Acid-Base Equilibria of Some Acids in Propylene Carbonate K. lzutsu,l I. M. Kolthoff,’ T. Fujinaga,* M. Hattori,’ and M. K. Chantooni, Jr. Department of Chemistry, University of Minnesota, Minneapolis, Minn. 55455
The dlssoclatlon constant K( HA), and homoconjugation constant, K‘(HA2-), have been determined at 25 O C in propylene carbonate of several weak acids. From conductometrlcdata pK(HA) and K(HA2-) were found equal to 8.Z7 and 2.5 X lo3 for methanesulfonic acid (I) and 4.g4 and 4.7 X lo2 for 2,5dichlorobenzenesulfonic acld (11). From spectrophotometric and conductometric measurements pK( HA) of dichloropicric acld (111) was found to be 6.74 f 0.05. KSP of sodium methanesulfonate was 7.5 X pK(HA) of picrlc acid (IV), spectrophotometricallydetermined in mixtures of methanesulfonic acid and its salt, was 9.3,~.The glass electrode in PC was calibrated in mixtures of I, II, 111, and IV wlth their tetraethylammonium salts. pK(HA) and K( HA2-) of salicylic and benzoic acids were determined potentiometrically with the glass electrode and found to be 15.23 and 1.6 X l o 3 for sallcyllc and 19.67 and 9 X l o 3 for benzoic acid. Propylene carbonate is a somewhat stronger base than acetonitrile, being of the same order of strength as acetone.
Propylene carbonate (4-methyl-1,3-dioxolan-2-one) is an aprotic dipolar protophobic solvent with a relatively high dielectric constant, e , of 64.4 at 25 OC and a dipole moment of 4.94 D. Considering that E is much larger than that of acetonitrile ( e = 36) and acetone (20), dissociation of salts should be greater in propylene carbonate, PC, than in the other two protophobic solvents, provided that ion solvation is of the same order of magnitude in the three solvents. Interesting and fundamental studies of relatively strong acids have been carried out by L’Her and Courtot-Coupez ( 1 ) .If we base the concept “basic strength” on the transfer coefficient of the proton between solvents (see Discussion), it may be concluded from Courtot-Coupez’s work that acetonitrile is a slightly weaker base than PC. Being still a very weak base, PC is a poor hydrogen bond acceptor, as is AN. In accordance with this property is the small value of the association constant of P C with the hydrogen bond donor p -chlorophenol in carbon tetrachloride. Courtot-Coupez (I)reports a value of K of 16.3 of PC, of 20.0 of acetone, and large values of protophilic aprotic solvents, e.g. of 476 of dimethylsulfoxide. Also, water as a solute in P C is present mainly as a monomer, the dimer formation constant being only 0.18 kg/mol a t 25 “C (2). Coetzee et al. ( 3 ) reported that in the slightly weaker base acetonitrile water up to a concentration of 1 M is present as a monomer. L’Her and Courtot-Coupez ( I ) determined conductometrically the dissociation constant of the following acids a t 25 OC: fluorosulfonic acid O, persulfuric acid, H ~ S Z O10-1 ~ , HSbClG 10-1 while they found H P F Gto be completely dissociated. These values were found in a solvent which had been made completely anhydrous by having the water react with HFS03 with formation of 1 H2S04, or with HzSz07 with formation of 2H2S04. The sulfuric acid formed does not interfere in the above measurements as it is quite a weak acid in PC. The French workers present a conductoPresent address, Department of Chemistry, Faculty of Science, Shjnshu University, Matsumoto, Japan. Present address, Department of Chemistry, Faculty of Science, Kyoto University, Kyoto, Japan.
