2946
J. Phys. Chem. 1980, 84, 2946-2952
to the carbonyl does not appreciably change the quenching efficiency. Additional information is obtained in the last few compounds. An essentially isolated carbonyl, as that in acetone, has no quenching ability. Two adjacent carbonyl groups (diacetyl) are effective quenchers. Two carbonyls which are conjugated through double or triple bonds are also effective quenchers as indicated by the rate constants obtained for diethyl fumarate and diethylacetylene dicarboxylate and, here again, as in the case of the benzene derivatives, the presence of the electron-donating ethoxy groups bonded to the carbonyls do not diminish the quenching efficiency. These results for the quenching of carbazole fluorescence by carbonyl-containing compounds are similar to the findings of Ricci and Nesta regarding the quenching of indole fluorescence. That paper and a number of references contained therein can be consulted for more detailed discussion.20 References and Notes (1) See, for example, J. B. Birks, "Photophysics of Aromatic Molecules", Wiley-Interscience, New York, 1970; N. Mataga and T. Kubuto, "Molecular Interactions and Electronlc Spectra", Marcel Dekker, New York, 1970; B. Stevens, Adv. Photochem., 8, 161 (1971). (2) Th. Forster, Angew. Chem., Int. Ed. Engl., 8, 333 (1969). (3) See, for example, W. R. Ware, D. Watt, and J. D. Holmes, J. Am. Chem. SOC.,96, 7853 (1974).
(4) D. Rehm and A. Weller, Ber. Bunsenges. Phys. Chem., 73, 834 (1969), H. Knibbe, D. Rehm, and A. Weller, Ber. Bunsenges. Phys. Chem., 73, 839 (1969). (5) G. Pfister and D. J. Williams, J. Chem. Phys., 59, 2683 (1973); see, however, 0. PASter, D. J. Williams, and G. E. Johnson, J. phys. Chem., 78, 2009 (1974). (6) 0. E. Johnson, J . Chem. Phys., 61, 3002 (1974). (7) See, for example, W. R. Ware in "Creation and Detectlon of the Excited State", Vol. 1, A. A. Lamola, Ed., Marcel Dekker, New York, 1971, Part A, p 213. (8) C. G. Swain and E. C. Lupton, Jr., J . Am. Chem. Soc., 90, 4328 (19681. (9) A. T. McCall, G. S. Hammond, 0. Yonemitsu, and 8. Wltkop, J. Am. Chem. Soc., 92, 6992 (1970). (10) R. F. Steiner and E. P. Kirby, J . Phvs. Chem., 73, 4130 (1969). (11) D. Rehm and A. Weller, Sei. Bunsenges. Phys. Chem., 73, 834 (1969). (12) J. F. Ambroseand R. F. Nelson, J. Electrochem. SOC.,115, 1159 (1968); J. F. Ambrose, L. L. Carpenter, and R. F. Nelson, I M . , 122, 876 (1975). (13) C. K. Mann and K. K. Barnes, "Electrochemical Reactlons in NonAqueous Systems", Marcel Dekker, New York, 1970, p 231. (14) R. W. Yip, R. 0. Loutfy, Y. L. Chow, and L. K. Magdzinski, Can. J . Chem., 50, 3426 (1972). (15) J. F. Ireland and P. A. H. Wyatt, Adv. Phys. Org. Chem., 12, 131 (1976). (18) H. J. men, L. E. Hakka, R. L. Hinman, A. J. Kresge, and E. B. Whipple, J . Am. Chem. SOC.,93, 5102 (1971). (17) A. C. Capomaccha and S. 0. Schulman, Anal. Chim. Acta, 59,471 (1972). (18) D. Dolman and R. Stewart, Can. J . Chem., 45, 903 (1967). (19) M. M. Martin and W. R. Ware, J . Phys. Chem., 32, 2770 (1978), and references therein. (20) R. W. Ricci and J. M. Nesta, J . Phys. Chem., 80, 974 (1976).
Ionization and Dissociation Equilibria in Liquid SO2. 12. The Behavior of Tetrahedral Ions Norman N. Lichtin,* Bernard Wasserman, Edward Clougherty, June Wasserman, Department of Chemistry, Boston University, Boston, Massachusetts 022 15
and John F. Reardon Depaflment of Chemistry, Boston State College. Boston, Massachusetts 021 15 (Received:March 6, 1980)
Electrolytic conductance of their solutions in liquid sulfur dioxide over a wide range of concentrations was measured for the 21 ionophores, Me,NCl, Me4NC104,PhMe3NBr,PhMe3NC1,PhMe3NI,Et4NI, Pr4NC1,Pr4NBr, Pr,NI, Bu4NBr, Bu4NI,Bu4NPc, (i-Am)4NBr,(i-Am),NI, (i-Am)4NB(i-Am)4,(i-Am)3NHBr,Hex,NI, Ph4AsC1, Ph4AsI, Ph4AsPc,and Ph4PPc, at 273.15 K and other temperatures. Limiting equivalent conductances and dissociation constants were determined for these solutes by Shedlovsky's procedure. Utilizing the data of this and other investigations, we calculated thermodynamic quantities for the dissociation equilibria of many of the solutes. Values of Bjerrum's contact distance parameter, a, were calculated from the equilibrium data and compared to sums of estimated ionic radii. Limiting ionic conductances were evaluated by a Fuoss-Coplan division of the limiting equivalent conductance of (i-Am)4NB(i-Am)4.Stokes radii were calculated for the ions employed. The results of the measurements are interpreted in terms of ion-ion and ion-solvent interactions.
