J. Phys. Chem. 1990,94, 6073-6079
6013
nation of the models ii-iv, models v and vi were tried. Model v leads to singular results for OAC and OAB, due to involvement of only two atoms viz., O(3) and C(8). On the other hand, for OPR and OBZ significant reductions in R, factor with reliable RMSLA values were obtained. The results from model vi are similar to that of v (Tables 6-7). Proximity and the consequent enhanced interaction leading to bond formation between N ( l ) and C(8) can be achieved either by libration (rotation) about the C(l)-C(7) bond (model i) or the C(2)-0(2) bond (model ii) or both in combination. In this connection it is important to note that the contribution from model ii is quite significant while that from model i is small. This trend perhaps indicates that the torsional librations about the C(2)-0(2) bond play a more prominent role than those about the C( 1)-C(7) bond during the reaction. Further, the role of models v and vi in combining the individual librations and in bringing the C(8) toward N( 1) is noteworthy. Figure 2. Schematic representation of the axes of libration used in the non-rigid-body analysis.
only to OPR and OBZ as evident from the significant reduction in R, and Z values and the reliable RMSLA values in these two cases. When possible combinations of the above models were attempted, one of the two problems mentioned earlier was encountered, despite significant reduction in R, and 2 values. To circumvent this difficulty and yet simulate the effect of combi-
3. Conclusion The thermal motion analysis of the reactants has indicated large internal motion between C(8) and N ( l ) and has suggested that the torsional libration about the C(2)-0(2) bond is apparently responsible for the observed solid-state reaction. Thus, despite the use of rmm temperature data with ADPs of limited accuracy and the inherent limitiations of the method, the results of the analysis are consistent with a plausible mechanism of the solid-state reactions as deduced from X-ray crystallographic studies.
The model docs not give reasonable agreement only for the ADPs of N(I) atom in the case of OBZ.
Acknowledgment. We thank Professor K. N. Trueblood for useful comments and suggestions. We acknowledge the valuable and encouraging comments of the referees.
(26)
Triple Ion Formation by the Hydrogen-Bonding Force in Protophobic Aprotic Solvents Masashi Hojo,* Akihiro Watanabe, Taiji Mizobuchi, and Yosbibiko Imai Department of Chemistry, Faculty of Science, Kochi University, Kochi 780,Japan (Received: August 14, 1989; In Final Form: January 5, 1990)
A large deviation was observed between the observed value of the equivalent conductivity (AoM) and the calculated value (Aaid) only with ion-pair formation constant ( K , ) for tributylammonium chloride (n-Bu3NHCI,(0.4-6.0) X IO-' M) in nitrobenzene and benzonitrile. The error was completely corrected by the symmetrical formation of triple ions (2M + X e M2X ( K 2 ) ,M + 2X a MX2 (K3),K2 = K,, where M = n-Bu3NH+,X = Cl-): K, = 2.65 X lo6, K2 = K3 = 1 . 1 X IO9, -2.0 to +1.6% in nitrobenzene; K , = 2.45 X IO6, K2 = K3 = 4.5 X IO8, -0.8 to +OS% in benzonitrile. In acetone, the triple ion formation constant was smaller ( K , = 1.85 X IO6, K2 = K 3 = 1.5 X lo8) than that in the above two solvents. Even in propylene carbonate with a high dielectric constant (c = 64.4), the triple ion formation could be observed to some extent. On the other hand, only the ion-pair formation corrected by the activity coefficients of simple ions explained the conductivity data in ethanol which is a hydrogen bond donor and acceptor. As for anions, the ion-pair formation constants of tributylammonium halides decreased in the order CI > Br > I, and so did the triple ion formation constants. The triple ion formation from the iodide was very small even in nitrobenzene. The triple ion formation from MX decreased in the following order: nitrobenzene > benzonitrile > acetone I acetonitrile > propylene carbonate. In the higher concentration range (4.0 X IO-' to 0.1 M) of n-Bu3NHC1in nitrobenzene or benzonitrile, the minimum was observed in the relation of A vs C'I2. The ion-pair and the triple ion formation constants caused a large relative error for the Aald to the Aokd (K,= 2.4 X IO6, K 2 = K 3 = 1.1 X IO9, +69.5% at the initial concentration of the salt, C, = 0.08 M in nitrobenzene; K , = 2.55 X IO6, K 2 = K 3 =. 4.5 X IO*,+50.0% at C, = 0.12 M in benzonitrile). The association between the triple ion and the simple ion (the formation of the quadrupole: M2X + X e M2X2 (K4),MX2 + M F! M2X2 ( K 5 ) )reduced the relative error within *2% ( K 4 = K5 = 1.8 X 104 in nitrobenzene; 2.0 X 104 in benzonitrile). The quadrupole formation was also observed for the bromide at the higher concentrations in these solvents.
Introduction
The concept of triple ion formation from a uni-univalent salt was introduced by Fuoss and Krausl as early as 1933 to explain the minimum in the relation between the equivalent conductivity (A) and the concentration (0of tetraisoamylammonium nitrate ( I ) Fuoss, R. M.; Kraus, C. A. J . Am. Chem. SOC.1933, 55, 2387.