metric titration curve of water with fluorosulfonic acid in PC. This curve has a puzzling appearance as the conductance remains close to zero until 1molecule of acid is added, and then it increases linearly with excess of acid. The only possible explanation seems to be that the reaction HFS03
+ HzO
-+
HzS04
+ HF
occurs extremely rapidly during the titration, the two acids formed being so weak that they virtually do not contribute to the conductance. If the reactions were not very rapid, HsO+FS03- should be formed, which is expected to be strongly dissociated. Hydration constants of the alkali ions Li+, Na+, and Kf ( 2 , 3 )as well as that of NO3- ( 4 )in P C appear to be of the same order of magnitude as those in acetonitrile ( 5 ) .PC does not form a lyate ion and the change in pH in the titration of a strong acid with a base is large, the magnitude of the break at the equivalence point depending on the strength of the titrant base. Courtot-Coupez (1)mentions that the hydrogen electrode does not function properly in strongly acid medium. Quite generally, titration curves of both acids and bases in P C are expected to be very similar to those in acetonitrile (AN). Since P C is a stronger base than AN, a slightly larger break in pH in the titration of very weak bases with a strong acid should be observed in AN than in PC. A host of titration curves of acids and bases, using the glass electrode as indicator electrode has been presented by Baranov et al. (6). Unfortunately, they used in most instances reagents containing considerable amounts of methanol and/or water. For example, since solutions of perchloric acid were found unstable in PC, they used a 5 to 1mixture of PC and methanol for the titration of bases with perchloric acid (the latter probably prepared from the dihydrate). The reagent is not stable and it would seem preferable to use another suitabje protophobic solvent as the titrant. In the titration of maleic acid in PC (their Figure 2,curve 3) with 0.1 M tetrabutylammonium hydroxide in a 5 to 1mixture of benzene and methanol they find only one break, whereas a large break should occur a t the end point when titrated as a monoprotic acid and a second one as a diprotic acid. When methanolic potassium hydroxide was used as titrant, the sparingly soluble potassium normal maleate precipitates, fesulting in two breaks. However, the normal salt probably precipitates already before the first equivalence point. T o appraise the properties of P C as a solvent in the titration of acids and mixtures of weak acids, we have determined the dissociation and homoconjugation constants of several weak acids. Values of pK(HA) and Kf(HA2-) of 2,5-dichlorobenzenesulfonic,methanesulfonic and dichloropicric acids were determined conductometrically and pK(HA) of dichloropicric acid also spectrophotometrically. Knowledge of these constants allows the calculation of p a H in mixtures of these acids and their tetraethylammonium salts which were used in the calibration of the glass electrode. Dichloropicric acid has the advantage of having a small homoconjugation constant and being sufficiently strong to allow both the spectrophotometric and the conductometric determination of K(HA). The K(HA) of picric acid was determined spectrophotometrically in mixtures of methanesulfonic acid and its tetraethylammonium salt. ANALYTICAL CHEMISTRY, VOL. 49, NO. 3, MARCH 1977
503
Table I. Molar Conductivity of Some Tetraethylammonium Salts,
Methanesulfonate
Perchlorate
- -
2,5-Dichlorobenzenesulfonate
Dichloropicrate
-
c,, M x 103
A
c,, M x 103
A
c,,M x 103
A
C,, M X lo3
A
0.56 1.11 1.66 2.21 2.76 3.44 4.11
30.7 30.4 30.3 30.05 29.9 29.7 29.5
0.56 1.12 1.67 2.22 2.77 3.32
27.7 27.4 27.2 27.0 26.85 26.7
0.59 1.17 1.75 2.33 2.90 3.47
24.1 23.85 23.7 23.5 23.3 23.2
0.16 0.32 0.56
24.6 24.35 24.15 24.0 23.8 23.65 23.2 22.9
A. = 31.4
0.80
1.12 1.60 2.80 4.01
-1, = 24.8
A, = 28.4
'1, = 24.9
Table 11. Limiting Molar Conductivities of Ions in PC at 25 "C
A,
13.1
12.9
18.3
15.3
11.7
Table 111. Conductance of Solutions Saturated of Sodium Methanesulfonate (NaA) in Presence of HA
C(HA), M X lo3 K x 10'
0
0.680
2.28 1.44
4.52 1.97
8.75 2.82
18.1 4.26
36.2 6.24
EXPERIMENTAL Solvent. Nakarai's extra pure grade PC was further purified by treatment with molecular sieves, 3 A. It contained traces of a basic impurity and was distilled twice at reduced pressure (bp about 80 "C) in the presence of p-toluenesulfonic acid which was added in 50% excess over the basic impurity. After the second distillation the solvent was free of basic impurity as found by conductometric titration with 0.1 M p-toluenesulfonic acid in PC. A third distillation was carried out without additive. An adiabatic vacuum fractional distillation column of 1 m in length and packed with stainless steel Dixon packing was used and the middle 80% fraction was collected each time. The conductivity at 25 "C of the purified PC was 2-3 X ohm-' cm-'. L'Her and Courtot-Coupez ( 1 )reported for a highly purified solvent 7 X 10-8 ohm-' cm-I. The water content as determined by Karl Fischer titration was less than 0.005%. The solvent, after