Introduction
Liquid sulfur dioxide dissolves a wide variety of organic and inorganic compounds and is one of the most thoroughly investigated aprotic nonaqueous solvents. Extensive reviews of its chemistry and solvent properties have been published by Lichtinl and Waddington.2 More recently, reviews have been contributed by Tokura3 on SO2 as an organic reaction medium, by Lichtin4 on carbonium ion stability in SOz, and by Burow5 and Zingaro6 on the solvent properties of SOz. The physical and thermodynamic properties of SOz have been summarized by Kuo7 and co-workers and a general review has been presented by Holliday and Nicholls.s 0022-3654/80/2084-2946$01 .OO/O
Recent contributions to the chemistry of liquid SO2 solutions have been by Lichtin and Wassermane on the reactivity of iodide and thiocyanate ions with p-nitrobenzyl bromide and TokuralO and associates on the apparent molar volume of a series of tetraalkylammonium halides in SOz at 298.15 K as well as on the electrical conductance of 34 electrolytes in SO2 a t 298.15 K.ll Very recently, interest has developed in electrochemical phenomena involving liquid SO2 as a s ~ l v e n t . ~ ~ . ' ~ In our earlier investigations in the series14J5concerning the kinetic and association behavior of ions in liquid SO2 we found that interpretation of the kinetic results must recognize ion-solvent interactions in this medium. The 0 1980 American Chemical Society
Behavior of Tetrahedral Ions in SO2
further eluciidation of the nature of the ion-solvent interaction wai the object of this study. Measurements have been made of the electrical conductance of 21 ionophores in liquid sulfur dioxide at 273.15 K and certain other temperatures. Experimental Section Procedure. The conductivity cell, bridge assembly,'e and procedures17have been described, as have both the vacuum line for the purification of the SO2 and the thermostat.18 Sulfur dioxide was dried by passage over Type 3A Linde molecular sieve pellets and degassed in three alternate freeze-thaw cycles on the vacuum line. Solvent conductance varied between 0.43 X lov8and 21.08 X lo4 mho/cm as comDaredl to a literature value at 273.15 K of 3 X mho/cm.6 Materials. Eastman White Label PhMeRNClwas recrystallized three times from 2-proipanol and dried for 1 day in vacuo at 118 "C over P206,mp 241-2 "C (cor); found 20.65% C1; calculated 20.65%. E)astman White Label PhMe3NBr was recrystallized six times by precipitation a t room temperature from absolute ethanol by addition of anhydrous diethyl ether and dried in the same manner as the chloride, dec. 205-7 "C (cor); found 49.83% C, 6.35% N, 37.01% Br; calculated 50.02% C, 6.53% H, 36.97% Br. Eastman White Label PhMe3NI was recrystallized three times from preboiled ethanol and dried in vacuo for 3 days at room temperature over P20s,mp 222-3 "C (cor); found 41.31% C, 5.36% H., 48.50% I; calculated 41.08% C, 5.38% H, 48.23% I. Etastman White Label (Me)4NC1w,m recrystallized three times by precipitation from absolute ethtllnol by addition of acetone and dried in vacuo over %;OHand CaS04for 48 1.1 at room temperature; found 32.39% C1; calculated 32.35% C1. (Me)4NC104was prepared by metathesis of aqueous ]Baker AR NaC104and aqueous Eastman White Label (Me)4NBr. The product was recrystallized from aqueous ethanol (1:l by volume) by chilling iin an ice bath and dried in vacuo over CaS04 for 48 h; found 275% C, 6.7% H, 20.7% C1; calculated 27.6% C, 7.0% H, 20.4% C1. Chemical Procurement Labs. Polarographic Grade (EtI4NIwas recrystallized twice from preboiled conductivity water under N2 and dried in vacuo over P205at 118 "C for 1day; found 37.64% C, 7.80% H, 49.59% I; calculated 37.37% C, 7.84% H, 49.35% I. Eastman White Label (PrI4NC1was recrystallized three times by precipitation from acetone by addition of anhydrous diethyl ether and dried in vacuo at 80 "C over P206for 24 h; found 16.02% C1; calculated 15.98% C1. Eastman Wlhite Label (Pr)4NBrwiis recrystallized three times by precipitation from chloroform by addition of ethyl acetate and dried in vacuo at 80 "C over P205for 24 h; found 29.94% Br; calculated 30.01%. Eastman White Label (Pr)4NI was recrystallized twice by precipitation from preboiled absolute ethanol by addition of anhydrous diethyl ether and dried in vacuo at 80 "C over P205for 24 h; found 40.65% I; calculated 40.5%. Eastman Yellow Label (Bu)&'Br was recrystallized at room temperature from benzene and precipitated by addition of ligroine and cooling. The crystals were dried in vacuo at 56.5 "C over Pz06for 72 h; found 59.66% C, 11.10% H, 24.62% Br; calculated 59.67% C, 11.22% H, 24.77% Br. Eastman White Label (BU)~NI was recrystallized three times by precipitation from methylene chloride by addition of benzene and dried in vacuo at room temperature over P205 for 4 days; found 52.02% C, 9.86% H; calculated 52.02% C, 9.82% H. (BU),~NPC was prepared by the method of Cox, Kraus, and Fuoss involving the neutralization of (Bu)4NOH with picric acid.lg The picrate was recrystallized twice from absolute ethanol and dried in vacuo at
The Journal of Physical Chemistry, Vol. 84, No. 22, 1980 2947
