1888
J. Phys. Chem. 1984,88, 1888-1892
negative than the Ho scale. Above this molarity, however, the H+ scale becomes more positive than the Ho scale. The reason for this change is unknown. That plots of H+ vs. log I for all the indicators in this work (except for 4-aminopyridine) have unit slopes suggests that the prototropic behavior of these indicators is consistent and that the H+ scale correctly describes their behavior. However, plots of Ho vs. log I for the same indicators in concentrated perchloric acid have slopes greater than unity (except for two indicators). The Ho scale, therefore, does not adequately describe the prototropic behavior of these compounds in concentrated perchloric acid. This finding is different from what was observed previously’ in sulfuric acid, where in concentrated solutions of the acid the Ho and H+ scales are colinear. A comparison of the dissociation constants of those indicators that were studied in both perchloric and sulfuric acids shows that the dissociation constants in HC104 tend to be slightly more negative than they are in HISO,, with the exception of 4-aminopyridine. This was also observed with the indicators used to establish the Ho scales in concentrated perchloric and sulfuric acids. The slope of the plot of H+ vs. log I for 4-aminopyridine is 0.89 f 0.01. This suggests that, as was the case of the H+ scale in H2S04,the H+ scale in HClO, does not adequately describe the prototropic behavior of 4-aminopyridine. This compound appears to be more basic in HClO, than it is in HISO,. This statement
is supported by the following observations. In sulfuric acid, 4aminopyridine is only 50% protonated when 4-bromo-6-nitro1,2-~henylenediamineis 90% protonated. In perchloric acid, however, the former is 80% protonated when the latter is 90% protonated. Furthermore, the acid-dissociation constant of 4bromo-6-nitro- 1,2-phenylenediamine is the same in perchloric and sulfuric acids. These observations suggest that 4-aminopyridine is structurally different in perchloric acid than in sulfuric acid, perhaps by virtue of differences in solvation. This raises a legitimate question as to the suitability of 4-aminopyridine as an indicator to define part of the H+ scale. However, the continuity of the curve in Figure 1 suggests that until a better indicator (i.e., a well-behaved arylamine) can be found, 4-aminopyridine will serve to establish the H+ scale (at least approximately) for perchloric acid solutions up to 11 M in concentration.
-
Registry No. HC104, 7601-90-3; 5-hydroxy-8-aminoquinoline, 89302-52-3; 6-aminoquinoline, 580-15-4; 5-aminoquinoline, 61 1-34-7; 1,2-phenyIenediamine,95-54-5; 8-aminoquinoline,578-66-5;4-chloro-ophenylenediamine, 95-83-0;3-aminopyridine, 462-08-8; 1,2-phenylenediamine-4-carboxylicacid, 6 19-05-6;2-nitro-p-phenylenediamine, 530714-2; 4-nitro- 1,2-phenylenediamine,99-56-9;2,6-diaminopyridine, 14 186-6; 3-nitro-l,2-phenylenediamine,3694-52-8;2,3,6-triaminopyridine, 43 18-79-0; 4-bromo-6-nitro-l,2-phenylenediamine,84752-20-5; 4aminopyridine, 504-24-5.
Proton Conductivity in Supercooled Aqueous HCI Solutions B, D. Cornish and R. J . Speedy* Chemistry Department, Victoria University of Wellington, Wellington, New Zealand (Received: June 1, 1983;
In Final Form: August 3, 1983)
Measurements of the electrical resistivity of 1,0.1, and 0.01 M solutions of HC1 and KC1 in water to -32 ‘C are reported. Values of the proton conductivity AH+ in the HC1 solutions are estimated. AH+ is a linear function of temperature in the range -32 to +45 OC, AH+ = A ( T / T , - l ) , and extrapolates to zero at T, = 227 K. Implications concerning the structure of water at T, are discussed.
