1/212
I(1)
= I(I)
+ e-
+ NO$- = ‘//zIz + NOz + ‘/zOz NO2
+ I-
=
l/zIz
+ N02-
(8) (5)
(10)
The net effect of this mechanism is summarized below: 21-
+ NOa- = + NOz- + 1/2O2+ 2e12
(12)
and therefore the overall reaction is simply a one-electron oxidation with respect to iodide. (At potentials greater than +0.5 V NOz- can be electrochemically oxidized to NOz (18, 19), but because the NOz can in turn react with another (19) H. S. Swofford, Jr., and P. 6. McCormick, ANAL.CHEM., 37, 970 (1965).
iodide, the net effect of this cyclic process does not change the above conclusions.) It is important to note that the chemical reduction of I (I) by either the above mechanism or via Reaction 9 results in an overall one-electron oxidation of iodide. However, reduction of I (I) by means of Reaction 5 results in a catalytic current at the electrode surface and therefore accounts for limiting current ratio of greater than unity. RECEIVED for review February 7, 1969. Accepted September 26, 1969. The authors thank the University of Minnesota, the National Science Foundat‘on, and the National Aeronautics and Space Administration for their support of this work.
Use of Electrical Conductivity for Determining Acetolysis rylmethyl p-Toluenesulfona Howell A. Hammond and Andrew Streitwieser, Jr. Department of Chemistry, University of Cal$ornia, Berkeley, Calif. 94720
A conductivity method is described for following the rates of solvolysis of substituted benzyl and polycyclic arylmethyl p-toluenesulfonates in anhydrous acetic acid. Small amounts of water and variations in temperature have important effects and precautions are described for handling these effects. Errors are somewhat larger than in titrimetric studies, but the averages of replicated experiments by conductivity agree well with independent determinations by other methods. The conductivity method is especially suitable for systems of high reactivity or low solubility, or in scarce supply. FORSOME YEARS we have been interested in acetolysis kinetic data for various arylmethyl p-toluenesulfonates (tosylates) for comparisons with molecular orbital calculations ( I ) . Although many of these data were available by titrimetric methods (2), limitations of solubility and reactivity precluded application to several polycyclic systems of interest. The convenient spectroscopic method of Swain and Morgan (3) cannot be applied in this case because of insufficient spectral differences between the aromatic sulfonate esters and p-toluenesulfonic acid in acetic acid. The successes of Dewar and Sampson (4), Huisgen and coworkers (3,and Fierens, Halleux, and Hannaert (6) with electrical conductivity as a kinetic method in aqueous formic acid and acetone suggested the possibility of using this method in acetic acid. The low dielectric constant of acetic acid and the consequent sensitivity of conductance to traces of water render impractical the evaluation of the parameters required (1) A. Streitwieser, Jr., “Molecular Orbital Theory for Organic Chemistry,” Wiley, New York, 1961. (2) A. Streitwieser, Jr., H. A. Hammond, R. M. Williams, R. H. Jagow, and C. J. Chang, in preparation. (3) C. 6.Swain and C. R. Morgan, J. Org. Chem., 29,2097 (1964). (4) M. J. S . Dewar and R. J. Sampson, J. Chern. Soc., 1956,2789. (5) . , R. Huisgen, E. Rauenbush, 6. Seidl, and I. Wimmer, Ann., 671,4i (i964j. (6) . , P. J. C. Fierens, A. Halleux, and H. Hannaert, Bull. SOC.Chim. Belg., 64, 191 (1955). 2032
0
in the Fuoss-Onsager conductance equation by standard solutions o f p-toluenesulfonic acid. However, Gramstad (7) found that plots of specific conductance 1;s.concentration were linear for acetic acid solutions of a range of acids varying from trifluoromethanesulfonic acid to methanesulfonic acid. This suggests that such a proportionality can be used directly for kinetic studies. EXPERIMENTAL
Apparatus. Resistance measurements were made with the circuit shown in Figure 1 connected to a Leeds & Northrup Speedomax-H recorder. The detector places an ac signal across a Wheatstone bridge containing the cell and a variable decade resistance box. Two choppers, 180” out of phase, are driven by the same ac signal and alternately display the potential between A and B to the recorder. The recorder reads zero when the decade resistance box is set equal to the cell resistance, R. If the decade resistance is decreased, the recorder reading increases. The difference between the decade resistance and the cell resistance at full scale can be adjusted by the span calibrator, S.C.; the recorder can be calibrated by substituting another standard resistance box for the cell, or during the run by periodically noting the value of IC required to zero the recorder. The system may be continuously monitored by interpolating between zero points. Procedure. The conductivity cell (Figure 2) was washed with warm cleaning solution and rinsed several times with distilled water before the first use. After each use the cell was washed with distilled acetone, blown dry with nitrogen, and aged 24 to 72 hours with the kinetic solvent, to reduce downward drift of resistance. A run was initiated by syringing an aliquot of substrate in carrier solvent into the “aged” cell. Mixing was accomplished by removing the cell, inverting it, replacing in the bath, and shaking. Two techniques were generally used. In the “zero technique” the decade resistance was set to a value slightly below the cell resistance and the recorder pen was allowed to fall to zero. (7) T. Gramstad, Tidsskr. Kjemi, Bergvesen, Met., 19, 62 (1959).
