Ionic Association of N-Methylpyridinium Iodide
The Journal of Physical Chemistry, Vol. 82, No. 4, 1978 387
A Thermodynamic and Kinetic Study of the Ionic Association of N-Methylpyridinium Iodide in Mixed Solvents' Paul Hemmes," James N. Costanzo, and Frank Jordan* Carl A. Olson Chemistry Laboratories, Rutgers, The State University, Newark, New Jersey 07102 (Received May 23, 1977)
The thermodynamics of ionic association of N-methylpyridinium iodide were investigated by UV and conductance, while the kinetics of the prpcess were studied by ultrasonic relaxation spectroscopy. The UV data were treated taking explicit account of the variable ionic strength existing in the solutions studied and this treatment led to essentially wavelength independent association constants in the 29&310-nm range. The high linear correlation obtained in the log K association vs. l/dielectric constant plot in aqueous ethanol for all UV and conductance data combined is suggestive of a classical ionic association process being monitored in the entire range of solvent compositions employed. Ultrasonic t$bsorption measurements demonstrated the existence of two relaxation processes in 95,90, and 88% acetone-water (v/v). The high-frequency relaxation was concentration dependent (at fixed solvent composition) and was due to the formation of ion pairs from free ions. The low frequency relaxation is due to a desolvation process which converts a solvent-separated ion pair to a contact pair. The relaxation frequency of the slower process is linearly dependent upon the water concentration in the solvent mixtures. This is shown to be evidence for the removal of a single water molecule in the process of interconverting the two ion pair species.
I. Introduction I t was shown by Kosower in 195Ei2 that N-methylpyridinium iodide (NMPI) gives rise to an ultraviolet charge transfer band in solution (reaction A). This band
I
CH3
CH3
supposedly arises due ,to transferral of electron density from an occupied orbital of iodide into the lowest vacant orbital(s) of the pyridinium ion. Subsequently, it was shown that the concentration dependence of the charge transfer band could be employed to calculate approximate association constants (K,,,,,) for the indicated process.2b On account of the fact that the K,, so obtained exhibited wavelength and salt concentration dependence, Kosower products suggested that the data could yield only Kassoc~ (c being the extinction coefficient of the charge transfer complex species). We have been interested in our laboratory in defining the solution events reflected by the charge transfer band behavior both from a thermodynamic and kinetic point of view. In a preliminary communication3 we noted that ultrasonic relaxation measurements gave rise to two relaxations in aqueous acetone solutions of NMPI: the lower frequency one concentration independent, the higher frequency one concentration dependent. A comparison with ultrasonic relaxation in NaI solutions indicated that the concentration independent relaxation only exists for NMPI and we concluded that NMPI existed as both solvent-separated and intimate (contact) ion pairs under our conditions. In this report we want to summarize our thermodynamic and kinetic results on NMPI obtained by a variety of physical techniques. With judicious treatment of the UV data we have been successful in separating K,,, and E and to obtain a wavelength independent K,,,,,. In addition, the dielectric constant dependence of K,,,,, obtained by the two methods over a wide variety of solvent compositions allows us to draw conclusions about the nature of the forces sustaining the complex. Since aqueous solutions 0022-365417812082-0387$01.OO/O
of NMPI show no excess sound absorption above solvent, only acetone rich mixtures were employed in the kinetic studies.