Introduction The unusual properties of supercooled water and aqueous solutions, recently reviewed by Angelll and by Lang and Ludemann? have generated much speculation3-’ about the nature of the impending singularity3at T, -45 OC and about the structural basis of the cooperative process in water that evidently generates long-range correlations as T + T,. Direct observations near T, are not possible because even the smallest samples of water freeze’ above -41 O C . Submicroliter samples are needed for studies below -20 OC. Thus, evidence about T, is based on the extrapolation of results measured under difficult conditions. A major motivation for conductivity studies on water is the fact that conductivity can be measured more precisely’ than most other properties of small samples and can therefore provide a more stringent test of the power law type equations3 that seem to describe the temperature dependence of the transport properties of water. In this work we examine the proton conductance AH+ in supercooled HCl solutions. The previous measurements on KC1 (1) C. A. Angell in “Water-A Comprehensive Treatise”, Vol. 7, F. Franks, Ed., Plenum Press, New York, 1981. (2) E. W. Lang and H.-D. Liidemann, Angew. Chem., Int. Ed. Engl., 21, 315 (1982). ( 3 ) R. J. Speedy and C. A. Angell, J . Chem. Phys., 65, 851 (1976). (4) H. E. Stanley and J. Teixeira, J . Chem. Phys., 73, 3404 (1980). (5) F. H. Stillinger, Science (Washingron, D.C.), 209, 451 (1980). (6) R. J. Speedy, J . Phys. Chem., 86, 982 (1982). (7) R. .I. Speedy, J. A. Ballance, and B. D. Cornish, J . Phys. Chem., 87,
325 (1983); R. J. Speedy, ibid., 87, 320 (1983).
0022-3654/84/2088-1888$01.50/0
solutions7 are extended to -32 OC and to 0.01 M and are used to estimate values of Aa-. Measurement of the resistivity of HCl solutions then yields AH+. The resistivities of the KC1 and HC1 solutions conform to power law equations of the form3s7 r = r , ( T / T , - 1)’
(1)
where r2, T,, and y are constants. The values of y are quite different for HC1 and KC1. The derived values of AH+ are, however, linear in T and the parameters A and T, vary in a simple way with concentration. There is extensive literature8-]’ on the anomalous magnitude of the proton mobility in water, none of which predicts this simple temperature dependence. (8) J. O M . Bockris, B. E. Conway, and H. Linton, J . Chem. Phys., 24, 834 (1956). (9) J. O’M. Bockris and A. K. N. Reddy in “Modern Electrochemistry”, Vol. l., Plenum Press, S e w York, 1970; T. Erdey-Gruz and S . Lengyel in “Modern Aspects of Electrochemistry”, Vol. 12, J. O M . Bockris and B. E. Conway, Eds., Plenum Press, New York, 1977. (10) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions”, 2nd ed., Butterworths, London, 1959. (1 1) H. S. Harned and B. B. Owen, “The Physical Chemistry of Electrolyte Solutions”, 2nd ed., Reinhold, S e w York, 1950; S . I . Smedley, “The Interpretation of Ionic Conductivity in Liquids”, Plenum Press, Sew York, 1980.
0 1984 American Chemical Society
The Journal of Physical Chemistry, Vol. 88, No, 9, 1984 1889
Conductivity in Supercooled Aqueous HCl Solutions
TABLE I: Values of the Cell Constants Obtained by Calibrating the Same Cell, with a 40-pm Capillary, with KCI Solutions of
Different Concentrationa
1 0. I 0.01 0.001
3
10.9 t 11.0 t 8.3 2 4.3 2
1.435 t 0.009 1.429 i 0.009 1.444 f 0.014 1.380 t 0.016
1.1 1.1
1.9 2.3
a The errors indicated are the standard deviations in the paramcters obtained by linear regression. The change of the cell constants for the 0.001 M solution is ascribed to surface conductivity effects which are not detectable at the higher concentrations.