purification, was stored under nitrogen atmosphere and was usually used on the day of the purification to avoid contamination by atmospheric moisture. Chemicals.The following reagents were prepared and/or purified according to methods used previously: picric acid (71, 2,5-dichlorobenzenesulfonic acid ( B ) , salicylic acid ( 9 ) ,benzoic acid (91, phenol ( I O ) , tetraethylammonium methanesulfonate (81, dichlorobenzenesulfonate ( B ) , benzoate (9),phenolate (10).Tetraethylammonium acetate was prepared by neutralizing an aqueous acetic acid solution and evaporating to dryness in vacuo (9).'I'etraethylammonium picrate was prepared according to the method of Coetzee and Padmanabhan ( 1 1 ) .Methanesulfonic acid was an analytical reagent grade product used without further purification. Dichloropicric acid was prepared from 3,5-dichlorophenol by the method of Willstatter and Schudel (12)and was recrystallized four times from cyclohexane.The acid was dried at ca. 40 "C in vacuo. The tetraethylammonium salt of this acid was prepared by neutralizing an aqueous solution of the acid with tetraethylammonium hydroxide solution. The salt was recrystallized four times from an ethanol-water mixture and was dried at ca. 40 "C in vacuo. Perchloric acid was a dihydrate (70% acid). Conductivity Measurements. A Yokogawa Hewlett-Packard universal bridge, Model 4255 A, was used for the conductivity measurements.Results are accurate to & 0.5%. A Yanagimoto conductivity cell, Type C, was used with cell constant 0.3685. The cell was equipped with a silicone rubber stopper and a measured volume of solution of ) injected to avoid the acid of known concentration (up to 300 ~ 1 was contamination by moisture. Before each measurement, the solution (about 17 ml) in the cell was well mixed using magnetic stirring. The 504
ANALYTICAL CHEMISTRY, VOL. 49, NO. 3, MARCH 1977
11.8
13.7
-8.6
measurements were carried out in a water bath maintained at 25.00 f 0.02 "C. Potentiometric Measurements. Potentiometric measurements were carried out at 25.0 f 0.1 "C using a Hitachi-Horiba glass electrode No. 1026 for paH determination. When not in use, the electrode was stored in pure PC. The reference electrode was Ag wire/O.O05M AgC104 in PC (+ 2% acetonitrile) and the salt bridge was filled with a solution of 0.05 M Et4NC104 in PC. Acetonitrile, which complexes silver ion, was added to the reference electrode solution. The potential of the electrode was stable within 1 mV for at least 2 weeks, while without AN the electrode potential was not quite stable. The potential of the glass electrode was measured to 0.1 mV with a Hitachi-Horiba pH meter, F7-SS. In paH measurement of mixtures of an acid and its salt, 50 ml of the salt solution was taken in the cell and appropriate volumes (up to 3 ml) of a stock solution of the acid were added. After each addition of the acid, the potential reached an equilibrium value within 5 min. Before each measurement, the glass electrode was M picric acid and 4 X lo-? M tetrachecked in a mixture of 4 X ethylammonium picrate (vide infra). Spectrophotometric Measurements. Absorption spectra were recorded with a Shimadzu multipurpose recording spectrophotometer, MPS-50L, and the absorbances were measured with a HitachiPerkin-Elmer UV-VIS spectrophotometer, Model 139. Quartz cells of 10-mm path length were used. RESULTS Conductometric Section. Ion Mobilities. T h e results of conductometric measurements of solutions of tetraethylammonium perchlorate, methanesulfonate, 2,fj-dichlorobenzenesulfonate, a n d dichloropicrate are presented in Table I. From a plot of A vs. v'i? the limiting molar conductivity, A,,, was obtained for each electrolyte. It is deduced from a comparison of the observed slope with the calculated Onsager slope that the above electrolytes are essentially completely dissociated under the experimental conditions. It is also found t h a t perchloric acid behaves as a strong electrolyte in PC in dilute solution. T h e perchloric acid used in preparation of t h e solutions was a dihydrate. T o correct for t h e effect of water M HC104 was deterpresent, the conductance of 2.65 X mined at water concentrations of 0.16,0.36, a n d 1.0 M. Conductivities were 7.99 X low5,8.10 X lop5, and 8.34 X lop5 ohm-l cm-1, respectively. T h e conductance increased almost linearly with the square root of the water concentration. B y extrapolating t o d C ( H a O ) = 0 the following values of A are obtained: 0.56 X M HC104,30.6; 1.12 X lop3 M, 30.4; 2.29 X 10-3 M, 29.9; a n d 3.41 X 10-3 M, 29.8; A,, being 31.2. For tetraethylammonium perchlorate, A, (EtdNC104) = 31.4. Literature values for X,(EtdN+) are 13.0 ( 1 3 ) ,13.28 (14),and 13.18 (15)at 25 "C. Using X,(EtdN+) = 13.1 we find X,,(C104-)
Table IV. Conductometric Determination of K(2HA) of Methanesulfonic Acid C(HMS), M X lo2
A
(calcd)
1.82 3.64 5.45 7.26 9.07
0.095 0.095 0.097 0.099 0.102
26.3 26.2 26.2 26.1 26.0
K(2HA)
A( 2HA) 01
x 10.3 3.61 3.63 3.70 3.79 3.92
Y
x 105
0.987 0.982 0.978 0.974 0.970
1.27 1.27 1.31 1.36 1.45 (1.33 f 0.09)
A(H(HA)z) = 26.6 - 3 1 . 7 f l . The confidence limits of the results are shown in 95% level.