ANALYTICAL CHEMISTRY, VOL. 41, NO. 14, DECEMBER 1969
TRIAD
4
F52X 6.3V
@RED
I
4 C
Recorder Out
Figure 1. Circuits used for conductivity system
I At the end of the run the times of the zero points were read from the recorder chart. For some of the faster runs, a "continuous monitoring" method was used, in which the span calibrator was set at a value such that the full-scale deflection was about equal to K O - K , and the decade box was set at R,. At the beginning of the run, the recorder pen was at full scale and, at the end, it was near zero. After the run was completed, the values of R were interpolated from the graph of recorder reading us. time. The bath temperature was generally checked repeatedly during a run because the conductance is a sensitive function of temperature, decreasing about 3z per degree rise. Since the total change in 1/R is typically about 2 to lo%, precise temperature stability is essential. In a few of the early runs a commercial bridge (ES1) was used. Chemicals. Anhydrous acetic acid was prepared by refluxing reagent grade glacial acetic acid with -10% acetic anhydride and an acid catalyst (sulfuric or p-toluenesulfonic acid). After refluxing overnight, the acetic acid was distilled through a 40-plate perforated glass plate column and collected over a 0.5" range (117" to 117.5' uncorrected). The acetic acid was stored in a flask equipped with a siphon-like arrangement so that it could be removed using a positive pressure of dry nitrogen without exposing it to air. The preparation and properties of the tosylates are described elsewhere ( 2 ) .
b
7
Figure 2. Conductivity cell used with anhydrous acetic acid solvolysis studies
I+-I
E
3 c m i.d.
A = Side a r m inlet w i t h serum cap B = Uranium-tungsten seals C = P l a t i n u m electrodes ( I I ' X l " X . 0 0 6 " ) D = Glass electrode-supports (-1.5 m m t h i c k )
ANALYTICAL CHEMISTRY, VOL. 41, NO. 14, DECEMBER 1969
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RESULTS AND DISCUSSION
Figure 3 shows the conductance-concentration relationship we observed for p-toluenesulfonic acid solutions at 40°C and shows that the concentration should be linearly related to conductance at concentrations less than 10-3M and above 10-ZM. Thus, we solvolyzed several arylmethyl tosylates, following their rates conductometrically by assuming the concentration of p-toluenesulfonic acid to be proportional to the inverse of the resistance of the solution, and independently compared the rates thus obtained with the titrimetric rates obtained. Evaluation of Data. For best results data were collected over a long enough period to allow short period temperature variations to go through several cycles but not so long that the change in conductance due to a drift in the average temperature was an appreciable fraction of the change due to solvolysis. This imposed a lower limit on the reactivities of samples that could be studied; when the acetolysis rate was too slow it was not possible to keep the drift small enough, In general, measurements were taken for about ten half lives and the rate constants were determined by least squares fitting of the data to Equation 1 by use of DeTar’s LSKIN program (8). When the data for only the first two or three half lives were used to determine the parameters of Equation 1 and the results were plotted on a semilogarithmic scale,
15
IO
c
/
/
/
/
/
Figure 3. Electrical conductance of p-toluenesulfonic acid in acetic acid
(8) D. F.DeTar and C. E. DeTar, “Computer Programs in Chemistry,” Vol. I, W. A. Benjamin, New York, 1968.
-
2-BIPMENYLENYLMETHYL TOSYLATE ACETOLYSIS FOLLOWED CONDUCTOMETRICALLY TEMP. 25.0 - 0.2 ML HOAC SOLUTION IN 30 ML HOAC NONLINEAR LEAST SOUARES F I T OF DATA TO X - X ( I ) - ( X ( I ) - X ( O ) ) E X P ( - K I T I 1
I
I
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1.1225E-03 2.0682E 00 2.1890E 00
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1-
0.
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200
10
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I
I
I
600 * 0
MINUTES
I
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600.0
I
1000.0
Figure 4. Direct reproduction of CalComp plot for a kinetic run Experimental points compared with calculated curve 2034
e
ANALYTICAL CHEMISTRY, VOL. 41, NO. 14, DECEMBER 1969
I
I
1200.0
I
1400.0
YEIGHTFO RESI0UAI.S
(OBSD.-CALCfl.l
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Figure 5. Residuals for run 3.083 1.4 to 1230 minutes b. 9 to 1230 minutes a.
