EQUILIBRIA INETHYLENEDIAMINE
2537
Equilibria in Ethylenediamine. 111. Determination of Absolute pK Values of Acids and Silver Salts. Establishment of a pH and pAg Scale'
by L. M. Mukherjee,2 Stanley Bruckenstein, and F. A. K. Badawi (Received January 4, 1966)
School of Chemistry, University of Minnesota, Minneapolis, Minnesota
+
The dissociation constant for the reaction HC1 H + C1- in ethylenediamine has been determined by spectrophotometric and cryoscopic measurements. The mean value of PKHC~, 4.01, has been used to calculate the potential of the saturated corrosive sublimate electrode (s.c.s.e.) and E ' A ~ , A using ~ electrodes of the first and second kinds. E.m.f. values obtained with the hydrogen electrode in solutions of acids and in solutions of salts were used to calculate pK values of acids. Similarly, from e.m.f. values obtained using the silver electrode in silver salt solutions, the corresponding pK values were evaluated. Cryoscopic determination of the pK value for hydrobromic acid in ethylenediamine is also reported.
Introduction
where
I n earlier papers3p4concerning equilibria in ethylenediamine (EDA)the potentiometric determination of relative dissociation constants of some silver salts, other uni-univalent salts, and a few acids were reported. In this work, a spectrophotometric study of solutions of the indicator acid, 3-methyl-4-phenylazophenol (HI), and mixture of the indicator with hydrochloric acid in EDA is described. Also, a cryoscopic investigation of dissociation of hydrochloric and hydrobromic acids is reported. Results obtained from these measurements are used to calculate the potential of the saturated corrosive sublimate reference electrode (s.c.s.e.) and the standard potential of silver-silver ion electrode.
(3) and 421KdH1= aH aH +I-
The bracketed quantities represent equilibrium concentrations. The observed absorbance, A , a t a particular wave length is
+
where b is the light path in centimeters, EHIis the molar absorptivity of the molecular species HI, and eI- is the molar absorptivity of all species (H+I- and I-) containing an I- ion.
Theory Spectrophotometry. Pure Indicator Solutions. An indicator acid, HI, dissociates in EDA in the following way KdHr
KiHI
H+I-
H+
basic color
+ I-
(1)
basic color
where both the ion pair H+I- and the dissociated anion I- have the same molar absorptivities. Accordingly, the over-all dissociation constant, &I, is given by5 KH[ =
aH +aI-
+
UH+I-
-K
~
1 3. KiH1
~
(2)
+
A = ~ ( E H I [ H I ] ~I-[H+I-] ~1-[1-]) ( 5 )
s14
HI acid color
(4)
~
(1) Taken, in part, from a thesis submitted by L. M. Mukherjee in partial fulfillment for the degree of Doctor of Philosophy (Aug. 1961) and by F. A. K. Badawi in partial fulfillment of the requirements for the degree of Master of Science (Aug. 1964) to the Graduate School of the University of Minnesota. (2) Chemistry Department, Polytechnic Institute of Brooklyn, Brooklyn, N. Y. (3) S. Bruckenstein and L. M. Mukherjee, J . Phys. Chem., 64, 1601 (1960). (4) S. Bruckenstein and L. hl. Mukherjee, ibid., 66, 2228 (1962). K ~ ~ ~ (5) I. M. Kolthoff and S. Bruckenstein, J . Am. Chem. Soc., 78, 1 (1956).