0022-3654/90/2094-6073$02.50/0
in dioxane-water mixtures (dielectric constant e < 12). They assumed the triple ion formation from a neutral molecule and a simple ion (AB + BAB2- and AB + A+ + A2B') by the action of electrostatic forces. Beronius and Lindback2 investigated the formation of triple ions, using conductance data of LiBr in (2) Beronius, P.; Lindback, T. Acta Chem. Scand., Ser. A. 1978,32,423.
0 1990 American Chemical Society
6074 The Journal of Physical Chemistry, Vol. 94, No. 15, 1990 CHART I: Triple Ion Formation
M' = R3NH' X- = CI-,Br-
1-octanol (e = 9.85 at 25 "C). However, Grigo' asserted that it was possible to fit conductance data by Beronius and Lindback2 without the additional assumption of triple ion formation. On the other hand, Salomon and Uchiyama4 showed the triple ion formation by fitting the extended full Fuoss-Hsia equation to the conductivity data. Very recently, Salomon et ala5reported the minimum in the A-C'I2 plot of LiAsF6 in methyl acetate. They treated the results in terms of alternative models either involving triple ions or neglecting triple ions. It is thought that the first and main cause of disagreement for the triple ion formation exists in the difficulty of estimating reliable & (the limiting equivalent conductivity) values for a salt in solvents with the low dielectric constants (e < 10). Barthel et a16 managed to obtain a reliable A. value for LiBF4 in dimethoxyethane (c = 7.15 at 25 "C) from the conductivity data at low temperatures (down to -45 "C). Regis and Corset' demonstrated the presence of the ion pair and a triple ion from lithium trifluoroacetate in acetonitrile by IR spectra. Bacelon et aI.* proposed the formation of triple ions (Li+NCS-Li+ and SCN-Li+NCS-) from LiSCN in nitromethane on the basis of IR and Raman spectra. Jansen and Yeager9 reported the formation of ion aggregates of lithium trifluoroacetate in propylene carbonate. We have reported the formation of [M2A]+ (M = Li" or Na+; A = CH3COO- or C6H5COO-) and [MA2]- (M = Li+, Na+, and K+; A = C6H5COO-) in acetonitrile.i0 The "leveling" effect of acids in pyridineIi was properly explained in terms of the species of [M2A]+.12 The formation of (CH3)3CN02'-(Na+)2was also suggested in a~etonitri1e.I~ In the previous study,14 we demonstrated the formation of the symmetrical triple ions from trialkylammonium halides in acetonitrile by conductivity data, with the formation constants of the ion pair and the triple ions obtained polar~graphically.'~~~~ Our polarographic s t ~ d y lshowed ~ , ~ ~that the interaction between the trialkylammonium ions (M+) and the halide ions (X-) is symmetrical in acetonitrile: both (M+)2X-and M+(X-), type species are formed with the formation constants similar to each other (Chart I). The protophobic aprotic solvents are very poor hydrogen bond acceptors as well as extremely poor donors.I6 In these solvents, both cations (substituted-ammonium ions) and anions (halide ions) can exist in the unsolvated or 'active" state. Therefore, it may be possible to observe the reactions caused by the hydrogenbonding force or by other minor interactions between or among (3) Grigo, M. J. Solution Chem. 1982, 1I , 529. (4) Salomon, M.; Uchiyama, M. C. J . Solution Chem. 1987, 16, 21.
(5) Salomon, M.; Uchiyama, M.; Xu, M.; Petrucci, S. J . Phys. Chem. 1989, 94, 4374.
(6) Barthel, J.; Gerber, R.;Gores, H.-J. Ber. Bunsen-Ges. Phys. Chem. 1984,88, 616. (7) Regis, A.; Corset, J. Chem. Phys. Lett. 1975, 32, 462. (8) Bacelon, P.; Corset, J.; de Loze. C. J. Solution Chem. 1980. 9, 129. (9) Jansen, M. L.;Yeager, H. L. J . Phys. Chem. 1974, 78, 1380. (IO) Hojo, M.; Imai. Y. Bull. Chem. SOC.Jpn. 1983, 56, 1963. (11) Tsuji, K.; Elving, P. J. Anal. Chem. 1969, 41, 1571. (12) Hojo. M.; Akita, Y.; Nishikawa, K.; Imai, Y. Bull. Chem. SOC.Jpn. 1987, 60, 509. (13) Hojo, M.; Nishikawa. K.; Akita, Y . ;Imai, Y. Bull. Chem. SOC.Jpn. 1986,59, 3815. (14) Hojo,M.; Takiguchi, T.; Hagiwara, M.; Nagai, H.; Imai, Y. J . Phys. Chem. 1989, 93, 955. (15) Hojo, M.; Nagai, H.; Hagiwara, M.; Imai, Y. Anal. Chem. 1987, 59, 1770; Chem. Lett. 1987,449. (16) Kolthoff, 1. M.; Chantooni, M. K., Jr. In Treatise on Analytical
Chemistry, 2nd ed.; Kolthoff, I. M., Elving, P. J., Eds.; Wiley: New York, 1979; Part I, Vol, 2, p 244.