Table V. Conductometric Data of 2,5-Dichlorobenzenesulfonic Acid
c,, M x 103 A
0.218 5.26
0.436 3.95
0.871 3.00
1.52 2.45
Table VI. Conductometric Determination of pK(HA) of Dichloropicric Acid in PC C (HPiClZ), M X lo3 3.69 I 0.171 pK(HA)" 6.75 a
7.37 0.119 6.77
11.07
20.2 34.3 73.7 0.100 0.07800 0.0667 0.0520 6.74 6.70 6.60 6.49
Calculated using the relation K(HA) = (A/Ao)*Ca.
= 18.3 as compared to values of 19.6 ( I ) , 18.8 ( 2 4 ) ,and 18.4 ( 1 5 ) .Values of A, of the various ions obtained in the present work are listed in Table 11. Determination of KSP(NaA),&(HA,-), and Kf(HA2-) o f Methanesulfonic Acid. As has been done in AN ( 8 ) ,we first determined the conductance of mixtures of methanesulfonic acid and its tetraethylammonium salt. By using a series of successive approximations ( 8 )a value of A,(HA2-) was found which was abnormally large. In order to obtain a more reliable value, the conductance of solutions saturated with the sodium salt and which contained various concentrations of free acid was determined. The sodium salt is slightly soluble and is a strong electrolyte in PC. T h e conductance of its saturated solution in the absence of free acid was 6.8 X ohm-' cm-l. Using AJNaMS) = 24.75 from A,(Na+) = 9.45 (15),we obtain as a first approximation [Na+]equal to 2.75 X lop4 M. Using the Onsager equation we find for the corrected value of A a t = 24.2:1a t a salt conthis ionic strength 24.75 - 31.2centration of 2.81 X M. From the limiting Debye-Huckel expression log y = - 0 . 6 9 d we obtain y = 0.97. Thus, the solubility product of NaMS is (2.8 X 10-4)2(0.97)2= 7.5 X at 25 O C . The conductances of solutions saturated with NaMS and containing various concentrations of free acid are presented in Table 111. In solutions prepared under conditions as in Table I11
2.17 2.19
3.25 1.97
4.31 1.85
5.38 1.78
6.43 1.74
8.53 1.67
10.6 1.64
Table VII. Spectrophotometric Determination of pK(HA) of Dichloropicric Acid in PC C(HPiCl*), M X 103 $4; 3.40 10.20 17.00 32.4 54.3
[PiClp-] M x 105
A,"
0.070 0.120 0.154 0.198 0.260
4,5,0 0.040 0.070 0.088 0.144 0.149
440 nm 2.8 4.7 6.0 7.7 10.1
450 nm 2.8 4.7 5.95 7.6 10.0
[HPiClz] M x 103 p
[H+],as a result of dissociation of the acid, is negligible. From this relation and approximate values of A(NaHA2) and A(NaA), we obtain an approximate value of Kf(HA2-) of -2.4 X lo3 and after successive approximations we arrive at values of A,(HA,-) = 13.7 and Kf(HA2-) = 2.5 X lo3. Determination of K(2HA)and K ( H A )of Methanesulfonic Acid. Conductivity data of dilute methanesulfonic acid solutions are presented in Table IV. T h e molar conductivity hardly varies with the acid concentration, indicating that the dissociation occurs practically completely into H + and HA2-
(
Av
2.8 4.7 6.0 7.65 10.05
3.37 10.15 16.94 32.3 54.2
6.63 6.66 6.67 6.74 6.73 Av. 6.69
a Correction was made for the absorbance of undissociated acid.
2HA
Hf
+ HAPK(2HA) = a(H+)a(HA2-)/[HAl2 = m2y2
where cy = A/Ao(2HA). By using A,(H+) = 12.9 and A,(HA2-) = 13.7, pK(2HA) was calculated to be 4.88. Thus, pK(HA) of methansulfonic acid is 8.27. Conductometric Determination of K ( H A )and K(HA*-) of 2,5-Dichlorobenzenesulfonic Acid. The conductometric results of 2,5-dichlorobenzenesulfonicacid are presented in Table V. From Table I1 we obtain A,(HA) of this acid equal to 24.6. In the estimation of the value of A0(2HA) it is assumed that the ratio Ao(HA)/Ao(2HA)in P C is equal to that in AN ( 8 ) (149/130) and hence A0(2HA) 21.5 in PC. T o obtain approximate values of K(HA) and K(HA*-) the French and Roe expression (16) was used, in which
-
A v'C a ( C
+ 1/ K (HAz-) = A, (HA ) V'K (HA)/ K (HA2 -) + CaAo(2HA). dK(HA)K(HA,-)
[HAP-] = [Na+l - [A-I = [Na+] - KSp(NaMS)/[Na+]y2
~
(1)
the degree of dissociation of HA into HA2- and A- is negligible as compared to unity. In Equations 1 and 2, C, denotes the analytical concentration of the acid and A the molar conductivity. Since the dissociation of acid in P C is more extensive than that in AN, the degree of dissociation being appreciable, the more exact form of the French and Roe equation was used. Ay{Ca[1/K(HA2-) + XCa])1/2 X 1'2 [1 - k (OX,) l/z/A,( HA)]
+ [K(HA)K(HA2-)]1/2C,XA,(2HA) ANALYTICAL CHEMISTRY, VOL. 49, NO. 3, MARCH 1977
(2) 505
~
~
)
Table VIII. Spectrophotometric Determination of K(HA) of Picric Acid CCH~SO~H, M x 103 0
CCH3SOnEt4N,
M x 103 = 4.42
0.634 1.04 1.66 2.07 3.09
4.42
4.42 4.43 4.44 4.44 4.47 4.48 4.48 4.49 4.50
4.12
1.09 1.72
2.15 3.22 4.29
Pa H
[Pi-]/[HPi]
pK(HA)
10.03 9.62 9.41 9.21 8.77 8.36 9.72 9.39 9.19 8.74 8.31
5.06
9.37 9.20 9.25 9.27 9.24 9.21 9.37 9.34 9.30 9.32 9.27 (9.29 f 0.04)
2.95 1.61 0.971 0.377 0.159 2.49 1.27 0.878 0.293 0.121
Corrected for the effect of the reaction with a picric acid-picrate mixture. The confidence limits of the results are shown in 95% level. E,rnv
+200r
- 3 4
'
d
'
'
I
'
'
;'
.