Volume 69,Number 8 August 1966
L. M. MUKHERJEE, S. BRUCKENSTEIN, AND F. A. K. BADAWI
2538
Defining the apparent molar absorptivity, eapP, as
Acid H X . In an EDA solution containing both the indicator acid, HI, and a nonabsorbing acid, HX, whose over-all dissociationis given by
where Ct, the total analytical concentration of the indicator, is given by Ct
=
[H:I]
+ [H+I-] + [I-] = CHI + [I-]
KHX
H X Z H + + X the rule of electroneutrality yields
(7)
and substituting eq. 3,4,5, and 7 into eq. 6 yields
[H+l = [X-I Assuming f H + = fX= 1, oneobtains
=
+ 11-1
fI- = f and
-[H+l - - KHX[HXl
Defining
[I-]
a = [I-]/Ct
yields 1-
=
cH,/ct
Substituting eq. 9 and 10 into eq. 8, one obtains a=-
- €I €1- - €‘
E.PP
fHX
(17) = fHI
-
fH+I-
+
KHICHI
where [HX] denotes’ the equilibrium concentration of the undissociated HX, and CHI represents the sum [HI] [H+I-] pertaining to the indicator acid HI. By transposing terms in eq. 18 and substituting [H+] = KHICHI/f2[I-]eq. 19 results
+
I
[HX - CHI
KHI --
CHI +--KH12 KHXf2[I-12
KHX
(19)
It is convenient to express eq. 19 in terms of a (given above by eq. 11)to yield
where €1
=
€HI
1
f EI-KiH1
+ KiH1
From the rule of electroneutrality
[H+] = [I-] Assuming fH+
= fI- =
f
where Ct is the total analytical concentration of the indicator present in the mixture used. The activity coefficient f can be obtained, as before, from the Debye-Huckel limiting law, -log f = 7.608&, p being given by
and fHI = fH+I-
1
substitution of eq. 7 , 11, 13, 14a, and 14b into eq. 8 yields
Thus, a plot of eapp vs. - E ’ ) ~ / ( ~ I - - e1)]f”Ctat any wave length permits evaluation of KHI. Equation 15a differs from a similar expression derived by Bruckenstein and Osugi6 in that it takes into account the presence of two undissociated species with different absorptivities. For evaluation o f f , we have used the Debye-Huckel limiting law. In terms of the experimental quantities
where CHX is the total analytical concentration of the acid, HX, in the mixture. If [HX] were known, a plot of [HX]/(l - a)Ct vs. (1 - a)/Sa2Ct would permit evaluation of KHX and KHI. However, [HX] cannot be obtained directly, and we have used a trial and error procedure. First, we assume a value for KHIIKHXand calculate p from eq. 21 and [HX]from
using the experimental value of a. A least-squares treatment is made according to eq. 20. The least-
Mixture of’ the Indicator Acid and a Nonabsorbing The Journal of Physical Chemistry
(6) S. Bruckenstein and J. Osugi, J . Phys. Chem., 6 5 , 1868 (1961).
EQUILIBRIA IN ETHYLENEDIAMINE
2539
squares value of the intercept yields another value of Cell 111: reference s.c.s.e. /jAgX(CA,x) 4- HX(CHx) IAg KHIIKHX. The above procedure is repeated and a plot The difference in e.m.f. values between cell I and cell I1 made of assumed value of KHI/KHx vs. the value of is KHIIKHx found from the least-squares treatment. Inspection of this plot yields the best value of KHIIKHX (see Figure 4). Cryoscopic Measurements. It has been demonstrated As was shown earlier3the difference in e.m.f. values of experimentally that cryoscopy in EDA' (f.p. 11.3") is cells I1 and I11 is represented by suitable for E'tudying dissociation of the type represented by eq. 16. The equilibrium constant, KHx, may be expressed in the form KHX=
[Ern - m,]2f2 2m, - Zm
where m, is the analytical concentration (molal) of HX, and Zm the sum of the equilibrium concentration of HX, H+, and X-. Zm is approximated, a t low concentrations of a solute, by dividing the observed freezing point depression by the molal freezing point depression constant. This treatment assumes that the activity coefficient of the solvent is not affected significantly by the variation in the ionic strengths of the acid solutions studied. Potentiometry. Our previous potentiometric studies3s4 in EDA have yielded only relative dissociation constants, i.e., differences in pK values, rather than absolute dissociation constants. A knowledge of the reference electrode potential vs. the hydrogen electrode in EDA is necessary to obtain the absolute pK values of acids. Similarly, the standard potential of the silver electrode must be known to obtain absolute pK values of compounds studied using the silver electrode. Classical aqueous techniques to evaluate the standard potentials are difficult to apply to EDA solutions since complete dissociation of even the strongest electrolyte would occur only a t analytical concentrations approaching -10-6 M. Evaluation of Reference Electrode Potential. To avoid the above problem, use was made of the spectrophotometric and cryoscopic values of KHc~to evaluate the reference electrode potential from e.m.f.-concentration data obtained from the cell Cell I: reference s.c.s.e./jHX(CHX)1H2 (1 atm.), Pt At 25", the e.m.f. of cell I is given by
EHX= E,,,, -t 0.0296 log KHx
+ 0.0296 log CHX(23)
taking E o ~ + , H 2 as zero. (We shall use the same notation as in ref. 3 and 4.) Evaluation of E o A g + , ~ g . Cells I, 11, and I11 were used to evaluate E o A g t , A g . Cell 11: reference s.c.s.e. jlAgX(CAgx)IAg
Thus, solving eq. 24 and 25 simultaneously yields E"A~+,A~. EoAg+,Ag
= EAgx -
EHX-t
Therefore, from the expression for the potential of cell
I1
and from the known values of E,,,, and E " A ~ + it ,isA ~ possible to determine Kagx. It is of interest to note that the determination of E" for a half-reaction in a solvent such as EDA does not require the knowledge of any absolute pK values, provided appropriate electrodes of second or third kind can be devised and used in conjunction with electrodes of the first kind.
