Lithium Aluminum Di-n-Butyl Amide as a Direct Acid-Base Tit rant for Quantitative Determination of Silanol Gene E. Kelluml and Kenneth L. Uglum Central Michigan University, Mount Pleasant,
Mich.
A new and general method for the determination of silanol and water was developed. Silanol was determined as a weak acid by direct titration utilizing lithium aluminum di-n-butyl amide as the base. Monomeric, simple, and polymeric silanols were analyzed along with several silicone resins. The end point in the titration was detected with N-phenyl-p-aminoazobenzene. Reaction times varied from 30 to 40 seconds for simple compounds and from 40 to 90 seconds for resins. Water was shown to react to only 75% of expected values in several experiments. Small, highly polar alcohols were also observed to react more efficiently than silanol or larger alcohols did with the reagent. Low results were obtained for alcoholic hydroxyl when the dielectric constant was greater than 23 and the area of the alkoxy group smaller than 33 A%. Several potential interfering functional groups were studied. Results indicated that no interference was present in the method from silicon hydride (SiH), alkoxy silane (SiOR), strained siloxane, or vinyl. The acetoxy silane (SiOAc) group produced indicator difficulties. Accuracy and precision of the new method were shown to be excellent on all samples tried. Relative standard deviations for simple and polymeric silanols were 0.25 to 1.2%. For resins, the relative standard deviation values varied generally from 0.25 to 3.0%.
USEOF LITHIUM aluminum amides for functional group analysis has been limited. This reagent was used for determination of hydroxyl in a few alcohols by Higuchi, Concha, and Kuramoto (1). They noted reaction with carbonyl-containing compounds when using back titration techniques. The hydroxyl in a few ethanolamines was determined by Small using a direct titration ( 2 ) . Jordan selectively titrated the hydroxyl in high molecular alcohols using the di-n-butyl amide derivative. The stoichiometry of the hydroxyl reaction has been suggested by Jordan (3)to be: 4 ROH
+ LiAl(N-Bu&
+
4 BuzNH
+ LiOR + Al(OR)$
(1)
The affinity of nitrogen for hydrogen is significantly greater than the affinity of oxygen for hydrogen; therefore, the equilibrium should lie far to the right in this reaction. A visual indicator may be utilized in this titration system. The indicator found most useful in previous work has been N-phenyl-paminoazobenzene (1-3). Silanols have been shown to exhibit greater acidity than the corresponding alcohols. They should, therefore, react at least as well as carbinol in the lithium aluminum amide system. The absence of strong acids and bases should eliminate most interfering side reactions, The structure of lithium aluminum amide is not known with certainty. No convincing evidence has been presented as to Present address, Gulf Research and Development Co., Kansas City Laboratory, 9009 W. 67th St., Merriam, Kan. 66204. (1) T. Higuchi, J. Concha, and R. Kuramoto, ANAL.CHEM.,24,
685 (1952). (2) L. A. Small, Analyst, 84,995 (1959). (3) D. E. Jordan, Anal. Chim.Acta, 30,297 (1964).
the stoichiometry of the hydroxyl reactions. The reaction of water has not been reported and apparently the visual end point has not been confirmed by potentiometric titration. In the work presented here a study was made into the reaction of lithium aluminum di-n-butyl amide (amide) with a wide variety of silanol-containing materials. The reaction of water in this system was characterized, and the reaction of alcoholic hydroxyl was studied using many different compounds. Potential interfering reactions in the silicone system were also studied in detail and the visual end point was confirmed by potentiometric titration. EXPERIMENTAL
