nitrated after 3 hours, It is possible that slow oxidation to adipic acid occurred in the later stages of the reaction. The only tertiary alcohol investigated, 2-methyl-2-propanol (tert-butyl alcohol), behaved somewhat like cyclohexanol. It was also more difficult to reproduce a particular result after a given time. Ninety minutes appeared to be the optimum nitration time; as the reaction time was increased, the titration showed a gradual decrease in per cent nitration. It is possible that decomposition to a nitroalkene occurred as has been observed with 98% nitric acid and 2-methyl-2-propanol at 0 to 5' C (18). When bromine was added to a nitration (18) C. A. Michael and G. H. Carlson, J . Am. Chem. Soc., 57,1268
(1935).
mixture after hydrolysis, decolorization of the bromine occurred, indicating the presence of some functional group such as a double bond. Interferences. Aldehydes, which are frequently impurities in alcohols, interfere in the nitration of primary alcohols by giving high results. A slight evolution of yellow fumes and formation of a yellow solution was observed upon addition of the reagent to octanal. By itself, octanal reacted about 25% with the nitrating reagent, Small amounts of aldehydes can be tolerated in the determination of primary alcohols, but amounts larger than 0.5 mmole cause high results (Table V).
for review September
1967* Accepted September
13, 1967.
Solubility and Complex Formation Equilibria of SiIver ChIoride in Propylene Carbonate James N. Butler Tyco Laboratories, Inc., Waltham, Mass. 02154 The equilibria of silver chloride i n propylene carbonate solutions containing excess chloride have been studied potentiometrically in a constant ionic medium (0.1N tetraethylammonium perchlorate) at 25" C. Equilibrium constants were fitted by a nonlinear least-squares pit-mapping technique. Only mononuclear complexes ASCI, were found. The overall formation constants for these complexes are: log p1 = 15.15 i: 0.15, log pz = 20.865 i: 0.015, log p3 = 23.39 i: 0.06 (for n = 1, 2, 3) and the solubility product of silver chloride is log K,, = 19.87 i: 0.02 (errors are standard deviations). The solubility of AgCl in excess chloride is approximately equal to the concentration of excess chloride, and the predominant soluble silver species is ASCI2-. The equivalence point of the titration of CI- with Ag+ occurs at [Ag+] = 1O-9*1, essentially independent of the concentration of reagents or supporting electrolyte. The thermodynamic equilibrium constants were estimated using the Debye-Huckel theory and neglecting ion-pair formation, and alternatively by assuming reasonable values for the ion-pairing constants.
PROPnENE CARBONATE (4-METHYLDIOXOLONE-2) has recently been used as a solvent for electrochemical studies relating to high-energy batteries ( I , 2) and free radical species (3). Its high dielectric constant (4) (64.4 at 25 C) permits ionic salts to dissolve at concentrations of several moles per liter, and its aprotic character permits electrode reactions with strongly reducing species such as radical anions or lithium metal to be carried out with little decomposition of the supporting electrolyte. One promising reference electrode system in this solvent is silver/silver chloride, and considerable effort has been expended in attempts to construct batteries using silver/silver (1) R. J. Jasinski, "High Energy Batteries," Plenum Press, New York, 1967. (2) R. J. Jasinski, J . Electroanal. Chem., 15, 89-91 (1967). (3) R. F. Nelson and R. N. Adams, J. Electroanal. Chem., 13, 184 (1967). (4) W. S. Harris, thesis, University of California, 1958; U. S. At. Energy Comm. Rept. UCRL-8381.
