deuterium isotope effect would be small. The expression thein would reduce to approximately
not inconsistent with the observed stoichiometry. The effect, of NO2 conrentration on the quantities of CO aiid COZ produced is not necessarily inconsistent with the observations of ref. 2, for if k6/ka[KO2] is sufficiently smaller than k6/lc3, as [KO,] is increased the ratio CO/C02 becomw decreasingly senhitive to extent of reaction and to NOz concentration, More data are required o n the changing stoichiometry with extent of reaction at low NO, concentrations The mechanism presented does not account for the variation in "second-order rate constant" with reagent ratio (Table 11).
Mechanism steps similar to I, 3 and 5 in the above mechanism were proposed by tho ma^.^ A chain mechanism for the oxidation of CHzO by 02 has been proposed by Scheer.'O Some thermodynamic quantities appropriate to the mechanism may be found in ref. 11 and 12. Acknowledgments.-The author wishes to acknowledge t'he advice and suggestions of Professor R. B. Bernstein throughout this work. The financial support from the Alfred P. Sloan Foundation and the U.S.A.E.C., Division of Research, is appreciat'ed. The author thanks Leslie B. Sims for criticisms. (10) & D. I. Scheer, "Fifth Symposium (International) on Cornbustion," Reinhold Publ. Corp., New York, N. Y., 1955, p. 435. (11) National Bureau of Standards, Circular 500, 1952. (12) W. A. Rosser, Jr., and H. Wise, J. Chem. Phys.. 26, 571 (1957)
TIIF: SOLGTIOS CONDUCTSSCE OF CY.0?OCA4RRON SALTS1 BY
%CHARD
H. BOYD
Cmtributinn \ o. 887 from thc Central Research l)epadment, Experimental Statzon, E I . du Pont de .%'emours and Company,. H'zlmzngton, Delaware I?ecezzed March 29. 1961
The conduc1,ances of sodium salts of tricyanovinyl alcohol, 1,1,2,3,3-pentacyanopropene, bis-( tricyanoviny1)-amine and 1,1,2,6,6,7-hesacyan0-1,3,5heptatrienehave been measured in water and those of the tetramethylammonium salts in acetonitrile and in acetone-carbon tetrachloride mixtures. The tetramet,hglammonium salt of pentacyanopropene also was studied in nitrobenzene-carbon tetrachloride mixtures. Sodium hexacyanoheptatrienide undergoes reversible dimerization in water as evidenced by the conductance curves and also by its electronic absorption spectrum. All of the salts exhibit normal behavior in acetonitrile with very slight ion-pairing. Ion-pair formation for the cyanocarbon salts in acetonecarbon tetrachloride mixtures is somewhat less pronounced than for comparable salts and solvents reported on in the literature. The ion-pair distance parameters derived from the dielectric constant dependence of the association constants reflect charge delocalization in the anions. Ion pairing has no appreciable influence on the optical spectrum of pentacyanopropenide. The variation of the Walden product ( A o ~ )with dielectric constant is very slight but noticeable in acetonecarbon tetr:tchloride mixtures. The variation for pentacyariopropenide in nitrobenzene-carbon tetrachloride mixtures is comparable to that found previously for other salts. Simplified Huckel-type molecular orbital calculations of the negative charge distrinution in three of the anions were m;tde :ind show estensive charge delocalization.