Experimental Reagents. Ethylenediammonium bromide was prepared by a method analogous to that described earlier4 for the corresponding chloride; a 40% aqueous hydrobromic acid solution was used instead of concentrated hydrochloric acid as was used for the preparation of the chloride. Analysis of the recrystallized sample gave a purity of 100.0%. Sodium Ethanolamine. Pure sodium metal was slowly reacted in a closed chamber with slight excess of freshly distilled ethanolamine. The excess ethanolamine was removed under vacuum; the solid residue was treated with small amount of pure EDA and again dried under vacuum a t -80". The latter treatment was repeated two more times to remove any remaining ethanolamine. A saturated EDA solution (0.00265 M ) of sodium ethanolamine was used in the indicator experiments. (7) L. D. Pettit and S. Bruckenstein,
J. Inorg. Nuc2. Chem., 13, 1478
(1962).
Volume 69, Number 8 August 1966
2540
L. 11.MUKHERJEE, S. BRUCKENSTEIN, AND F. A. K. BADAWI
Purification of the solvent and other reagents are described elsewhere. 3,4 Spectrophotometric Technique. A battery-operated Beckman Xodel DU spectrophotometer equipped with a photomultiplier attachment was used. The cell compartment was maintained a t 25 f 0.5". All cells were calibrated, and the constancy of calibration was checked periodically by measuring the absorbance of standard potassium chromate solutions in 0.05 M potassium hydroxide. The experimental solutions were made by dilution of concentrated stock solutions with the help of a Gilmont ultramicroburet (Model No. G 15401). All manipulations were carried out in a glove box free from water and carbon dioxide. Cryoscopic Technique. A VECO -4 5902 Type thermistor (100,000 ohms resistance a t 25" ; temperature coefficient = -4.6%/"C.) was used as the temperature-sensing device in an equal-arm Wheatstone bridge. The unbalanced bridge voltage was amplified by a Keathly 150 AR microvolt amplifier and recorded using a Sargent potentiometric strip chart recorder. The freezing point cell was the same as that used prev i ~ u s l y . Cooling ~ curves were recorded following the previously reported p r ~ c e d u r e . ~The mean deviation of a freezing point measurement was always less than 0.001'. The limiting factor appeared to be the reproducibility of initiating nucleation, not the temperature measurement. Potentionzelric Techniques. These have been described previously.3,
350
550
450 A, m r .
Figure 1. Spectra of 3-methyl-4phenylazophenol: curve A, 2.23 x 10-6 M HI in EDA; curve B, 2.028 x M Na+I- ( H I 0.00265 M sodium ethanolamine); curve C, 3.325 X M HI in 0.00455 M acetic acid; curve D, 2.65 X loF5M HI in 0.4720 M acetic acid.
+
Results and Discussion Molar absorptivities of the indicator acid, HI, are given in Figure 1. In the pure indicator solutions (curve A, Figure 1) there is a single maximum a t 490 mp, followed by a shoulder a t 430 mp. The 490mp peak is also present in the completely ionized form of the indicator (Na+I-) (curve B, Figure 1). On acidification, the peak tends to shift to 470 mp (compare curves C and D, Figure 1) accompanied by reduction of absorbances a t 490 mp. Plots of molar absorptivities of the indicator os. the concentrations of an added nonabsorbing acid, e.g., acetic (or hydrochloric) acid, a t 470 and 490 mp are given in Figure 2. These plots are linear over -0.1 to -0.5 M acetic acid added and correspond to the equilibrium mixture of H I and H+Igoverned by eq. 3; a t very high acid concentrations heteroconjugate ions of the type (1HX)- may form. The linear portions of Figure 2 are extrapolated to zero acid concentration and the extrapolated values of eapp so obtained are taken to give E' (eq. 12) for the particular wave lengths used. The value of e' is found to be 2.00 X lo4a t 470 mp and 1.74 X lo4a t 490 mp. The Journal of Physical Chemistry
490 nw
1'41 I
I
I
I
0.2
I
0
I
0.4
Molarity.