Reagents. Ansul 121 ether (dimethyloxyethane) dried over molecular sieves, Ansul Go. Lithium aluminum hydride, 95+% pure, Metal Hydride, Inc. Di-n-butyl amine, Eastman Org. Chemical No. 1260. A'-phenyl-p-aminoazobenzene, Eastman No, 1714, (prepared in a 0.1% benzene solution). Tetrahydrofuran (THF), reagent grade; and pyridine, reagent grade. Apparatus. Three-necked flask, lOOO-ml., round-bottomed, with 29/42 T joints. Three 29/42 T plugs, two with hose fittings. Water condenser, 20-cm., with 29/42 T upper and lower joints. Dropping funnel, 50-ml, with 29/42 T joint on bottom. Magnetic stirrer. Heating mantle, lOOO-ml, and Variac. Source of dry nitrogen gas flow. Titration Apparatus. The titration buret was a 10-ml autozeroing type with attached closed reservoir and Teflon stopcock, available from Arthur H. Thomas Co. The titration cell was constructed from a 55/50 T joint with the bottom closed off for stirring. The top was closed OR and two 1j2-inch and two l/.,-inch ports were added so like-sized holes were across from each other. The large holes were used for sample introduction and to hold the buret tip. Serum bottle stoppers were employed to seal these ports with the one holding the buret drilled to fit tightly around the tip. This arrangement allowed easy removal of the buret from the cell and a tight seal when it was in place for titrations. The two small ports were fitted with serum bottle caps holding 19-gauge, 3-inch needles. The titration cell and buret reservoir were maintained under a dry nitrogen purge of 10 to 20 ml per minute. The nitrogen was first passed through molecular sieves, then into a chamber containing calcium sulfate. The line was then split into two lines, one going to the titration cell and the other to the reagent reservoir. In the line leading to the titration cell the nitrogen passed through a drying tube filled with barium oxide. A drying tube filled with calcium sulfate was connected to the inlet of the reagent reservoir. This apparatus allowed a continual supply of very dry nitrogen. Procedure. The reagent was prepared by reacting lithium aluminum hydride with di-a-butyl amine: LiAlH4
+ 4(CdH&NH
4Hz
+ LiAI[N(CkH9)2]4
(2) The dry 1000-ml round-bottomed flask was positioned above the magnetic stirrer and 700 ml of dry ether added along with a Teflon-covered stirring bar. The ether was dried by passing it slowly through a 15 X 1-inch column of 5A molecular sieves. One T plug with a hose fitting was put in place along with the water condenser. The T joints were lubri-+
VOL. 39, NO. 13, NOVEMBER 1967
o
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Table I. Determination of Total Hydroxyl in Monomeric Silanols Mean Compound CH3)3SiOH (CeH5)(CHs)&OH (CeHa)dX3SiOH
No obs 6 6 3 4 (C6H&SiOH 6 4 (CeH&Si(OH)a 6 (CH2=CH)(CH3)sSiOH 5
OH
18.6 11.0
8.40 7.48 6.32 6.27 15.0 16.8
Std dev (=I= OH) 0.0800 0.128 0.0531 0.0735 0,0800 0.0539 0.0960
z
0.129
Re1 std dev (rt %) 0.429 1.16 0,632 0.983 1.27 0.860 0,638 0.768
Table 11. Determination of Total Hydroxyl in Simple Silanols Re1 Mean Std dev stddev Compound Noobs % O H (=I= %OH) (.t %> [HO(CHa)aSilG& 6 15.0 0.284 1.90 [HO(CH3)2Silp0 4 19.9 0.294 1.48 4 19.7 0.206 1.05 [(CH3)3Si0]2CH8SiOH 6 6.95 0.120 1.74 6 7.26 0.284 3.91 [(CHa)aSiO]~C&&OH 6 6.02 0.0920 1.53 4 5.82 0.103 1.77 5 5.89 0.0989 1.68 5 5.86 0.107 1.83 4 5.83 0.00980 0,168 {HO[(CH3)3SiO]aSi) 2 0 6 8.13 0.212 2.61 Table 111. Determination of Total Hydroxyl in Polymers and Silicone Resins Re1 Mean Std dev stddev Sample No obs Z OH (.t %OH) (=t%) 0.0430 0.883 HO[(CsH5)(CH,)SiO].H 5 4.83 0.0774 HO[(CH2=CH)(CH3)SiO].H 5 3.75 2.06 0.0602 1.60 HO[(CH3)&O],H 5 3.75 0.0637 Resin 1 4 2.66 2.40 0.150 Resin 2 6 7.24 2.08 0.0295 Resin 3 3 0.933 3.16 0.00245 Resin 4 4 0.717 0.345 0.0885 3.32 Resin 5 3 2.66 0.127 Resin 6 4 2.79 4.55
cated with Kel-F stopcock grease. A nitrogen purge of 10 ml per minute was begun. A few drops of indicator were then added. Small portions of lithium aluminum hydride were added to the ether, which was being stirred at a moderate rate, until the indicator changed from yellow to purple permanently, signifying an excess of hydride present. An additional 2 grams of LiAlHd was added and the last standard taper plug put into place. The magnetic stirrer was removed and replaced with the heating mantle. The heating mantle was turned on and the Variac adjusted to give a moderate rate of reflux which was maintained for 20 minutes. The reflux was then adjusted to a gentle rate while 40 ml of di-nbutyl amine was placed in the dropping funnel which was positioned on top of the water condenser. The stopcock of the dropping funnel was opened to allow 1 drop of amine to fall directly into the reaction flask each 3 to 4 seconds. The rate of reflux increased from heat of reaction and evolution of hydrogen. After about 50% of the amine was added, the rate of addition was increased to a drop every 1 to 2 seconds. After the last of the amine was added, the Variac was turned up to give a rapid reflux for 10 minutes. The Variac was turned off. The water condenser was replaced by the second standard taper plug with a hose fitting. The reagent was 1624