Hojo et al. solutes. For the present study, we have chosen the protophobic aprotic solvents with high or moderate dielectric constants (20 < t < 65) in order to minimize the dipole-dipole interaction between cations and anions. We would like to stress that, in our system, the reliable &value for an electrolyte (e.g., n-Bu3NHCl) can be obtained by the Kohlrausch's law because tetraalkylammonium perchlorate and halides and trialkylammonium perchlorate behave as rather strong electrolytes in the solvents with higher dielectric constants. In the present study, the conductivities of n-Bu3NHX (X = CI,Br, and I) are measured in several aprotic solvents (acetone, benzonitrile, nitrobenzene, and propylene carbonate) and an amphiprotic solvent (ethanol). The formation constants of the ion pair, the triple ions, and the quadrupole are evaluated in these solvents. We will demonstrate that the triple ion formation from the trialkylammonium halide is caused mainly by the hydrogenbonding forces between (or among) the solutes in the protophobic aprotic solvents with high dielectric constants. Theoretical Section
The following formulation was made for the analysis of the conductivity of the salt in the protophobic aprotic solvents. The dielectric constant is high enough to dissociate the salt to some extent. The ion-pair-formation reaction is expressed by eq 1 (the electric charges are omitted) and the triple ion formation reactions [MXI (1) [MI [XI are eqs 2 and 3. In addition, the quadrupole formation reactions M+XsMX,
Kl=-
between the triple ion and a simple ion are eqs 4 and 5. The mass
balance for M of the salt is C, = [MI + [MX] + 2[MzX]
+ [MX,] + 2[M,X2]
(6)
where C, is the analytical concentration of the salt. M2X2 is derived both from M2X and MX2. [M2X2l = K4[M2Xl [XI + KJMX21 [MI
(7)
If K2 = K3 and K4 = K5, then [MI = [XI because of the symmetry in eqs 4 and 5 as well as eqs 2 and 3. In this case, eq 6 can be reduced to a very simple form: 4K4K2[XI4 + 3K2[XI3
+ K1[Xl2 + [XI - C, = 0
(8) When the formation of the quadrupole can be ignored (K4 = K5 = 0), eq 8 is reduced to the third-order equationI4 3K2[XI3 + KI[XI2 + [XI - C, = 0 (9) When the formation of the triple ions does not occur (K2 = K3 = 0), eq 9 is simplified to eq 10. These equations are solved by KI[X]2 + [XI - c, = 0
(10)
the Newton's method or a modified method until the relative error reaches less than *0.01% for each C,value or until the function value of eqs 8, 9, or 10 reaches less than flO-IO with the electric computer. Once the [XI value is calculated, the concentration of each species can be easily obtained. [MX] = KI[Xl2
(1 1)
The Journal of Physical Chemistry, Vol. 94, No. 15, 1990 6075
Triple Ion Formation in Aprotic Solvents [MZX] = K2[XI3 = [MXJ = K3[XI3
(12)
Equation 7 gives the M2X2concentration. The total value of the equivalent conductivity, A, is given by the summation of those of simple ions ([MI = [XI) and the triple ions ([M2X] = [MX,]):
where & represents the sum of the limiting equivalent conductivity for the simple ions and AT the sum of the limiting equivalent conductivity of two kinds of triple ions (A, = A,,(M2X+) Xo(MXc)), As mentioned above, providing K4 = K5in eqs 4 and 5 as well as K2 = K3 in eq 2 and 3, then [MI = [XI. In this case, it is not necessary to divide the boor A T value in two parts (the cation and the anion). At first, the activity coefficients of all the species were assumed to be unity. Then, the activity coefficients of ions were calculated by the Debye-Hiickel limiting law (-log f* = for the lower salt concentration range ((0.4-6.0) X IF3M). The ionic strength was evaluated by the sum of [XI and [MX,]. The activity coefficients of uncharged species were assumed to be unity. The correction with the activity coefficients was repeated until the equilibrium constants reached constant. In spite of the relatively high dielectric constants of the solvents, the association between M2X and X, or MX2 and M (the formation of the quadrupole, M2X2)should be considered for the high salt concentrations. The higher aggregates above the quadrupole (the formation of M3X3 etc.) were ignored.