room temperature over P205for 3 days, mp 89-91 "C (cor); found 56.36% C, 8.26% H, 11.95% N calculated 56.15% C, 8.14% H, 11.91% N. (i-Am)4NBr was prepared by heating equimolar amounts of Eastman White Label (iAm)3N and l-bromo-3-methylbutane in a sealed Pyrex tube at 70 "C for 10 days. The product was washed with petroleum ether (30-60 "C), recrystallized six times by precipitation from ethyl acetate with petroleum ether, and dried in vacuo at 56.5 "C over P205for 48 h, mp 87.5-89.5 "C; found 20.80% Br; calculated 21.11% Br. (i-Am)4NI was synthesized by heating equimolar amounts of Eastman Yellow Label (i-Am)3Nand l-iodo-&methylbutane in a sealed Pyrex tube at 80 "C for 1weekemThe product was washed with petroleum ether, dissolved in 10% ethanolic KOH, filtered, and precipitated by pouring the solution onto ice with vigorous stirring; it was then filtered and washed with petroleum ether, recrystallized three times by precipitation from acetone with diethyl ether, and dried in vacuo at 81 "C over Pz06for 18 h, mp 146-7 "C (cor); found 29.73% I; calculated 29.83% I. (i-Am)4NB(i-Am)4 was prepared by the method of Coetzee and CunningThe compound was recrystallized eight times from aqueous acetone (81, vokvol) and dried in vacuo over P205 a t 56.5 "C, mp 240-241 "C (uncor); found 80.96% C, 14.80% H, 2.43% N; calculated 80.89% C, 14.93% H, 2.36% N. (i-Am),NHBr was prepared by heating equivalent amounts of Eastman White Label l-bromo-3methylbutane and Eastman Yellow Label (i-AmI3Nin a sealed Pyrex tube at 135 "C for 7 days. The solid product was recovered after cooling the tube to 0 "C. The compound was recrystallized three times by precipitation from ethyl acetate by addition of petroleum ether and dried in vacuo over P205a t 64.5 "C for 2 days; found 58.42% C, 10.82% H, 26.15% Br; calculated 58.43% C, 11.11% H, 25.91% Br. Eastman White Label Hex4NI was recrystallized three times by precipitation from acetone by addition of diethyl ether and cooling to 0 "C and dried in vacuo at room temperature for 2 days, mp 103-4 "C (cor); found 26.41% I; calculated 26.35% I. Calbiochem A.R. Grade Ph4AsCl was recrystallized three times from hot ethanol by addition of diethyl ether and cooling gradually in a dry ice-trichloroethylene bath and dried in vacuo over Pz05at 56.5 "C for 3 days, mp 255-257 "C (uncor); found 8.35% CI; calculated 8.47% C1. Ph4AsI was prepared by metathesis of equivalent amounts of Ph4AsC1and Fisher Certified Reagent KI in conductivity water, recrystallized three times from ethanol by addition of diethyl ether, and dried in vacuo over P205at 118 "C overnight, dec. 316-8 "C (uncor); found 24.78% I; calculated 24.87% I. Ph4AsPc was prepared by metathesis of equivalent amounts of Ph4AsC1and Baker AR Grade picric acid dissolved in hot absolute ethanol, recrystallized three times from hot ethanol, and dried in vacuo over P205at 56.5 "C for 5 days, mp 203-5 "C (uncor); found 58.76% C, 3.63% H, 6.93% N; calculated 58.93% C, 3.63% H, 6.87% N. Ph4PPc was prepared by adding an equivalent amount of Calbiochem AR Grade Ph4PC1 in conductivity water to Baker AR Grade picric acid in hot absolute ethanol, recrystallized three times from ethanol, and dried in vacuo at 56.5 "C for 3 days, mp 201-3 "C (cor); found 63.20% C, 3.45% H, 7.46% N; calculated 63.49% C, 3.91% H, 7.41% N. All solvents were reagent grade or equivalent and were dried or redistilled as needed. Analyses were carried out by Galbreath Labs except for the analyses of (CH3)4NC104 and (CH&NCl which were carried out by Dr. Carol Fitch, Needham Heights, MA. Data Equivalent conductance data from representative single
2940
The Journal of Physical Chemistry, Vol. 84, No. 22, 1980
Lichtin et al.
TABLE 11: Conductance Parameters salt
temp, K
lo4&, mol/dm3
273.38 262.60 254.16 247.57 273.38 262.60 254.16 247.57 273.15
8.41 i. 0.63 9.67 i: 1.68 12.04 t 3.01 12.92 f 0.63 10.05 f 0.42 15.47 f 2.17 13.95 f 1.63 23.01 f 4.49 17.95 f 1.11 18.16 f 1.17 25.27 f 3.32 35.33 f 4.11 53.85 f 5.37 51.43 f 5.98 54.99 i: 10.07 72.25 i: 13.59 66.14 f 8.57 30.9 f 5.3 63.9 f 7.2 46.0 f 5.0 61.3 i: 4.8 2.04 f 0.03 112.0 i. 48.8 68.6 f 7.7 81.35 i: 8.76 45.6 i. 5.4 48.0 f 2.3
Me,NC10,
Me,NCl
PhMe,NCl PhMe ,NBr PhMe NI Et,NI Pr,NC1 FY,NBr Pr,NI Bu,NBr Bu, NI Bu, NPc (i-Am),NBr (i-Am),NI (i-Am),NB(i-Am), (i-Am),NHBr Hex,NI Ph, AsCl Ph,AsI Ph,AsPc Ph,PPc
273.15
273.15
A,,
mho cm2/mol
219.4 f 1.8 202.3 f 3.8 183.9 f 4.5 170.3 i: 0.6 243.7 f 0.9 218.3 i: 2.3 204.4 f 1.9 184.0 f 1.9 216.0 f 0.7 214.0 f 0.8 206.3 f 1.3 208.5 f 0.8 197.4 i: 0.4 195.1 f 0.6 194.7 f 0.8 188.0 f 0.7 184.7 f 0.5 197.6 f 1.0 187.1 f 0.5 186.5 f 0.6 124.5 i. 0.2 193.0 f 0.75 174.4 i: 0.9 188.7 i: 0.4 183.3 f 0.3 127.3 i: 0.4 128.6 f 0.2
r+ + r-, A"
sl,f A"
4.7Ba
4.65 f 0.10 4.57 f 0.22 4.67 i: 0.40 4.62 f 0.08 4.91 i 0.08 5.41 i: 0.32 4.92 f 0.22 5.91 f 0.62 6.25 f 0.20 6.29 f 0.21 7.62 f 0.73 9.49 i 0.74 12.21 f 0.59 11.92 ?I 0.69 12.34 f 1.01 13.94 f 0.88 13.47 f 0.83 8.67 i 0.94 13.23 f 0.65 11.19 f 0.75 12.97 f 0.45 3.53 f 0.03 15.97 f 2.77 13.64 f 0.72 14.58 f 0.54 11.13 f 0.79 11.48 f 0.32
5.2Bb
6..26' 6.40 7.26 6.16 6.33 6.47 6.68 6.89 7.10 10.04d 7.07 7.28 10.24 3.43e 11.80' 8.86' 9.21 12.15 12.05'
a Quaternary cation radii from Robinson and Stokes.24 van der Waals radius of 0, 1.4 A , used for C10,- radius. Radii of halide ions from Pa~ling.'~ Cation radius estimated from plane projection drawings with values of bond distances and bond angles taken from P a ~ l i n g . ' ~ Radius of picrate ion from Lichtin and Pappas.' e Cation radius taken t o be the N-H radius of 1.48 A. f Bjerrum's value.