Figure 2. Determination of E': 470 mp, A acetic acid, A, HC1; 490 mp, 0 acetic acid; 0 HC1.
Beer's law is valid a t 470 and 490 mp for solutions of Wa+I- (HI sodium ethanolamine or the sodium salt of HI) over the range of concentration of in-
+
EQUILIBRIA IN ETHYLENEDIAMINE
2541
I
I,
Table 11: Spectrophotometry with 3-Methyl-4-phenylazophenol in EDA a t 490 mpa
1.125 2.015 2.23 2.675 3.33 4.40 5.47 7.58 9.60
Table 1: Spectrophotometry with 3-Methyl-4-phenylazophenol in EDA at 470 mp"
x
10s
1.125 2.015 2.23 2.675
3.33
4.44 5.47 7.58 9.60
%PP470
A
O.64Ob 0.570" 0.191d 0.225d 0.27gd 0.36Qd 0.456d 0.625d 0.76gd
x
10-4
2.85 2.83 2.85 2.81 2.79 2.795 2.78 2.76 2.67
fl(C%ppdio
f2 0.8920 0.8598 0.8513 0.8420 0.8273 0.8028 0.7857 0.7568 0.7435
(EL-470
- C'4d'Ct x -
10
C'470)
0.807 1.326 1,525 1.642 1.913 2.505 2.903 3.589 3.563
= 2.90 :x 104 and = 2.00 104. b Light path = 2.00 cm. c Light path = 1.00 cm. d Light path = 0.301 cm. [0.3009 cm. (1.00-cm. cell 0.70-cm. spacer used; whole Calibrated against standard KtCrOd in 0.05 N KOH)]; slit width < 0.015 mm. a
+
0.8908 0.8585 0.8525 0.8410 0.8237 0.8036 0.7852 0.7551 0.7379
1.519 2.497 2.687 3.061 3.785 4.503 5.307 6.691 7.119
+
terest. The eI- values obtained are 2.90 X lo4a t 470 mp and 3.37 X lo4 at 490mp. Plotting the data given in Tables I and I1 according to eq. 15a yields straight lines as shown in Figure 3. Least-squares constants for these data are given in the legend to Figure 3. KHI equals 2.58 X (standard deviation = 0.41 X on the basis of the 490-mp data and equals 3.04 X (standard deviation = 0.55 X using the 470-mp data. The internal consistency of approach is shown by excellent agreement of the int'ercept (€1- in eq. 15a) with the experimental value of €I-.
Concn.,
3.32 3.275 3.26 3.23 3.24 3.18 3.16 3.14 3.02
a €1-493 = 3.37 X 104 and d 4 9 0 = 1.74 X lo4. Light path = Light path = 0.301 cm. 2.00 cm. Light path = 1.00 cm. [0.3009 em. (1.00-cm. cell 0.70-cm. spacer used; whole calibrated against standard K&rOa in 0.05 N KOH)] ; slit width < 0.015 mm.
Figure 3. Plot of eq. 15a. Least-squares constants and standard deviations are given in the format: (mp), intercept (standard deviation), and slope (standard deviation) are 470, 2.874 x 104 (0.013 x 104)) -0.3297 X lo4(0.013 X lo4); 490, 3.378 X lo4 (0.025 X lo4), -0.3870 X lo4 (0.061 X lo4). Leastsquares lines are shown in the figure.
M
0. 745b 0.660' 0. 21gd 0. 2595d 0. 324d 0. 420d 0. 520d 0. 710d 0 . 870d
Table 111: Spectrophotometry of Mixtures of 3-Methyl-4-phenylazophenol and Hydrochloric Acid in EDA a t 490 m p a Concn.
1.99 1.97 2.015 2.015
CHp
Conon. ( M ) of
( M ) of HI X lo3
HC1 X 103 '
1.04 2.575 5.25 10.50
BPP
X
3.14 3.025 2.99 2.88
P 0.8403 0.8219 0.7889 0.7526
[HC11/
CHI^
P[I-I2 x 10-4
1.034 2.40 4.70 8.73
1.132 2.081 2.49 4.09
= 3.37 X lo4, E'490 = 1.74 X lo4, and KHIIKECI = See eq. 19.
a €1-490
2.38.