11. Experimental Section A. Chemicals. NMPI, synthesized from pyridine and methyl iodide refluxed in absolute ethanol or bought from Fisher Scientific, was twice recrystallized from absolute ethanol to give white crystals, mp 118-120 "C. After drying, NMPI was stored in a desiccator over CaC12. NMR and x-ray studies confirmed the structure. Solutions were prepared by dissolving weighed samples of NMPI in solvent mixtures prepared as v/v solutions. All dielectric constants were interpolated from literature valuesa4 B. UV Measurements. All UV spectra were recorded with a Cary 14,spectrophotometer thermostatted at 25 f 0.1 O C with a Forma bath. The solutions contained only NMPI to avoid complications in data treatment due to the unknown extent of multiple ion pairing likely to occur in different low dielectric solvent mixtures. Thus thiosulfate was not employed (could be needed to keep the iodide reduced and to avoid estiblisliment of the Is- I2 + I- equilibrium5). For all measurements only those freshly prepared NMPI solutions were employed for which the UV spectrum lacked the characteristic triiodide band (350-360 nm) throughout the course of the experiments. Nor was inert electrolyte added during the measurement of K,,,,, from the concentration dependence of the NMPI spectral characteristics. Instead, the variation in ionic strength was taken into account explicitly in the data treatment. UV Data Treatment. The equation employed by Kosower and BurbachZbfor calculation of K,,, and t from the concentration dependence of the long wavelength UV behavior of NMPI solution is X J A= Z * / K a s s o c f+ l / e (1) where X = C2/(2Co - x ) ; Z* = 1/(2Co - x ) ; Co is the initial NMPI concentration (weighed); x is the concentration of complex; 6 its absorption coefficient;K,, is the association constant; and A is the absorbance of the solution. In a spectral region where only the complex absorbs A is 1978 American
Chemical Society
P. Hemmes, J. N. Costanzo, and F. Jordan
The Journal of Physical Chemistry, Vol. 82, No. 4, 1978
388
TABLE I: K and e from UV Measurements 290 nm %EtOH
Dn
95 90 85 80 70 60 50
27.0 29.2 32.2 34.8 40.6 46.8 52.8
69.2 41.7 27.2 21.2 14.1 6.7 7.7
1058 1079 1119 1095 926 1342 911
Dielectric constant interpolated from ref 4.
300 nm 0.993 0.982 0.950 0.988 0.979 0.939 0.968
71.7 35.6 25.1 22.8 12.1 7.1 5.7
Molar extinction coefficient.
proportional to xc. An iterative procedure would assume x = 0 as an initial guess to yield an initial value of K,,,,,. The K,,,,, would generate an x value to give a new value of K,,,,,, and the process repeated until a constant value of K was obtained. As the ionic strength changed with changing NMPI concentration the following modified form of eq 1 was employed:
-=-[ c,"
1 (1+ .)Co
AF
E
]+-
1 KE
K' = [AB],/ [A],[B],;
concentration equilibrium constant
K' = KF-' =
X
c, - x )
(3)
where Cot, eo-are the initial cation and anion concentrations, respectively, and x is the concentration of complex. Replacing x by A / €
K F - ~=
A /e ( C c - A / E ) ( C ,- A / € )
(4)
if Co+ = Co- = Co by rearrangement
-=-[ c," AF
. 1 2 c o - x I t -1 E KE
(5)
and as
x
=
(1- .)C,
+
2C0 - x = (1 a)C0,and this substitution into ( 5 ) leads to (2). Equation 2 is employed by first setting a = 1 to allow calculation of an t for a particular solvent composition. a,for each concentration in a particular iteration is generated as (Yi
=
(CO- A / € ) CO
and the iteration on E is recycled until for two successive iterations Ifi
- Ei+ll/Ei
< 0.001
Equation 2 is treated by linear least-squares statistics yielding intercepts and slopes at each iteration as well as linear regression coefficients, r.
0.996 0.986 0.986 0.987 0.989 0.942 0.902
71.6 44.3 24.7 22.5 12.6 7.5 5.3
897 880 961 777 686 735 712
0.997 0.985 0.981 0.986 0.988 0.999 0.884
Linear regression coefficient.
C . Conductance measurements were performed in 95% (v/v) aqueous acetone and 99% (v/v) aqueous ethanol solutions employing a Beckman Model RC 16 conductivity bridge. The cell was a dipping type and the cell constant was determined employing KC1. All solutions were thermostatted at 25 f 0.02 "C using a Forma bath. Solvent properties were taken from the l i t e r a t ~ r e . ~ Association constants for NMPI solutions were calculated from the conductance equation derived by F u o ~ s : ~
F
where the new symbols are as follows: a is degree of the Debye-Huckel dissociation; log F = AI'l'z/(l + mean activity coefficient; r = 2Z2aCo;a is ion size parameter in A; A = 2 (1.290 X 106)Z2/(DT)3/z; B = 35.56/(DT)1/2;Z is the ionic charge; D is the solvent dielectric constant; T is the temperature in K. Equation 2 describes the association process A+BZAB
(C,' - x ) (
1014 1172 1109 932 901 1049 929
-
310 nm
K TCAf'l
1
h is the equivalent conductance; hois the same at infinite dilution; C is the concentration (in equiv/L); K is the association constant; F = 4 / 3 cos' [1/3 c0s-l (-33/2z/2)]; z = [ S / ( h o ) 3 / 2 ] ( C h ) 1S/ 2=; a b o B; (Y = 0.8204 X lo6/ (DT)3'2;D is the dielectric constant, Tis the temperature in K; /3 = 82.50l/.rl(DT)'/' where .rl is the viscosity (cP);f = 10[2p'c112/(1 K O ! ) ] ; 20" = (3.6494 x 106)/(DT)312; K = 0.50294 X 1010C1/z/(DT)1/2; a is the interionic radius (cm). This technique was only used in media in which the expected association constant was moderately large. D. Ultrasonic Relaxation Measurements. The sound absorption instrumentation was described previ~usly.~ A Matec Model 765 plug-in was employed for measurements between 90 and 300 MHz so as to make available vastly increased power. Acetone was purified by literature methods.* Water was conductivity grade.