Introduction The synthesis of tetracyanoethylene and a number of its percymo derivatives recently has been reported.? A number of theqr compounds have the interesting property of tieing acids and forming salts.3 The pirpose of this paper is to report the physical beha1:ior of some of these cyanocarboii anions ill solution. These ions should be particularly interesting since they form a new class in which the negative charge appears to be highly delocalized over the molecular surface. Ileasurenier t of electrolytic conductance u as chosen as the principal experimental means of investigatioii i n view of its generality, precision and theoretical foundation Measurements in water and a number of organic solvents were made. Salts of tricyanovinyl alcohol (TCV alcohol), 1,1,2,3,3-peiil:icyunopropeiie(PCP), his-(tricyanovinyl)-ammf [bis-(TCY)-amine] and 1,1,2,6,6,7hexaryano-l,3 5-heptatricne (HCHT) 11 ere chosen as a wieb rixpresentatne of the various cyanocarbon anions r m eriiig a raiigc of sizes and type. 1) P.i;,er S X I 111 t h e scrles C>anocarhon Chemistry 11)T I Cairns eL al J A m Chem S o c 80, 2776 (19.58) 3 ) (a) W J I T ddlrton L 1 I ttle D D Codriian a n d V 1 Engelhardt zbzd EO, 2705 (1958) (b L3 1% Wileg J K JT illiarns
s s d B C. A l c K u w k
TO
be puhlishtd
Their structures are shown in Fig. 1. Sodium salts were studied in water because of their high solubility. Tetramethylammonium (TMA) salts were qtudied in acetonitrile, nitrobenzene-carbon tetrarhloride mixtures, and acetone-carbon tetrachloride mixtures. F u 0 ~ s 4recently has published a summary of the final version of the Fuoss-Onsager theory of the c*onductunce of symmetrical charge type electrolytes The conductance measurements reported here arc analyzed in terms of that theory. The physieal processes that occur then will be discussed i i i terms of the parameters calculated from the fitting of the theory to the data Experimental Details The conductance bridge consisted of a Leeds and Northrup Co. shielded ratio box (Cat. N o . 1553) and a calibrated General Radio Corp. decade resistance box (Type 1432-N) (together with single 10 k./step and 100 k./step decade resistances t o extend the range). A Leeds and Northrup C o . ( S o . 1185) air capacitor was used for the capacitance balance, 4 Hewlett-Packard Corp. audio oscillator (Type 200.4B) and a DuMont oscilloscope (Type 350-R)(together with a Ballentine Laboratories a.c. voltmeter as a preamplifier) nere used as signal source and detector, respectively. T R Oconductancc cells of the design of Mukerjee, ~t al.,6 (4) R. M. Fuoss, %bid.,81, 2659 (1959).
Oct., 1Nil
1835
SOLUTlOS CON1)UCTrZNCE OF CYANOCARBON SALTS
-
10%-
-7.2%-
z.
‘ ’CT
%
+&/“=“O@
1
II
c t.318
12;
I
TRICYANOVINYL (TCV) ALCOHOLATE r = 3.5% R=3.IA
.
N -.372
I
t 2?7c
m
N N PENTACYANOPROPENIDE (PC P-) r = 4 . 3 i R13.6; -494
12.4 %
15.0%
.
Bi s [TR ICYANOVI N Y L(TCV)l AMI NE r = 4.8i R = 38 ;
HEXACYA NOHEPTATR I E N I DE (HCHT) r = 5.2% R.4.0; of anions studied. Effective charge distributions froni simple LCAO-hlO calculations are
Fig. 1.-Struct,ures shown for three of the anions. T = radius of equivalent disk and K ments on Stuart-Briegleb models.
were used. A oell. consists of two bright platinum electrodes sealed into a Florence flask and contains a “Teflon” polytetrafluoroethylene covered magnetic stirring bar. The volumes and cell constants are 1 liter and 0.07092 and 250 ml. and 0.15050. They m r e calibrated with potassium chloride over the useful concentration range using the conductance data of Shedlovsky, et al.6 The same volume of liquid was used in all experiments with the smaller cell to avoid changes of cell constant with cell content,. The stirring motor can be immersed directly in the oil-bath, a convenience deserving of use in other experiments. The bath was set a t 25“ and controlled to f 0.01’. TMA +/TCV alcoholate- and tetraethylammonium bis(TCV)-amine were obtained as laboratory samples that had been prepared by 1 he methods of Middleton, et al.3and were repurified by recrystallization from ethanol. TMA T / PCP- and NIT, ’H CIIT- were prepared for 11s by the niethods of reference 3, wspectivcly. Aqueous solutions of sodium salts were prepared by making solutions of tho arids by ion exchange by the method of hliddleton, et nl.3 The acids then were titrated potentiometrically with 0.1 .Y KaOH solution. This served both to prepare the salt and to determine its amount’. The conductance measureinents were made by adding increments of the fairly concentrated solution from the titration to thr 1-liter conductancr cell hy means of a weight’ pipet. ThiA+/bis.(TC\*)-amine- and TMA+/HCHT- were prepared from :qimus solutions of the sodium salts by adding an esccss of TllA*,’H-. The precipitated salts were purified by wveral recrystallizations from hot water. TMA salts werc added to the 250-ml. conductance cell dry by dropping in the sample in a small “Tcflon” cup. The samples were weighed to 3~ 1 pg. on a microbalance. Distilled water in equilihrinm wit,h air was used for conduct,ance me:tsrircments and had a specific conductance (K) of 1.5 X IO-6(%cm.)-’. J3astman (yellow label) acetonitrile was redistillrd several times from phosphorus pentoxideand had a of 1 X 10-7(Q-cm.)-1.