m
ANALYTICAL CHEMISTRY
left under a slow nitrogen purge for 24 hours to allow the solids to settle out. The reagent was filtered rapidly through a Buchner funnel filled with glass woo! into a 1-liter flask. An alternate approach was to siphon the reagent carefully into the titration apparatus. The apparatus was closed and a drying tube containing calcium sulfate was connected to the reservoir vent. Titration Procedure. Forty milliliters of dry 1 : I THFpyridine and 5 drops of the 0.1% indicator solution are added to the titration cell and titrated to a purple-red color persisting for about 1 minute. A weight of sample or standard sufficient to give about 5 ml reagent consumption is added to the cell and titrated to a red color persisting for about 2 minutes. This serves as a pretreatment for the solvent and indicator system. Liquid samples are added from a small weighing-dropper bottle, or solids are added from an iodine cup in sufficient quantity to give about 4 or 5 ml consumption. Sample weights are obtained by difference before and after sample addition. The titration generally requires 30 to 40 seconds to a stable end point. The standardization procedure employed 3-methyl-lbutanol as the source of hydroxyl. The alcohol had been dried carefully through a 15-inch by 1-inch column of chromatographic 5A molecular sieves of 80- to 100-mesh size. The water content was reduced to less than 0.05% generally, making the total hydroxyl content 19.4z. Four determinations were made each time the reagent was standardized. The reagent was restandardized at the beginning of each day of use. RESULTS AND DISCUSSION
The silanol compounds used in this study were of unknown purity. Some were expected to be pure, but others were between 80 and 100% pure. The materials were considered to contain unknown amounts of hydroxyl, siloxane, and water. To determine how pure the reference materials were, three published hydroxyl methods were applied to samples for which they were known to be accurate. The small quantities of water present were determined by a modified Karl Fischer reagent titration method ( 4 ) . To determine the purity of monomeric and simple silanols, the NMR method described by Hampton, Lacefield, and Hyde et al. was employed (5). Total hydroxyl in polymers was determined by the LiAlHd method described by Barnes and Daughenbaugh et a/. (6) and the condensation method presented by Smith and Kellum (7). The hydroxyl in silicone resins was also determined by the condensation method of Smith and Kellum. The total hydroxyl was determined by titration with amide reagent before the purity of any reference compound was established. This set up a real analysis situation where purity was an unknown and limited the possibility of bias due to having known materials. Table I presents the titration data for determination of total hydroxyl in six monomeric silanols. The number of observations is given along with the standard deviations and relative standard deviations. Table I1 gives the data obtained for total hydroxyl present in the simple silanols employed for study. Five different compounds were available for study. A few of the samples were analyzed more than once over a period of several months. The precision for determination of total hydroxyl in the various materials was (4) R. C . Smith and 6.E. Kellum, ANAL.CHEW., 38,67 (1966). (5) J. P;. Hampton, C. W. Lacefield, and J. F. Hyde, Inorg. Chem., 4, 1659 (1965). (6) G. H. Barnes, Jr., and N. E. Daughenbaugh, ANAL.CHEW, 35, 1308 (1963). (7) R. C . Snuth and G. E. Kellum, Ibid., 39, 338 (1967).