Figure 1. Diagram of the conductivity cell (not to scale). (1) Thermostated flask (30 "C). (2) Platinum electrodes. (3) Perspex disks separating the two thermostated cells. (4)Pyrex capillary containing test solution. (5) Thermostated flask (-35 to +45 "C).
Because the present results are precise and fit a simple linear equation, they yield a precise estimate of T," = 227 f 2 K. Previous e~timatesl-~ of T," (Le., T, for pure water) agree with this value but are less precise.
Experimental Section Solutions. Aqueous HCl and KC1 solutions were made up volumetrically at 20 "C to 1.00, 0.100, and 0.0100 mol dm-3 by using analytical grade reagents and multiply distilled water. Conductivity Cell. The cell is illustrated in Figure 1. The solution is contained in a U-shaped Pyrex capillary, about 16 cm in length with a 10- or 4O-~m-diameterbore. The bottom part of the capillary is thermostated by circulating ethanol from a cryostat. The top ends of the capillary were sealed into two larger bore tubes (with epoxy resin), which contained the platinum electrodes. The electrode tubes were thermostated by circulating paraffin oil at 30 "C. Resistance Measurement. A potential of 120 or 950 V dc was applied across the cell and a dc voltmeter in series. The current flowing through the cell and through the input impedance of the voltmeter (10' R f 0.1%) was measured as a potential on the voltmeter. The resistance of the cell was independent of the applied potential. The resistances measured were in the range 10s-lO1l R. The higher voltage was necessary to obtain sensitivity at the higher resistances. Calibration. The measured resistance R is the sum of two parts. The major part is that of the solution in the lower part of the U-shaped capillary. However, about 2 cm of the capillary protrudes into the upper part of the cell, thermostated at 30 OC, so R = Re + l r / a
(3)
where Re is the resistance of the solution at the ends of the capillary and is constant. I is the length, a the cross-sectional area, and r is the resistivity of the solution in the main part of the capillary. Values of R were measured from 45 "C to the freezing temperature of each solution. The resistivity of each solution was also measured independently from 0 to 45 "C, with use of a conventional conductivity cell calibrated with Jones and Bradshaw's standards.12 Plots of R vs. r were linear, and values of the intercept Re and slope I/a were obtained by linear regression. The resistivities of 1 and 0.1 M KC1 solutions measured to -32 "C in IO-pm capillaries agreed to within 1% with those obtained previously to -27 "C in 20-pm capillaries.' However, there was (12) G. Jones and B. C. Bradshaw, J . Am. Chem. SOC., 55, 1780 (1933).
evidence of surface conductivity e f f e ~ t s lfor ~ , the ~ ~ 0.01 M KC1 solution in a 10-Fm capillary, so the measurements were repeated in 40-pm capillaries. Capillary Surface Effects. The resistivities of all the solutions were also measured in 40-pm capillaries to -22 "C, where the solutions froze. Values of r agreed to within 0.5% with the measurements in 10-pm capillaries, except for the 0.01 M KC1 solution, which had an apparently lower resistance in the smaller capillary (by 10% at -20 "C). To verify that surface effects were significant, a single 40-1m capillary cell was calibrated with KC1 solutions in the concentration range 14.001 M. The cell constants should be the same if surface effects are absent. For the purpose of the comparison we define a cell constant for the ends of the capillary by Ie/a
Re/rc
where re is the resistivity of the solution in the ends of the capillary at 30 "C. The measured values of Ie/a and l / a are given in Table I. Results for the 1-0.01 M solutions are the same to within the standard errors (the standard deviation in the linear-regression parameters), but there is a substantial change on going to 0.001 M. These tests indicate that the resistivities obtained for the 0.01 M KCI solution in a 40-pm capillary are probably reliable but that surface effects are likely to be significant at lower concentrations or in smaller capillaries. Churaev et al.13 have also shown that surface effects become significant at about 0.01 M in 10-pm capillaries.