-
-
(5) P. Mukerjve, K . Mysels and C. I. Dulin. J . Phys. Chem., 62, 1390 (1958). 10) T . Shedlo\.sky. A . S. Broan a n d T). A . MacInnes. Trans. I:‘/ectrochern. S O C . . 66, I (iA (1934).
=
radius of equivalent sphere from measure-
Acetone (Baker and Adamson, ACS specification) was dried over calcium chloride and distilled from alumina according to t,he directions of Reynolds and Iiraus.7 I t had B K 1 1 7 X 10-8(
Pure Organic Coinpounds,” Elsevier Pub. Co., New York, N. Y., 1950. 4 ‘i YIaryott and E. R. Smith, ref. 9. J,
The visible arid dlrsviolet spectra were measured in a Cary Model 14 recording spectrophotometer. The experimeiital values of equivalent conductances and concentrations in the various systems are listed in Table
11.
A = equivalent conductanre; AD, its value a t infinite
S
dilution
= a f AoB (“Onsager” slope) = EiAo - Et = vi& -t 02
E J c = molar concentration
TABLE I1 EQUIVALENT CONDUCTANCE DATA,25’
-rr
cx
11
10‘
tir,i:l t ?---
mtration T Y W R 4 . 7 : a :c. : ( I ' .w. i r w
84.607 77.384 73.931 68.638 64.310 60.573
Nitrobenzene-carbon tetrachloride
0.4676 c x 104 2.0093 4.0978 6.1600 10.5810 14.4684 20.6157 tetrachloride.
1.0027 2.0360 3.0047 4.9731 7.0345 10.100
cx
10'
0.9588 1.9061 2.8637 4.7507 6.6402 9.4884
0.6241 ' I
39.529 37.941 36.757 34.997 33.675 32.130
cx
10'
1.0798 2.2246 3.4976 5.9497 7.8757 11.0295
13.68 A
37.832 35.388 33.482 30.897 29.448 27.649
the conductance results for aqueous solutions of soaps, such as lauryl sulfate.6J2 The authors of rtlferences 5 and 12 review arguments for believing that dimerization is the only reasonable type of ion association to account for conductance greater than expected for a normal electrolyte. Furthermore, aqueous solutions of ionic dyes are believed to undergo extensive dimerization and higher nggrcgation.13 Naturally the effects of this beharior on the optical absorption have been more thoroughly stiidicd in these compounds than on t,ht. dectrolvtic. cwiductance. However, equivalcnt conductanre behavior similar to that of S a + HCHT- has been found in aqueous solutions of several dyes. l 4 Further evidence for dimerization comes from tlie elecatronic spectrum of Ka+HCHT-. This shows the presence of a band a t iiitermediate conrentration (- 10-8 M ) not present in very dilutr M ) (see Fig. 4). Sa+HCIfTsolution (-shows deviations from Beer's law for the principal ahsorption a t 635 mp that can be explained by a dimerization equilibrium. With the assumption that only the monomer absorhs a t this wave length anti that its concentration is controlled by the (13) P. Mnkerjee, J . Phys. Chem., 62, 1401 (1958). (13) 'rhere is an e-.tensi\e literature on this phmomanon 7Ve a i U cite only thr awellent earlv study of E Itahinowitch and F. ?,patein [ J A m . ('hem. Roc 63, 69 (1941iI Ser also T Forster. A n n irn ! ' h v s ('h-m., 19.57, Annual R e \ v u s . i n c Palo h l t o Calif.,
-.
Io- i w e n t H mk. 114) C . Robinson and 11. 3. Garrett, Tvnnv Porodoy Rx.. SP, 771 (1Q W ) I
RICHARD H. BOYD
1838
I
I
I
I
I
82t
I
-I
JFX
Vol. 65
Xdl
Fig. 4.-Visible ultraviolet spectra for cyanocarbon anions [tricyanovinyl (TCV) alcoholate, pentacyanopropenide (PCP-), bis-tricyanovmyl-( TCV)-amine and hexacyanoheptatrienide (HCHT-)] in water. Molar extinction coefficient, C, of HCHT- is plotted on scale a t right, others on left. Dashed line for P C P - is for acetone-carbon tetrachloride mixture. Dielectric constant was 10.31.
150
to:
Fig. 2.-Equivalent conductances of sodium mlts of cyanocarbon anions [tricyanovinyl(TCV) alcoholate, pentacyanopropenide ( PCP -), bis-tricyanovinyl-( TCV)-rtmine and hexacyanoheptatrienide (HCHT-) 1 in water a t 25.00' plotted against square root of concentration (mole/l.). Short dashed curve is a calculated curve allowing for presence of dimerization. Long dashed lines show Onsager slopes.