'
TABLE 111: Single Ion Conductances and Stokes Ionic Radii in Sulfur Dioxide h c , mho cm2/equiv
ion
I- '
(i-Am),N+ Me,N+ PhMe,N+ Et,N+ Pr,N' Bu,N+ (i-Am),"' Hex," Ph,As+ Ph,P+ B(i-Am),-
62.3 109.5 82.1 84.3 70.5 60.5 68.4 50.2 59.1 62.5 62.3 126.9 124.6 124.2 109.9 104.1 66.1
c1Br1-
c10, BF,PcU
- m i c radii from TL-- 11.
Br-
av'
62.3 111.7 89.3 89.8 70.4 63.3 68.3 50.2 61.7 63.0 62.3 127.0 124.7 124.2 107.7 101.9 65.6
62 111 86 87 70 62 68 50 60 63 62 127 125 124 109 103 66
R , is the hydrodynamic radius.
runs for sample salts are presented in Table I (see paragraph at end of text regarding supplementary material). At least three independent runs were performed for each solute. Dissociation constants (&) and limiting equivalent conductance (A,) values for each salt were calculated by means of Shedlovsky's procedure.22 The slope (1/KdAo2) and the intercept (l/A,) of the resulting straight line were calculated by the least-squares method with l/AS(z) as the dependent variable. Results are presented in Table 11. Indicated uncertainties were calculated from the square roots of the variances (95% confidence limits) in the slope and intercept of the linear Shedlovsky plots. The formation of triple ions was investigated. For all salts studied no minima were observed in plots of A vs. log V. It can be concluded that concentration of ion triplets was negligible.23
d
142 123 101 90.6
160 156 149 137 85.3
r ~ A/ 5.12 3.47 4.45 4.00 4.52 4.94 5.12 5.61 7.05 6.97 5.40 1.81 1.95 2.16 2.00 2.17 5.10
' 273.15 K.
Rs,b3CA 3.26 1.83 2.37 2.34 2.91 3.28 2.99 4.07 3.39 3.23 3.26 1.60 1.63 1.64 1.87 1.98 3.08
rC/RsC 1.57 1.90 1.88 1.71 1.55 1.51 1.71 1.38 2.08 2.16 1.66 1.13 1.20 1.32 1.07 1.10 1.66
R,,bpd
A
1.85 2.17 2.60 2.90
1.64 1.68 1.76 1.90 2.24
298.15 K.
The values of the dielectric constant and viscosity of sulfur dioxide employed in the calculations were taken from ref 4, 1OOOq = 4.03 - 0.0363t ("C) and D = 95.12 exp[-6.676 X 10-3T (K)], and were 4.03 mP and 15.35 at 273.15 K, respectively. As stated previously, solvent conand 21.08 X ductance varied between 0.43 X mho/cm and was at most 5% of solution conductivity. All calculations were carried out on an IBM 1620 computer. Discussion Single Ion Conductances. Limiting single ion conductances in liquid SO2 at 273.15 K are listed in Table 111. They were determined by a Fuoss-Coplan division of the limiting equivalent conductance of the reference electrolyte, (i-Am)4NB(i-Am)4, equally between cation and anion.