11,'
1:
P ~ H Flgure 1. Calibration plot of the glass electrode in PC ( 0 )2,5dichlorobenzenesulfonic acid, (0)methanesulfonic acid, (a) picric acid, ( A ) dichloropicric acid. Slope 60.4 rnV/paH
in which y is the activity coefficient, k the Onsager slope, a is [H+]/C, and can be assumed to be approximately equal to h/A,(HA), while X , which is equal to [HA]/Ca,is found from calculation of [HA] in Equation 3.
+
(4K(HA)K(HA2-) - 1]K(HA2-)[HAl3 [4K(HA)K(HA2-) -, t 2CaK(HA2-) - 1)[HA12 {K(HA) 2Ca - K(HA2-)Ca2}[HA]- Ca2 = 0 (3)
+
+
For 2,5-dichlorobenzenesulfonicacid the exact French and Roe treatment yields pK(HA) = 4.94 and K(HA2-) = 4.7 X lo2 which differ only slightly from the values of 5.02 and (4 f 1)X lo2,respectively, found from Equation 1. Dissociation Constant of Dichloropicric Acid (HPiC12). Results of the conductometric measurements of tetraethylammonium dichloropicrate solution are in Table I. A value of h,(Et&IPiClZ) = 24.9 was obtained. Using X0(Et4N+)= 13.1 and X,(H+f'= 12.9 we obtain X,(PiC12-) = 11.8and h,(HPiClz) = 24.7. The results of conductometric measurements of dichloropicric acid solutions are presented in Table VI. The average value of pK(HA), obtained from the relation K(HA) = (A/AJ2Ca, was 6.68. However, as is apparent from Table VI, the pK(HA) value decreases with increasing acid coqcentration, indicative of homoconjugation. The French and Roe treatment (Equation 1)was therefore applied. T o estimate X,H(PiC12-)2, A, was considered to be inversely proportional to the square root of the molecular weight of the ion. Thus X,H(PiCL-)2 XO(PiC12-)//fi = 8.3 and Ao(H H(PiC12)z)
-
506
ANALYTICAL CHEMISTRY, VOL. 49, NO. 3, MARCH 1977
= 21.2 From these values, we obtained pM(HA) = 6.80 and K(HA2-) = 2 X 10. Spectrophotometric Section. Determination of K(HA) of Dichloropicric a n d Picric Acids. Dichloropicric acid is considerably stronger than picric acid, and trace amounts of basic impurities in the solvent would have a negligible effect on the degree of dissociation of the former in PC. The molar absorptivity of the dichloropicrate ion (PiC12-) at A,, = 397 nm was 5.75 X lo3. A t X = 440 and 450 nm a t which the absorbances were measured for the determination of acid dissociation, the molar absorptivities were 2.57 X lo3 and 1.48 X lo3, respectively. At 440 and 450 nm undissociated acid, which was obtained by adding 0.058 M perchloric acid (70% HC104 was used) to the dichloropicric acid solution, showed slight absorption. In the determination of pK(HA) values these absorbances were taken into account. Results are presented in Table VII. The average value of pK(HA) equal to 6.69 is in satisfactory agreement with the conductometric value, 6.80. No indication of homoconjugation was obtained fro the speqtrophotometric data. In the estimation of pK(HA) of picric acid the ratio of [Pi-]/[HPi] in mixtures of methanesulfonic acid and its tetraethylammonium salt was found from the spectrophotometrically determined picrate concentration. Data are in Table VIII. Absorbances were measured a t 400 nm. At this wavelength the molar absorbance of picrate determined with tetraethylammonium picrate was found equal to 1.41 X lo4. Using pK(HA) = 8.27 and Kf(HA2-) = 2.5 X lo3 of methanesulfonic acid, the hydrogen ion activities, a ( H + ) , in the above solutions were calculated from Equation 4 (8)
+
y2C,a2(H+)- y a ( H + ) K(HA)((C, C,) K(HA2-)(CS - Ca)2] K2(HA)C, = 0 (4)
+
+
