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Chemical affinity systems—I
]. inorg,aucl.Chem.Vol.42.pp.1559-1575
PergamonPressLtd.,1980. PrintedinGreatBritain
CHEMICAL AFFINITY SYSTEMS--I pH D E P E N D E N C E OF BORONIC ACID--DIOL A F F I N I T Y IN A Q U E O U S SOLUTION PAUL A. SIENKIEWICZtand DAVIDC. ROBERTS* Department of Chemistry, Rutgers, The State University of New Jersey, New Brunswick,NJ 08903,U.S.A. (First received 2 August 1979; received [or publication 20 February 1980)
Abstract--A comprehensivetheory of complexformation between boronic acids (R-B(OH)2)and organic diols is introduced and comparedwith experimental results for two exemplary systems using a direct spectrophotometric method over a wide range of pH values. The complexes of benzeneboronic acid with 4,5-dihydroxynaphthalene2,7-disulfonate (4,5-diol) and with 2,3-dihydroxynaphthalene-6-sulfonate(2,3-diol) were found to dissociate to the extent of one part in 3.39x 104 and 4.37x 104,respectively, at optimal pH values. The conjugate acid form of a complex is observed for the first time in equilibria of this type.
INTRODUCTION
more, the pH dependence of the complexation was not well understood even for the better-characterized systems, and, since it would be necessary to "tune" the complexation equilibrium in order to utilize it conveniently as the basis of a separation method, a full understanding of the nature of this type of equilibrium was sought.
The association of boronic acids with diols has been utilized as the basis for chromatographic separations[l]; it occurred to us that this phenomenon might serve as the basis of a new separation method paralleling the ease and efficiency of biochemical affinity chromatography. Accordingly, we sought examples of boronic acid--diol equilibrium which exhibit a very high degree of association. Although there are several instances of isolation of boronic acid-diol complexes[2], no quantitative studies exist, to our knowledge. We expected the catechols and 1,8-naphthalenediols to favor complex formation most strongly, by analogy to the complexes of boric acid with these species, which were indicated in previous work to be among the most stable of this type[3, 4]. Unfortunately, reliable data concerning the extent of association in these cases were unavailable. Further-
THEORY The most widely-used model, upon which numerous quantitative studies have been based, is one developed by Edwards[3a] and Antikainen[5]; the treatment given here is an extension of their model to account for the ionization of the diol or other chelating species. In accord with the original formulation of Hermans[6], the following species may be postulated to exist in equilibrium upon combining aqueous solutions of a monoalkylboronic acid, R-B(OHh, and a diol:~ capable of forming a cyclic chelate,
*Author for correspondence. tHenry Rutgers Scholar, 1978--79. /-OSAlthough a doubly ionized species X also is possible, ~.Oit is being neglected, since, for the cases studied, its concentration is vanishinglysmall at moderate pH values.
OH
/---OH
OH
X ~--OH
R~B~ HA
/OH R -- B'-- OH
~OH A-
HL
/---OX
~.--OH L-
1559
f---OH X ~---OH
R - - B ' ° ' - ~X
\o__./
H2AL
HO\ BI_O'-'~X R / \0__/ HAL-
1560
P. A. SIENKIEWICZand D. C. ROBERTS
The case involving a boronic acid is identical to that for boric acid, except that, by virtue of the alkyl group, complexes containing more than one diol molecule are not possible, and the equilibrium is further simplified. The use of a boronic acid also avoids additional equilibria involving polyborate ions, which are sometimes observed in the case of boric acid[4b]. The value of practical interest in such a system is the ratio O/~
E[bound species X-Y] " E[unbound species X] E[unbound species Y]
Direct spectrophotometric measurement of a (1)
which in this case takes on the form [H2AL] + [HAL-] a = ([HAl + [A-])([HL] + [L-l)'
(2)
The model of Edwards and Antikainen is based on the use of the apparent acidity of borate--diol mixtures as a measure of the degree of association. Assuming for the present purposes that [H+] = a~, the experimentally determined "apparent K~" of the mixture, K ~ - [H+][HAL-] [HA]tilL]
(3)
=
can be used to obtain approximate values for a (say, a') by virtue of the approximation [HAL-] ~, [H2AL]; that is; a' =
[HAL-] ([HA] + [A-])([HL] + [L-])"
(4)
By substituting into this expression a rearranged form of eqn (3), and then further simplifying, using the definitions K . A = [H+][A-] KnL= [H+][L-] [HAl ' [HL] we arrive at an expression for a' as a function solely of [H +] and experimentally measurable constants [7]: ~, =
g~ [H +] + K.~, + KHL+ KHLKriA" [H ÷]
(5)
This function will reach a maximum value at [H ÷] = X/KHLK.A (i.e. at a pH intermediate between pKHL and p K , A); if the diol is a considerably weaker acid than boric acid (i.e. K,A>>K,L), the value of a' at the optimal pH reduces to: t O/max
~
Kl KHA"
concerning the pH behavior of all borate--diol association equilibria in which Kt has been experimentally determinedt and the values of /(HA and K,L are known or easily estimated. In general, a plot of (log a') vs pH will exhibit a bell-shaped curve, in which the function will level off at height log ((Kr)/(K.A + KUL)) at pH values intermediate between the pKo's of the boron species and diol, and drop off with slopes of 1 and -1 in the lower and higher pH regions, respectively (see Fig. 1).