Results Resistivities. The resistivities are given in Table 11. The results for 0.01 M KCl are those measured in a 40-pm capillary. Figure 2 shows the temperature dependence and the difference between the HC1 and KC1 solutions. The lower temperature limit is determined by the freezing of the solutions. Results obtained before and after freezing and remelting agreed to within 1%. The resistivities were fitted to eq 1 with the best-fit parameters listed in Table 111. The precision is about 1% in each case. The Proton Conductance X H t . The calculation of the proton conductance X H t involves some assumptions, as follows. The molar conductance of a solution is defined by A = l/rC
(4)
where C i s the molar concentration of the electrolyte. It is reasonable to assume that the relative density of each solution (the density at T relative to that at 20 "C) is the same as the relative density of pure water p/p20 so that
c = C2OP/P20
(5)
The variation in the density, p, of pure water is only 2% over the (13) N. V. Churaev, I. P. Sergeeva, V. D. Sobolev, and B. V. Derjaguin, J. Colloid Interface Sci., 84, 451 (1981). (14) C. A. Angell, J. Shuppert, and J. C. Tucker, J. Phys. Chem., 77,3092 (1973).
1890 The Journal of Physical Chemistry, Vol. 88, No. 9, 1984
Cornish and Speedy
TABLE 11: Resistivity, r/(ncm), for the 0.01,0.1, and 1 M HC1 and KC1 Solutions KC1
c,
a
HC1
c,, = 0.10
= 0.010
TI'C
r/(R em)
45.0 35.0 25.0 18.0 10.0 5.0 0 -5.0 -7.7 -11.6 -16.2 -20.4 -22.1
498.0 586.9 711.1 820.1 987.4 1124 1295 1517 1659 1917 2311 2823 3067
T/"C
c,, = 1.00
c,,
r/(R em)
T/"C
r / ( nem)
55.8 65.0 77.7 89.5 140.1 161.2 192.0 242.3 290.5 316.1 354.2 403.6 445.9 490.1
45.0 35.0 25.0 18.0 10.0 0 -5.1 -10.0 -15.6 -20.5 -22.4 -24.5 -26.6 -28.7 -30.3 -32.8
6.72 7.72 8.98 10.22 12.07 15.35 17.61 20.29 24.51 29.50 31.77 34.55 38.21 41.21 45.44 51.00
45.0 35.0 25.0 18.0
0 -5.1 -10.1 -16.2 -20.3 -22.1 -24.2 -26.6 -28.2 -29.8
T/"C 45.0 35.0 25.0 15.0 5 .O
0 -5.1 -10.0 -15.2 -20.1 -23.0 -25.1 -27.2 -29.3 -31.1
c,,
= 0.0ta
c,
= 0.10
= 1.00
r/(R em)
T/"C
r/(R em)
T/"C
r / ( n cm)
187.6 210.0 240.3 281.5 342.0 383.1 432.6 497.3 585.1 701.8 787.0 869.0 965.3 1081 1226
45.0 35.0 25.0 15.0 5.0 0 -5.1 -10.0 -16.2 -20.3 -22.4 -24.1 -26.1 -28.3 -30.2 -32.2
19.89 22.23 25.33 29.60 35.86 40.11 45.56 52.49 64.31 75.19 82.22 88.40 97.68 108.9 121.6 138.1
45.0 35.0 25.0 15.0 5.0 -0.1 -5.2 -9.5 -15.0 -19.4 -21.8 -24.0 -25.9 -27.5 -29.9
2.354 2.636 3.009 3.521 4.252 4.623 5.181 5.754 6.557 7.752 8.562 9.320 10.13 10.80 12.21
C,, is the molar concentration of the solutions at 20 "C.