where C, and C, represent the concentrations of tetraethylammonium methanesulfonate and methanesulfonic acid, respectively. The dissociation constant, K ( H P i ) , was calculated from values of a ( H + ) and [Pi-]/[HPi]. The p a H was varied between 10.03 and 8.31, an average of pK(HPi) of 9.3 f 0.04 being found. Potentiometric Section. Calibration of the Glass Electrode in PC. For purposes of calibrating the glass electrode, mixtures of methanesulfonic, 2,5-dichlorobenzenesulfonicor dichloropicric acids with their tetraethylammonium salts were used. Values of p a H in the above mixtures were calculated using Equation 4. For picric acid K(HA2-) = 0. In Equation 4 the conductometric value of pK(HA) was used for the sulfonic acids, the spectrophotometric value for picric acid and the average of the conductometric and spectrophotometric values for dichloropicric acid. When the concentration of
Table IX.pK(HA) and Kf(HA2-) of Acids in PC and AN Acid
PC
AN
pK(HA) Kf(HA2-) pK(HA) Kf(HA2-) 2,5-Dichlorobenzene sulfonic Methanesulfonic Dichloropicric Picric Salicylic Benzoic Acetic
4.7 X lo2
6.2
8.27 6.74
2.5 X lo3 (2 X lo1) -0 1.6 X lo3 9 X 10'
10.1
3 X 10'
11.0
2 2 X 10,' 4 X 10'
9.29
15.23 19.67 (22.2)
16.7 20.7 22.3
3X
lo2
4.94
4.7 X
10'
I Q
3.
2,5-dichlorobenzeriesulfonic acid was greater than that of its salt, Equation 5 was used in which [H+] is not negligible as compared to the concentration of the tetraethylammonium salt. ( ~ K ( H A ) K ( H A ~ - )/ Yy)a3(H+) - {4K(HA)K(HA2-)(Ca- C,) y2CJa2(H+) K(HA)y(K(HAz-)(C, - C,)' (C, C,) K ( H A ) / y 2 ) a ( H + ) K2(HA)C, = 0
+
+
+
+
+
(5)
In Figure 1the paH values are plotted vs. E. In the paH region between 5 and 10, a good linear relation was obtained with a slope of 60.4 mV/paH. Below p a H 5 , however, a deviation from linearity was observed. Values of Kf(HA2-) for methanesulfonic and 2,5-dichlorobenzenesulfonicacids were calculated from the potentiometric data using Equation 6 ( 8 ) , assuming theoretical response of the glass electrode, 59.1 mV/pa H,
where r = a(H+)y/a(H+)1/2yl/zand in which a(H+)llz and are values a t 50% neutralization. For methanesulfonic acid, Kf(HAp-) by this method is 3.3 X lo3, which is in satisfactory agreement with 2.5 X lo3obtained conductometrically. For 2,5-dichlorobenzenesulfonicacid, however, Kf(HA2-) of 1.9 X 10' is considerably smaller than the conductometric value, 4.7 X lo2, while the reverse relation is found for dichloropicric acid, the potentiometric and conductometric values of Kf(HA2-) being 5 X lo1 and 2 X lo1, respectively. The glass electrode was calibrated before each measurement M in picric acid and 4 X 10-3 using the buffer solution 4 X M in tetraethylammonium picrate of p a H = 9.3. Potentiometric Determination of K(HA) a n d Kf(HA2-) of Salicylic, Benzoic, Acetic Acids a n d Phenol. Plots of p a H vs. log C,/C, of mixtures of these acids with their tetraethylammonium salts are presented in Figure 2. Values of pK(HA) were found from Equation 4,while Kf(HA2-) values were calculated from Equation 6. Results are summarized in Table IX. Constant values of Kf(HA2-) were obtained in the salicylic and benzoic acid systems but not in the acetic acid and phenol systems. The approximate value of pK(HA) of acetic acid was taken equal to the half-neutralization p a H of 22.2. In phenol-phenolate mixtures varying values of pK(HA) and Kf(HA2-) were obtained; apparently the glass electrode did not function properly a t p a H values 2 25.