+
Experimental Section Soluents. Commercially obtained nitrobenzene (Wako Pure Chemicals, GR grade) was purified by drying over calcium chloride for several days and distilled at 5 Torr (cf. ref 17). Benzonitrile (Wako, GR grade) was dried with CaH, several days, decanted, and then refluxed for 1 h with freshly added CaH,, which was distilled at 10 Torr (cf. ref 18). Propylene carbonate (Wako, EP Grade) was dried with molecular sieves (Wako type 5A) and distilled in vacuo (cf. ref 9). Ethanol (Wako, Super Special Grade) was refluxed over magnesium, activated with iodine, and then distilled. Acetone (Wako, SP Grade) was used as received. These solvents had specific conductivities of 7.2 X IO4, 2.3 X IO4, 1.2 X lo-*, (, 10, 3.50 X lo3, and 6.55 X lo3,respectively, by the Shedlovsky analysis, as is shown in Table I. The apparent hovalues given by the Shedlovsky method were much smaller than those given indirectly by the calculation with Kohlrausch's law for the chloride salt: &, = 1.55 directly obtained; A. = 34.78 by Kohlrausch's law (Ao(n-Bu3NHCI) = Ao(nBu3NHC104) Ao(n-Bu4NCI) - Ao(n-Bu4NC104). A similar difference occurred for the bromide and even for the iodide. These phenomena of n-Bu3NHX suggested that some additional reactions other than the ion-pair formation between n-Bu3NH+ and Xoccur. Here, we would like to mention that all the Shedlovsky analyses were done for the salt concentrations of (0.4-4) X M. Wynne-JonesZ2stated that the abnormal conductivity behavior exhibited by the partially substituted ammonium salts in nitrobenzene or in non-hydroxylic solvents had been explained on the assumption that they exist in a nonionic form. However, Witschonke and KrausI7 concluded that the occurrence of such a nonionic species from pyridinium picrate in nitrobenzene is not excluded but the fraction of total solute occurring in such form must be very small. Figure 1 shows the A vs C1I2relation for n-Bu3NHCI in nitrobenzene. The A values calculated by eqs 9 and 13 coincided with the observed value within f2.0% error, at most, over the
+
(20) Janz, G. J.; Tomkins, R. P. T. In Nonaqueous Elecrrolyres Handbook; Academic: New York, 1972; Vol. 1, Chapter 1. (21) Taylor, E. G.; Kraus, C. A. J . Am. Chem. SOC.1947, 69, 1731. (22) Wynne-Jones, W. F. K. J. Chem. SOC.1931, 795.
6076 The Journal of Physical Chemistry, Vol. 94, No. 15, 1990
Hojo et al.
TABLE I: 4and Apparent K, Values of Tributyl- and Tetrabutylammonium Salts in Several Protophobic Aprotic Solvents and Ethanol by Three Different Methods of Analysis A
I1
..” P1/2 vs ’ L
salt
A,”
n-Bu4NC104 n-Bu3NHC104 n-Bu4NCI n-Bu4NBr ~I-Bu~NHCI n-Bu3NHBr
187.0 189.2 185.7 188.0
n-Bu4NCIOI ~I-Bu~NHCIO~ ~I-Bu~NCI n-Bu4NBr n-Bu3NHCI n-Bu3NHBr
47.45 49.5 47.8 49.14
II-Bu~NCIO~ n-Bu3NHC104 n-Bu4NCI n-Bu4NBr n-Bu4N1 wBu~NHCI n-Bu3NHBr n-BuJNHI
33.25 35.18 34.17 34.22 33.8
~I-Bu~NCIO~ n-Bu3N HClO4 n-Bu4NCI n-Bu4NBr n-Bu3NHC1 n-Bu,NHBr
28.06 28.87 27.94 28.74
n-Bu4NCIO4 n-BujNHCIO4 n-Bu4NCI n-Bu4NBr n-Bu,NHCI n-Bu,NHBr
54.65 54.55 43.00 45.78 43.43 46.50
Arrhenius-Ostwald Kab Acetone 178.57 1.41 X IO2 178.25 1.41 X IO2 172.41 2.91 X IO2 176.37 2.47 X IO2 50.00 1.15 x 105 80.65 2.58 X IO4
A0
Shedlovskv
K.
Ao(calcd)e
185.44 192.76 180.87 185.01 13.8 1 88.31
9.41 X IO’ 3.06 X IO2 3.10 X IO2 2.64 X IO2 2.40 x 103 3.34 x 104
188.19 192.33
45.33 46.40 45.1 1 46.51 6.90 28.57
Benzonitrile 9.92 X IO’ 2.66 X IO2 1.81 x 102 1.59 X IO2 3.80 x 104 4.76 x 104
47.03 48.51 47.01 48.35 2.60 21.32
6.03 X 2.98 X 1.74 X 1.41 X 6.02 X 2.56 x
IO’ IO2 IO2 IO2 IO2“ 104
48.49 49.83
32.21 32.89 32.50 32.71 32.49 2.60 11.76 29.41
Nitrobenzene 5.25 X I O 1 3.52 X IO2 7.67 X I O 1 7.17 X IO’ 6.63 X 10) 8.53 x 103 1.91 x 104 6.41 x 103
33.1 1 34.20 33.69 33.71 33.37 1.55 6.43 29.32
1.66 X 3.94 x 5.60 X 4.49 x 3.28 X 7.31 X 3.50 x 6.55 X
IO’ IO’ IO’ IO’ 10’“ 103 IO3
34.78 34.80 34.46
27.69 28.48 27.56 28.26 27.03 29.07
Propylene Carbonate 2.19 X IO’ 1.77 X IO’ 2.18 X IO’ 2.04 X IO’ 4.43 x 103 5.04 X IO2
28.04 28.93 27.90 28.72 26.69 29.7 1
0 0 0 1.59 4.14 x 103 5.29 X IO2
28.79 29.61
5 1.28 5 1.47 40.82 43.10 40.82 43.67
EtOH 2.78 X IO2 2.17 X IO2 1.28 X IO2 1.49 X IO2 2.73 X IO2 2.46 X IO2
53.11 53.21 42.21 44.73 42.45 45.28
2.88 X 2.05 X 6.32 X 1.03 X 2.66 X 2.32 X
IO2 IO2 IO2 IO2 IO2 IO2
42.30 44.82
A0
“Equivalent conductivity (cm2.S/mol). bAssociation constant, M+ + X‘ Shedlovsky’s plot made a convex curve with a maximum.