Table IV. Titration and Recovery of Water in Absence of Other Hydroxyl-Containing Materials Re1 OH HzO, OH, N Amide, recovered, regrams grams amide ml grams covery 75.1 4.80 0.0135 0.166 0,0180 0.00950 0.0165 74.7 0.147 6.59 0.0117 0.0221 75.0 10.85 0.0247 0.134 0.0174 0.0329 0.0155 76.8 0.134 6.80 0.0107 0.0202
z
relatively constant even though the silanol and water concentrations varied considerably. Table 111 shows the data for determination of total hydroxyl in three polymers and six silicone resins. The precision obtained for polymers was consistent with that obtained for the simple compounds, but in this study resins produced poorer and somewhat variable precision. This was attributed to slightly slower reactions and inexperience. A marked improvement in precision would occur with greater experience. In some instances the precision was as good as reported for simpler materials. The reaction of water had never been reported; therefore, it was studied in some detail here. It is imperative to be able to correct for water present in silanols, so it was necessary to ascertain how water reacted with the amide reagent. Table IV gives the data obtained in several experiments where water was titrated by itself over a period of several months. The data show conclusively that only 75% of the water added is recovered. In some instances the titrations were performed before alcohol or silanol had been titrated, but in others water was determined after silanol or carbinol. A back titration ex-
Experiment H20
SiOH
Table V. Titration and Recovery of Water with and without Silanol % OH in THF Re1 % Run No by KFR by Amide recovery 2.06 I 2.72 75.7 1.45 1.90 76.3 I1
I I1
Mixture
periment was run where water was added to a fourfold excess of reagent. Table V gives the data from a study where a known concentration of water in T H F was determined by titration with amide, then a silanol compound added to it, and the total hydroxyl determined, Under all titration conditions, the recovery of water was only 75 %. The total hydroxyl results from the new procedure were compared to theory and data obtained employing the previously reported methods, Table VI presents comparative data from the new and other procedures for monomeric and simple silanols. Results on the monomeric silanols were compared with those by NMR, LiA1H4, and BF3 condensation. The simple silanols listed were compared with the same reference methods. The results show that the new method is as accurate as the methods used for reference. Agreement with NMR and condensation results were excellent in every case. The new method generally agreed with NMR results to within a relative 0.25 to 1.2%. The lithium aluminum hydride data tended to be high in most instances. The new method is capable of accurate determination of silanol plus water in any type of simple silanol compound. Table VI1 presents comparative data for the polymers and resins used for study. The condensation method and LiA1H4 procedure were employed as reference methods for these materials. The new method agreed well with the supporting schemes in every instance, varying typically by a relative 0.7 to 3.2% from the condensation procedure and a relative 0 to 1.8 % from the LiAlH4 method. The small difference in results from the various procedures indicates the accuracy of the new method. The reaction of water indicated that a major difference in stoichiometry existed between it and the reaction of hydroxyl
I
I1
Silanol compound (C6Hd(CH&SiOH (CsH&SiOH Calcd total % OH With 100% With 75 recovery of water recovery of water 9.03 8.88 3.29 2.99
% OH in Compound 10.90 6.27
% OH found 8.87 2.69
% THF in mixture 22.9 66.7
% Compound in mixture 77.1 33.3 Re1 of water recovered, assuming 75 % reaction 100 91
Table VI. Accuracy of New Procedure by Comparison of Results for Purity of Monomeric Silanols with Values from Other Methods Purity Compound OH theory By Amide By NMR By LiAIHl By BFa-Cond 18.9 80.9 78-80 90.3 11.2 88.3 86.9 88.3 7.94 89.0 88.9 90.2 6.17 92.7 91.4 15.7 90.1 90.0 91.7 90.0 16.6 98.7 97-99 15.0 99.3 100 102.5 7.13 97.7-99.6 97.8-98 101 5.67 98.8-99.8 100 97.3-97.7 7.21 95.8 93 113 95.7
VOL. 39, NO. 13, NOVEMBER 1967
e
1625
80
c, I
20
10
30 DIELECTRIC
40
V
80
CONSTANT
76
12
Figure 1. Recovery of alcoholic hydroxyl as a function of dielectric constant X H20 0 CWjOH A CH3CHzOH
I
I
1
28
32
36
I
I
I
40
44
48
ALKOXY GROUP AREA, A'
Figure 2. Recovery of alcoholic hydroxyl as a function of alkoxy group area
CHB(CH~)ICH~OH 0' (CH3)zCHCHzCHzOH '0 CHj(CHn)sCH20H @ CHdCHz)ieCH:OH
8.CsHjCHzOH
HOCHzCHZOH HOCHzCHzCHzOH CH3CHOH(CH2)2CHOHCH3 .'HOCHzCHOHCHzOH
H
by BFs
cond 4.80-4.92 3.73-3.88 3.78 3.75 3.78-3.82 0.939 7.13 0.732 2.70
By LiAlHa
CH30H
B (CH3)sCOH
zOH
Table VIII. Comparison of Calculated and Observed Reagent Normalities Re1 LiAIH4, BuzNH, A-121, N diff grams ml ml Caicd Found flc 2.32 46.5 750 0.308 0.222 75.9 44 2.23 780 0.286 0.199 73.3 2.01 41 750 0.266 0.187 74.2 2.00 40 0.251 0.167 800 70.2 2.20 44 660 0.330 0.232 74.2
ANALYTICAL CHEMISTRY
I
24
0