Table I11 presents the results of the HI-HC1 mixture experiments obtained a t 490 mp. Using the trial and error procedure outlined in the second section of Theory, a plot of assumed KHI/KHXvs. the corresponding least-squares values was made (Figure 4). The shape of this plot makes the determination of KHI/KHX very precise and yields a value of 2.38 for KHIIKHx. The standard deviation of this ratio for the best leastsquares fit is 0.49. The calculated value of KHI with a standard deviafrom these data is 1.13 X tion of 0.23 X The difference between the various estimates of KHI is not outside the range of our experimental error. Therefore, we have averaged all values of KHI weighting inversely as the square of the standard deviation of each value. The average K H Iis equal to 1.68 X and, using the average value of the ratio K H I / ~ H X equal to 2.38, KHc~calculates to 7.06 X Volume 69,Number 8 August 1966
L. na. MUKHERJEE, S. BRUCKENSTEIN, AND F. A. K. BADAWI
2542
Table IV: Cryoscopic Data for Hydrochloric Acid and Hydrobromic Acid in EDA AT^ x HX
HC1
Conon., Ca 103, 'C.
7.18 14.90 19.53 24.02 43.50
22 46 59 74 119
ZCc
I
KHX
8.0 17.3 22.1 27.4 46.7
0.682 0.566 0.560 0.529 0.534
0.49 1.46 1.22 1.55 0.724
x
104
Mean K ~ c lX l o 4 = 1.1 i0.38 HBr
1.41 7.54 15.78 17.17 24.06
5 25 49 54 75
1.9 9.3 18.9 20.0 28.0
0.732 0.601 0.536 0.549 0.512
1.40 1.97 2.21 1.683 2.025
Mean K H BX~ lo* = 1.86
2 KHi/Knx, least-squares.
4
Figure 4. Plot of assumed values of KHI/KHXws. the corresponding least-squares values (eq. 20).
The cryoscopic results obtained with HC1 and HBr are given in Table IV. The molar concentration scale has been used to permit comparison between the spectrophotometric and cryoscopic results. The Marshall-Grunwald equation8 has been used to evaluate the activity coefficients. KHCIis found to be 1.1 X rt 0.38 X and K H B ~1.9 , X f 0.25 X a t -11.2'. The uncertainty of these K values is probably larger than that due to change in temperature from -11 to 25'. Schaap and co-workersg have reported a conductometric value for PKHCl of 3.98 while a value of 3.935 was found by Fowles,'* et al., from similar measurements. The difference between these values and our values is not large, and we have averaged our mean spectrophotometric result, cryoscopic result, and the a grand above conductometric r e s ~ l t s ~to~ 'obtain ~ mean of 4.01 f 0.07 for ~ K H c ~ This . value of p K ~ c 1 was used below to calculate E,,,, from potentiometric experiments using cell I. On repeating our previous potentiometric experiments involving hydrochloric acid in cell I and silver chloride in cell 11, lines of theoretical slope were obtained, but these lines were displaced 34 mv. for hydrochloric acid and 10 mv. for silver chloride, as comDared to Our previoiisly reported value^.^#^ For other cases, substantial agreement with previously reported e.m.f. data was obtained. The difficulty was found to be the time dependence of the reference electrode potential. The Journal of Physsical Chemistry
0.25
' Analytical concentration of HX (mmoles/liter). Freezing point depression, average of three cooling curves on same sample, rounded to 0.001'. Mean deviation is always less than 0.001'. E Concentration of HX (mmoles/liter) as determined from freezing point depression using naphthalene as standard.
