56
S. N. BHATTACHARYYA AND A. MUKHERJEE
+
intercept ( k k * ) / k . From the slopes and intercepts of the plots in Figure 4, values of k/kco2 and L*/kco, can be obtained. These values are listed in Table I. The present results are insufficient to define specifically the nature of reactions 5 , 5*, and 6. However, the observation that t-BuOH does not undergo reaction 5, whereas MeOH, EtOH, and i-PrOH do, would suggest the necessity of an a-hydrogen atom for this reaction to occur. Reaction 5 therefore, most probably involves either hydrogen atom abstraction 0-
R + Ri Rz>CHOH + '>C-OH + OHRz
(7)
or proton abstraction 0-
+ RiR2>CHOH +R2R '>C-OH- + OH
(8)
from the a-carbon atom. Reaction 5*, which occurs with EtOH, i-PrOH, and t-BuOH, could then be hydrogen atom abstraction 0-
+ ROH
--3 RO
+ OH-
(9)
or proton abstraction
0-
+ ROH -+RO- + OH
(10)
from the hydroxyl group. Apart from the hydroxyl radical, which would be expected to react exclusively with the hydrocarbon under the present conditions, the fate of the products of reactions 7-10 cannot be predicted. Preliminary mass-spectrometric studies8 indicate reaction between 0- and alcohols to occur. With MeOH, using SO2 as the source of 0-, secondary ions of mass 17 (OH-) and 31 (H&O-) are observed. However, the probable excess kinetic energy of the 0- ions in these experiments makes extrapolation of these data to radiolysis conditions somewhat doubtful. Acknowledgment. The author wishes to thank Mr. G. K. Buzzard for carrying out the mass spectrometric analyses. (8) G. K. Buzzard and J. M. Warman, work in progress.
Excess Thermodynamic Functions of Some Binary Nonelectrolyte Mixtures.
I.
Measurements of Excess Gibbs Free
Energy, Enthalpies, and Volumes of Mixing
by S. N. Bhattacharyya and A. Mukherjee' Indian Association for the Cultivation of Science, Jhdavpur, Calcutta, India
(Received March 22, 1967)
Excess Gibbs free energies, enthalpies, and volumes of the systems toluene-fluorobenzene and methylcyclohexane-fluorobenzene have been measured a t different temperatures over the entire mole fraction range. The excess Gibbs free energies have been studied at 50, 60, and 70", the excess enthalpies a t 10, 25, and 40°, and the excess volumes a t 40" for all the systems.
Two major approaches to a molecular theory of solulattice rigid lattice theories and theories, are already fairly well developed. The rigid lattice models have been extensively used before, but The Journal of Physical Chemistry
(1) J. Barker, J. Chem. Phys., 20, 1526 (1962).
(2) J. R. Goates, R. L. Snow, and M. R. James, J. Phys. Chem. 67, 335 (1961). (3) J. B. Ott, J. R. Goates, and R. L. Snow, {bid., 66, 1301 (1962).
57
THERMODYNAMIC FUNCTIONS OF SOME BINARYNONELECTROLYTE MIXTURES feature of this theory is that it can take into account the effects due to the difference in the number of sites occupied by the component molecules of the mixture and also of those molecular interactions which are directional in character. This theory could also be applied, with much profit, to general cases as mentioned above. Very little systematic work has been done until now along these lines, particularly in interpreting both excess free energies and enthalpies of such nonelectrolyte mixtures. With this object in view, we have measured the excess Gibbs free energy gE, excess enthalpy hE, and excess volume vE of the systems toluene-fluorohenzene and methylcyclohexane-fluorobenzene. Bhattacharyya, Anantaraman, and Palit have already measured the excess functions for the systems benzene-fluorobenzene and cyclohexane-flu~robenzene.~A good volume of data already exists in the literature on allied systems such as benzene-cyclohexane or toluene-cyclohexane so our investigations, along with data that are available, would enable us to test very systematically the scope and applicability of the Barker quasi-lattice theory. The deformable lattice theory of solution due to Prigogine may, as well, be utilized for the analysis of the experimental excess functions. Bhattacharyya, Anantaraman, and Palit4 demonstrated that average potential theory could effectively be extended to a mixture composed of spherical nonpolar molecules and spherical weakly polar molecules. I n reality, a polyatomic molecule would be nonspherical in shape and would be the source of other types of weak orientational forces. It has lately been shown5 that with the help of a single potential all types of weak forces, central, dipolar, globular, or those due to polarizabilities, that are encountered in a real solution could be approximated. This could very well be tested in our proposed investigations. Moreover, an attempt would be made to eliminate the limitations inherent in the average potential model; i.e., the theory could be applied to systems where the force constants of the molecules are very close to each other by utilizing some of the features of the deformable lattice theories of polymer mixtures which are in a rapid state of development. The results of the measurements of hE and vE of the system toluene-fluorobenzene at 25" have been reported earlier.s Samples of fluorobenzene from a different source have been used for present work. To ensure that the results obtained with the two samples are not different, a few more measurementsof hE at 25" have been made. As the two sets of data have been found to be in agreement with each other within experimental error, the combined data of this system for hE a t 25' have been subjected to analysis. The experimental methods used and the results obtained for this work are described in this paper. The applications of the generalized rigid-lattice theory and deformable-
lattice theory to the data are reported in two subsequent papers.