chloride cathodes with lithium anodes (5-7). This paper re ports studies of the silver/silver ion electrode, and of the solu bility and complex formation equilibria of silver chloride. EXPERIMENTAL Propylene carbonate (Matheson, Coleman and Bell) was purified by distillation in a Podbielniak vacuum-jacketed column of approximately 50 theoretical plates, operated under total reflux for several hours before any distillate was withdrawn. The reflux ratio was then changed to 1O:l. The first 200 ml of distillate were discarded. From an initial charge of 3500 ml, approximately 2700 ml of purified solvent were collected, The distillation proceeded at a pressure of 1 mm Hg and a stillhead temperature of 78 to 80" G. Analysis for water and volatile organic impurities was made by gas chromatography (8), on a column of Porapak Q, using thermal conductivity detection and helium as a carrier gas. The only detectable impurity was 15 to 20 ppm of water. Organic impurities were less than 4 ppm. Silver perchlorate (Chemical Procurement) containing 0.5 % water, tetraethyl ammonium chloride (Eastman) containing 1.5 water, and tetraethyl ammonium perchlorate (Eastman) containing less than 0.1 water, were dried over anhydrous CaS04 in a desiccator before solutions were prepared but were not otherwise purified. Soltldions were analyzed for chloride ion by potentiometric titration with aqueous silver nitrate, and for silver ion by potentiometric titration with a nonaqueous chloride solution of known concentration. The cell consisted of two electrode compartments connected by a salt bridge. Coarse glass frits separated the two ends of the salt bridge from the electrode compartments, and one of the electrode compartments contained a Teflon-coated (5) J. E. Chilton, Jr., Tech. Documentary Rept. ASD-TDR-62-1
(April 1962), AD 277 171. (6) H. F. Bauman, J. E. Chilton, W. J. Conner, and G. M. Cook, Tech. Doc. RTD-TDR-63-4083, (October 1963)AD 425 876. (7) J. E. Chilton, Jr., W. J. Conner, G. M. Cook, and R. W. Holsinger, Tech. Rept. AFAPL-TR-64-147 (February 1965), AD 612 189. (8) R. J. Jasinski and S. Kirkland, ANAL.CHEM., 39, 1663 (1967). VOL. 39, NO. 14, DECEMBER 1967
e
1799
Table I. Titration Data" CAg
CCl
E
E
CCl
CAS
Experiment No. 1 Experiment No. 3 (sat'd only) E" = 0.0687, C H ~ O = 0.0013M E" = 0.0687, C H ~ O = 0.0028M 0.969 - 1,0347 0.105 5.49 7.95 -0.8838 0.969 - 1.0207(?) 0.157 Experiment No. 4 0.968 -0.9973 0.210 E" = 0.140, C H ~ = O 0.004.M 0.968 -0.9766 0.262 0.968 -0.9566 0.314 0.452 9.050 -1.0468 (?) 0.967 -0.9302 0,366 0.463 6.944 -1.0336(?) 0.967 -0.8881 0.419 0.474 4.739 - 1,0125(?) (0.966) ( -0.8480)b (0.437) 0.481 3.365 -0.9877 0.966 -0.8477 0.471 0.485 2.427 -0.9604 0.966 -0.8464 0.523 0.488 1.951 -0.9378 0.965 -0.8418 0.575 0.490 1.471 -0.9033 0.965 -0.8377 0.627 0.492 1.180 -0.8641 0.964 -0.8315 0.679 (0.493) (0,962) ( - 0 , 7708)b 0.964 -0.8225 0.730 0.493 0.888 -0,7650 0.963 -0,8118 0.782 0.494 0.790 -0.7553 0.963 -0.7959 0.834 0.494 0.692 -0.7437 0,962 -0.7524 0.886 0.495 0.593 -0.7201 0.495 0.544 -0.6972 Experiment No. 2 0.495 0.505 -0,6803 E" = 0.0687, C H ~ O = 0.0020M 0.495 0.500 -0.6516 4.36 -0.9896 1.49 Experiment No. 5 4.34 -0.9128 1.98 E" = 0.1139, C H ~ O = 0.0047M (4.34) (-0. 8890)b (2.01) 4.32 -0.8830 2.47 0.060 0.194 -0.8730 4.30 -0.8728 2.95 0.075 0.194 -0.8522 4.28 -0.8588 3.42 0.094 0.194 -0.7824 4.26 -0.8321 3.89 (0.114) (0.194) ( - 0 , 7336)b 4.25 -0.8000 4.08 4.25 -0.7100 4.18 a Caa, Ccl in mmoles/liter, E in volts. All data at 25.0" C in 0.1M EtaNClOr solutions in distilled propylene carbonate, containing less than 4 ppm propylene oxide or propylene glycol. * Interpolated saturation point ; following this are for saturated solutions.
magnetic stirrer. Etched silver wires were used for electrodes in both compartments, and a uniform ionic strength of 0.100M was maintained in all three compartments with Et4NC1O4. The reference electrode compartnient contained 0.004M Ag+; and the compartment with the stirrer contained various concentrations of Ag+ and C1-, which were added from 2-ml RGI micrometer burets containing 0.1M AgC104 or 0.1M Et4NC1 in propylene carbonate. Potentials were measured with a Fluke high-impedance differential voltmeter, and were usually steady to +0.1 mV. Solution preparation, storage, and all experiments were carried out in a dry nitrogen atmosphere in a glove box. The cell was jacketed and the temperature was maintained at 25.0 i 0.05" C by means of a Haake circulating thermostat.
