NOTES
2458 The Dissociation of Trityl Perchlorate in 1,2-Dichloroethane
sey's simplified equation7 -In Kd = e2/aDkT. The value of AH" was obtained from a plot of In Kd against 1/T, and A G O and A#' by standard thermodynamic relations.
by W. Y. Lee and F. E. Treloar Department of Physical Chemistry, University of Melbourne, Parkville, Victoria 3068,Australia (Received January 88, 1969)
We have studied the ionization of trityl perchlorate in l12-dichloroethane in connection with its use as a ca,talyst for cationic polymerization. A recent crystallographic study' shows that it is an ionic solid; hence, in solution we only consider the dissociation equilibrium between ion pairs and free ions.
The salt was prepared as describedS2 The solvent was carefully dried with Pz06and then fractionated and dried again over BaO or CaH2. A special vacuum cell with bright platinum electrodes was used; the cell constant was 0.2328 cm-' (calibrated by aqueous KC1 solution). The mixing of solutions was performed at a vacuum line. A Wayne Kerr universal bridge B 221 operating at 1592 He was employed for the conductivity measurement which was made in an oil bath controlled to within *0.05". The concentration of the salt was determined spectrophotometrically at A,, 4120 8; the molar extinction coefficient was determined3 to be 3.30 X lo4. I n Table I are given the values of the dielectric constant and viscosity of 1,2-dichloroethane, taken from the literature.4 The conductance measurements were made at concentrations in the range of 1.6 X to
Table I : Dielectric Constant and Viscosity of 1,2-Dichloroethane Temp, OC
Dielectric constant
Visoosity, mP
20 25 30 40
10.65 10.36 10.08 9.535
0.8385 0.7820 0.7360 0.6520
M a t 20, 25, 30, and 40". Work on the 1.8 X same system at 0, 10, and 21.5' has been reported.6 The results as listed in Table I1 were treated by the Shedlovsky method6 and calculated by IBiLl 7074 computer. The method of least squares was used for all linear plots. The derived values of A, and Kd, together with other parameters of interest are in Table 111. The value of a was calculated by using Denison and RamThe Journal of Physical Chemistry
Table I1 : Conductivity of Trityl Perchlorate in 1,2-Dichloroethane Tamp,
C X loa,
OC
M
A
20
1.67 2.51 3.79 4.58 6.51 7.40 11.7 17.1 17.3
64.0 63.2 61.8 60.2 60.6 58.7 54.5 50.6 50.3
2.90 3.62 3.82 6.47 7.76 8.37 12.9 14.6
63.8 61.4 60.0 56.3 56.9 55.5 52.1 50.8
25
Temp,
cx
loa,
O C
M
A
30
3.13 5.31 6.79 8.96 10.8
69.1 64.2 64.1 60.6 58.0
40
2.11 3.16 3.74 6.06 6.91 8.10 9.12 11.5 16.7
81.8 79.2 79.9 70.9 74.4
70.8 71 .O 66.0 61.9
It is noted that these results differ markedly from the recently published values of Longworth and Mason5 to a much greater extent than could be accounted for by the temperature difference. The crystallographic study' indicates that C+-C1 distance in the solid state is 4.1 8, and its value is expected to be greater in solution. Therefore, our result, a = 6.5 8, seems to be more reasonable than Longworth's (a = 8.7 8). The value of AH' obtained in this work confirms that the previous value5 of AH" = +2 kcal/mol is indeed too high. Furthermore, a positive value of AHo for the dissociation of trityl perchlorate in l12-dichloroethane is very difficult to understand in the light of Denison and Ramsey's theoretical approach ; 8 p 9 using their equations (1) A. H. Gomes de Mesquita, C. H. Mac Gillavry, and K. Eriks, Acta Cryst., 18, 437 (1965). (2) H.J. Dauben, Jr., L. R. Honnen, and K. M. Harmon, J . Ora. Chem., 25, 1442 (1960). (3) W.Y.Lee, B.So.(Hons.) Research Report, Melbourne (1965). (4) (a) Maryott and Smith, Natl. Bur. Std. (U. S.),Circ., No. 514 (1951); (b) "Handbook of Chemistry and Physics," Chemical Rubber Co., Cleveland, Ohio, 48th ed., 1967-1968. (5) W. R. Longworth and C . P. Mason, J , Chem. Soc., A , 1164 (1966). (6) R. M.Fuoss and T. Shedlovsky, J . Amer. Chem. Soc., 71, 1496 (1949). (7) J. T.Denison and J. B. Ramsey, ibid., 77, 2616 (1955). (8) N. Kalfoglou and M. Swarc, J . Phys. Chem., 72, 2233 (1968). (9) For example, see eq 7 of ref 7.