ANALYTICAL CHEMISTRY, VOL. 41, NO. 14, DECEMBER 1969
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Run No. 2.053 2.042 2.041 2.071 1.211 1.123 1.235 1.129 1.207 1.223 1.225 1.229 2.248 2.250 2.253 2.255 2.258 2.262 2.264 2.107 2.121 2.125 2.131 2.154 2.156 2.133 2.142 2.145 2.149 2.152 2.199 2.201 2,271 2.286 2.273 2.277 2 280 2.282 2.284 3.071 3.073 3.085 3.083 3.088 3 090 3.092 I
Table I. Conductometric Rates for Acetolysis of Arylmethyl Tosylates Observation lo5 X k , sec-l, Temp., “C Concn, molar Methoda interval, sec f std error p-Chlorophenyl 39.9 C1-A 1000-170,000 0.0002 0.86 f 0.08 60.0 0,0002 CI-A 1000-114,000 6.41 i 0.14 60.0 0,0004 C1-A 1600-85,000 7.55 f 0.08) 60.0 0.0004 C1-A 4000-71,000 7.67 f 0.08 p-Fluorop henyl 25 .O 0.08 CI-A 4000-175,000 0.75 f 0.06 12.2 f 0.4 Cl-A 1000-35,000 50. 0.0004 12.3 f 0.3 C1-A 3000-63 ,OOO 50.1 0.05 41.6 f 1.3 60.0 0.0004 C1-A 900-8,500 60.0 44.2 f 0 . 4 C1-A 1000-17,400 0.2 60.0 C1-A 800-7,700 37.6 f 2.3 0.0004 60.0 C1-A 1000--17,000 0.0004 34.7 f 1.0 43.8 f 1 , l 60.0 C1-A lOOO-17,OOO 0.0004 60.0 36.1 i 0.6 C3-B 900-20,600 0.003 60.0 0,005 42.5 f 0 . 9 C3-B 800-19,200 60.0 c3-c 0,0008 900-1 5,600 36.5 f 1.5 32.8 f 0.7 60.0 0.0004 c3-c 900-20,400 36.9 4 0.6 60.0 0.0002 c2-c 900-21,000 42.9 f 0.2 60.0 0.0002 c2-c 900-18,000 37.8 i 0.5 J 60.0 C2-B 900-18,000 0.0008 p-Methylphenyl 40.0 0.06 C3-A 600-2,500 95.9 i 0 . 7 C3-A 980-3,lOO 40.0 99. =t 1 0.03 100. i 0.3 C3-A 708-3,500 40.0 0.0004 85.8 f 1 . 8 C3-A 740-5,400 40.0 0,001 C3-A 645-3,600 240. f 3 50. ... 267. =t 3 C3-A 500-2,700 50.0 0.008 C3-A 190-1,200 60 0.0004 (400 f 62)) 59.8 701 = t ~16 C3-A 260-1,800 0.0004 C3-A 210-1,200 0.0005 (766 i 30)/ 59.8 C3-A 180-1,200 0.0005 709 f 10 } 59.8 C3-A 0.008 59.8 280-1,200 712 f 7’ 0.002 60.1 C3-D l80-1,500 731 f 8 1 C3-D 230-1,800 59.8 0.008 740 f 10 J 3-Phenanthryl 39.8 o.oO01 C3-B 130-11,OOO C2-B 500-12,500 39.9 ... 59.7 C2-B 300-1,800 o.oO01 C2-B 138-650 567 =t 4 59.7 0.0006 C2-B 85-1 ,000 59.7 0.0001 f 12 750 C2-B 110-610 683 f 17 , 59.7 o.OOO1 59.7 o.oO01 C2-B 75-1 ,000 617 f5 1 2-Anthracyl 290 f 23 C2-B 190-2,200 40.0 O.ooOo4 280 C2-B 170-2,100 f 16 O.ooOo6 40.0 2-Biphenylenyl 1.72 f 0.03 25.0 0.0007 C2-A 1500-90,000 9.65 f 0.27 C2-A 540-74 ,000 40 0.0007 9.2 f 0.12, C2-A 2COO-82, 000 40 0.001 55 i 1 C2-A 900-15,000 60 0.0005 80 h 2 , C2-A 960-17, OOO 60 O.aO07
t
1
1
t
c
Av k X lo6, f est error
0.86 f 0.1 7.2 f 0 . 4
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39
f2
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i4
254
=t20
712
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85
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653
f 35
285
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20
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f9
a C1 = conductivity followed with commercial (ESI) impedance bridge; C2 = conductivity followed with ac to dc conductivity detector using “zero technique”; C3 = conductivity followed with ac to dc conductivity detector using “continuous monitoring technique.” A = acetic acid carrier; B = ethyl ether carrier; C = chloroform carrier; D = acetonitrile carrier. Instrumental difficulties encountered making analysis uncertain-e.g., for interval 1.7 to 207 minutes, k = 85 =k 8 but residuals were not distributed randomly.
