number 7, July 1975 / 441