(6)
This was undertaken to verify eqn (5) independently and accurately and to assess the contribution of [H2AL] to the overall value of a. The present method is related to that introduced by Bruice[4b] but differs in its experimental approach. Our method involves the observation of the effect of increasing concentrations of boronic acid upon the UV spectrum of a dilute diol solution, while other parameters (volume, pH, temperature, ionic strength) were maintained constant. Since well-defined isosbestic points were obtained in all cases (see Fig. 2), the equilibrium was shown to be well-behaved, and could be treated in much the same way as a simple two-species equilibrium. The following symbols will be used throughout the remainder of this discussion: CHA and Cr~L, total concentration of all boronic acid and diol species, respectively; Aob,, absorbance of experimental boronic aciddiol mixture; A,~o~, absorbance of pure diol solution (in absence of boron species); A~omeex, absorbance of a solution of entirely complexed diol. For each set of curves obtained in a given buffer, a value of wavelength giving maximum AA was chosen, and by plotting (l/Aobs-A~oO vs (I/C.A), an absorbance value at infinite boronic acid concentration (assumed to be A~om¢ox) could be obtained by extrapolation (Fig. 3). The total concentration of complexed species may then be obtained using the expression: A~llol [H2AL] + [HAL-] = C.L(A oA°b~-_-~iol) = X (7) \
complex
(see Appendix for a derivation) and the true value of a for each individual CHA value determined using a modified form of eqn (2): X
a = ( C . L - X)(C.A - X)"
(8)
These values were then averaged, affording an overall a for the pH value used in the experiment. EXPERIMENTAL
Materials. All buffers were prepared using commercialreagent grade chemicals. 4,5-dihydroxynaphthalene-2,7-disulfonic acid disodium salt dihydrate (4,5-diol) was obtained from Aldrich (purity 98%) and 2,3-dihydroxynaphthalene-6-suffonic acid sodium salt (2,3-diol) was obtained from Sigma; both were used as supplied. Benzeneboronic acid was prepared by the procedure of Washburn et al.[8]; it was further purified by dissolving in a minimum volume of hot CCI4 (affording the anhydride plus water, which is removed by filtration through absorbent cotton) tUnder conditions where only a 1:1 complex forms, viz., at and allowing to crystallize upon cooling; filtration and brief air low diol concentration. The same sort of behavior will be obser- drying afforded fluffywhite crystals of the anhydride, m.p. 209212°C (uncorr.; lit[8] 214-216"C), which were stored in a desicved for the process (diol+ l : 1 complex~ I : 2 complex).
This value has been used by Antikainen (as k~) as a means of expressing the extent of borate-diol association in his potentiometric studies; clearly the assumptions used to arrive at such a simple expression for a' are not valid in the context of the present study. The value of eqn (5) is that it affords predictions
Chemical affinity systems--I
1561
'
.\
• (.
,~
\
. /Z
~
~1 0 -I
)\
. "
\
/
.
.\
I
\\
/ 0
/
I
""J(
:•/ t
2
3
4
/
//
~\\',
"
~
6
7
~
8
9
-- -- -- -
11
10
l
1
~\~
12
13
'
~4
pH
Fig. I. Log a' vs. pH for various diols with boric acid ( ): 4,5-diol[4b]; (.......): 2,3-diol[3e]; ( . . . . . ): 4,5-dihydroxy-l,3-benzenedisuifonie acid (R. N/is~.nen et al., Suomen Kemistilehti 33, 111 (1960);( ............ ): 3,4-dihydroxybe~aldehyde[3d]; (. . . . . . . . . ): dl-2,3-bu~anediol[3c]; ( - - ) : ethylene giycol[3c].
,.o '1; iii~
i! :'"
lliii,~ii: !!~I,Ii~ir'
T III ~ I
l i~r'fil
" t
~t~lr*'iii!
iii!
!,, 4 ~i,!Jili
~ ii!
IIil I!i! illi ~
o.~
~'~~ ~ m H 1 1 H ~
11~!i
I.!!I !il,,i tilt
o ~ ilil ~,',!
if!
~H, !' ;hi !"
i!:
:
+lif Li
i!
.~ L.! I!! ;i;i '
!19
o Ii:
:i
3,00
I J: I qii!li i, [:, ~i i I: J ti i,i'i Iti:l 310
B~O
3,$0
34,0
WAVELENGTH,
I
I ;[ 350
I
I
, 360
,
,
.
i:
370
nm
Fig. 2. UV spectra of 4,5-diol solutions containing increasing amounts of benzeneboronic acid; pH = 3.73, [4,5-diol] = 8.75 × 10-5 _M; Curve D is that of pure diol solution; other curves correspond to increasing total boronic acid concentrations up to a maximum of 3.87 × 10-3 _M(Curve C). cator and used directly to prepare solutions of benzeneboronic acid. Apparatus. All pH measurements were performed using an Orion Model 601A pH meter equipped with a combination glass/Ag-AgCI electrode; it was standardized against two of the three Fisher standard buffers (pH 4, 7 or 10) which were closest in value to the pH being measured. UV spectra were recorded at 25*(] on ~qther a Cary 118 or a Cary 17-D spectrophotometer at a sweep speed of 0.2 nm/sec. Absorbance values (vs buffer) were obtainod by careful reading of the chart and corrected for absorbance obtained from a baseline run at the beginning of each set of spectra using buffer in the sample cell.