tential read immediately, the broken curve is obtained. This potentiometric titration is suitable for analysis of either the silver or chloride content of nonaqueous solutions; its lower concentration limit is determined principally by the trace impurities in the solvent and supporting electrolyte, which react with silver ion and thus distort the shape of the titration curve. Although the equivalence point is not precisely at the point of maximum slope, because of the multiple equilibria involved, the two points are identical within experimental error for all practical titration conditions. This is discussed later. Titrations were carried out in solutions ranging in concentration over a factor of 20 in chloride and a factor of 40 in silver. The experimental data are given in Table I.
RESULTS
Detailed studies of the kinetics of the silver/silver-ion electrode reaction in solutions based on propylene carbonate were not made, but our experience has been that under the small current drains encountered in these measurements, only ohmic resistance polarization was observed, even in solutions containing less than 10-4Msilver. In the constant ionic strength medium used, the Nernst equation was obeyed within kO.1 mV, the error in the potentiometric measurement. Equilibrium was reached within one minute. Solutions saturated with AgCl showed similar reproducibility, but often required as long as half an hour to reach eqiilibrium. Figure 1 shows a typical curve obtained when an aliquot of Cl- was titrated with Ag+. It is possible to supersaturate the solution slightly. If the titrant is added quickly and the po1800
e
ANALYTICAL CHEMISTRY
CALCULATIONS
We have considered here only solutions containing excess chloride. The following equilibria were assumed to hold in saturated solutions: AgCl(s) e Ag+
+ C1-
Ka0 = [Ag+][Cl-]
(1)
and in both saturated and unsaturated solutions : Ag+
+
Cl- $AgCl(sol)
[AgCl]
KJAg+][Cl-]
(2)
23
23.
I
-0.41
-Equivalence
-a5
II
E
(volts) -0.6
-
-0.7
-
-08
-
-o,$
-1.0
i
point
I
23
log 8:
23
b
Unsaturated
1,pB
4
Saturated with AgCl
23
I.
-1.1
I
I
1
,5
1.0
1.5
cAg’cCl
Figure 1. Titration curve for Experiment 1 (See Table I).
23
I
I
I
I
I
I
20.80
I
I
I
I
I
20.85
I
I
20.90
109 Pz
Mononuclear complexes were expected by analogy with aqueous solutions (9, IO) and other nonaqueous solutions (11) and their predominance was confirmed (see below). Unsaturated Solutions. Of the five species present (aside from supporting electrolyte), only [Ag+] is directly measured. The other four are defined in terms of the three equilibria (Equations 2-4) and two mass balance conditions which utilize the known total concentrations of silver and chloride (12). Substituting the equilibrium relations in the mass balances, we obtain :
Figure 2. Contours of deviation function U (see text) as a function of the constants pz and pd,with log pl fixed at 15.0 The broken line indicates the possible variations of pz and the standard deviation
within
The constants were therefore obtained by a nonlinear leastsquares pit-mapping technique, similar to that used by Sillen and coworkers (13). The equilibrium constants &,Pz, and P 3 were adjusted to minimize the function
3
CAE = [&+I CCl
=
0-I
PJC1-I“
(5)
no0
+ [&+I
3
n=l
nPn[C1-1”
(6)
where
PO = 1, Pi
and =
K I , P 2 = K&, and
0 3
=
KIKzKa
(7)
From Equations 5 and 6 it is clear that the measured quantities C A ~CCI, , and [Ag+] are sufficient to determine the equilibrium constants, but the function with which the data are to be fitted is defined by two sumultaneous fourth-order polynomial equations. The elimination of [Cl-] between the two equations leads to a polynomial of 16th order in which the 16 coefficients are combinations of the three constants desired, and for which conventional least-squares methods yield inconsistent answers.
(9) I. Leden, Scensk. Kem. Tidskr., 64, 249 (1952). (10) E. Berne and I. Leden, Ibid.,65,88(1953). (11) D. C . Luehrs, R. T. Iwamoto, and J. Kleinberg, Inorg. Chern., 5, 201 (1966). (12) J. N. Butler, “Ionic Equilibrium,” Addison-Wesley, Reading, Mass., 1964, Chapters 8 and 9.