1
APPARENT EXTINCTION COEFFICIENT I C - I W FOR 7 4 9 I: IO" Y O L I R l
vs
8 C
I
140 t . 130
120
110
0
5
15
10
G
x 10-1. of anion dimerization constant for Z
Fig. 5.-Determination hexacyanoheptatrienide (HCHT-) from plot of e us. s*c, e = apparent extinction coefficient at 635 q and c = stoichiometric concentration (mole/l.).
anion dimer, it can be shown that e = eo
-
(F)
e*c
where is the apparent extinction coefficient at 635 mp is the true one for monomer e is concn., moles/l. e
€0
A plot of e2c us. r should be a straight line of slope 2K/eo and intercept eo. It is seen in Fig. 5 that such a plot does give a good straight line. K i s found to be 217 l./mole and eo = 138,000. The I 81.0 IO 20 dimer band at 568 mp is poorly resolved, and CXIO' (rn/l). analysis of the absorption a t that wave length inFig. %-A' = A + SC''; - Ec log c plotted against square volves much greater error. However, analysis root of concentration (mole/l.) for Na+/tricyanovinyl (TCV) correcting for monomer absorption a t 568 mp inalcoholate-, Na +/pentacyanopropenide (PCP-) and Na +/ dicates an equilibrium constant of 500 l./mole bis-tricyanovinyl- (TCV)-amine. and e (dimer) = 104,OOO is indicated. The difference in K's from the two bands probably is due to equilibrium the assumption of no dimer absorption a t 635 mp. 2A- t-)14Allowance for some dimer absorption here would result in a higher K and still give a straight plot. An attempt was made to calculate the conductwhere A- is the anion monomer and Az- is the ance behavior of Na+HCHT- from the measured I
-
SOLUTION CONDUCTANCE OF CYANOCARRON SALTS
Oct., 1961
1839
K in the manner of Mukerjee, et aLs The simple Onsager theory was used, and suitable values for the equivalent conductance of the monomeric and dimeric anions were chosen. Figure 2 shows {dotted line) a calculated curve using &- = 28.1, Xo- = 1.47 &- and K = 500. This somewhat higher value for K than found from the Beers law deviation ‘of the monomer was required. Even so, the calculated conductance does not continue to rise as f;ast as the experimental curve. No effects on the electronic spectra of the otther salts were noticed, ie., they obey Beer’s law and no additional bands were found. This is consistent with the normal conductances. The cause of the dimerization is interesting to speculate on. Apparently it is an example of the type of dimerization taking place in ionic dye solutions. It is the result of unusually high intermolecular forces, (van der Waals in nature) that exist in moleculles that are also very strong absorbers in the ultraviolet and visible regions. The high dielectric constant of water results in a ratJher moderate electrostatic repulsion energy so that stable dimers can form. The three anions that show no dimerization are moderately strong absorbers (see Fig. 4). HCHT- is a very strong absorber (Fig. 4),and it shows pronounced dimerization. The dimer band a t 568 mp apparently is an example of an “IH”band as described by West and Carroll.l5 The dimer absorbs a t a different frequency due to resonance interaction between excited and unexcited molecules in the dimer. The cyanocarbon salts thus provide a striking demonstration 01the correlation between electronic absorption and aggregation. The salts studied are similar in cherriical structure and size and shape. But only the very strong absorber, HCHT-, shows pronounced dimerization. 2. Behavior ‘of Tetramethylammonium Salts in Acetonitrile.