Table \'EL Comparison of Results from New and Other Procedures for Total Hydroxyl in Polymers and Resins
a
I
20
A CH3CH20H o CHsCHzCHzOH A (CH3)zCHOH
on carbon and silicon. We found that comparison of normalities of various lots of reagent obtained and calculated from the lithium aluminum hydride used did not agree. The normalities found were 25 % lower than calculated, based upon the 95+ % EiAIHl employed for reagent syntheses. Table VIII presents comparisons of normalities for several differenr lots of reagent. These data indicate that hydroxyl groups on silicon and carbon possibly reacted with only three of the four amino groups on the reagent molecule, whereas water removed all
1626
16
X HzO
CHaCH2CHzOH A fCH3)zCHOH CH3(CH&CHzOH 8 (CH3)sCOH d (CH~)ZCNCHICH~OH b CH3(CH2)iCHzOH @ CH8(CH2(iGCH20H -@ CeHjCHzOH iY HOCHzCH20H P HOCHzCHzCHsOH CH3CHOH(CHz)zCHOHCH3 HOCHzCHOHCHzOH @
Compound By Amide PWQ[(C8H6)CH3SiO],H 4.83 HO[(CH2=CH)CH3SiO].H 3.75 HO[(CHa)~SiQ],H 3.75 Resin No 1 0.933 Resin No 3 7.12-7.34 Resin No 4 0.717 Resin No 5 2.79
X I
four. This would oppose the reaction proposed by Jordan. It was hypothesized that small polar alcohols might exhibit reactions which led to low results in the same way as water. The stoichiometry, however, was expected to be nearer that of silanol and higher alcohols than to water. Figures 1 and 2 present the data obtained from titration of 14 different alcohols. All samples were of reagent grade and the small water concentrations present were corrected for by Karl Fischer reagent titration. The sample of methanol was analyzed by LiAlH4and acetylation procedures and was shown to be pure. The coordinates in Figure 1 and Figure 2 are dielectric constant and alkoxy group area cs. relative per cent recovery of the alcoholic hydroxyl. Figure 1 shows that small polar alcohols and diols do not react the same as silanol or higher alcohols, based upon the standard hydroxyl sample. Monohydroxy1 alcohols give a different trend than di- and trihydroxy1 alcohols. Both curves coincide at a dielectric constant of 22 to 24 and greater than 99% recovery. Figure 2 gives the plot of alkoxy group area cs. relative per cent recovery of hydroxyl and shows a single trend existing between alkoxy group area and recovery. This would indicate that mostly a steric effect influenced the yield of the hydroxyl reaction. At an alkoxy group area of 32 to 34 A2, results were quantitative and remained so up to at least the CIFalcohol. The polarity or steric requirements established from the above experiments have little practical effect upon the analysis of silanol. The dielectric constants of even simple silanols are probably lower than 24 and the area of the various siloxy groups is larger than 34 A2. Higuchi, Concha, and Kuramoto titrated a few alcohols during their studies ( I ) . Their data did show a relative 2 tcr 3 difference in results for ethanol and butanol, but they did not correlate it to anything. Jordan titrated fairly large al-
cohols; therefore, he did not encounter the difficulty of variable results (3). Several potential interfering side reactions were studied in depth. Results indicated that silane hydrogen (SiH), alkoxy silane (SiOR), strained siloxane, and vinyl did not interfere under any titration conditions. Acetoxy silane (SiOAc) produced an unknown reaction with the indicator which prevented the color change from being observed easily. No positive evidence was obtained that the group was actually reacting with the reagent, Potentiometric end points were measured with glass combination and platinum-graphite electrodes in an attempt to confirm the color change of the visual indicator. The curves obtained were not of excellent quality but definitely showed the indicator color change occurring within the last 20 of the curve. This was satisfactory for a visual indicator in this weak acid system. Tetrahydrofuran (THF) was used as titration solvent by previous workers (1-3). We found that initial titration r’esults for carbinol and silanol were always high with T H F as the solvent. This had not been reported previously, With two or three successive determinations, results dropped to expected values and remained there. After the first of a series of sam-
z
ples was run, no further difficulties were encountered. The problem most likely arises from production of di-n-butyl amine in the titration which changes the basic strength of the overall system, at least at first. The solution to the problem was found by employing a 1 :1 co-solvent of THF and pyridine. This largely eliminated the effects noted above. Since the standardization and sample analysis procedures employed multiple determinations, the only important difference in data obtained using the co-solvent was improved precision. RSD values were generally improved by a relative 20 to 5 0 z employing THF-pyridine as the solvent. The majority of the data given in this paper was obtained employing THF as solvent, but most of the relative standard deviation values of less than 1 were obtained with the co-solvent.