Cell IV was used to study this effect together with cells
I and I1 containing freshly prepared hydrochloric Cell IV: (new) reference s.c.s.e./]references.c.s.e. (old) acid and silver chloride solutions, respectively, us. a s.c.s.e. electrode aged over different periods of time. The results are shown in Figure 5 . Stock" has also observed similar drifts. Apparently, unsuspected drifts in the s.c.s.e. potential occurred in our previous hydrochloric acid and silver chloride study. In all e.m.f. experiments reported in this paper, the s.c.s.e. electrode was between 1 and 2 days old. We can offer no explanation for the drift in the s.c.s.e. potential. In Table V, least-squares constants for eq. 23 (cell I),on fitting EHx us. log CHX,obtained for hydrochloric acid and hydrobromic acid dilution experiments and for eq. 27 (cell 11)on fitting EAgx us. log CAgX obtained for silver chloride, silver bromide, and silver iodide experiments are given. In the least-squares treatment the numerical value of 0.0296 (=2.303RT/25 at 25") was not adjusted since the two-parameter fit including the adjustment of 2.303RT/25 did not fit the data (8) H. P. Marshall and E. Grunwald, J . Chem. Phys., 21, 2143 (1953). (9) W. B. Schaap, R. E. Bayer, J. R. Siefkar, J. Y. Kim, P. W. Brewster, and F. C. Schmidt, Record Chem. Progr., 22, 197 (1961). (10) G. W. A. Fowles and W. R. McGregor, J . Phys. Chem., 68, 1342 (1964). \----,-
(11) J. T.Stock, private communication.
EQUILIBRIA IN ETHYLENEDIAMINE
2543
Table V : Potentiometric Results Obtained Using Cells I and 11s
- 10
$
HX or AgX
CHX or Ckx,M
E, v.
HCI
0.1192 0.0597 0.0264 0.0130 0.0035
-0.6718 -0.6814 - 0.6924 -0.7013 -0.7214
HBr
0.1490 0.1011 0.0508 0.0254 0.0108 0.0051
-0.6602 -0.6651 0.6721 -0.6824 -0.6908 0.7043
AgCl
0.4948 0.3947 0.2036 0.1565 0.0947 0.0620 0.0333 0.0148 0.0019
0.1006 0,0980 0.0907 0.0874 0.0802 0.0736 0.0669 0.0553 0.0322
AgBr
0.3332 0.1663 0.1065 0.0214 0.0123
0.0887 0.0800 0.0737 0.0567 0.0484
0.2259 0.0988 0.0502 0.0187 0.0101 0.0048
0.0584 0.0490 0.0408 0.0302 0,0227 0.0187
1
8
w' -5
20
40
Time, days.
Figure 5. Time dependence of the reference electrode (s.c.s.e.) potential: 0, cell I (with HCI); A, cell I1 (with AgC1); A, cell IV.
significantly better. Aside from the hydrochloric acid and silver chloride data, agreement with our previously reported data is good. We calculate E,,,, to be -0.5272 v. using the mean value of ~ K H C=I 4.01. Data obtained using cell I11 are given in Table VI. The two sets of hydrochloric acid-silver chloride mixture data were obtained independently by two of the authors some 3 years apart. The value of pK~gclpKHcl calculated from eq. 25 for these two sets of hydrochloric acid-silver chloride data are shown in Table VI. The value of E ' A ~ + - ,calculated A~ from the present set of data using eq. 26 is equal to 0.7571 0.0030 v. as compared to 0.7339 v. given by previous HCl-AgC1 data. 3,4 We have taken previously reported dataa4 along with data obtained in this study of cells I and I1 and Calculated absolute pK values using E,,,, (= -0.5272 (=0.7571 v.) obtained above. These v.) and EoAB+,bg values are listed in Table VII; also listed in Table VI1 are the acid dissociation constants obtained using cell V.
*
Cell V: reference s.c.s.e.1 IMXlHz (1atm.), Pt where M = Li or Na. Salts investigated included chloride, bromide, nitrate, and perchlorate of lithium and sodium, and sodium phenylacetate.
a
-
+ 0.0296 log C=cI + 0.0296 log C H B ~ Ekcl = 0.1105 (&O.OOlO) + 0.0296 log C k c l (f0.0014) + 0.0296 log CA~B? E A ~ B0.1039 ~ E q r = 0.0810 (10.0032) + 0.0296 log CA,,
Cell I: Ea01 = -0.6459 (10.0015) E H B=~ -0.6349 (&0.0013) Cell 11:
As was shown earlier,4in an EDA solution of a pure salt U H + = ~ K H x K B / K M thus, s; relative pK values for a series of acids may be calculated from the e.m.f. values of cell V with the corresponding solutions of lithium and sodium salts. Alternatively, the relative dissociation constant of Lis and NaS (HS denotes EDA) may be obtained by comparing the e.m.f. values found with cell V using the lithium and sodium salts of the same acid. Such comparisons yield pKNas - p K ~ i s 0.22 i 0.01. We have not included the e.m.f. data obtained with any sodium salt of a phenolic compound. ExperiVolume 69,Number 8 Augwd 1966
L. M. MUKHERJEE, S. BRUCKENSTEIN, AND F. A. K. BADAWI
2544
mentally, for such compounds no change in u H + is observed wit,h varying concentrations of salt, but we have evidence, both cryoscopic and conductometric, that for sodium o-phenylphenolate, for example, a X-, simple monomeric dissociation, MX $ M + is not sufficient to explain the observed behavior.