Behavior of Tetrahedral
The Journal of Physical Chemistty, Vol. 84, No. 22, 1980 2949
Ions in SO,
This compound has been shown%to provide values of ion mobilities in nonaqueous solvents that may be accurate to 0.1%. Two series of values of Xi0 were obtained, one by proceeding through (i-Am),NI, the other by proceeding through (i-Ani)4NBr. The two sets of values agreed to within 3%. Their average is also reported. Included in Table I11 are (datafor several previously studied27tetrahedral ions. Tokura and co-workers prepared a similar table for ions (st 298.15 K, based on a split of the limiting equivalent coriductaince of Bu4NBBu4,3a less proven reference electrolyte, and their values lhave been included. Hydrodynamic radii, Rs, were calcullated for the ions at both temperatures from Stokes’ law: Rs = 0.820zi/Xpq. In for the ions are plotted Figures 1 andl 2 values of against r;l (frlom Table 11) for 273.151and 298.15 K. The Stokes’ law for perfect sticking solid lines h f q = zFe/6a(300)ri
I
I
273.15 K
’
SLIP
STOKES STI(
QMe,N*c
(1) *ANIONS
0 CATIONS
and Stokes’ law for perfect slipping X i 0 ~= zFe/4a(300)ri
(2)
Boydm and Zwanzig30 have developed a fuller expression for which takes into account the retarding effect of the dielectric relaxation of the solvent dipoles on the mobility of the ions. Equation 3 is a recent version31 of the imzFe Xior = -(3) A V v i+ rld(ze)2(eo- e,)7/r~eov(2eo+ 1) perfect sticking: A, = 6, .Ad = 3/8 perfect slipping: A, = 4, .Ad = 3/4
proved equation. In this equation eo and e , are the static and optical frequency dielectric constants and 7 is the dielectric relaxation time of the solvent. Values of e, and T were not available for liquid SO2, ‘but were estimated. 7 was taken as s,32and e, = (refractive index)2 = (1.338)2 (from Burow’s review5). This Boyd-Zwanzig treatment predicts conduction maximia28for both slip and stick cases at (4)
(drnax = (3Ad4)li4/&T
(5)
4 = (zeI2(r/v)(eo - em)/eo(2eo + 1)
(6)
with The dielectric relaxation correction term, the second term in the denominator of eq 3, is small and always positive, 15.87 X for SOz at 273.15 K. Thus it predicts negative deviations from Stokes’ law that increase as the ionic radius r, decreases. For the tetrahedral cations studied here such is nlot the case at all. For SO2solutions the maximum values predicted are as follows: at 273.15 K stick
(X/’~I)~,
= 0.197
(rJm, = 3.12 8,
slip
(Xoi qt),
= 0.225
(rJrn, = 4.11 8,
at 298.15 K stick
= 0.167
(rJrnax= 3.67
slip
= 0.191
(ri)mag= 4.84 A
(Xiop),,
01
05
03
r-l/tH-
7
)
Figure 1. Ion mobilities agalnst reciprocal crystal radlus: (0)experimental A:?, C,, denotes the ion (C,H2,,+,),Nt.
these lead to the following maximum values of the limiting ionic conductance: at 273.15 K stick Xi0 = 48.9 = 55.8
slip
Xi0
at 298.15 K stick
Xf’ = 41.4
slip
Xi0
= 47.4
For the ions studied here the maximum values of A/‘ are about 125 for the halide ions, 2.5 times the predicted values, and the (rJmaxvalues are considerably larger than the values of rc usually associated with haiide ions, 1.8-2.2 A. Curves calculated with eq 3 for both the perfect slipping and sticking cases at 273.15 and 298.15 K are included in Figures 1 and 2. Even if we allow for the approximate data used in the calculations there is seen to be little agreement between theory and experiment, even though SO2with a dipole moment of 1.62 D would not be expected to display a much smaller dielectric relaxation effect than H20 with a dipole moment of 1.87 D. Use of the correct values of 7 and e, might reveal a completely different picture. Fernandez-Prini and Atkinson31have carried out an analysis of the mobilities of the alkali metal ions and tetraalkylammonium ions in a variety of nonaqueous solvents and solvent mixtures. Only with methanol was the disagreement as serious as here. Kay28and S p i r ~ ~ ~ have presented discussions of the improved Boyd-Zwanzig equation, its usefulness, and its limitations. On examining the Stokes’ law plots in Figure 1we see that the R4N+ions either display positive deviations from Stokes’ law for slip or lie on the line, a not surprising result for a solvent commonly regarded as nonpolar (dielectric constant = 151, aprotic, and unassociated. We conclude that these quaternary cations do satisfy Stokes’ law for slippage and attribute their displaced positive deviations from the Stokes’ law line to the assignment of incorrect radii to the ions. Two recent compilations of ionic radii
2950
The Journal of Physlcal Chemistry, Vol. 84, No. 22, 1980
Lichtin et al.
TABLE IV: Ionic Radiia of Quaternary Ions ion Me," Et,N+ Pr,N+ Bu,N+ (i-Am),N+ Hex,N+ Ph,As' Ph,P a
RL 2.16 2.54 2.85 3.15 4.24 4.70 4.25 4.14
All radii in angstroms.
7
RS
RH
Rub
2.76 3.50 4.33 4.94 4.90 6.09 5.06 4.86
3.47 4.00 4.52 4.94 5.40 9.60b 7.05b 6.94b
3.47 4.00 4.52 4.94 5.12 9.60 7.05 6.94
STOKES
Table 11.
by S p i r and ~ ~ by ~ K r ~ m g a l zhave ~ ~ pointed up the uncertainty in our knowledge of the radii of these quaternary ions. In Table IV are listed the lowest values given, RL, the highest values given, RH,the values needed to fit the Stokes' law slip line, Rs, and the values we used for Figures 1and 2, RU. The values we used which were from Robinson and Stokesz4or estimated from molecular models or drawings are seen to be the largest values given. SpiroS6 has suggested that smaller values of ionic radii deduced from van der Waals radii might be more appropriately used in aprotic nonaqueous solvents in place of the larger Robinson and Stokes values. It is of interest to note that the hydrodynamic radius, Rs, calculated for Me4N+from eq 2, Rs = 2.76 A, is only 0.09 A larger than an ionic radius deduced for this ion from crystal structures by Hepler, Stokes, and StokesSS6 The data of Table I11 show that the ionic conductances of the tetrahedral cations decrease with increasing number of carbon atoms in the alkyl chain. The regular decrement in conductivity in going from methyl to ethyl to propyl derivatives does not suggest any unusual interaction of the Me4N+ion and solvent dipoles, as might be expected because of its greater charge density and as was found in dimethyl sulfoxideaZ6However, a glance at column 6 of Table V which is a measure of dX:/dT reveals that the mobility behavior of Me4N+is more like that of an anion (known to be solvated in SOz) than like the other R4N+ ions. The difference in the ionic conductivities found for the Me4N+and PhMe3N+ions parallels that found for the , ~ ~and 10.7, respectively. The bulky ions in f ~ r m a m i d e12.5 phenyl group both increases the effective hydrodynamic radius of the ion and, perhaps, interacts with SO2, a Lewis acid. Little difference in ionic conductivity is found between Bu4N+and the (i-Am)4N+ions as would be expected since they must possess essentially the same hydrodynamic radius. For the ion, substitution of a hydrogen atom for an isoamyl group could lead to a decrease in the hydrodynamic radius and consequent increase in mobility. The possibility of increased interaction with the solvent through either hydrogen bonding or increased ion-solvent
r%Yi
Figure 2. Ion mobilities against reciprocal crystal radius, symbols as in Figure 1.