-The tetramethylammonium salts in acetonitrile behave normally, and the A’ plots are straight lines giving reasonable values of the distance parameter UJ (see Table 111). However, the UJ (except for HCHT) are somewhat smaller than indicated by the behavior in the other organic solvents indicating some slight association is probably present (see the end of Sec. 3). Thus, in a solvent like acet>onitrile( D = 36.0) the dielectric constant is low enough that anion dimerimlion is effectively prevented through increased elec t h static repulsion. The dielectric constant is high mough, however, that ion pairing betwcrn anion and cation is ve.ry slight,. The A9 values are listed Table V and are discussed separat,ely under 4. Lind arid l k o s s * l find negligible associat,ion for TF:t,hyLI +,;PC;P- and his-(TCV)-rtminr in acet,oilit,rile which is consistent, with our rtsults asslImIng the larger size of the TEt,hylA+ion niduces thr :issociation from very slight to negligible. 3 , The Behavior of Tetramethylammonium Salts in Acetone-Carbon Tetrachloride and Nitrobenzene-Carbon Tetrachloride Mixtures. Ion Pairing ---.‘‘The conduct,ance data in “XI? ontedby hand with the I’uoss “y - 2’’m e t ’ h ~ d . ~ The agreement, between the methods was good. S o correction was made for the effect of solute on jolveiit viscosit,y. The distance parameter in the Debye-Huc-kel activity coefficient term was takcn (L priori to be 6 8. In pure acetone the ion-pair association constant, K , was found to be slightly negat,ivc for the salts, except TMA+:TCP alcoholate--. Therefore, the results were recomput’ed with K , constrained to be zero. The results for TMA+/TCP alcoholate- in pure acetone and ‘ThI A+; PCP- in pure nitrobenzene were ocnlculatctl by hand assuming UJ to bc fised at 6.5 A., a value infcrnd from the results a t lower dirleot,ric constant, xvhorc thc swxiation is more pronounccd and both Ka and a~ can hc calrulatd with highcr accurary. This procedure swms justified ;ts t,hc IC’, valucs a s d d a t e d agree mcll with rstrapola.t>ion of K , from lower dielectric (*onstant mixtures. T h r associalion c:onstant.s, ICa, and t,hc ,I par:imp”:>r (along with a.r) arc listrd iii Tabk 111. Thr ~ x l i i w of thr limitling condiict’ances, iio.u p lisitctd i i : T:thli? 1-and are discussed in t>hrnext, section. We are inter&cd i n the iriflucucc of the ( y i i i o carbon anion struct,iire 011 ion-pair T h tlniori chargC is r s p ! v . t r d t r t highly deiocdized, resul t,ing i 1 1 dwrc3a sod c~lrct~rwt ntic :it 1,r:tction l)c%wwti anion :~ndcat ioii at :I givrii d i st a n w . I1ovicvcr : t IF w p r c i c d fl :it st r 11 tu r w \vt>\iid mak(>close appro:icl: dist,a,ncrs possil)lr, x ( 8
siit+irig
iii
r:tt,hvr high c>!rctrosta.tic* att’i,:irt,ir:1!.
RICHARD H. BOYD
1840
D
---TCV K.
... 20.61 15.18 13.47 12.19 10.31 36.0
(47.21 234.7 533.1 4633
...
ION PAIR alcoholat J x lo-' e a d . ;
0.0315
7.2
Vol. 65
TABLE I11 ASSOCIATION CON6TANTS AND ION SIZE FROM J(a), 25" ' K.
...
PCP -Bia-(TCV)-arnine--HCHTx IO-* a~(A.j K. J x 10-4 w(A.) K. Sodium salts: Water 0.025 6.0 0.0270 7 . 3 J
...
Tetramethylammonium salts: Acetone-carbon tetrachloride mixtures (1.553) (6.5) ... 1.423 6.5 ... 1.317 6 . 5 2.931 6.5 54.8 2.475 5.5 4.012 7.1 137.4 3.360 5.9 124.3 3.246 6.2 442.9 4.468 6.6 214.7 4.009 6.2 8.467 9.7 2179 7.434 8.4 945.5 6.091 6.8 0.221
4.1
Acetonitrile" 0.203 3.9
...
...
0.205
4.4
J
x
10-4
a~ (A.)
...
...
..
...
1.182
6.0
53.0
3.031
6.4
6.082
7.6
0.264
6.8
863
...
Nitrobenzene-carbori tetrachloride mixtures* 34.69 (10.7) (0.0660) (6.5) 18.90 106.1 0.3060 5.6 15.80 331.3 0.7311 7.4 13.69 631.8 1.030 6.4 a The values of dielectric constant, viscosity and density used in the computations are those reported by F. ,Qccascina, S. Petrucci and R. M. Fuoss, J . A m . Chem. Soc., 81, 1301 (1960). b The values of dielectric constant, viscosity and density used in computation were interpolated from data reported by H . Sadek and R. M. FUOSS,ibid., 76, 5905 (1954). The parameters enclosed in parentheses indicate calculations made with a fixed value of a ~ .