Preparation of buffers. The buffers shown in Table 1 were prepared, using glass-distilled water, by acidifying a solution of an appropriate salt with its conjugate acid so as to result in INn+] = 0.1 _M in all cases. Arsenite buffers were prepared iby suspending As203 in 0.1 _M NaAsO2 and filtering off the excess upon reaching the desired pH. Two liters were sufficient for erich set of spectra. Preparation of stock solutions. Solutions of 4,5-diol were found to discolor (with change in spectrum) with time and exposure to light, and therefore were prepared immediat~.ly before use by dissolving the solid and diluting to the mark with the desired buffer. Solutions of 2,3-diol appeared to be stable;
1562
P.A. SIENKIEWICZ and D. C. ROBERTS Table 1. Buffers used in experiments (all 0.1 M Na+)
Buffersystem (0.i M HCI) H3PO4-H2PO 4 HCOOH-HCO0-
I.ii 2.12
3.73 4.75
Molar ionicstrength 0.i 0.i 0.i
CH3COOH-CH3C00-
6.24~ 6.49
0.1
/
0.1145 0.1240 0.1564
6.99 7.00
7.24 / 7.97/ 8.00/
9.16~it 9.20
9.85~-~HC0 10.25/
Total
H2P04 _ HF04-< ~
0.1572 0.1776 0.2278 0.2291
~
AsO 2
-
-
3
AsO 2
_ ~ o . 1 0.i
,~0.I166 C03= ~-0.1325
conc.0.05M; restCI for pH 9.85case.
these were prepared by diluting a known volume of a single standard aqueous solution with the appropriate buffer. Benzeneboronic acid solutions were freshly prepared from the anhydride for each set of spectra at a given pH; gentle heating on a steam bath was required to assist solution of the anhydride; the solution was cooled to 20°C before diluting. Preparation and study o[ working solutions. For each set of spectra at a given pH, a single total diol concentration (CnL) was maintained, and a range of boronic acid concentrations (CH^) were employed, as shown in Tables 2 and 3. Each working solution was prepared by transferring 50 mL of stock diol solution via pipette to a 100 mL volumetric flask (the same pipette and flask were used here in all experiments), adding via pipette the appropriate volume of stock boronic acid solution, and diluting to the mark with buffer. The spectrum of each working solution was obtained immediately after preparation (the spectrum was found not to change with time, indicating that equilibration was nearly instantaneous, as previously reported [4b] and the recorder chart caused to wind back automatically prior to.the recording of the next spectrum so that the chart drive and wavelength drive maintained their original engagement. This was repeated until spectra representing a wide range of boronic acid concentrations (and hence, degrees of complex formation) were obtained. The raw data were treated as described in the text of this paper and the a values thus obtained are reported in Tables 2 and 3. Calculations were performed using a programmable hand calculator, and verified using a computer program written in APL. Curve-fitting was performed using a computer program written in BASIC, implemented on a Tektronix 4051 computer equipped with a 4662 digital plotter, upon which plots were prepared. RESULTS The values in Tables 2 and 3 are illustrated graphically in Fig. 4. The expected bell-shaped behavior predicted by eqn (5) is observed in both cases, with a deviation in the low-pH region in the 4,5.diol case. This is to be expected
in certain cases, since our original assumption of [H2AL] ,~ [HAL-] may not be valid at sufficiently low values of pH; the leveling off thus represents the first observation in equilibria of this type of the conjugate acid of the complex. Returning to our original expression for a, eqn (2), we may rewrite it: [H2AL] a = ([HA] + [A-])([HL] + [L-]) + [HAL-] ([HA] + [A-])([HL] + [L-])
(9)
or
[H2AL] ¢X=
KHA
+
K, [H ÷] + K~A + KHL + KHAKHL" [H +1
(10)
Since the equilibrium HA+HLO---H2AL involves no charged species, K/~.2At.,=- ([H2AL]/[HA][HL]) is a true equilibrium constant, and our expression simplifies to 5=
Kt'(H2AL)
KHA
K,
(u)
K.AKHL' [H+] + K~A + KHL + - -
[H +1
The parameters of this equation were adjusted to give
Chemical affinity systems--I
1563
Table 2. Summ~y of data for 4,5~iol-benzeneboronic acid complexes pH
CHL(~)
CHA(max)(~)
log a
std.dev.)