For each point, Equation 5 was solved by Newton’s approximation method t o obtain [C1-li consistent with the assumed values of the Pn. If the equilibrium expressions are correct, and the mass balances are obeyed, Zishould be equal t o Z i ’ for each point of the set (see Equations 5 and 6) and U should be zero. Because of experimental errors, Uis finite, provided the number of points in the set exceeds the number of adjustable parameters. The function U was chosen to give the points a weight which reflects their relative errors; the deviation (1 Z,’/Z,) is normally distributed about zero for our data. The data for unsaturated solutions from experiments 1 , 2 , 4 , and 5 (Table I) were combined to obtain a set of 19 points for (13) N. Ingri and L. G. Sillen, Acta Clrem. (1962).
S c a d . , 16,
VOL. 39, NO. 14, DECEMBER 1967
159-172 1801
I
I
1.10
I I I Ill1 I I Experlment No ( S e e table I ) I + 2 D
I I I I I I I
I
I
I
I11111
I
I
I
4 A 1.05
A
n A 0
--I
v
15.0
14.5 log
15.5
PI
A 0
For this figure, we assumed log p1 = 15.15, log pz = 20.865, and log Pa = 23.39
calculating the best values of the constants Pn. Four points (question marks) in Table I were not included in this curvefitting procedure as they appeared to contain systematic errors, and their inclusion would result in a false fit to the theoretical equations. In particular, the three points at the beginning of Experiment No. 4 were rejected because the concentration of chloride is greater than 5 of the total ionic strength, and the assumption of constant liquid junction potentials and activity coefficients (on which the calculation of [Ag+] is based) may not be correct for these points. Figure 2 shows the map of the deviation function U obtained for various values of p2 and P 3 with the set of 19 chosen points. For this map, log 61 was fixed at 15.0. The pit is not quite orthogonal, because [Cl-] depends on the asmned values for the constants pa, and the function Z'/Z is not precisely a polynomial in [Cl-1. The contour of the standard deviation was drawn at
where IC' = 19 is the number of points (J3),and Umin= 0.050 is the Iowest value of U. The variation of U with PI is shown in Figure 3. For this curve, log B2 was fixed at 20.863 and log p3 was fixed at 23.4. From these calculations, the best values of the constants fitting this set of data are found to be: log P1 = 15.15 z!c 0.15 log Pz
=
20.865 A 0.015
log p3
=
23.39
* 0.06
where the errors are standard deviations. We made an attempt to fit a value of P4to this data set by including the three discarded points from Experiment 4 at high chloride concentration, and including extra terms in Equations 5 and 6 corresponding to n = 4, but this attempt was unsuccessful. The best fit was obtained with p4 = 0, and even with this assumption, the three points deviated systematically from the calculated function. Thus this deviation reflects the failure of the constant ionic medium assumption, and not the presence of additional complexes. e
+
Figure 4. Deviation of individual experimental points from theoretical values for mononuclear complexes
Figure 3. Variation of U with PI. Log PZ was fixed at 20.86, and log Os was fixed at 23.4, for this calculation
1802
+ +
+
+
.9 5
14.0
I
t
0
04
ANALYTICAL CHEMISTRY
Figure 4 shows the deviations ( Z ' / Z )of the individual points from the theoretical curve obtained for the best values of the constants Pn (given above). The agreement is within experimental error, even though CAEdiffered by a factor of 20 between experiments 2 and 5, and provides strong evidence that the complexes present in solutions containing excess chloride are predominantly mononuclear, as we have assumed. If there were substantial concentrations of polynuclear complexes present, we would expect to see a systematic variation in Z ' / Z as C Ais~ varied; perhaps by as much as a factor of ten for the range of C.he;covered in our experiments. Saturated Solutions. In the region of the titration curve where excess chloride and solid AgCl are present, the solubility product equilibrium, Equation 1 applies, and the mass balances include an additional term for the amount of solid AgCl precipitated. Elimination of this term between the two mass balances gives
CCI- CA, = lC1-1 - CAS+]
+ [AgCk-l + 2i'AgC1~-1
(12)
Making use of the equilibria, Equations 1-4, as well as Equation 7, this becomes: (Cci
- CA,
+ [&*I)
[&+I2
=
K d
+ Pz~sJCAg+l + 2 P&m3
(13)