TABLE 111: Best-Fit Parameters in the Equation
r = r,(T/T,
500
- 1)-Y at 1-atm Pressure
T range/"C
elec- c201 tro- (mol lyte dm-3)
-33 -30 -22 -30 -32 -31
KC1 KCI KC1 HCl HC1 HC1
r,c,0/
c
% std
(Rmol
$4
E
dm-')
y
TJK
dev
0.2242 0.1639 0.1455 0.09629 0.07350 0.07047
1.496 1.469 1.497 1.026 1.097 1.083
214.1 221.5 222.6 224.4 225.5 225.8
1.08 0.45 0.15 1.05 1.01 0.61
N
to45 to45 to45 to45 to45 to45
1.0 0.1 0.01 1.0 0.1 0.01
5 m
. tr
4
300
5001
200
100
0
I
-40
-20
0
T Io[
40
Figure 3. The proton conductivity AH+ plotted against temperature: 0, 0.01 M; 0 , 0.1 M; 0,1 M. Values from Table IV.
We assume that Aa- in an HC1 solution is the same as Xcl- in the KCI solution of the same concentration. (This approximation becomes exact in the limit of infinite dilution but is suspect at higher concentrations where HC1 and KCl solutions have different T, values.)
Figure 2. The resistivity r of 0.1 M aqueous solutions, KC1 and HC1, plotted against temperature. Data from Table 11.
temperature range of this work, so this approximation is probably valid to within the 1% precision of the resistivity measurements. A is the sum of the individual ionic conductances A = A+
+ A-
(6)
so that
AH+ =
h ~ c -l
(7 )
XCl- = lCI-AKCI (8) The transport number tcr in KCl solutionslO,llis close to 0.5 and is insensitive to both concentration and temperature above 0 OC. The linear relation tCI- = 0.504 + 0.00019(T/K - 273) (9)
represents tC1-in KC1 solutions, in the ranges 0 I1 M and 0 I T 5 50 OC, to within 0.2% We assume that eq 9 applies, to within 1%, below 0 OC. Values of Xcl- were calculated from eq 4, 5, 8, and 9 and values of r from eq 1 by using the parameters in Table 111. Values of AH+, calculated from eq 4, 5, and 7 by using the experimental values of r for HCl solutions from Table 11, are listed in Table IV and plotted in Figure 3.
Conductivity in Supercooled Aqueous HC1 Solutions Tg
?
Ts
The Journal of Physical Chemistry, Vol. 88, No. 9, 1984 1891 TABLE V: Parameters in Eq 10-12 with Ts"= 227 Ka
Tm
I/
PI
,.t
. ej -I t
1-
I
300 AKC~ AHC~
l -
AH+
p\
A"/(S
ai
bl
dmz mol-')
dm3")
dm3',)
y
R!vISD,~%
7.49 14.80 11.20
0.749 0.398 0.329
0.046 0.019 0.011
1.40 1.07 1.00
1.44 1.35 1.26
Data from Tables I1 and IV (with use of eq 4-9 to estimate c and A). RMSD% Is the square root of the mean square percentage deviation. The maximum deviation of any point is 2.5 X
.
a
vr
12
RMSD'%.
O I 4
1100
-
/I I,
/I 1 I ,
,
,
,
Figure 4. AH+ (0.01 M) and q-s/8, where q is the shear viscosity, plotted against temperature. The dashed extrapolations to zero at 227 K seem more plausible than would be any extrapolationsto zero at Tg< 160 K. Viscosity dataz'.23with a precision of 1% extend to -24 O C . MeasurementsZ2to -34 "C may be less reliable due to the small capillary used (1
w-4.
TABLE IV:
__
AH+
in HCI Solutions
c,, = 0.1 o o a
c,, = 1.ooa hH+/(R-'
c m z mol-')
45 35 25 15 5 -0.1 -5.2 -9.4 -15.0 -19.4 -21.8 -24.0 -25.9 -27.5 -29.9
34 7 313 276 23 8 198 184 165 149 132 111 101 92 85 80 71
" C,
c,, = 0.01" hHt/(R-'
hH+/(R-'
7'1°C
T/"C cmz mol-')
45 35 25 15 5 0 -5.1 -10.0 -16.2 -20.3 -22.4 -24.1 -26.1 -28.3 -30.2 -32.2
414 373 330 285 23 7 214 190 165 136 117 108 100 91 82 74 66
T/"C cmz mol-')
45 35 25 15 5 0 -5.1 -10.0 -15.2 -20.1 -23.0 -25.1 -27.2 -29.3 -31.1
434 391 345 297 24 7 222 198 173 149 125 112 102 92 83 74
is the molar concentration of the solutions at 20 " C .