No. of points
i.ii*
1.669 x 10 -3
8.28 x 10 -2
1.325
.0062)
5
2.12"
3.687 x 10 -4
5.108 x l0 -2
1.588
.040)
6
3.73
8.750 x 10 -5
3.869 x 10 -3
2.987
.013)
7
4.75
8.140 x 10 -5
3.887 x 10 -3
3.845
.039)
8@
6.24
7.785 x 10 -5
4.152 x 10 -3
4.52
6.99
7.615 x 10 -5
3.915 x 10 -3
4.536
.063)
i0
7.00
8.36 x 10 -5
3.886 x 10 -3
4.524
.071)
io
7.97
7.785 x 10 -5
4.068 x 10 -3
4.070
.098)
8.41
7.440 x 10 -5
3.997 x 10 -3
3.64 (.41)
7
3.41 (.27)
5¢
.i0)
9
7~
9.20
8.200 x 10 -5
8.00 x 10 -3
3.036 (.124)
7
9.85
6.145 x 10 -5
7.843 x 10 -3
2.18
8
(.36)
6#
1.979 (.099)
1 mm cells used in these cases; in all others, 1 cm cells were used. One or two poorly behaved points excluded from averaging (in cases where two points were excluded, average for all points is also given).
Tables 2(a-k). Raw data used to calculate values in Table 2 (note: A~ in these tables refers to A°ornplexas defined in text.) pH = 1.11
CHL = 1.669x10 -3 M
0.1 M HC1 Solution
CHA
Abs.
0
0.675
1.04xi0 -2
0.760
I/A-A~iol
I/CHA
K
log K
11.76
96.15
21.46
1.3317
2.08x10 "2
0.818"
6.99
48.07
21.09
1.3241
4.14xi0 -2
0.895*
4.54
24.15
21.07
1.3236
8.28xi0 -2
0.975*
3.33
12.07
20.73
1,3166
Plot of 1/A-Adiol vs. 1/CHA : A ~ * Points used to extrapolate A ~ Average log K = 1.3248
extrapolated
= 1.152
in Double Reciprocal Plo%
Standard Deviation = 0.0062
over all point~
1564
P.A. SIENKIEWICZand D. C. ROBERTS
Table 2(b). pH = 2.12
CHL = 3.687xi0 -4 M
Sodium Phosphate Buffer
CHA
Abs.
o
O.lO7
° l/A- A diol
I/CHA
K
log K
37.98
1.5795
4.882xlO -3
0.142-
28.57
204.9
9.728x10 -3
o.167"
16.67
lO2,8
37.53
1.5744
1,945x10 -2
0,212
9.52
51.3
45.01
1.6533
3.373x10 -2
0.229
8.20
29.6
34.98
1.5438
5.108x10 -2
0.257*
6.67
19.6
38.82
1.5891
o
Plot of 1/A-Adiol vs. 1/CHA : A oo extrapolated = 0,333 * Points used to extrapolate Ace in Double Reciprocal Plot Average log K = 1.5880
Standard Deviation = 0.0402
over all points
Table 2(c). pH = 3.73
Sodium Formate Buffer
CHA 0
Abs.
1/A-A~iol
CHL = 8.75x10 -5 M 1/CHA
K
log K
0.207
9.708x10-5
0.250
23.26
10300
928.1
2.9676
1,934xi0 "4
0.290
12.05
5170
973.0
2.9881
4.851x10 -4
0.377
5.88
2060
960.9
2.9826
9.708x10 -4
0.475*
3.73
1030
1002.1
3.0009
1.934xi0 -3
0.568*
2.77
517
986.2
2.9939
3,869xi0 -3
0.645*
2.28
258
976,8
2.9898
Plot of 1/A-Adiol vs. I/CHA , Aooextrapolated
= 0.763
* Points used to extrapolate A oo in Double Reciprocal Plot Average log K = 2.9866
Standard Deviation = 0.0126
over all points
Chemical affinity systems--I
1565
Table 2(d). pH = 4.75
CHL = 8.14xi0 -5 M
Sodium Acetate Buffer o
CHA
Abs.
o
0.295
1/A-Adiol
I/CHA
K
log K
1.932xi0 -5
0.352
17.54
51760
11654
4.0664
4.871x10 -5
0.399
9.60
20530
7601
3.8808
9.746xlO -5
0.474
5.58
10260
7443
3.8717
1.942xi0 -4
0.573
3.60
5150
7476
3'8736
4.874x10 -4
0.691-
2.52
2052
7252
3.8604
9.754x10 -4
0.748*
2.20
1025
7029
3.8469
1.943x10 -3
0.779*
2.06
515
6445
3.8092
3.887x10 -3
0.797*
1.99
257
5936
3.7731
o
Plot of ~/A-Adiol vs. I/CHA : A ooextrapolated
= 0.8192
* Points used to extrapolate A~in Double Reciprocal Plot Average log K = 3.8727
Standard Deviation = 0.0864
over all points
Average log K = 3.8451
Standard Deviation = 0.0398
excluding first point
Table 2(e). pH = 6.24
Sodium Phosphate Buffer
CHA
Abs.