102
MX (K,).‘The A,, value calculated by the Kohlrausch’s law. “The
; i
TABLE 11: Ion-Pair (K,)and Triple Ion ( K 2= K,) Formation Constants of Tributylammonium Halides in Protophobic Aprotic Solvents salt An“ K, K, = K > re1 errorb/% KI re1 errorr/% 188.19 192.33
1.85 X IO6 1.70 x 105
Acetone 1.5 X IO8 1.0 x 107
-0.69 to +0.98 -1.02 to +0.80
1.83 X IO6 1.70 x 105
-13.25 to +O.Ol -8.23 to +0.36
~I-BU~NHCI n-Bu3NHBr
48.49 49.83
2.45 X IO6 1.60 x 105
Benzonitrile 4.5 x 108 -0.79 to f 0 . 4 8 1.0 x 107 -0.84 to +OS2
2.35 X IO6 1.60 x 105
-23.27 to +0.06 -9.05 to +0.20
WBU~NHCI n-Bu3NHBr n-Bu3N H I
34.78 34.80 34.46
2.65 X IO6 2.10 x 105 9.3 x 103
Nitrobenzene 1.1 x 109 -2.03 to 3.0 x 107 -0.96 to
2.50 X IO6 2.10 x 105
-41.32 to +0.01 -18.77 to -0.40
n-Bu,NHCI n-Bu3NHBr
28.79 29.61
5.5 x 103 5.7 x 102
n-Bu,NHCI n-Bu3NH Brd
+ 1.60 + 1.09
Propylene Carbonate (2 x 105)
“The A. value obtained by the (Kohlrausch’s law) calculation with the A. data from the Shedlovsky method. bThe relative error (over the range of (0.4-6.0) X IO-’ M salt concentration) in the calculated A value to the observed A value. (The value when only ion pair is accounted. “For (0.5-6.0) X IO-, M salt concentration.
initial concentration of the salt (C,) of (0.4-6.0)X M. For instance, at C,= 1.0 X M, the values of K I = 2.65 X IO6, K2 = K 3 = 1 .I X IO9, bo= 34.78, and AT = 11.59 gave the AaId value of 0.749, which has a -0.78% relative error compared with the Aobd value of 0.755. Only with KI,the relative error in A values was -40% at C, = 6 X M (cf. Table 11). The concentrations of simple ions, ion pair, and triple ions are calculated to be [XI = [MI = 1.90 X IO” M, [MX]= 9.57 X IO4 M, and
[M2X] = [MX,] = 7.56 X 10” M. The reasonable A,, values of n-Bu3NHCI are evaluated by Kohlrausch’s law with the & values of “strong” electrolytes (by the Shedlovsky’s method). The limiting equivalent conductivity of triple ions, AT, was assumed to be one-third of simple ions, Ao. Fuoss and Kraus made the same assumption for the triple ions from tetraisoamylammonium nitrate in low dielectric constant media.] We thought that the assumption is quite reasonable from the viewpoint of the mean diameter of
Triple Ion Formation in Aprotic Solvents
I
I
I
I
I
A
I
I
I
I
I
0
TABLE Ilk Equilibrium Constants, KI and K2 = K,, Corrected by the Activity Coeflcients" salt KI K, = K, (K,/K,)b re1 error/%
Acetone n-Bu'NHCI 2.0 X IO6 n-Bu3NHBr 1.92 X IO5
1.2 X 10' 2.0 X IO6
(60.0) (10.4)
-0.58 to +0.63 -0.57 to +0.58
(155.8) (31.1)
-0.82 to +0.61 -0.32 to +0.49
(409.4) (124.4) (18.6)
-0.91 to +1.09 -0.46 to +OS8 -0.47 to +0.39
Benzonitrile n-Bu3NHCI 2.568 X IO6 n-Bu3NHBr 1.766 X IO5
4.0 X 10' 5.5 X IO6
Nitrobenzene n-Bu3NHCI 2.76 X IO6 n-Bu3NHBr 2.25 X IO5 n-Bu3NHI 1.077 X IO'
1.13 X IO9 2.8 X IO7 2.0 X IO5
Propylene Carbonate 1.5 X IO5 (28.3) -0.20 to +0.22 n-Bu3NHCI 5.3 X IO' n-Bu3NHBr 6.12 X IO2 -0.45 to +0.47 "Other conditions are same to those in Table 11. bK2/Kl = aMIX/ (aMXaM) and K3/K1 = %X2/(hXaX)* the triple ions as the result of free rotation. And the assumption was successfully applied to the conductivity data of trialkylammonium chloride (R3NHCl, R = Me, Et, and n-Bu) in acetonitrile." If the activity coefficients of the ions were corrected with the Debye-Hfickel limiting law (-log ft = 1 . 