y1/2
DISCUSSION From the analytical point of view, P C has few advantages for acid-base titrations over other protophobic solvents, like acetonitrile (AN) or acetone (Act). Advantages are that PC is nonpoisonous, has a high dielectric constant (which makes it a popular solvent for electrochemical studies), but is about
Figure 2. Relation between log (C,/C,) and paH in PC (1)phenol, C, = 2.6 X acid, C, = 2.71 X =4.11~10-3~
M: (2) acetic acid, C, = 2.93 X M; (4)salicylic acid, (0) C, = 2.85 X
M; (3) benzoic M, ( 0 )C,
10 times a stronger base than AN. A disadvantage is that standard solutions of strong acids are not stable in PC as is also the case in AN and Act. The conductance of 3 X M perchloric acid prepared by dilution of a 0.23 M stock solution was found 4% smaller upon dilution after 4 h than that obtained upon dilution of the freshly prepared stock solution. On the other hand, the conductance of the dilute solution obtained from the freshly prepared stock solution remained constant for 4 h. Another disadvantage is that the glass electrode becomes somewhat erratic a t p a H < 5 and at high pH. As far as titration of acids is concerned, it has hardly any advantages over any of the other protophobic solvents. Resolution of acid strength is of the same order of magnitude as in AN or Act. The mobility of the proton is practically equal to that of the tetraethylammonium ion (Table 11) and of the cesium ion (12.66 ( 1 5 ) ) Thus, . the proton appears to be solvated with at least one and possibly two molecules of solvent. A fairly exact comparison of basic strength of PC with that of AN is obtained by comparison of the transfer coefficient p r A N P C ( H += ) -log r A N P C ( H + of ) the proton between the two solvents. A negative value of p7*"PC(H+) indicates a larger decrease in free energy of the proton in PC as compared to that in AN. In previous work a t Minnesota ( I 7) use of the following relation has been made
PCAANpK(HA) = pyANPC(H+) pyANPC(A-),l - pyANPC(Ha) (7a)
+
In this relation p-yANPC(Ha)is an expression of the difference in hydrogen bond accepting capacity between the two solvents. Recently L'Her and Courtot-Coupez ( I ) estimated from IR measurements the complexation constants of PC and AN (as solutes) with p-chlorophenol in carbon tetrachloride as solvent. They find the difference ActAPClogK = +0.09, which may be regarded equal to -p-yACtPC(H,). This estimation appears to be justified as there is agreement in AH of hydrogen bond accepting capacities of a large group of solvents toward 4-fluorophenol as donor from the pure base and high dilution ANALYTICAL CHEMISTRY, VOL. 49, NO. 3, MARCH 1977
507
methods (18).Calorimetric and IR methods were used. Since pyACtAN(H,) = -0.1 (17), pyANPC(H,) = pyACtPC(H,) p-yACtAN(H,)= -0.1 - (-0.1) = 0.0. This is verified from comparison of homoconjugation constants in AN and PC (vide infra). As has been done previously, we consider in deriving Equations 7a and 7b that py(A-) = py(A-),l py(n) and py(HA) = py(n) py(Ha), p(n) being the transfer coefficient of the nonelectrical contribution of HA and of A-. An estimate of py(H,) can also be obtained from Equation 7b:
+
+
ANAPClog Kf(HA2-) = -pyANPC(Ha) - pyANPC(A-),1 pyANPC(HA2-),1 (7b)
+
From the values of Kf(HA2-) in the present paper and previously (9) reported values in AN we find that ANAPClog K(HA2-) = -0.1 f 0.2. Since pyANPC(A-),l - pyANPC(HA2-),1 must be close to zero, pyANPC(Ha) +0.1 f 0.1. As solvents AN and P C appear to have practically the same hydrogen bond accepting capacity. I t may be somewhat fortuitous that their hydrogen bond accepting capacity as solutes in dichloroethane is of the same order of magnitude. Gutmann and Schmid (19)report that the donor number of PC is 1unit greater than for AN. Coming back to Equation 7a we must consider that part of pCAANlogK(HA) is due to the Born effect: PCAANlogK(HA) = -1.22 X 10-6[l/r(H+) l/r(A-)] [1/64.4 - 1/36.1] (Born effect only) in which 64.4 is the dielectric constant of PC and 36.1 that of AN. Taking r ( H + ) = 5 A and r(A-) = 7 A, the Born effect is +0.5. Using r ( H + ) = 3 A and r(A-) = 7 A, the effect is +0.7. The first value seems more probable (the proton is solvated). From the experimental values of K(HA) in this paper and those reported previously in AN (9) we find an average value for PCAANlogK(HA) of -1.5 f 0.3, or, corrected for the Born effect, -1.0 f 0.3. From Equation 7a we then get for pyANPC(H+)= -0.9 f 0.1. If we consider that pyANPC(A-) is determined only by the Born effect and r(A-) = 7 A, we find for pyANPC(H+)= -1.5 0.2
+
+
= -1.3 f 0.3. Thus AN is of the order of 10 to 40 times a weaker base toward the proton than is PC.
ACKNOWLEDGMENT One of the authors (K.I.) expresses his thanks to M. Furukawa of Shinshu University for his assistance in experimental work.