0
0.909
1/A-Adiol
CHL = 7.785x10 -5 M 1/CHA
K
log K
2.075x10 -5
0.770
7.19
~8209
27254
4.4354
5.206x10 -5
0.586
3.09
19206
30606
4.4858
1.041x10 -4
0.380
1.89
9597
34052
4,5321
2.076xi0 -4
0,222
1.45
4816
36875
4.5667
5.206x10 -4
0.132"
1.28
1921
42429
4.6276
1.042x10 -3
0.110"
1.25
960
43534
4.6388
2.076xi0 -3
0.102"
1.24
482
36696
4.5646
4.152xi0 -3
0.100"
1,23
241
22058
4.3435
Plot of i/A-Adiol vs. CHA : Ao~extrapolated
= 0.091
* Points used to extrapolate A oo in Double Reciprocal Plot Average log K = 4.5243
JINC Vol. 42, No. I I---C
Standard Deviation = 0.0995
over all points
1566
P.A. SIENKIEWICZ arid D. C. ROBERTS
Table 2(f). pH = 6.99
Sodium Phosphate Buffer
CHL = 7,615x10 -5 M
o
OHA
Abs.
0
0.950
I/A-Adiol
I/CHA
K
log K
9,760x10 "6
0,871
12.66
102460
35159
4,5460
1.952xi0 ~5
0.789
6,21
51230
41909
4,6223
4,899xi0 -5
0,590
2.78
20410
~0448
4.6069
9.804x10 "5
0,391
1.79
10200
36662
4.5642
1.961x10 "4
0,231"
1.39
5100
35859
4.5546
4.903x10 -4
0,135"
1.23
2040
35630
4.5518
9.810xi0 -4
0.III*
1.19
1020
30212
4.4801
1,962xi0 "3
0.097*
1.17
510
27226
4.4349
3.915xi0 -3
0.088*
1.16
255
29540
4.4706
o
Plot of !/A-Adiol vz, I/CHA : A oo extrapolated = 0,0804 * Points used to extrapolate A oo in Double Reciprocal Plot Average log K = 4.5368
Standard Deviation = 0.0628
over all points
Table 2(g). pH = 7.00
Sodium Phosphate Buffer
CHL = 8.36x10 -5 M
a
CHA
Abs.
0
1.038
I/A-Adiol
1/CHA
K
log K
9.662xi0 -6
0,984
13.51
103930
28142
4.4493
1,932x10 "5
0.915
6.99
51760
27558
4.4402
4,849x10 "5
0,700
2.79
20620
37532
4.5744
9,707x10 ~5
0.463
1,68
10300
39755
4.5994
1.9~Ix10 "4
0,280*
1.28
5152
39569
4,5974
4.855x10 "4
0.183
1,14
2060
35331
4.5481
9.715x10 -4
0.157"
1,11
1029
29057
4.4633
1.943xi0 -3
0,145"
1.09
515
21~12
4.3326
3.886x10 "3
0,135"
1.08
257
18958
4.2778
o
P16t of i/A-Adiol vs. 1/CHA : A co extrapolated = O,1222 *Points used to extrapolate A ~ i n
Double Reciprocal Plot
Average log K = 4.4758
Standard Deviation = 0.1155
over all points
Average log K = 4,5245
Standard Deviation = 0.0712
excluding last 2 points
Chemical affinity systems--I
1567
Table 2(h). pH = 7.97
CHL = 7.785x10 -5 M
Sodium Phosphate Buffer
CHA
Abs.
0
0.950
5.101x10 -5
0.736
1.021xi0 -4 2,034x10 -4
i/A-Adiol °
K
log K
9909
3.9960
1/CHA
4.67
19600
0.584
2.73
9795
10088
4.0038
0.345*
1.65
4916
14382
4.1578
5,101x10 -5
0.188"
1.31
1960
13982
4.1455
1.021xi0 -3
0.124"
1.21
980
14762
4.1691
2.034xi0 -3
0.113"
1.19
492
8894
3.9491
4.068xi0 -3
0,104-
1.18
246
5431
3.7349
o
Plot of 1/A-Adiol vs. 1/CHA : A~extrapolated = .065 * Points used to extrapolate A ~ i n Double Reciprocal Plot A~erage log K = 4.0223
Standard Deviation = 0.1549
over all points
Average log K = 4,0702
Standard Deviation = 0.0976
excluding last point
Table 2(i). pH = 8.41
0-Chlorophenol Buffer CHA
Abs.
0
0.884
CHL = 7.44x10 -5 M
1/A-Adiol
1/CHA
K
log K
1,007x10 -4
0,780
9.61
9930
1745
3.2419
2.0C6xi0 -4
0.725
6.29
4980
1424
3.1537
5,000x10 -4
0.430
2.20
2000
3234
3.5098
1.003x10 -3
0.243
1.56
997
5634
3.7508
1,998xi0 -3
0.152"
1.36
500
12665
4.1026
3,997xi0 -3
0.138"
1.34
250
11881
4.0708
Plot of I/A-A~iol vs. !/CHA : A~extrapolated = 0.122 *Points used to extrapolate A ~ i n
Double Reciprocal Plot
Average log K = 3.6382
Standard Deviation = 0.4058
over all points
Average log K = 3.4140
Standard Deviation = 0.2707
excluding last two points
1568
P.A. SIENKIEWICZand D. C. ROBERTS
Table 2(j). pH = 9.20
CHL = 8.20x10 -5 M
Sodium Arsenate Buffer
CHA
Abs.