NOTES
2459
Table 111: Dissociation Constant and Associated Parameters of Trityl Perchlorate in lJ2-Dichloroethsne Temp, "C Ao,cm$/(ohm equiv)b Kd x lo4, mol/l." AGO, kcal/mol
AS", cal/(deg mol) AH" , kcal/mol
20 70.2 2.85 6.5 4.75 -25 -2.6
(21 , 5)a (66.5) (12.58)
(8.7) (3.91) (-20) (f2)
25 70.7 2.52 6.5 4.88 -25 -2.6
30 78.4 2.41 6.5 5.02 -25 -2.6
a Values in brackets are those of Longworth and Mason,6 being included here for comparison. within 12%.
we calculate AH" and AS" to be -2.4 kcal/mol and -24 cal/(deg mol), respectively, in very good agreement with our results. For the systems trityl hexachloroantimonate and trityl hydroxypentachloroantimonate in methylene chloride, Kalfoglou and Szwarcs also find that AH" is negative. It has been suggested* that the large Kd values obtained by Longworth and Mason were due to the presence of moisture which thus increased the measured conductance. However, we have deliberately added water to our system and found a large decrease of conductance, which contradicts this suggestion. The effect of water is probably the hydrolysis of trityl perchlorate to triphenyl carbinol and perchloric acid which almost certainly has a lower conductance than trityl perchlorate; Gandini and Plesch'o have determined the specific conductance of perchloric acid (4 X M ) in methylene dichloride at 20" to be 9 X loMsohm-l cm-' compared with our value of 7.4 X lod4 ohm-' cm-' for trityl perchlorate a t a comparable concentration (3.5 X M ) in a solvent of similar dielectric constant (1,2-dichloroethane) at 25". I n fact, reexamination of Longworth and NIason's data reveals that they probably placed too much reliance on values of the conductance a t high concentrations in making the extrapolation to obtain a trial value of no. Such reliance is hazardous, since at higher concentrations than M, higher order aggregated ions may be formed. Deviation from linear behavior in the conductance plot is generally regarded as an indication of the formation of triple ions in solvents of low dielectric constant.l' If a value of 39.2 is taken to be the ionic conductance of C104- in 1,2-dichloroethane at 25",12 the ionic conductance of trityl carbonium ion would be 31.0. This rather low value of Ao+ is attributed to its bulkiness only. Apparently the trityl carbonium ion is not solvated as evidenced by the low -AS" of dissociation. (10) A. Gandini and P. H. Plesch, J . Chem. SOC.,B , 7 (1966); Eur. Polyn. J . , 4, 55 (1968). (11) The original paper is that of R. M. Fuoss and C. A. Kraus, J . Amer. Chem. Soc., 55,2387 (1933). A recent example is given by D. N. Bhattacharyya, C. L. Lee, J. Smid, and M. Szwarc, J . Phys. Chem., 69, 608 (1965). (12) L. F. Gleysteen and C. A. Kraus, J . Amer. Chem. Soc., 69,451 (1947).
40 90.1 2.14 6.6 5.25 -25 -2.6
Reliable within 3%.
' Reliable
Acknowledgment. We wish to acknowledge the Melbourne University Research Grant (to W. Y. L.) for support of this investigation.
On the Tait Equation of Compressibility for Solids
by Y. E(. Huang Research Laboratory, Watervliet Arsenal, Watervliet, New York (Receieed January 20, 1969)
It is of interest to consider the well-known Tait compressibility equation from an analytical point of view. The Tait equation'v2 may be written as K/v
=
-(bp/dv).
=
(voC*)-'[p
+ B*(T)I
(1)
where K-' is the isothermal compressibility, v is the volume, p is the pressure, T is the temperature, and v0, C*, and B* (2') are three parameters to be specified. As pointed out by earlier investigator^,^-^ this equation is applicable not only to liquids but also to solids. I n this note we are concerned with solids a t high pressures. We find a useful connection between eq 1 and the Slater formula6 for the Gruneisen parameter y. On the basis of this link, we can explicitly determine C* and B*(T) in terms of known solid properties. Thus a new model of Tait-Gruneisen solids is formulated. I n what follows, it will be seen that this model is analytically simpler than the Gruneisen-Debye model.' Let vo be the volume of solid under standard conditions of po = 1 atm and TO= 293°K. It will become (1) A. T. J. Hayward, Brit. J . A p p l . Phys., 18, 965 (1967). (2) G. A. Neem and D. R. Squire, J . Phys. Chem., 7 2 , 128 (1968). (3) H. A. Bethe, "The Theory of Shock Waves for an Arbitrary Equation of State," OSRD Report No. 545 (1942). (4) M. A. Cook and L. A. Rogers, J . A p p l . Phys., 34, 2330 (1963). ( 5 ) R. Ginell and T. J. Quigley, J . Phy.9. Chem. Solids, 26, 1157 (1965). (6) J. C. Slater, "Introduction to Chemical Physics,'' McGraw-Hill Book, Co., Inc., New York, N. Y., 1939, p 239. (7) Y. K. Huang, J . Chem. Phys., 45, 1979 (1966). Volume 78, Number 7 July 1969