7 3 ~ ~ /the ~), relative error in A values decreased to f l % . The equilibrium constants corrected by the activity coefficients, Kl and K2 = K3 (K,= Kl/ft2 and K2 = K2/ft2), are listed in Table 111. In Figure 2 is shown the A vs C1/2curve of the higher concentrations (3.8 X to 8.1 X M) of n-Bu3NHCl in nitrobenzene. In this concentration range, a minimum was observed in A a t C, = 2.6 X IO-* M. We had a very large relative error (+69.5% at C, = 8.0 X M) for Acalcdto AoM, even though both the ion pair and the triple ions were considered. In order to explain the very large deviation, the formation of the quadrupole was introduced (Chart 11), which is based on the association between the triple ion and the simple ion (eq 4 and 5). The M with the was evaluated to be 0.4649 at C, = 1.0 X equilibrium constants K, = 2.4 X lo6, K2 = K3 = 1.1 X lo9, and K4 = K5 = 1.8 X IO", provided that the A. and AT values are the same as those a t lower salt concentrations. This A=,& value M, the coincided with AoM value of 0.465. At C, = 1.0 X equilibrium concentrations of the simple ions, the ion pair, the triple ions, and the quadrupole were calculated to be that [XI =
I
0.1
I
I
0.2 c112/,~12.d,-3/2
I
0.3
Figure 2. The observed and calculated A values of n-Bu,NHCI ((0.38-8.1) X M) in nitrobenzene: (0)observed; ( 0 ) calculated altogether with the ion pair, the triple ions, and the quadrupole, K , = 2.4 X106,K2=K3=1.1XlO9,K4=K5=1.8XIO4,&=34.78,A~= &/3; (A)calculated with only the ion pair and the triple ions, K I = 2.4 X lo6, K 2 = K , = 1.1 X IO9, A. = 34.78, AT = &/3. CHART II: Quadrupole Formation
& & 0
(3
M, [MX] = 8.33 X [MI = 5.89 X M, [MZX] = [MX2] = 2.24 x lo4 M, and [M2X2]= 4.76 X IO4 M, respectively. The quadrupole can be produced by the association between the triple ions and the simple ions (eqs 4 and 5) and also the association between the ion pairs (eq 14). As for n-Bu3NHCl
of the higher concentrations in nitrobenzene, we did not find the proper K41 value for fitting the data, but the calculation with eqs 4 and 5 fit the Acalcdto the AoM within f2% relative error over the concentration range of 4.0 X to 8.0 X M. As the summary of the results for the chloride in nitrobenzene, the conductivity data of the low concentration range ((0.4-0.6) X M) can be explained only by the ion pair, that of the medium concentration range ((0.6-6.0) X M) is explained by the ion pair and triple ions, and that of the high concentration M) should be considered with the range ((0.6-8.0) X quadrupole formation. We have used same values of A,, and AT for all concentration ranges. A better fit may be given by the appropriate equivalent conductivity corrected by viscosity change with the salt concentration. Figure 3 shows the A vs Cl/2 curve of n-Bu,NHBr (the lower concentration range: (0.38-7.1) X M) in nitrobenzene. As in the case of the chloride, the A,lcd values with the triple ion formation fit to the L & ~values within f l % over the concentration of (0.4-6.0) X IO-) M of the bromide. In Figure 4 is shown the A vs C1/2curve of n-Bu3NHBr (the higher concentration range, 3.8 X 10" to 0.13 M). The bromide did not give the minimum in the observed A values. The A values calculated only with the ion-pair formation caused a very large negative error in the observed A values (e.g., -69.69% a t C, = 0.12 M) at high concentrations. On the other hand, a positive error was made by calculation with the ion pair and the triple ions
Hojo et al.
6078 The Journal of Physical Chemistry, Vol. 94, No. 15, 1990
4.0t
301
1
0.5
1.01
I
LA
OO
0.02
0.04
008
0.06
c1/2/mo11i2dm-3/2
1
Figure 3. The observed and calculated A values of n-Bu’NHBr ((0.38-7.1) X IO-, M) in nitrobenzene: (0)observed; (A) calculated with both the ion pair and the triple ions, K,= 2.1 X I@, K2= K, = 3.0 X IO’, 4 = 34.80, AT = &/3; ( 0 )calculated without the triple ions, K, = 2.1 X IO’, A0 = 34.80. I
9 l
I
I
I
I
01
02 03 ~112,’ mo$/2 dm-3/2
J
Figure 5. The observed and calculated A values of n-Bu’NHCI (4.0 X IO-’ to 0.13 M) in benzonitrile: (0)observed; (0) calculated altogether with the ion pair, the triple ions, and the quadrupole, K I = 2.55 X IO6, K2 = K3 = 4.5 X IO8, K4 = K5 = 2.0 X IO‘, &, = 48.49, AT = &/3; (A) calculated only with the ion pair and the triple ions, K I = 2.55 X IO6, Kz = K’ = 4.5 X IO*,A0 = 48.49, AT = Ao/3.