+
+
111. Results and Discussion UV Spectrophotometry. The UV absorptions of M NMPI solutions increase with increased percent ethanol in the wavelength range 280-315 nm. The charge transfer band shifts to longer wavelengths as the percentage of ethanol is increased in accord with Kosower and Burbach's report.2b A typical plot of Coz/AFvs. (1 + a)Co/F (according to eq 2 ) is shown in Figure 1 in 95% aqueous ethanol representing the final interated values. The scatter increases somewhat at lower percent ethanol and was compensated for by increasing the number of points employed. 4-20 X M NMPI was employed in the UV studies. The final iterated K and t values along with the linear regression coefficients are quoted in Table I at 290, 300, and 310 nm. The essential agreement in K at three different wavelengths shows random scatter and is reasonably good. Figure 2 presents a plot of log K vs. 1/D at 300 nm. Eigeng and Fuoss10 derived the equation for ionic association:
(
K = -4 7 r ~ aexp ~ z1z2e2) 3000 clDKT
(7)
where N is Avogadro's number, a is the ion size parameter,
The Journal of Physical Chemistry, Vol. 82, No. 4, 1978 309
Ionic Association of N-Methylpyridinium Iodide
9.0
0.22 8,O
h
Find
0.20
70 0.16
6.0
0.1
0.14
02 cnf2/
0.3
0,4
F
Figure 3. Conductance plot for NMPI in 95% acetone-water (vlv).
a2 0.4 0.6 OB (l+a)C, / F * IO2 Flgure 1. UV absorption data for NMPI in 95 % aqueous-ethanol plotted according to eq 2.
1.8
I
0.02
I
I
a a06 CAf2/
0.08 OJO
F
Figure 4. Conductance plot for NMPI in 99% ethanol-water (v/v).
Q 1.
2. 3. 4. 5. 1 / D -IO2
Figure 2. Is. 1/D plot for NMPI. Circles from UV, triang s from conductance measurements. ~
z1 and z2 are charges, e the unit electrostatic charge, and K is the Boltzmann constant. The correlation coefficient for the linear plot is 0.988. The value ext,rapolated to the dielectric constant of water is 2.4 M-l in excellent agreement with the 2.3 f 0.3 M-l value reported at constant 0.01 ionic strength by Kosower and Burbach.2b The slope of the line in Figure 2 allows an estimation of the interionic distance a i.e.
slope = 0.4343e2/akT
The association constants obtained by both conductance and UV spectroscopy follow a very similar dielectric constant dependence (Figure 2) with a very high linear regression coefficient (0.996 for nine observations). Thermodynamically, both sets of measurements apparently follow a classical ionic association model. Theoretical calculations also suggested that electrostatic forces are responsible for the association.12 Ultrasonic Relaxation. In any given solvent the sound absorption coefficient, cy, will vary with frequency, f,via the equation (9)
where fr, is the relaxation frequency for the ith process; Ai is an amplitude term for the process; and B is the limiting 00 for all f,,. The related quantity, value of c y / f as f / f r , I*, is given by the expression
(8)
yielding 4.19 A for a. Conductance. The conductance data analyzed according to eq 6 are seen in Figures 3 and 4 respectively for 95% aqueous acetone and 99% aqueous ethanol. The slope and intercept yield K = 217 M-l and .lo= 167 for 95% aqueous acetone ( D = 22.14) and K = 107 and ho= 53.6 for 99% aqueous alcohol ( D = 24.85). The Walden products h o q are 0.605 and 0.619. Assuming that the ionic mobilities of the positive and negative ions are nearly equal, one can estimate the interionic distance a employing Walden's rulell to give 5.32 A for a in 95% aqueous acetone and 5.24 A 99% aqueous ethanol. Considering the approximations involved these two values are certainly similar to each other.