As the equilibrium constants Pn are known from the analysis of the unsaturated region of the titration curve, and all other quantities in Equation 13 are directly measured except K,,, a value of the solubility product K,, can be obtained for each point of the titration curve. The constancy of this value as the titration progresses serves as a check both on the validity of the constant ionic medium method and on the values of the constants Pn obtained from the unsaturated solution. No mathematical difficulties are encountered with this calculation; K,, is easily obtained from Equation 13 by Newton's approximation method. Figure 5 shows the values of K,, calculated for each of the saturated points in Table I. The slight systematic deviation to larger values of K,, at smaller values of Ccl/C~, is not attributable to polynuclear complexes such as Ag,C1+, as these would cause the apparent value of K,, to deviate in the opposite di-
I
I
I
I
I
I
I
-20.0-
-19.9-A
Figure 5. Calculated values of solubility product K,, from the saturated region of the titration curves Horizontal line represents the best value: log K,, = -19.86
0
-
-19.8
=
+
-
log K,
t
m
m
4-19.7
+-
X
o
+ n
+ A
+ A E l m
-
-19.6
I
Experlmcnt No. (See iablel) -19.5
-19.4
-
1.2
rection. Neither is the deviation due to a change in ionic strength as C1- and AgC1,- ions are removed by precipitation, because the deviation is less for experiment 2 ( C A ~= 2 to 4mM, C O = ~ 4.3mM) than for experiment 1 ( C A ~= 0.4 to 0.8mM, Ccl = 0.96mM). The possibility that the deviation is due to an error in the analytical concentrations, or in the conand 02 within reasonable stants p,, was tested by varying e~~ limits, but this did not remove the deviation. Thus it may simply reflect a failure to reach equilibrium. As the most reliable data are those with high values of Call CA=,the best value of K,, is given by the line in Figure 5 : log K,, = -19.87 i 0.02 The error is the standard deviation of the mean of points from experiments 1, 2, and 3 with Ccl/CAg greater than 1.4. Preliminary experiments with added water have shown that K,, increases with increasing water content, so that the data from experiment 4 (with the highest water content) give systematically high values of Kso. The extrapolated value of K,, in perfectly anhydrous propylene carbonate is not smaller than lO-lg.9, so that our estimate above is correct within experimental error. Although the interpolated saturation points (Figure 1) give values of the solubility of AgC1, no additional information is obtained from these points treated as solubility data. DISCUSSION
Solubility of AgCl in Excess Chloride. From the equilibrium constants obtained in this work, we can predict the solubility Q of silver chloride in chloride-containing media. From the various equilibria and the mass balance on silver, we have = (LJC1-1)
+ + KsdC1-1 + Ks&1-12 Ks1
4f3
-
- 19.3
S
I + 2 E l 3 x
(14)
where Ks, = PnKsofor n = 1,2, 3. The equilibrium constants Ks, have been calculated from our experimental results, and are listed in Table 11. Figure 6 shows how the total solubility of AgC1, as well as the concentrations of the various soluble species, varies with the concentration of free chloride. The total added chloride concentration (Ccl-C,,) needed to obtain a given value of free chloride concentration [CI-] must be calculated from the equilibria and the mass balance on chloride. As a rough
I
I
I
1.4
I.6
1.8
I
I
2 .o
2.2
c C l ''Ag
approximation, AgClz- may be taken to be the predominant species; under this assumption, S is approximately equal to the concentration of additional chloride. The actual variation of C& is shown in Figure 6. Even if no chloride is added, the solubility of AgCl cannot be lower than Ksl, or 2 X 10-6M. This is the solubility of pure AgCl in pure propylene carbonate, and the predominant species is the undissociated AgCl complex. The square root of the solubility product for AgCl has no simple relation to its solubility in any propylene carbonate solution. Equivalence Point and Point of Maximum Slope. We mentioned earlier that the equivalence point for the titration of Ag+ with C1- (or vice versa) in propylene carbonate is approximately, but not precisely, the point of maximum slope. This can be shown quantitatively by differentiation of Equation 13. The point of maximum slope occurs (12) when
Table 11. Summary of Equilibrium Constants for AgCl in Propylene at 25" C Zero ionic Zero ionic strength Experimental strength without with ionvalue. ion-pairingc pairingd logpi logpz log Pa log K,, logK,1 log Kaz log Ke3
$15.15 f 0.15 +20.865 f 0.015 +23.39+ 0.06 -19.87 f 0.02 -4.7 f 0.2b +1.00 i 0.03b +3.52 i 0.07b
$ 1 5 . 5 A 0.2 +21.18 zt 0.03 +23.4 i 0 . 1
-20.18 3 0.05 -4.7 jr 0 . 2 +1.00 i 0.05 +3.2 i 0.1
+16.1 +21.8 +24 ? -20.8 -4.7 +1.00 +3 ?