0
1.233
1/A-Adiol °
Z/CHA
K
log K
9.857xi0 "5
1.008
4.44
10145
2754
3.4400
1.966x10 -4
0.976
3.89
5086
1542
3.1882
4.916xi0 -4
0.853
2.63
2034
1023
3.0102
1.008x10 -3
0.733*
2.00
992
763
2.8967
1.966x10 -3
0.518"
1.40
510
820
2.9139
3.920x10 -3
0.291"
1.06
255
1081
3.0341
8.000x10 "3
0.157"
0.93
125
1488
3.1727
o
Plot of 1/A-Adiol vs. 1/CHA : A ooeXtrapolated = 0.082 * Points used to extrapolate A oo in Double Reciprocal Plot Average log K = 3.0936
Standard Deviation = 0.1900
over all points
Average log K = 3.0359
Standard Deviation = 0.1239
excluding first point
Table 2(k). pH = 9.85
g CHL = 6.145x10 "~ M
Sodium Carbonate Buffer o
CHA
Abs.
0
0.828
1/A-Adiol
1/CHA
K
log K
1.928x10 "4
0.813
66.67
5185
99.83
1.9992
4.837x10 "4
0.784*
22.73
2067
121.33
2.0839
9.679x10 "4
0.780
20.83
1033
66.29
1.8214
1.928x10 "3
0.684
6.94
518
114.69
2.0295
3.857x10 "3
0.621-
4.83
259
91.03
1.9591
6.775x10 -3
0.234*
1.68
148
430.58
2.6340
7.843x10 -3
0.176"
1.53
128
569.16
2.7552
o Plot of I/A-Adiol vs. 1/CHA , A~extrapolated = 0.0982
* Points used %o extrapolate A ~ i n
Double Reciprocal Plot
Average log K = 2.1831
Standard Deviation = 0.3602
over all points
Average log K = 1.9786
Standard Deviation = 0.0989
first five points
Chemical affinity systems--I
1569
Table 3. Summ~y of data for 2,3-diol-benzeneboronic acid complexes pH
CHL(M)
CHA(max)(~)
log a (std. dev.)
No. of points
4.75
1.924 x l0 -4
5.852 x I0 -2
1.6735 (0093)
6.49
4.062 x 10 -4
2.288 x 10 -3
3.601 ( 034)
6#
7.24
4.812 x l0 -5
2.153 x i0 r3
4.269 ( 065)
9
8.00
4.812 x l0 -5
3.082 x 10 -3
4.647 ( 095)
9
9.16
4.812 x I0 -5
7.995 x 10 -3
3.700 ( :359)
8
10.25
9.623 x 10 -5
1.566 x i0 -2
3.537 ( 024)
l0 #
I0
One poorly behaved point excluded from averaging.
Tables 3(a-f). Raw data used to calculate values in Table 3 (note: As in these tables refers to A°ora~,lexas defined in
text.) pH
=
4,75
CHL
Sodium Acetate Buffer
CHA
Abs,
0
0,215
1,924x10-4. M
=
1/A-Adiol °
1/CHA
K
log K
1,302xi0 "3
0,276
16,40
768,0
46,92
1,6713
2,605xi0 -3
0,336
8.25
383,7
49,46
1,6942
5,191xi0 -3
0,425
4,75
192,6
47,49
1,6766
7,339xi0 -3
0,484
3,70
136,2
46,17
1,6644
1,038x10 -2
0,568*
2,85
96,3
47,85
1,6799
1,468xi0 -2
0,648*
2,30
68,0
46,69
1,6693
2,202x10 -2
0,758*
1,85
45,4
47,18
1,6737
2,926x10 -2
0,830*
1,60
34,2
46,57
1,6681
5,852x10 -2
0,994*
1,28
17,0
46,17
1,6643
Plot of i/A-Adiol vs, 1/CHA : A~extrapolated * Points used to extrapolate A ~ i n Average log K = 1,6735
= 1,283
Double Reciprocal Plot
Standard Deviation = 0,0093
over all points
1570
P.A. SIENKIEWlCZ and D. C. ROBERTS
Table 3(b). pH = 6.49
CHL - 4.062x10 -4 M
Sodium Phosphate Buffer o
CHA
Abs.
0
0.042
I/A-Adiol
I/CHA
K
log K
2,870xi0 "5
0.062
50.00
34750
4423
3.6458
1.147x10 -4
0.102
16.66
8~10
48986
4.6900
2.869x10 "4
0.156"
8.77
3480
4071
3.6097
5,740xi0 "4
0,297
6.45
1740
4133
3.6163
1.144xi0 -3
0.224*
5.49
875
3739
3.5728
2,288xi0 "3
0,244-
4,95
437
3641
3.5613
Plot of
1
o /A-Adiol vs • I/CHA : A ~
extrapolated : 0.269
• Points used to extrapolate A~o in Double Reciprocal Plot Average log K = 3,?826
Standard Deviation = 0.4402
over all points
Average log K - 3.6012
Standard Deviation = 0.0342
excluding second point
Table 3(c). pH = 7.24
CHL = 4.8115x10 "5 M
Sodium Phosphate Buffer
CHA
Abs.