11. Experimental Section Measurement of gE. A dynamic-type equilibrium still has been designed and built to measure gE. The still is similar to the one developed by Brown and Ewald,' with certain modifications, as it appears to fulfill the requirements suggested by Fowler.8 The sample tubes with magnetically operated ball valves used by Brown and Ewald have been replaced in the still by overflow traps, as the former were found to be troublesome. The stopcock over the disengagement chamber for introduction of liquid mixture to the still has also been eliminated, the mixture being introduced through the overflow tubes. The same tubes, of which the overflow tubes are an integral part, are designed with a view to minimize any error caused by a change in composition of the equilibrium samples due to evaporation during their removal. At the sampling end is a specially designed ground joint with a capillary opening which has been used for this purpose, the sample being taken out with a long needle immediately after the still is stopped. The capacity of the boiler has been made deliberately as large as 180 ml to obtain very accurate results. The traps each hold about 8 ml. The disengagement chamber has been altered to take a ten-junction copper-constantan thermocouple, and a drip counter has been built into the condensate return. The drip counter also prevents liquid from flowing back to the vapor condensate trap as a result of surging during the initial stages of boiling, The equilibrium still is connected to a manostat and manometer system, which is the same as that of Scatchard, Raymond, and Gilmanngand which has been used before in this laboratory. An Invar scale cathetometer with a precision of *0.02 mm was used to read the heights of the mercury. The 90-1. manostat and the manometer were kept in oil and air thermostats, respectively, where the temperatures were maintained at 35 f 0.01". The mercury heights were corrected for the mean temperature and the gravitational constant. The correction for the weight of the column of the confining gas over the mercury in the lower arm of the manometer to the line of condensation and the weight of the column of vapor from the line of condensation to the lower end of the thermometer well is (4) €3. N. Bhattacharyya, A. V. Anantaraman, and S. R. Palit, Trans. Faraday Xoc., 59, 1101, (1963); Indian J . Chem., 1 , 459 (1963). (5) 8. N. Bhattacharyya, Indian J . Phys., 41, 579 (1967). (6) S. N. Bhattacharyya and A. Mukherjee, Indian J. Phys., 38, 93 (1964). (7) I. Brown and A. H. Ewald, Australian J . Sci. Res., AS, 306 (1953); I. Brown, ibid., A3, 530 (1952). ( 8 ) R. T. Fowler, Ind. Chemist, 24, 717 (1948). (9) G. Scatchard, C. L. Raymond, and H. H. Gilmann, J . Am. Chem. Xoc., 60, 1275 (1938). Volume 78, Number 1
January 1968
S. N. BHATTACHARYYA AND A.
58 less than 0.008 mm, so this correction was not applied. No correction has been made for the pressure gradient required to accelerate the vapor from the disengagement chamber to the condenser as this is believed to be negligible. The pressure of the vacuum side of the manometer was checked by a McLeod gauge and was always kept below 0.005 mm. The ten-junction thermocouple was calibrated by measuring the vapor pressure of pure benzene at various temperatures and subsequently fixing the temperatures by the data of Scatchard, Wood, and Mochel. lo For this, benzene was purified with special care, and its density was repeatedly checked until it agreed quite well with the standard values in the literature. A LN I