An important object of these conductivity studies is to obtain precise data on the temperature dependence of a property of water so that a reliable extrapolation can be made to determine T,. Previous e~timatesl-~ of T, have an uncertainty of at least 1 5 K because they have been based on the extrapolation of less precise data from a three-parameter equation (1) or its equivalent. The present values of AH+ have a precision of 1.2% and fit the two-parameter equation (2), as shown in Figure 3. They yield the more reliable estimate of T," = 227 f 2 K for pure water. It is comforting that this value agrees with the original estimate of 228 K suggested by Speedy and Angell.3 With the value of T," = 227 K it is possible to represent all the measurements reported here by
AH+,
on c. However, the square root dependence gives a significantly better fit in the KCI case. An implication of the dependence of T, on c112,discussed previ~usly,~ is that the limiting slope (8 In A/&1/2)Tas c112 0 changes sign at low temperatures, in obvious conflict with the Onsager limiting law.1o,'' However, the testing of this implication would require more extensive measurements to lower temperatures and concentrations, which are precluded at the moment by the freezing and surface conductivity problems. Values of the limiting conductances
= A ( T / T , - 1)'
(10)
A'H+,
A'KCI, A'HCI = A'( T / T,o - I)?
with use of the parameters in Table V, all lie within 2% of literature values" above 0 "C, so the extrapolation of eq 10-12 to infinite dilution, below 0 "C, seems justified.
Discussion It is clear that an understanding of the state of water as T T, is a prerequisite for any interpretation of AH+ and its temperature dependence, so this discussion focuses on current ideas concerning the significance of T,. When water is cooled slowly, it always freezes' above -41 OC. However, recent experiments by Briiggeller and Mayer,15 which suggest that freezing can be avoided by rapid (-lo6 K/s) cooling of very small samples, open up the question of what happens to water below -41 "C. One possibility is that the properties of water vary continuously to a glass transition temperature Tg < 160 K and that the glass formed there is the same as the amorphous solid water, ASW, formed by vapor deposition. In this case ASW can serve as a model for the underlying structure of water.16 The existence of a glass transition at Tg = 140-150 K, from ASW to liquid water, was reported by McMillan and Los," but a recent study'* has suggested that ASW freezes directly at 160 K with no sign of a glass transition or of an intermediate liquid phase. The alternative proposal is that liquid water tends to a state of mechanical i n ~ t a b i l i t yat ~ . ~T, 227 K where the isothermal compressibility extrapolates to infinity. The long-range density-density correlations that are associated with a diverging compressibility'' imply correspondinglylong structural relaxation times (the "critical slowing down" effectlg), so the viscosity is also expected to diverge at T, and water should become a rigid gel there.6 The formation of the gel at T, differs from a glass transition in three respects.6 (1) The rigidity of the gel derives from long-range structural effects (the growth of low-density domains to macroscopic size, for example4s5)whereas the glass transition is a simple locking of the local structure and does not involve long-range correlations. The glass transition in the hard-sphere fluid can be understood2' on the grounds that the isothermal (15) P. Briiggeller and E. Mayer, Nature (London), 288, 569 (1980); ibid.,
with
298, 715 (1982). (16) M. G . Sceats and S. A. Rice in "Water-A
and the parameters listed in Table V. The decrease in T, with concentration for the HC1 solutions is much less than for KCl solutions, so it is not possible to discriminate between a linear and a square root dependence of T,
Vol. 7, F. Franks, Ed., Plenum Press, New York, 1981. (17) J. A. McMillan and S . C. Los, Nature (London), 206, 806 (1965). (18) D. R. MacFarlane and C. A. Angell, J . Phys. Chem., in press. (19) H. E. Stanley, "Introduction to Phase Transitions and Critical Phenomena", Oxford University Press, New York, 1971. (20) R. J. Speedy, Physica B (Amsterdam), 121B, 153 (1983). (21) J. Hallett, Proc. Phys. Soc., London, 82, 1046 (1963). (22) Ya A. Osipov, B. V. Zheleznyi, and N. F. Bondarenko, Russ. J.Phys. Chem. (Engl. Transl.), 51, 1264 (1977). (23) L. D. Eicher and B. J. Zwolinki, J. Phys. Chem., 75, 2016 (1971).