z
ACKNOWLEDGMENT
The authors thank Dow Corning Corp. for supplying the reagents, apparatus, and silanol materials for this study. RECEIVED for review June 5,1967. Accepted August 10, 1967. In partial fulfillment of requirements for the degree of Master of Science, Gene E. Kellum, June 1967. Presented at the 1967 Anachem Conference, Detroit Mich., October 1967.
Titration of Bases in Acetonitrile I. M. Kolthoff, M. K. Chantooni, Jr., and Sadhana Bhowmik School of Chemistry, Unicersity of Minnesota, Minneupolis, Minn. 55455 The neutralization curves in acetonitrile (AN) of bases of various charge and of mixtures of bases with perchloric acid can be calculated provided the dissoclation constants, K:E+, of the protonated forms of the bases are known. Knowing the dissociation constant of a large number of indicators, the best indicator for the titration of a single monoprotic base or a mixture of monoprotic bases or of a diprotic base can be selected. Bases with pKBi+in water of 4 or greater have been visually titrated accurately and precisely with p-naphtholbenzein as indicator. Bases with pK&+ in water of the order of 1 (dimethylsulfoxide, formamide, urea, anthraquinone) can be titrated spectrophotometrically using m-cresolsulfonephthalein as indicator. The pK&+ i n AN of the above bases in the order mentioned is 5.8, 6.1, 7.7, and 3.5. Mixtures of an aliphatic amine with aniline can be titrated to the first equivalence point, either potentiometrically or with neutral red as indicator. The conductometric titration of uncharged bases with perchloric acid does not give a distinct break at the equivalence point. Good titration lines are obtained by adding an excess of a weak acid, HA, which transforms the base into the homoconjugate salt, BH-AnH-, which is highly dissociated. The homoconjugate anion, itself a base, i s then titrated with perchloric acid.
NUMEROUS acid-base titrations in nonaqueous solvents, including acetonitrile (AN) have been described in the literature ( I ) . In most instances titrations have been carried out potentiometrically, usually with the glass electrode as pH indicator electrode. However, visual indicators have also been used in many instances. (1) J. Kucharskg and L. Safafik, “Titrations in Nonaqueous
Solvents,” Elsevier, Amsterdam, 1965.
On the basis of the acid-base properties of a given solvent it is usually possible to predict its suitability as a medium for titration of acids and bases. However, no calculation of titration curves and of the break in paH at the end point have been made in nonaqueous solvents, except in the protogenic solvent acetic acid (2). For many years acetic acid has been a popular solvent for the titration of bases; however, the break in paH at the end point is much greater in many aprotic protophobic solvents. During the last several years we have been studying acidbase equilibria in AN and have determined the dissociation constant of several acids in this solvent (3-8). Although AN is a solvent with good resolving power for acids, it is not very suitable for the successive titration of acids in their mixtures because of homoconjugation of most acids with their own anions, and heteroconjugation with other anions, homoconjugation being the cause of greatly drawn-out titration curves with an inflection at 5 0 z neutralization (5). Only in very dilute solutions (about 0.001N) homoconjugation usually becomes negligibly small and titration curves, like those in water, are obtained (5). (2) I. M. Kolthoff and S. Bruckenstein, “Treatise on Analytical Chemistry,” Part I, Vol. 1, Interscience, New York, 1959, p. 475. (3) I. M. Kolthoff, S. Bruckenstein, and M. K. Chantooni, Jr., J. Am. Chem. SOC.,83, 3927 (1961). (4) I. M. Kolthoff and M. K. Chantooni, Jr., Ibid.,85,426 (1963). (5) I. M. Kolthoff and M. K. Chantooni, Jr., Ibid.,87,4428 (1965). (6) . , I. M. Kolthoff. M. K. Chantooni., Jr.,. and S. Bhowmik, Ibid.. 88, 5430 (1966).’ (71 . , I. M. Kolthoff and M. K. Chantooni., Jr.., J . Phvs. Chem.., 66., 1675 (1962). (8) I. M. Kolthoff and M. K. Chantooni, Jr., Ibid.,70,856 (1966). VOL. 39, NO. 13, NOVEMBER 1967
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