\
’
1.01
0
°
7
1
I
6.0 4
4.01
20[
I
1
1
0.1
I
0.3
0.2
C1/2/,$/2,d
I
-,312
Figure 4. The observed and calculated A values of n-Bu’NHBr (3.8 X IO-) to 0.13 M) in nitrobenzene: (0)observed; (0) calculated altogether with the ion pair, the triple ions, and the quadrupole, K, = 2.4 X IO5, K2= K, = 3.0 X IO7, K4 = K5 = 2.2 X IO’, A, = 34.80, AT = &/3; (A) calculated only with the ion pair and the triple ions, K I = 2.4 X lo5,K2 = K3 = 3.0 X IO’, A. = 34.80, AT = A0/3; ( 0 )calculated only with the ion pair, K , = 2.4 X IO5, A0 = 34.80.
(+36.88% at C,= 0.12 M). Therefore, the quadrupole formation was introduced also to the bromide. Over the concentration of values with to 0.13 M, the Aald values fit to the 4.0 X the relative error of -2.14 to +1.65%. In the case of n-Bu3NHBr in nitrobenzene, the AOM values can be explained by the quadrupole formation based on eq 14 (&, = 2.3, the relative error, -2.15 to +1.57%). As for n-Bu3NHI in nitrobenzene, although the A values calculated only with the ion-pair formation deviated from the M), the observed values (-5.17 to +1.93% for (0.4-6.0) X deviations can be almost explained by the correction for activity coefficients of the simple ions. However, as mentioned above, the &values obtained directly by the Shedlovsky method (&, = 29.32) are slightly smaller than those obtained indirectly from the Kohlrausch’s law (& = 34.46). Therefore, the triple ion formation
-.
4
i
0.5
b\ ‘?
00
i
,
,
0.02
0.04
I j
I
006
cl/2/ml‘”
008 &.)-3/2
Figure 6. The observed and calculated A values of n-Bu,NHCI ((0.38-7.1) X IO-’ M) in acetone: (0)observed; (A)calculated with both the ion pair and the triple ions, K, = 1.85 X IO6, K2 = K3 = 1.5 X IO8, A. = 188.19, AT = Ao/3; ( 0 )calculated without the triple ions, K, = 1.83 X IO6, A. = 188.19.
is probable even for the iodide in the solvent (cf. Table 111). In Benzonitrile. In Table IV are shown the observed and the calculated A values for n-Bu3NHCI of (0.4-6.0) X M in benzonitrile (c = 25.2, = 0.0122 P).23 Considering the triple ions, the relative error in the calculated value to the observed value of the conductivity is small. At the initial concentration of 1 .O X M, the concentrations of the simple ions, the ion pair, and the triple ions were calculated to be [XI = [MI = 1.99 X M, [MX] = 9.70 X lo4 M, and [M,X] = [MX,] = 3.54 X 10” M, respectively. Figure 5 shows the A-C1/*curve for n-Bu3NHCI of the higher to 0.13 M). The minimum appeared concentrations (4.0 X at C, = 4.6 X lo-* M in the observed A values, as was the case in nitrobenzene. In the calculation, we had a very large relative error (+50.5%) at high concentration of the salt (C, = 0.12 M) ~
(23) Coetzee, J. F.;McGuire, D. K. J . Phys. Chem. 1963, 67, 1810.
The Journal of Physical Chemistry, Vol. 94, No. 15. 1990 6079
Triple Ion Formation in Aprotic Solvents
TABLE I V Comprison of the Calcuhted A Values with the Observed A Values for Tributylammonium Halides in Benzonitrile I 03c: 105[X] I Os[M2X] L C ld 4bda re1 error/% re1 erroP/% n-Bu3NHCI, K, = 2.45 X IO6, K2 = K3 = 4.5 X IO8, A0 = 48.49,AT = &/3 (K,= 2.35 X IO6) 1.555 +0.00 +0.06 0.088579 1.555 1 0.4 1.25326 1.400 +0.06 -0.42 0.124269 1.4008 0.5 1.40297 1.285 +0.18 -0.83 0.163786 1.2873 0.6 1 .S3823 1.135 -0.54 -2.60 0.252991 1.1289 0.8 1.77813 -3.88 1.030 -0.79 1.0218 1.o 1.98924 0.354220 -0.64 -6.73 0.841 0.718 347 0.8357 I .6 2.51791 0.768 -0.54 -8.57 1.00403 0.7637 2.0 2.81 5 22 -13.15 0.661 -0.71 0.6563 3.0 3.446 54 1.8423 1 -0.58 -17.07 0.600 2.83088 0.5965 4.0 3.97713 -20.49 0.560 -0.26 0.5585 5.O 4.44336 3.947 71 -23.27 0.530 +0.48 0.5326 6.0 4.86387 5.17796 n-Bu3NHBr, K, = 1.6 X
lo5,K2 = K3 = 1.0 X
IO’, A. = 49.83,AT = A0/3
(K,= 1.6 X IO5) 0.4 0.6 1 .o 2.0 4.0 6.0
4.67806 5.78945 7.54824 10.767I 15.2887 18.7340
0.102376 0.194049 0.430068 1.24823 3.57364 6.57495
5.870 4.862 3.833 2.786 2.053 1.738
5.84 4.84 3.85 2.81 2.07 1.74
+0.52 +0.45 -0.45 -0.84 -0.82 -0.12
+0.20 -0.15 -1.64 -3.60 -6.71 -9.05
‘The total concentration of a salt and the A value, read out from the A vs C1/*curve. bThe relative error of the calculated A value to the observed value, when only the ion-pair formation (M’ + X- F? MX, K,)is accounted.