By means of log Ka tis. 1/D (D = dielectric constant) plots and comparison with other systems, some conclusions can be made. Figure 6 shows such a plot. Appropriate data for comparison are not plentiful, but the picrate ion (Pi-) has been studied. It is similar in size and shape, although not necessarily in charge distribution, to the cyanocarbon anions PCP- and bis-(TCV)-amine -. Values of Ka for TMA+/Pi- in pure acetoneM and pure nitrobe~izenel~ are shown in the figure. Tetrabutylanmonium picrate (TBA+/Pi-) has been studied in nitrobenzene-carbon tetrachloride mixtures,'* and the results also are shown. Presumably for TMA+/Pi- in nitrobenzene-carbon tetrachloride mixtures the curve would be similar but lying above the TBA+/Pi-(CeH6NOZ-CCL) curve by an amount suggested by the single measurement in pure nitrobenzene shown. The picrate ion behaves similarly to ions such as bromide, iodide and nitrate.ls Thus it may be seen that association in the cyanocarbon solutions is somewhat less pronounced than for other ions that have been studied. However. it is seen that the lower Ka values for cyanocarbons are not simply a matter of lower slopes. TMA +/PCP- in acetone-carbon tetrachloride, for instance, has a higher slope in the same dielectric constant range than TBA+/I'ibut a lower K . It may also be noticed that the Ka values for TMA+/PCP- are higher in nitrobenzene-carbon tetrachloride than in acetone-carbon tetrachloride and the slopes are slightly different. The Ka valucs for the four cyanocarbon salts in the same solvent are in the order expected on the basis of size, but the slopes of the log K , us. 1/D plots do not appear to behave in a simple manner. Table IV shows the a~ (ion pair contact distance) (16) M. J. Mcl)oweil and C. A. Kraris. J . Ani. Chem. Soc., 73, 3293 (1951). Their datn mere recalculated rising the complete Onsnperk'uoss theory with the computer. The n e w X a value is us. 89
71.2
calculated by them. (17) E. G. Taylor arid C. A. Kraus, cbd.. 69, 1731 (1947). (18) E. IIirsch and R. M. Fuoss, tbtd., 89, 1018 (19601.
values calculated from the slopes of the log Ka vs. 1/D plots, and the relation slope = s2/2.303a~kT which holds for spherical ions in a continuous medium. It is not immediately clear to what molecular distance this should be compared for a flat ion such as a cyanocarbon. One extreme would be to compare it with the radius of the TMA ion , plus the radius calculated from ( 3 / 4 ~ V ) ' / ~where V is the molecular volume found from models (Stuart-Briegleb). The other extreme would be to use the contact distance of the TMA ion against a point on a flat face of the anion (that is, 3.5 A., the radius of TMA+ 1.6 A., the half thickness of s electron orbitals or less). Distances calculated by these two methods also are listed in Table IV. Calculations likewise are included for TBA+/Pi-(C,H6N02-CCl.J. It seems physically unreasonable to identify the distance a~ calculated from the slopes with contact a t a point since the U K are comparable to or larger than the contact distance ( 2 5.1 A.). Work on other ions has given distances from slopes that are consistently smallpr than those found from models.1s-20 Thus, it is fair to conclude that the ion-pair configuration is not one of contact of the cation a t a point of localized charge on the anion. This conclusion is, of course, consistent with the supposed delocalized charge in these anions. The first approach above (average distances from volumes) gives distances which a t least in the case of PCP- seem to be too large in comparison with U K . An alternative method of calculating the pair distance, instead of assuming point charges in spherical ions ( a K ) , would be to assume an idealized model where the cation is a sphere with a point charge a t the center but on the axis of the center of a thin circular disk that is uniformly charged. Distances ( a ' K ) can be calculated by equating t,he clectrostatic attraction energy of this configura-
+
(19) H. Sadek and R. M. Fuoss. ibrd., 81, 4507 (1959). (20) D. 8. Berns and R. M. Fuoss,%bad.,89, 5585 (1960).
SOLUTION CONDUCTANCE OF CYANOCARBOS SALTS
Oct., 19G1
tion with 2.303kT X :(slope of the log Ka us. 1/D plot). The distances calculated in this way (a'=) are listed in Table IV. This model seems more physically reasonable than the one with contact at a point with localized charge since it gives distances that are either comparable to or less than the contact distance from models (5.1 A.).
I
0.41
TCV ALCOHOL-
T a m IV
.-
ION PAIRDISTANCE PARM~ETERS~ (IN A.) Acetonecarbon tetrachloride mixtures Salt
aK
TMA +/TCV alcoholate- 5.78 TMA+/PCP4.53 TMA+/bis-(?'CV)-amine- 6.21
&el
6.6 7.1 7.3
&on