Table VI1 : Absolute p K Values of Acids and Silver Salts in EDA
+
HX or AgX
Present authors
HCl HBr
Table VI : Results Obtained Using Cell 111. Calculation of E ' A ~ + ,According A~ to Eq. 26 CApCI,
M
0.01085 0.01085 0.01085
CHCli
M
0.2410 0.1200 0.0525
AE,
V.a
0.0419 0.0337 0.0236
PKAgCl
- PKHCl
0.055 0.06 0.04
Mean 0.05 i 0.01 0.0108 0.0108 0.0108
0.2410 0.2076 0.1222
0.0408 0.0395 0.0328
0.733gb
0.014 0.03 0.025
Mean 0.023
' AE
EoAg+,Ag, V.
0.01
0.7571'
= E.m.f. difference between cell I1 and cell I11 both con-
'
taining the same CA~CI. Previous measurements (cf. ref. 3 and 4). Cell I: E H C=~ -0.6122 (10,0019) 0.0296 log C H C ~ Cell 11: E A ~ C=I 0.1202 (i0.0015) 0.0296 log CAgCl c This paper (Table V).
+ +
With the exception of HC1 and AgCl the agreement between the pK values calculated from the previously reported results3r4and the present ones is as close as can be expected. (As mentioned earlier, this discrepancy in the case of HC1 and AgCl has been traced to the accidental drift of the potential of the reference electrode used in the previous measurements.) It should also be mentioned in this connection that our absolute pK values of HC1, HBr, " 0 3 , AgBr, and AgI reported in t)his paper compare favorably with those obtained by conductance measurements. 9,10
The Journd of Physical Chemistry
2 . 87,"'b 4 . O l C s d 3. 76,bt03 , 64"td 3.73,Q'h3.734; Hydriodic acid 2.97'10 HNOa 3 . 2OoPh HClOi 3 . 1OoSh Acetic acid 5. 1gbSi Phenylacetic acid 5. 19,b8i4 . 48b10 3-Methyl-4phenylazophenol 3 , 77d3k p-Phenylphenol 7. 02,a'b3t 7 .02",h3' o-Phenylphenol 7. 131asb*' 7 . 02"3h,' Phenol 7 . 13"3'8' Thymol 8.21"8b21 AgCl 3.70,"," 4.04d'0 AgBr 4.23,msn 4. 26d10 AgI 5.06,m x n 5 . 03dt0
Others (conductometric values)
3.98," 3.935' 3. 62e
3 . 48e
4.08" 4.95'
a Cell I ; E,,., = -0.5272 v. 'See ref. 4. Grand mean of spectrophotometric, cryoscopic, and conductance values (see text). This paper. E See ref. 9. 'See ref. 10. Cell V; P K H C= ~ 4.01. F. A. K. Badawi, M.S. Thesis, University of Minnesota, 1964. Cryoscopic value (see text). Cell I ; pK based on comparison of calculated e.m.f. for CHX = 0.01 M using the corresponding least-squares constants, given in the legend to Figure 2 of ref. 4, us. EHCI= -0.7051 v. a t CHCI= 0.01 M (cf. footnote to Table V); PKHC1 = 4.01. This pK value is only approximate. Weighted average (see text). See eq. 5d in ref. 4. Cell 11; E,,,,= -0.5272 v.; E ' A ~ + ,=A0.7571 ~
'
V.
= 0.1202 (*0.0015) f 0.0296 log CAgCl E A ~ B=? O.lOM5 (10.0022) 0.0296 log C A ~ B ~ E A ~=I 0.0801 (10.0012) 0.0296 log C A ~ I EAgCl
+
+
~ " See ref. 3. ' Cell 11; E,,,, = -0.5272 v.; E ' A ~ + ,=A 0.7571 X given in the footnote to Table V. v. Equations for E A ~are
Acknowledgment. This work was sponsored by the Army Eesearch Office.