A = Ao/(l
+
T, = T,o(1 - b C q
(11)
(12)
Comprehensive Treatise",
J . Phys. Chem. 1984, 88, 1892-1896
1892
compressibility goes to zero there, for instance. (2) Glass transitions are not anticipated by thermodynamic anomalies in the liquid as Tgis approached from above, in contrast to the situation in water where a variety of anomalies’ anticipate the approach ~ , ~gel to T,. (3) According to the stability limit c o n j e c t ~ r e ,the is mechanically unstable so that any structural relaxation that can occur on the experimental time scale will be toward a more stable phase (Le. ice), rather than toward equilibration within amorphous phase space. Despite these differences, the formation of a gel in a rapidcooling experiment should be like a glass transition in some respects. In particular, the heat capacity of water, which increases rapidly as T T, as a consequence of the rapid structural change (e.g., growth of the low-density domain^^!^), should drop sharply to a value similar to that of ice when the structural relaxation time exceeds the experimental time scale and structural change is arrested, just as at a glass transition. Angell and Tucker2shave discussed this point in some detail. The experimental evidence, from studies of cooling liquid water1J5and of heating ASW,18 suggest that between about 160 and 232 K any structural relaxation that occurs in the amorphous state of water leads to the formation of ice. There is no evidence for the existence of an internally equilibrated metastable amorphous state in that temperature range. Given this “stability gap”, there is no reason to expect that the structure toward which T, is closely related to ASW. The evidence water tends as T on this point is not yet conclusive because the rapidly quenched samples are contaminated with the hydrocarbon cooling fluid.lS The debate concerning the possible continuity of states between ASW and liquid water has focused’J4~16~2s~26 on attempts to resolve the “entropy paradox”. Plausible extrapolations to estimate the entropy that liquid water would have if it could be equilibrated in the “stability gap” become less than the entropy of ice above 160 K. It is important to recognize in this connection that attempts
-
-
(24) P. V. Hobbs, “Ice Physics”, Oxford University Press, London, 1974, Chapter 2. (25) C. A. Angell and J. C. Tucker, J . Phys. Chem., 84, 268 (1980). (26) C. A. Angell, Annu. Rev. Phys. Chem., in press.