dipole interaction because of the higher charge density of (i-Arnl3NH+over (i-Am)4N+must be prevented by the presence of the remaining bulky isoamyl groups. The tetraphenyl cations, Ph4As+and Ph4P+,should be roughly the same size in solution, but since rcov(P)= 1.10 A is less than rcoV(As)= 1.21 A37 a difference in ionic mobility is expected. The ionic conductivities of the Ph4As+ and (i-Am)4N+ions are nearly the same, as in a ~ e t o n i t r i l e 55.8 , ~ ~ and 56.0, respectively. Since we can assume negligible interaction between the well-shielded (i-An&N+ ion and solvent molecules it would appear that there is none between the Ph4As+ion and solvent as well. The phenyl groups introduce no different interaction. The ionic conductances of the halide ions in SOz at 273.15 K parallel those in DMSO at 298.15 K, 24.0, 23.6, 23.4, from C1- to I-. The order given, C1- > Br- > I-, is usually interpreted as evidence for nonsolvation, but considerable independent evidence exists for S02-anion interaction. From a study of partial molar ionic volumes in SOz, Tokura et al. concludedlO that anion-solvent interaction is strong in SOz. In addition, association constants of charge-transfer complexes of halide ions and SOz have been determined in acetonitrile, water, and methanoL6 In our investigation, the position of the halide ions
TABLE V: Walden Productsa
so2 273.15 K
ion Me ,N+ Et,N+ Pr,N+ Bu,N+ Am,N+
c10,Pc-
c1Br-
1-
xp
H2O 298.15 K
273.15 K
xp
87 70 62
0.447 0.351 0.282 0.250
0.363 0.314 0.258 0.232
142 123 90.6
b 0.279 0.413 0.443 0.461
109 66 127 125 124
0.439 0.266 0.512 0.504 0.500
0.350 0.218 0.409 0.399 0.381
137 85.3 160 156 149
0.256 0.292 0.260 0.248 0.202
111
hP7)
hi%
Units of h f : mho cm'lequiv.
Units of
7):
poise.
101
h?
24.1 16.4 11.5 9.6 8.8 36.9 15.1 41.0 42.6 41.4
- kp,273)/hp.273.
(hf929*
298.15 K
vll
hC7)
xp
0.431 0.293 0.206 0.172 0.157 0.659 0.269 0.733 0.761 0.740
0.400 0.290 0.208 0.173 0.155 0.600 0.271 0.680 0.695 0.684
44.9 32.6 23.4 19.4 17.4 67.4 30.4 76.4 78.1 76.8
Behavior of Tetrahedral Ions in
The Journal of Physical Chemistty, Vol. 84, No, 22, 7980 2951
SO2
TABLE VI: Thermodynamics of Dissociation
I
Me,NCl
Me,NBr Me,NI Me,NC10,
Figure 3.
The variation of
30 I / T IO3/('K-')
4.0
log 10Kdwith 1 / T .
on the Stokes' law plots for both temperatures, with the X?Q values closer to the stick than sli,p values with C1-, the smallest ion with the greatest charge density, the "stickiest" ion, furthers the anion solvation thesis. The behavior of the halide ions will be discussed more fully in a subsequent paper on spherical ions. The Walden products for the (YO4-, BF4-, and Pc- ions lie almost on the Stokes' stick line as; expected for anion solvation. The Walden products, &OQ, for all ions for which we have data at 273.15 and 208.15 K in both H20 and SO2solutions are presented in Table V. The WaXden products for all ions decrease with increase in temperature for SO2 solutions, but not for H20 solutions. In the SO2solutions the change in X?Q is particularly large for Me4N+,about 19%, and decreases as the size of the R group increases, perhaps disappearing at (n-b~m)~N+ or Hex4N+ions. For aqueous solutions only for the Me4N+is there a change. For the anions the changes in Walden product are about 20% in SO2solutions and about 9% in aqueous solutions. We note that the change for the Me4N+ion i s about the same as for the anions;, -20%. It would appear that not only are anions solvated, but cations are alslo. Kay has recently shown that in the solvents H20, MeOH, CH,CN, and HCONH2quaternary ions larger than E t a + show negative deviations from the Stokes' slip line which get larger as the ion gets larger.?* The same ions in SO2 all display positive deviations. These negative deviations in the other solvents are pierhapal explainable on the basis of ionic retardation cawed by dielectric relaxation of the solvent and hydration effects on true ionic size. I[n SO2 solution these negative deviations never appear, but, dielectric relaxation of solvent must occur and, if the Walden products are to be believed, solvation exists. The solvation (ion-solvent interaction) rnust have been of such a type as to compensate for dielectric relaxation retardation. Solvation effects are of ti limited number of types, among them local dielectric constant changes, local viscosity changes, hydrophobic hydration where possible, and acid-base effects. Local dielectric constant changes are ruled out because of the success of the Bjerrum model in interpreting ionic association in SO2. ,4local viscosity decrease as perhaps would accompany a local structural breakdown would serve to keep the mobility high. There is some evidence from X-ray studies" that SO2 has a degree of order. More data on temperature dependence is needed. Ion Association. 'Values of dissociation constants, Kd, and thermodynamic functions for dissociation are pres-
104Kd,a AGO, cal/ mol/ mol dm3
247.57 254.16 262.60 273.38 298.15 264.22 273.27 298.15 264.25 273.33 298.15 247.57 254.16 262.60 273.38 298.15 273.33 298.15 273.15 298.15 273.31 298.15 273.15 298.15 273.15 298.15 273.31 298.15 273.15 298.15 273.15 298.15 273.15 298.15
23.01 18.94 15.47 10.05 5.52 14.68' 11.45' 5.95b 16.76d 14.10d 7.63b 12.92 12.04 9.67 8.41 4.36b 20.56d 10.81b 24.6ge 13.93b 22.78d 11.47b 36.33 16.08b 51.43 18.55b 36.29 20.10b 72.25 26.74b 66.14 36.63b 30.90 13.7gb
K
' o o l -
34
temp,
Me,NPc Et,NCl Et,NBr Et,NI Pr,NBr Pr, NI Bu,NBr Bu,NI Bu,NPc
2990 3170 3380 3750 4440 3430 3680 4400 3360 3570 4250 3270 3409 3620 3850 4580 3360 4050 3260 3900 3300 4010 3060 3810 2860 3730 3050 3680 2680 3510 2720 3320 3140 3900