o
0.078
I/A~A~iol
1/OHA
K
log K
1.350x10 -5
0.111
30.30
74060
24914
4.3964
2.700x10 "5
0,134
17.85
3?000
20679
4.3155
5.380x10 -5
0.169
10.98
18575
18478
4.2666
1.076x10 -4
0.217
7.19
9287
18973
4.2781
2.700x10 -4
0.262
5.43
3700
16534
4.2183
5.~00x10 -4
0.286*
4.80
1850
17442
4.2416
1.076x10 -3
0,298*
4.54
928
17792
4.2502
2.153x10 -3
0,303*
4.44
464
15260
4.1835
o
Plot of 1/A-Adiol vs. 1/CHA : A ~ * Points used to extrapolate A ~ i n Average log K = 4.2687
extrapolated = 0.310 Double Reciprocal Plot
Standard Deviation = 0.0648
Chemical affinity systems--I
1571
Table 3(d). pH = 8.00
Sodium Phosphate Buffer
CHA
Abs.
o
o.150
CHL = 4.8115x10 -5 M"
l/A-Adiol
I/CHA
K
log K
1.937xi0 -5
0.188
26.31
51624
62081
4.7929
3.876x10 -5
0.212
16.13
25796
47587
4.6774
7.724xi0 -5
0.241-
ii.00
12947
42541
4.6288
7.758x10 -5
0.243
10.75
12890
45768
4.6605
1.545xi0 -4
0.268
8.47
6469
52047
4.7163
7.736xi0 -4
0.283
7.52
1293
36577
4.5632
1.541xi0 -3
0.285*
7.40
649
30121
4.4788
3.082xi0 -3
0.287*
7.29
324
45151
4.6546
Plot of
1
o /A-Adiol vs. I/CHA : A oo extrapolated = 0.288
* Points used to extrapolate A oo in Double Reciprocal Plot Average log K = 4,6465
Standard Deviation = 0.0946
over all points
Table 3(e). pH = 9.16
Sodium Arsenate Buffer
CHA 0
Abs.
CHL = 4.8115x10 -5 M
i/A-A~iol
1/CHA
K
log K
0.157
4.020x10 -5
0.133
41.70
24900
6543
3.8158
1.005xlO -4
0.114
23.25
9950
5231
3.7186
2.012xi0 -4
0.089*
14.70
4970
5390
3.7316
4.008x10 -4
0.066*
11.00
2500
5133
3.7104
8.017xi0 -4
0.049
9.25
1250
4558
3.6587
2.006x10 -3
0.032*
8.00
500
4549
3.6579
3.997xi0 -3
0.025*
7.57
250
4772
3.6787
7.995xi0 -3
0.022*
7.40
125
4246
3.6280
Plot of i/k-A~iol vs. I/CHA : A ~
extrapolated = 0.018
* ~oints used to extrapolate A co in Double Reciprocal Plot Average log K = 3.6999
Standard Deviation = 0.0585
over all points
1572
P. A. SIENKIEWICZ and D. C. ROBERTS Table 3(f). pH = 10.25
Sodium Carbonate Buffer
CHA
Abs.
0
0.527
CHL = 9.623x10 -5 M
1/A-A~iol
i/CHA
K
log K
3.951xlo -5
0.480
21.27
25309
37o6
3.5689
7.907xiO "5
0.443
11.90
12646
3506
3.5488
1.575xlO -4
0.379
6.75
6347
3600
3.5563
3.150xlO -4
0.302
4.44
3173
3399
3.5314
3.940xlO -4
0.272
3.92
2537
3452
3.5382
7.885xlO -4
o.192-
2.98
1268
3420
3.5341
1.571x10 -3
0.141-
2.59
636
3043
3.4833
3.929xlo -3
0.089*
2.28
254
3456
3.5386
7.862xlo -3
0.073*
2.20
127
3437
3.5362
1.566xlo -2
0.069*
2.18
64
2263
3.3547
Plot of 1/A-A~iol vs. 1/CHA : A ooextrapolated
= 0.056
* Points used to extrapolate A oo in Double Reciprocal Plot Average log K = 3.5191
Standard Deviation = 0.0618
over all points
Average log K = 3-5373
Standard Deviation = 0.0236
excluding last point
the best visual fit for both the 4,5-diol and the 2,3-diol data; the resulting theoretical curves are displayed in Fig. 4 along with the experimentally determined points. The parameters giving the best fit are collected in Table 4 along with available literature values for comparison. The determination of glf{'H2Ag) further allowed the first measurement of the true acid dissociation constant of the complex: K _ [H+][HAL-] g~ (12) ~('~L) = [I2I~ALi.....Kf(H'--~AL) in equilibria of this general class. Interestingly, no complex formation whatsoever could be observed at pH 2 in the 2,3-
\/
~'OH2
o B .o
I
reported values was in the apparent PKHA for the 4,5diol case, which is at least 1.15 units lower than expected. Neither of two possible explanations, viz., covalent interaction of the buffer species with the diol or boronic acid ("buffer competition") and incorporation of the buffer species into the complex itself (substitution of OH by the buffer anion in the HAL- structure), seem plausible, since the averaged a values would have to be low by the same factor to correlate so well with eqn (11), and this is unlikely given the wide variety of buffer anions used. The optimal log a values reported here of 4.52 (for 4,5-diol) and 4.65 (for 2,3-diol) represent the largest degrees of association ever observed in 1:1 complexes of this type, and, for reasons previously mentioned, the values are more reliable than those obtained by potentiometric methods. The spectrophotometric observation of H2AL for the 4,5-diol case allows a tentative conclusion to be drawn concerning its structure. As can be seen in Table 5, little change occurs in the spectrum of HL in the presence of high HA concentrations, on passing from pH 7 (complex entirely in the HAL- form) to pH l.ll (complex at least 90% in H2AL form). This may be interpreted as suggesting a water-coordinated species, I, as the structure of H2AL rather than II, since Ph
Ph
I
I +o B\o
II
1573
Chemical affinity systems--I E+l 2 $0
2.0~
o &
1 +5B
J
o \
J
1 OB
e. 5 g
B.BB
B.PB
B.4B
+.6B
B Be
I .00
|/CHA
Fig. 3. Double reciprocal plot: 4,5-diol, pH 3.73.