l/R1= 1/R - (1/R- l/Ro).e-kt
(1)
curvature was observed in many of the plots, but when data over a period of ten half lives were included, the curvature disappeared. Correspondingly, the plot on a linear scale gave a smooth exponential curve as in Figure 4. The residuals plot from DeTar’s program was very helpful in evaluating the 2036
*
data. If data from too early or too late in the reaction were included, they forced an erroneous fit to Equation 1 and this was reflected in the residuals plot. For example, in run 3.083, if data taken prior to reaching thermal equilibrium are included, the residuals are obviously not random (Figure 5 , a). When they are omitted (Figure 5, b) the distribution of residuals is random.
ANALYTICAL CHEMISTRY, VOL. 41, NO. 14, DECEMBER 1969
Rate Constants. The conductometric rates are presented in Table I. The comparison (Table 11) shows that the conductometric method is sufficiently accurate to warrant its use when the reactivity, solubility, o r availability of a compound makes the titrimetric method useless. However, several points concerning the properties of the system should be emphasized. Precautions. First, anhydrous acetic acid has a dielectric constant of 6.2 at 20 OC; hence, the dissociation of ion pairs into free ions which conduct the electricity is drastically affected by even small amounts of water. Thus, it was necessary to exclude moisture leaks in the cell rigorously and to age the cell with the kinetic solvent for at least 18 hours. This usually resulted in a steady value for the solvent conductance. Second, the resistance of acetic acid solutions is a sensitive function of temperature, decreasing about 3 for each 1'C rise in temperature. Since the total change in conductance in a typical experiment is only 2 to 10 a gradual change in temperature can greatly affect the calculated rate constant. For example, if one is examining a reaction where the infinity conductance is 10 x 10-6 ohm-1 and the zero conductance is 9 x 10-8 ohm-1, a change of 0.03OC can change R by (0.03 X 108/9 x 0.03) 'V 0.1 kiloohm, or about 1 of the total change in R from time zero to time infinity. Even if the temperature change is periodic, the effect on a rate constant derived from a segment of the data can be great. Thus, the temperature should be carefully controlled and recorded with each reading. As shown in Figure 3, there is evidently a region of concentration in which 1/R is not a linear function of the concentration of p-toluenesulfonic acid. It appears that this region is between loM3and 10-2M. However, these limits probably vary with changes in temperature and the concentration of other conductors present, so that the region of nonlinearity is not generally known beforehand. This problem was handled by trial and error determination of the concentration of a tosylate that would give data fitting Equation 1 such that there was no over-all curvature in the fit. These limitations produce errors that are well demonstrated by the results in Table I. For precise work, replicate results are necessary. The average of several runs agrees well with the titrimetric studies. On the other hand, a kinetic run can be carried out conveniently with only micromoles (-1 mg) of material, a feature that is especially important when solubility and availability of material are limited.
Table 11. Comparison of Conductometric Rates with Titrimetric Rates k X lo5,sec-l ConductoAryl group % difference Titrimetric" metric and temperature +2.4 0.84 0.86 p-Chlorophenyl, 40' -4.0 7.5 7.2 p-Chlorophenyl, 60" f4.0 0.72 0.75 p-Fluorophenyl, 25" +s.4 37 39 p-Fluorophenyl, 60" -1.0 96 9s p-Methylphenyl, 40 -5.9 254 270 p-Methylphenyl, 50" 0.0 85 85 3-Phenanthryl, 40" -1.0 300 297 2-Anthracyl, 40' Av. ' ~ 3 % O
z
z,
ACKNOWLEDGMENT
We are indebted to D.F. DeTar for a copy of his program. RECEIVED for review February 12,1969. Accepted September 15, 1969. Study supported in part by grant 1002-66, Air Force Office of Scientific Research, by a grant from the Petroleum Research Fund of the American Chemical Society, and by a National Institutes of Health predoctorai fellowship to H.A.H. for 1964-7.
CORRECTION
A Single Scale for Ion Activities and Electrode Potentials in Ethanol-Wa,ter Solvents Based on the Triisoamylbutylammonium Tetraphenylborate Assumption In this article by Orest Popovych and Aloys J. Dill [ANAL. CHEM.,41, 456 (1969)l the final sentence of the text on page 462 should read "In anhydrous ethanol, all Eo's exhibit a positive shift by about 0.1 volt, relative to their nonaqueous values, $Eo(i,SH)."
ANALYTICAL CHEMISTRY, VOL. 41, NO. 14,DECEMBER 1969
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