AH', cal/ mol
AS", eu
-4310
-29.1
-4170
-28.7
-3630
-26.4
-3170
- 25.8
-4190
- 27.6
-3710
-25.5
-4470
-28.5
-5100
- 29.9
-6600
- 34.6
-3850
-25.3
-6430
- 33.4
-3830
- 24.0
-5220
- 30.6
a Values of lo4& are from this report unless otherwise indicated. Reference 11. ' Reference 40. Reference 1. = Reference 15.
ented in Table VI for all tetrahedral ionophores measured at two temperatures in this work and by Tokura's gr0up.l' For the two salts studied over the widest temperature range, Me4NC1and Me4NC104,log Kd is seen in Figure 3 to be a linear function of T1. Linear correlation coefficients were calculated and are included in the figure. Accordingly, it is assumed for all ionophores reported that both and Asd do not vary significantly over the observed temperature range. For the two salts, Me4NCl and Me4NC104,A",was evaluated from the slopes of the plota by the method of least squares, for all other ionophores by the Gibbs-Helmholtz equation. A& was evaluated from the standard thermodynamic relation. Especially to be noted are the negative entropies of dissociation. The decrease in entropy of dissociation observed in every case is interpreted to mean that the decrease in entropy of the solvent due to the greater ordering of the solvent molecules by the free ions (relative to that by the associated ion pairs) exceeds the increase in entropy accompanying the dissociation of the unsolvated ion pair into free unsolvated ions. This greater ordering of the solvent molecules by the free ions must be largely attributed here to the anions of these quaternary ionophores. However, since X-ray studiesb indicate that SO2 is an ordered liquid, the free, separated, bulky cations might disorder the solvent less. Of the anions used here, the halide ions are known to be strongly solvated in SO2,and picrate ions are expected to interact strongly with solvent SO2because of dispersion forces (vide infra) and the picrate ion dipole.b As a general rule, in SO2 quaternary ammonium salts tend to be highly dissociated because of the low surface
2952
The Journal of Physlcal Chemlstty, Vol. 84, No. 22, 1980
charge density of the bulky cations. Previous publications in this series'4J6 have established that the application of the Bjerrum model to conductance data of ionophores in SOz yield Bjerrum a values, interpreted as averaged ion pair center-to-center distances, which fall within 0.2 8, of the sum of appropriate estimated ionic radii. This has been shown to be particularly true for the alkali halides, tetramethylammonium halides, and even certain tetraethylammonium halides, all of which would appear to be composed predominantly of contact ion pairs. For the PhMe3N+ halides dissociation constants presented in Table I1 increase with increase in anionic size from chloride to iodide and Bjerrum a values are quite close to sums of ionic radii. Evidently the charge density of the cation is sufficiently large to permit penetration of the solvation sheath of the corresponding halide ion. As cation size increases and charge density decreases this ability to penetrate the anion sheath is seen to diminish. We have previously reported for Et4NC1and Et4NBr 104K,'s of 24.7l and 22.8,13 respectively. To these we now add 104Kd= 35.3 for Et4NI. Tokura et al. found the same order at 298.15 K, lo4& of 13.9,11.5, and 16.1 for the chloride, bromide, and iodide, respective1y.l' This order for Kd, I > C1> Br, is understandable if it is assumed that the tightly held solvent sheath of the chloride ion (formed predominantly by ion-solvent dipole interaction) resists penetration by the cation, but the less tightly held bromide ion sheath permits penetration and the creation of a tighter ion pair with a lower dissociation constant. In the case of the iodide ion, the most polarizable halide ion, we have, in addition to the ion-solvent dipole interaction, a large dispersion energy contribution to the solvation energy.5 The usually high solubility of iodide salts and the intensity of the color of iodide solutions in contrast to the feeble color of solutions of the other halides can be interpreted as caused by these large dispersion forces. The result is a tightly held solvent sheath, low charge density, less tightly held ion pair, and a large dissociation constant. Kd values for the Pr4N+salts fall in the same sequence as for the Et4N+salts, but the small value of the difference of &(I) - Kd(BI') presaging an impending bromide-iodide inversion should be noted. Also the fact that Kd for the chloride is almost equal to that of the iodide is indicative of diminishing cation charge density. In the Bu4N+series the chloride proved to be too hygroscopic for effective handling, but inversion of the values of Kd for bromide and iodide emerges: &(Br) > &(I). The charge density of the cation has diminished to the point that penetration of the solvent sheath of the bromide ion is not possible and the results for the (i-Am)4Nt series substantiates this view. The data for (i-Am)3NHBrare striking and important. Substitution of the much smaller H atom for the isoamyl group reduces the hydrodynamic radius of the cation, leading to a corresponding increase in its limiting conductance over that of the Bu4N+and (i-And4N+bromides. A preferred orientation of the cation with respect to the anion, one closer to the anion, arises because of the possibility of hydrogen bonding to the anion or to its solvent sheath. In fact, the dissociation constant of the (iAm)3NHBr is less than that of the (i-Am)4NBrby a factor of 32, and the Bjerrum a value is within 0.2 8, of the sum of the radii of N-H and Br-.