Results of this investigation, in 0.1M Et4NClO4 containing 1.3 to 4 mM HzO. Errors are standard deviations. No significant Q
differences are expected at zero water concentration. b Calculated from the relation K,, = &KBo. c Assuming that the actiyity coefficients are given by the Debpe Huckel Theory with a = 3 A. d Assuming that for AgClOa, Et4NAgCh,and EtdNCl, the formation constant is Kl = 10.
VOL. 39, NO. 14, DECEMBER 1967
e
1803
4 Figure 6. Concentrationsof various soluble species in saturated AgCl solutions containing excess chloride
S is solubility of AgCI; CCIis total concentration of chloride. Concentration of excess chloride required to achieve a given free chloride concentration is given by Ccl - S
This may be compared with the relation for the equivalence point, obtained by setting C A=~ COL in Equation 13 :
The only difference between the two conditions is the coefficient of the term containing P3, and thus the equivalence point is indistinguishable from the point of maximum slope if
For the values of the constants given in Table 11, Equation I7 gives [Ag+i >> 10-17.4 At the equivalence point, [Ag-] is given by Equation 16 to be 10-9. 4, so this is certainly satisfied for all realistic conditions. The equivalence point potential (see Figure 1) is essentially independent of the concentrations of reagents or supporting electrolyte, and a “dead-stop” end point is appropriate. Estimation of E ~ u ~ l i ~ Constants r i u ~ at Zero Ionic Strength. It is of interest to estimate thermodynamic equilibrium constants from our concentration equilibrium constants measured in 0.1M EtlNC184. In the first instance, we have neglected the possibility of ion-pairing with the supporting electrolyte. By analogy with water (which has only a slightly higher dielectric constant) we would expect ion-pairing to be negligible. Conductance measurements in LiCl0,-propylene carbonate solutions (14) and calorimetric measurements in solutions of a number of salts (15) indicate that ion-pairing is probably small. If ion-pairs are neglected, activity coefficients may be calculated from the extended Debye-Huckel Equation 12. For propylene carbonate (dielectric constant 64.4) at 25” C, A = 0.687 and B = 0.360. At ionic strength 0.1, with a = 4 A, a singly charged ion has y1 = 10-0.18 and a doubly
charged ion has y z = Using these values of activity coefficients, the equilibrium constants were corrected to zero ionic strength, and the results are listed in Table 11. Note that ionic strength has negligible effect on Kal, ICsB,and p3. The limits of error have been increased to account for the uncertainty in the Debye-Huckel calculations. Ion-pairing equilibria in a number of solvents of lower dielectric constant have been studied (16) and from these a rough estimate can be made of the ion-pairing equilibrium constants in propylene carbonate. In acetonitrile, the ion association constant for EtlNCl is 101.64 and for EtrNCIOl is 101.06. If the logarithm of the ion-pairing constant is inversely proportional to the dielectric constant of the solvent, we can predict that in propylene carbonate, the ion-pairing constant for EtdNCl is 101.O and for Et4NC104 is 100.5. The values in the last column of Table I1 were calculated assuming that the ion-pairing constants for all oppositely-charged ions (except Et4N+ and C D - ) were 10. The difference from the constants calculated neglecting ion pairing is not large; and these values represent an extreme limit of the ionpairing effect. The ion-pairing effect on P3 and & is uncertain, because of the uncertainty in the association constant of the divalent ion AgC13-2 with IEt4K. Note that Ksl and Kszare virtually unaffected by ion-pairing, as well as by ionic strength. ACKNOWLEDCrMENT
-
The author thanks Walter Zurosky, Marcel Fajnzylber, and Benjamin Marshall for assisting with the experimental work, Mrs. Susan Kirkland for distilling the propylene carbonate, and Dr. Raymond Jasinski for numerous helpful and informative discussions. RECEIVED for review June 5, 1967. Accepted September 19, 1967. Work supported by, but does not necessarily constitute the opinion of, the Air Force Cambridge Research Laboratories, Office of Aerospace Research, under Contract AF 19(628)-6131.
(14) D. P. Boden, A. R.Buhner, and V. J. Spera, Contract DA 28~ ~ 2 “ ~ ~ C September - ~ ~ 3 1966. ~ 4 ~ AD ~ 639 ) , 709. (15) U.C. Wu and N. L. Friedman, J. Phys. Chem., 70, 501 (1966).
(16) 6. W. Davies, “Ion Association,” Butterworths, London, 1961, p. 96.
4
e
ANALYTICAL CHEMISTRY