LITERATURE CITED (1) M. L'Her and J. Courtot-Coupez, J. Elecfroanal. Chem., 48, 265 (1973). (2) D. R . Cogley, M. Falk, J. N. Butler, and E. Grunwald, J. Phys. Chem., 76, 855 (1972). (3) W. Muney and J. F. Coetzee, J. Phys. Chem., 66, 89 (1962). (4) R. L. Benoit, D. Lahaie, and G. Boire, Nectrochim. Acta, 20, 377 (1975). (5) M. K. Chantooni, Jr., and I. M. Kolthoff, J. Am. Chem. Soc., 89, 1582 (1967). (6) N. A. Baranov, N. A. Vlasov, L. P. Potekhenia, and 0. F. Shepot'ko, Zh. Anal. Khim., 25, 2069 (1970); J. Anal. Chem. USSR (Eng. Trans/.), 1774 (1971). (7) I. M. Kolthoff, S. Bruckenstein, and M. K. Chantooni, Jr., J. Am. Chem. Soc., 83, 3927 (196 1). (8) I. M. Kolthoff and M. K. Chantooni, Jr., J. Am. Chem. Soc., 87, 4428 f 1965). (9) i.MI Kolthoff and M. K.Chantooni, Jr., J. Phys. Chem., 70, 856 (1966). (10) I. M. Kolthoff, M. K. Chantooni, Jr., and S. Bhowmik, J. Am. Chem. Soc., 88, 5430 (1966). (11) J. F. Coetzee and G. R. Padmanabhan, J. Phys. Chem., 66, 1708 (1962). (12) R. Willstatter and G. Schudel, Chem. Ber., 51, 787 (1916). (13) J. Courtot-Coupez and M. L'Her, Compt. Rend. Acad. Sci., 271, 357 (1970). (14) L. M. Mukherjee and D. P. Boden, J. Phys. Chem., 73,3965 (1969); 74, 1942 (1970). (15) M. L. Jansen and H. L. Yeager, J. Phys. Chem., 77, 3089 (1973). (16) C. M. French and I. G. Roe, Trans. Faraday Soc., 49, 314 (1953). (17) M. K. Chantooni, Jr., and I. M. Kolthoff, J. Phys. Chem., 77, 527 (1973). (18) E. M. Arnett, L. Joris, E. Mitchell, T. S. Murty, T. M. Gorrie, and P. v. R. Schleyer, J. Am. Chem. Soc., 92, 2365 (1970). (19) V. Gutmann and R. Schmid, Coord. Chem. Rev., 12, 263 (1974).
RECEIVED for review October 11,1976. Accepted November 29, 1976. I.M.K. gratefully acknowledges financial support from the National Science Foundation through grant CHE75-22642.
I CORRESPONDENCE
1
Clipped Free Induction Decay Signal Analysis Sir: Fourier transform (FT) NMR spectroscopy has numerous advantages compared to conventional continuous wave (CW) NMR techniques ( I ) . Contributing to the efficacy of this technique is the efficiency with which the Fourier cosine absorption spectrum can be computed via the fast Fourier transform (FFT) algorithm. T h e free induction decay signal (FID) is the primary measured quantity and a single time scan corresponds to a realization of the stochastic process consisting of an ensemble of such FID's. The Fourier frequency spectrum of an average of many (often 2K) skans is thus a reasonable statistical estimate of the spectrum of the stochastic process. The purpose of this communication is to call attention to the advantages of computing the Fourier frequency spectrum of the stochastic process consisting of (an ensemble of) clipped free induction decay (CFID) signals. A clipped signal c ( t ) is derived from a signal s ( t ) by the simple, although highly nonlinear, operation c ( t ) = sgn s ( t ) . In this manner, c ( t ) takes on the values f l only. An important 508
ANALYTICAL CHEMISTRY, VOL. 49, NO. 3, MARCH 1977
restriction on s ( t ) is that it have zero mean; Le., E [ s ( t ) ]= 0. An FID satisfies this condition and is, in addition, bandlimited in (0,W).By this clipping operation, all amplitude information in the FID is destroyed. However, the important point is that the essential frequency information within s ( t ) , the FID, is still retained in the zero crossings of c ( t ) . T h a t this is the case may be seen in Figures 1and 2 which show the FID, the CFID, the Fourier power spectrum of the FID, and the Fourier power spectrum of the CFID for both ethylbenzene and toluene. The Fourier power spectrum of the CFID is virtually identical to the Fourier power spectrum of the unclipped FID, confirming, in essence, that the essential frequency information required by a spectroscopist is embedded in the zero crossings of the FID. Additional insight into clipped signals is obtained if one computes the Walsh sequency spectrum of the CFID. The Walsh transform (WT), like the FT, is a unitary transform, is information preserving, and also possesses fast computational algorithms (FWT's) (2,3).The W T is considerably more