to estimate an entropy by integrating the heat capacity along an arbitrary irreversible path do not resolve this paradox. The evidence that most measures of structural relaxation times in supercooled water are tending to di~erge’J9~ at T,, rather than at Tg, is not explained by the continuity of states hypothesis. Figure 3 shows plots of q-5/8and AH+ against T, which is intended to show that the extrapolation to zero at T, N 227 K, particularly the linear extrapolation of the precise AH+ results that extend to 242 K, is more convincing than would be any extrapolation to zero at Tg < 160 K. We therefore take the view that liquid water forms a rigid gel at T, 227 K, if it does not freeze above T,, and it is the structure of this gel rather than the structure of ASW that should serve as a model for the underlying structure and properties of liquid water. The structure of the gel is as yet unknown, and it may turn out to be the same as that of ASW. However, in view of the stability limit conjecture3f’ and the recent models of the structure of supercooled ~ a t e r >it~is~likely ~ * ~that the gel contains extensive domains of some low-density clusters immersed in a more dense background random network and is, thereby, distinguishable from ASW. For example, the frozen in density fluctuation of the gel should scatter light and make it opaque. The proton mobility in the gel at T, may be similar to that in ice. In HF-doped ice24AH+ is about 10 Q-’ cm2 mol-’ at -10 OC, which corresponds to the extrapolated XH+ in water at about -42 O C from Figure 3. The rate-limiting factor for proton migration in the gel, and in supercooled water, is probably the concentration of the kind of defects that limit proton migration in ice.24 This conclusion is in contrast to most models of proton transfer in ~ a t e r ,which ~ , ~ postulate that the rate-limiting step is a structural relaxation process (e.g., the reorientation of a water molecule adjacent to the hydronium ion) and therefore should have a similar temperature dependence to other measures of structural relaxation times in water. The Walden product qXoH+doubles between +25 and -25 “C, whereas qXocr, 7XoK+, V / T ~(7, is the reorientational correlation time), and qD ( D is the self-diffusion coefficient) are relatively constant.2 Registry No. HC1, 7647-01-0; H’,
12408-02-5; water, 7732-18-5.
Kinetic Behavior of Cetyltrimethylammonium Hydroxide. The Dehydrochlorination of 1 , l ,l-Trichloro-2,2-bis(p -chlorophenyl)ethane and Some of I t s Derivatives Eduardo Stadler, Din0 Zanette, Marcos C. Rezende, and Faruk Nome* Departamento de Qdmica, Universidade Federal de Santa Catarina, 88,000 Florian6polis, S.C., Brazil (Received: June 7 , 1983; In Final Form: September 19, 1983)
The dehydrochlorination of 1,l,l-trichloro-2,2-bis(p-chlorophenyl)ethane (DDT), l,l-dichloro-2,2-bis(p-chlorophenyl)ethane (DDD), and l-chloro-2,2-bis(p-chlorophenyl)ethane(DDM) with hydroxide ion was studied in the presence of hexadecyltrimethylammonium hydroxide (CTAOH) micelles at 25.0 “C. The experimental results clearly deviate from the theoretical behavior expected by the pseudophase-ion-exchange model and can be explained by considering a n additional reaction pathway across the micellar boundary. This additional reaction pathway in which hydroxide ion in the aqueous phase reacts directly with the organic substrate in the micelle is probably of a phase-transfer catalysis type.
Introduction Although in the last few years significant progress has been made in the quantitative treatment of micellar catalysis,’-I0 we (1) Fendler, J. H.; Fendler, E. J. “Catalysis in Micellar and Macromolecular Systems”; Academic Press: New York, 1975. (2) Romsted, L. S. Ph.D. Thesis, Indiana University, Bloomington, IN, 1975. (3) Bunton, C. A. Prog. Solid State Chem. 1973, 8, 239. (4) Cordes, E. H.; Gitler, C. Prog. Bioorg. Chem. 1973, 2, 1 . (5) Tsujii, K.; Sunamoto, J.; Nome, F.; Fendler, J . H. J . Phys. Chem. 1978, 82, 423.
are still far from a complete understanding of the different processes involved in these phenomena. Indeed, at high counterion (6) Morawetz, H. Adv. Catal. 1969, 20, 341. (7) Berezin, I. V.; Martinek, K.; Yatsimirskii, A. K. Rum. Chem. Reu. (Engl. Transl.) 1973, 42, 187. (8) Nome, F.; Schwingel, E. W.; Ionescu, L . G. J . Org. Chem. 1980, 45, 705. (9) Martinek, A. K.; Yatsimirskii, A. K.; Levashov, A. V.; Berezin, I. V. In “Micellization, Solubilization and Microemulsions”; Mittal, K. L., Ed.; Plenum Press: New York, 1977; Vol. 2, p 489. (10) Quina, F. H.; Chaimovich, H. J . Phys. Chem. 1979, 83, 1844.
0022-3654/84/2088-1892$01.50/00 1984 American Chemical Society