where u is the sound velocity pLmaxi is an amplitude factor for the ith process. The amplitude terms are related via
where T~ is the relaxation time of the ith process. It can be shown13that pm is basically a pure amplitude term (although some kinetic expressions can arise in the coupling of one process to another). The Ai value is a relaxation time weighted amplitude factor. Due to this distinctly different weighting of amplitude, all curves were analyzed in such a way as to produce the best fit of both
390
P. Hemmes, J. N. Costanzo, and F. Jordan
The Journal of Physical Chemistry, Vol. 82, No. 4, 1978
r----l 501
TABLE 111: Rate Constants 95% acetone 2.9 X 10" 2.7 X l o 7 1.7 X lo' 1.1 X 10' 90%acetone 5.9 x I O 9 5.4 x 10' 2.0 x IO6 2.2 x 10'
30
solvent molecule. The relaxation times for this system are given by the expression = '/z[S i:
TIJ-1
(S2
-
4P)"ZI
in which
S = k10 t h-1 t hz t h - 2 P = hl8(kz + h - 2 ) +
12-112-2
From the above it is easy to see that Figure 5. p plot of 0.40 M NMPI in 90% acetone-water (v/v). The circles represent experimental points; the broken curves theoretical plots for the two relaxations; the solid curve is the resultant of the two contributions.
TABLE 11: Results of Fitting Ultrasonic Data to Two Relaxations NMPI Composition concn, M l O O e 95%acetone
0.35 0.30
0.20 0.15 0.10 90%acetone
88% acetone
0.20 0.40 0.60
2.62 2.45 2.05 1.81 1.54 5.19 4.27 3.08
0.45
fr,,
MHz 160 120 100 90 72
fr,,
MHz 1017B 20 53 20 50 20 46 20 40 38
135 125 115
35 35 35
65 70
140
42
65
75
curves simultaneously. A representative data set is shown in Figure 5. This procedure was adopted since a / f curves are more sensitive to assumed parameters for low frequency relaxations (large 7)while I* plots are more sensitive for high frequency effects. The final results of B, f,,, and fr2 are given in Table 11. Also shown in this table are values of 0. The term 0 is given by the equation14
in which d is the degree of dissociation; y* is mean activity coefficient; and c is the total electrolyte concentration. Values of % were calculated from the auxillary relationship
s =T I - 1 + TI;l P = TI-lTII-l Values of the rate constants were obtained by plotting S and P vs. 0. The values of the rate constants are given in Table 111. No values are presented from the 88% mixture since the electrolyte concentrations were so high that the Debye-Huckel law is probably not accurate. Hence 8 cannot be calculated with any degree of confidence. The presence of two relaxations immediately suggests the presence of two or more ion pair types in solution. This was the subject of our preliminary comm~nication.~ The values of kl are in reasonable agreement with that estimated for diffusion-controlled rate constants which were calculated from hoto be 9 X 1O1O M-l s-l (in 95% acetone) by the method of Petrucci.14 The values of kz and k+ are such that the ratio K2 = k z / k - 2 is small. Thus it is evident that the solvent-separated ion pair always predominates. It should be noted also that k-l is subject to large errors since it is obtained as a difference of two large numbers. One feature of the multistep association scheme which has not been previously tested is the presence of the solvent molecule, S. Kinetically, the low frequency relaxation which is concentration independent could be any type of isomerization or pseudoisomerization. Rarely has the process been proven to be a desolvation and never has the order of the reaction with respect to solvent been determined. In pure solvents such determinations are impossible but in mixed solvents one can vary the concentrations of the various solvent components. It is easy to see that the low frequency relaxation is given by the expression 7-1
wherelK is the association constant. This latter was obtained from conductance studies. The quantity yk2was calculated from a Debye-Huckel expression by an iterative process. The value of the ion size parameter a was taken as 4.19 A (from log K vs 1/D plot). For the initial calculation g was taken to be 0.5. A refined value of cr was then calculated from the initial guess of y*2 and the value of K. This new cr value was then cycled in an iterative scheme until lcrl - cri+l[/uL5 0.01. For an analysis of the data, a two step mechanism was assumed in which M+ + L-
k , k2 ;=t M,L F? k-1 k-2
ML
+S
where M+ and L- are the free ions; M,L is the solventseparated ion pair; ML is the contact pair, and S is a
P
--=
N
+ h-2) + h-ih-z + h-1 + hz +
hlO(k2
s
hi0
k-2
If k2,k-2
