1010
The Journal of Physical Chemistry, Vo/. 82, No. 9, 1978
(e;M2+)+ t NO;
-+
products
T. Kato, S. Hyodo, and T. Fujiyama
(7)
If we can safely assume that the ascending part of the curve in Figures 3-5 is not due to reaction 7 there remains the possibilities that the decreasing part is due entirely or partly to the reaction (e;M2')'
t (NO;MZt)+
-+
products
(8)
with k8 l2By plotting l h * against If*for the various
concentrations, a line with a slope of -(rb/rf)is generated as far as the absolute intensities, I'f and rb, are independent of concentration. In Figure 2, a plot of I h * vs. If* is shown. It can be seen from the figure that a linear relationship exists between Ib* and If*. From eq 34, on the other hand, the relation (37) is obtained, where R is the ratio of chloroform-d molecules in the free and bonded states. As X A B defined by eq 16
0.5 mole fraction of ethanol
The Journal of Physical Chemistry, Vol. 82,No. 9, 1978
Local Structures Formed in Ethanol Solutions
25
1015
-
20-
0
0.5 mole fraction of ethanol
Flgure 5. Dependence of (IA), on K,,
1
at various concentrations.
1 ’ IO
20 30 50
100
500 1000 KAA
x,
Figure 7. Dependence of ( lA), on KAA at = 0.3. The upper and lower curves corresponds to ethanol-carbon tetrachloride and ethanol-chloroform systems, respectively.
0
0.5
1.0
EA Flgure 6. Theoretical values of ( l A ) , calculated for KAB= 0, 10, and 100.
KAA
= 30 and
KAA and ( lA)w in Ethanol-Carbon Tetrachloride Solution. In the case of the ethanol-carbon tetrachloride system, KAA and are obtained rather easily in comparison with those in the ethanol-chloroform system, because interaction between ethanol and carbon tetrachloride molecules is weak. From eq 27-31, together with the observed concentration fluctuation values at XA= 0.3: the values of 0, ( l A ) w = 6, a n d K A A = 30 (40) are obtained for KAAand ( I A ) w . It is of much interest to compare the results obtained for ethanol-chloroform and ethanol-carbon tetrachloride systems. It is seen from eq 39 and 40 that the mean association number, ( lA)w, of ethanol molecules in carbon tetrachloride solutions is much larger than in chloroform solutions, although the association equilibrium constant, KAA,between ethanol molecules is not very different in carbon tetrachloride and chloroform solutions. This indicates that the association tendency of ethanol molecules in these solutions does not govern the size of the associated local structure of ethanol molecules. In the next paragraph, we discuss this point in more detail on the basis of KAA and KAB. Equilibrium Constant and Mean Association Number. As was discussed in the Theoretical Section, the mean association number can be calculated, if we know the equilibrium constants, KAAand Km, and the macroscopic mean concentration. As an example, the calculated ( lA)w values for KAA = 30 and KAB = 0, 10, a n d 100 are illusKAB =
trated in Figure 6. Obviously the mean association number depends on KM. In other words, the stronger the interaction between A and B molecules the smaller the association number of A molecules. Ethanol-chloroform and ethanol-carbon tetrachloride systems correspond to the results for Km = 10 and KAB= 0 at X A = 0.3 in Figure 6, respectively. In order to see the effect of KAAon the mean association number of ethanol, was calculated at X A = 0.3 for various KAA values. The results are shown in Figure 7. The upper curve shows the results obtained for the system where the interaction between A and B molecules is negligibly small, i.e., KM = 0. In this case, therefore, the mean association number increases with an increase of K M or an increase of the associative tendency of A molecules. The lower curve corresponds to the results for ethanolchloroform systems. Obviously, the interaction between ethanol and chloroform arrests the formation of a large aggregate of ethanol molecules and keep the mean association number almost constant for all KAA values.
Acknowledgment. The infrared data used in the present work has been obtained by Miss Yumiko Katayanagi. The authors are pleased to express their sincere thanks to Miss Katayanagi for her permission to use her unpublished data in the present report.
References and Notes (1) K. Iwasaki, M. Tanaka, and T. Fujiyama, Bunko Kenkyu, 25, 134 (1976). (2) K. Iwasaki, M. Tanaka, and T. Fujiyama, Bull. Chem. Soc. Jpn., 49, 2719 (1976). (3) T. Kato and T. Fujlyama, J . Phys. Chem., 80, 2771 (1976). (4) K. Iwasaki, Y. Katayanagi, and T. Fujiyama, Bull. Chem. Soc. Jpn., 49, 2988 (1976). (5) T. Kato and T. Fujiyama, J . Phys. Chem., 81, 1560 (1977). (6) K. Iwasakl and T. Fujiyama, J . Phys. Chem., 81, 1908 (1977). (7) M.Tanaka and T. Fujiyama, to be publlshed. (8) I. Prlgoglne and R. Defay, “Chemlcal Thermodynamics”, Longmans Green and Co., London, 1954, Chapter 26. (9) L. SarolBa-Mathot, Trans. Faraday. Soc., 49, 8 (1953). (10) S. R. Polo and M. K. Wllson, J . Chem. Phys., 23, 2376 (1955). (11) M. Okazaki, I.Hara, and T. Fujiyama, J. Phys. Chem., 80, 64, 1586 (1976). (12) T. Fujiyarna and M. Kakimoto, Bull. Chem. SOC.Jpn., 4B,2346 (1976).