Lichtin et al.
The picrates are seen to be less highly dissociated than the corresponding halide ion pairs. This increased stability of the picrate ion pair has been attributed to the increase in the interionic attraction force contributed by the charge-picrate dipole interaction over the normal charge-charge interaction which would primarily exist in the corresponding halide ion pair^.^^^^^ Acknowledgment. This work was supported by the National Science Foundation under Grant No. GP 4023. Supplementary Material Available: Equivalent conductance data are listed in Table I (2 pages). Ordering information is given on any current masthead page.
References and Notes Lichtin, N. N.; Pappas, P. Trans. N . Y . Acad. Sci. 1975, 20, 143. Waddington, T. C. "NmAqueous %vent Systems"; Academic Press: New York, 1965; p 253. Tokura, N. Synthesis 1971, 72, 639. Lichtin, N. N. "Carbonium Ions"; Olah, G. A.; Schleyer, P. von R., Eds.; Interscience: New York, 1968; pp 135-151. Burow, D. F. "Chemistry of Nonaqueous Solvents"; Logowski, J., Ed.; Academic Press: New York, 1970; p 305. Zingaro, R. A. "Nonaqueous Solvents"; D. C. Heath Co.: Boston, MA, 1968; p 128. Kuo, C. H.; LI, K. Y.; Yaws, C. L. Chem. fng. 1974, 7 7 , 88. Holiiday, A. K.; Nicholis, D. fduc. Chem. 1974, 87, 85. Lichtin, N. N.; Wasserman, 8. Polym. Prepr. 1968, 9(2), 1056. Tokura, N. Bull. Chem. SOC.Jpn. 1972, 45, 871. Tokura, N.; Takezawa, S.;Kondo, Y. J. Phys. Chem. 1973, 77,2133. Tinker, L. A.; Bard, A. J. J . Am. Chem. SOC.1979, 707, 2316-9. Lacaze, P. C.; Dubois, J. E.; Delamar, M. J . Nectroanal. Chern. Interfacial Electrochem. 1979, 102, 135-7. Lichtin, N. N.; K h a n , H. J . Chem. fng. Data 1963, 8 , 178. Lichtin, N. N.; Puar, M. S.;Wasserman, B. J. Am. Chem. Soc. 1967, 89, 6677. Lichtin, N. N.; Vignale, M. J. J . Am. Chem. SOC.1957, 79, 579. Lichtin, N. N.; Bartlett, P. D. J . Am. Chem. Soc. 1951, 73, 5530. Lichtin, N. N.; Glazer, H. J . Am. Chem. SOC.1951, 73, 5537. Cox, R.; Kraus, C. A.; Fuoss, R. M. Trans. Farao'ay Soc. 1935, 37, 749. Coetzee, J. F.; Cunningham, J. P. J . Am. Chem. Soc. 1964, 86, 3403. Coetzee, J. F.; Cunningham, J. P. J . Am. Chern. SOC. 1965, 87, 2529. Shedlovsky, T. J. Franklin Inst. 1038, 225, 739. Davies, C. W. "Ion Association"; Butterworths: Washington, DC, 1962; p 130. Robinson, R. A.; Stokes, R. H. "Electrolyte Solutions"; Butterworths: London, 1959; p 125. Pauling, L. "The Nature of the Chemical Bond", Cornell Unlversity Press: Ithaca, NY, 1940; Chapter X. Arrington, D. E.; Griswoid, E. J . Phys. Chem. 1970, 74, 123. Wasserman, B. "Equilibrium and Kinetic Studies in Liquld Sulfur Dioxide", Ph.D. dissertation submitted to Boston University, 1969. Kay, R. L. "Water, A ComprehensiveTreatise"; Frank, F., Ed.; Plenum: New York, 1973; Voi. 3, Chapter 4. Boyd, R. H. J . Chem. Phys. 1961, 35, 1281. Zwanzig, R. J. Chem. Phys. 1970, 56, 3625. Fernandez-Prini, R.; Atkinson, G. J . Phys. Chem. 1971, 75, 239. Smyth, C. P. "Dielectric Behavior and Structure"; McGraw-Hill: New York, 1955; Chapter IV. Conway, B. E.; Bodvis, J. O'M. "Modern Aspects of Electrochemistry"; Plenum: New York, 1972; Vol. 7, p 62. Krumgaiz, B. Discuss. Faraday SOC.1977, 64, 337. Spiro, M. "Physical Chemistry of Organic Soivent Systems"; Covington, A. K.; Dickinson, T., Eds.; Plenum: New York, 1973; p 615. Heoler. L. G.: Stokes, J. M.: Stokes, R. H. Trans. Faraday Soc. 1965, 6 i , 20.
(37) Gould, E. S."Inorganic Reactions and Structure"; Henry Holt and Co.: New York, 1955; p 452. (38) Inami, Y. H.; Bodenseh, H. K.; Ramsay, J. B. J . Am. Chem. Soc. 1961, 83, 4745. (39) Accaslna, F.; D'Aprano, A,; Fuoss, R. M. J. Am. Chem. Soc. 1951, 81, 1058. (40) Lichtin, N. N.; Leftln, H. P. J. Phys. Chem. 1956, 60,100.