even with the ion pair and the triple ions. However, the quadrupole formation solved the problem, again. On the other hand, the observed A values of n-Bu3NHBr did not exhibit the minimum up to 0.13 M. In Other Solvents. Figure 6 shows the LI-CI/~curve of nBu3NHCI ((0.38-7.1) X IC3M) in acetone (c = 2 0 . 7 , ~= 0.00302 P),23 The calculated A values only with the ion-pair formation ~ in give the relative error of -1 3.25 to +0.01% to the A o values the range of C, = (0.4-6.0) X M. The triple ion formation reduced the error (cf. Table 11). Incidentally, assuming that conductance is based only on the simple ions, the concentrations of the (simple) ions present in the solution are evaluated. Thus, the correction of the activity coefficients explained the one-fifth of the relative error (-13.25% comes to -10.9%) at C, = 6.0 X M. Tributylammonium bromide was examined by the similar way. The correction of the activity coefficients of the simple ions explained two-thirds of the error of -8.23% at C, = 6.0 X M. Thus, the K 2 and K 3 values seem to be estimated too large to some extent unless the K Ivalue is large enough (1106)because the activity coefficients are not corrected in the calculations. The situation can be easily grapsed by comparing the K2 = K3 values with the K2 = K3 values in Tables I1 and 111. In propylene carbonate (c = 64.4,20,24r) = 0.0254 PZo),the conductivity data of n-Bu3NHCI gave the relative error of -3.54% at C, = 6.0 X lo-’ M. The correction of the activity coefficients for the simple ions reduced the error to -1.21% from -3.54%. About the half of the error must be caused by the triple ion formation ( K 2 = K3 = 2.0 X IO5). As for n-Bu3NHBr in propylene carbonate, the Acalcd values only with the ion-pair formation could fit to the value, after the activity coefficients are corrected. In an amphiprotic solvent, ethanol (c = 2 4 . 5 5 , ~= 0.01078 P),25 the correction of the activity coefficients for the simple ions made the relative error less than *I%, although the Amid value had a large negative error to the AoW at C, = 6.0 X M (-13.4%
-
(24)Mukherjee, L. M.; Boden, D. P. J . Phys. Chem. 1969, 73, 3965. (25) Riddick, J. A.; Bunger, W. B. In Techniques ofchemistry, Vol. 2 Organic Solvents, 3rd ed.; Weissberger, A., Ed.; Wiley-Interscience: New York, 1970;p 146.
and -12.2% for the chloride and the bromide, respectively) with the ion-pair formation. The calculation with the triple ion formation did not reduce the error at all but made it worse. The A. values obtained directly by the Shedlovsky method and indirectly by the Kohlrausch’s law coincided with each other (cf. Table I). The above results show that triple ion formation reaction does not occur in ethanol. The cation (R3NH+) and the anion (CI-or Br-) are stabilized through the hydrogen bonding between the solute and the solvent, which prevents the triple ion formation in ethanol, despite the relatively small dielectric constant. Recent studiesZ6J7show that the halide ions interact with multiple numbers of HO- or HC- function groups through the hydrogen bonding. In the protophobic solvents, the results in the present study show that the tendency for the formation of triple ions decreases in the order nitrobenzene > benzonitrile > acetone Iacetonitrile14 > propylene carbonate. Popovych and Tomkins28 described that, generally, the anomalies in conductance behavior have been encountered most frequently in the solvents having lower cationsolvating power. They proceeded that, according to the Parker scheme,29the ability of dipolar aprotic solvents to solvate cations varied in the order dimethyl sulfoxide = dimethylacetamide > dimethylformamide > acetone > acetonitrile = nitromethane > benzonitrile = nitrobenzene. Our results are quite similar to Parker’s classification, except the order of acetone and acetonitrile. The order obtained in the present study can be acceptable from the viewpoint of the donor and the acceptor number by Gutma” We believe that many contradictory results in conductometric studies could be accounted for by the triple ions and the higher aggregates which are revealed by the poor solvation toward both anions and cations. Registry No. n-Bu3NHC1, 6309-30-4; n-Bu3NHBr, 37026-85-0; nB u ~ N H I34 , 193-29-8. (26)Meot-Ner (Mautner), M. J . Am. Chem. SOC.1988, 110, 3854. (27)Hiraoka, K.;Mizuse, S.;Yamabe, S.J. Phys. Chem. 1988,92, 3943. (28) Popovych, 0.; Tomkins, R. P. T. Nonaqueous Solution Chemistry; Wiley: New York, 1981;p 285. (29)Parkar, A. J. Q.Rev. (London) 1962, 16, 163. (30)Gutmann, V. The Donor-Acceptor Approach to Molecular Interactions; Plenum: New York, 1978;Chapter 2.