Table 4. Equilibrium constants from curve fitting of spectrophotometric data using eqn (l 1) 4,5-Dioi
2,3-Dioi
-o
Fit
Lit.
Fit
Lit.
PK I
0.84
1.3 [13]*
3.o0
P~L
5.45
5.36 [12]
8.12
8.12 [3e]
8.70
8.7 [13]
p~
7.55
5.53
[9]
5.33
[4a,lO]
8.7 [13] 9.71 [ii]
log Kf(H2AL )
1.30
pKa(H2AL )
2.14
pK I for H3BO 3 + 4,5-dioi:
#pK I for H3BO 3 + 2+3-dioi:
9.71 [ii]
1.55 [4a]
3.89 (extrap. to I = O.i) [3e]
Table 5. pH dependence of UV spectral data for complexed 4,5-diol __
1 max
max E
pH
i.ii
pH
7.00
332.5
336.5
8027
9796
347.5
351.5
9249
11093
1574
P. A. SIENKIEWICZ and D. C. ROBERTS r
l
o
2 o
.J /
\ \
II
~" ~-~i
//
L~ ~..~ , , / / / / v . . . 0
1
2
3
/ , 4
5
~__, 6
7
,
~_
__
8
9
18
, II
, 12
13
14
pH Fig. 4. Log a vs pH for 4,5-diol and 2,3-diol.
in going from HAL- to structure II we would expect a substantial change in the UV spectrum, rather than the almost negligible pH effect observed (expected for simple protonation). In view of the fact that the aryloxy groups in II are quite electron-withdrawing, it seems quite plausible that II would prove to be a sufficiently strong Lewis acid to form a stable adduct with water. Further studies of these systems in our laboratory are presently focusing on the use of diol-functionalized solid supports, in conjunction with boronic acids, in new separation methods. Acknowledgements--Acknowledgement is made to the donors of The Petroleum Research Fund, administered by the ACS, for partial support of this research. Additional financialsupport from the Rutgers Research Council and the Rutgers Biomedical Research Support Grant Program (funded by NIH) is gratefully acknowledged. REFERENCES 1. H. L. Weith, J. L. Wiebers and P. T. Gilham, Biochemistry 9, 4396 (1970); H. Schott, E. Rudloff, P. Schmidt, R. Roychoudhury and H. Krssel, Biochemistry 12, 932 (1973) and Refs. therein. 2. I. M. Pailer and W. Fenzl, Monatsh. 92, 1294 (1961); W. Kliegel, Organometal. Chem. Rev. AS, 153 (1972); O. C. Musgrave and T. O. Park, Chem. Ind. (London) 1552(1955). 3. For catechol itself, see (a) G. L. Roy, A. L. Laferriere and J. O. Edwards, £ lnorg. Nucl. Chem. 4, 106 (1957); (b) P. J. Antikainen and A. Kauppila, Suomen Kemistilehti !132, 141 (1959); (c) J. M. Conner and V. C. Bulgrin, J. Inorg. Nucl. Chem. 29, 1953 (1967); for relevant catechol derivatives, see (d) P. J. Antikainen and H. Oksanerl, Acta Chem. Scand. 22, 2867 (1968) and Refs. therein; (e) R. N~is~inen,P. Tilus and P. Helander, Suomen Kemistilehti I~3, 331 (1970). Values in the range of 103-105are reported for the "association constants" in these papers, using potentiometric methods, although, as pointed out by Conner and Bulgrin, the method of calculation used in these cases incorrectly assumes that the diol component is less acidic than boric acid, and is, to this extent, inaccurate. 4. The association of 4,5-dihydroxynaphthalene-2,7-disulfonate
(chromotropic acid) with boric acid has been studied potentiometrically: (a) M. Bartugek and L, Havelkovfi, Coll. Czechoslov. Chem. Commun. 32, 3853 (1967)--and qualitatively by spectrophotometric methods: (b) D. W. Tanner and T. C. Bruice, J. Am. Chem. Soc. 89, 6954 (1967); however, an actual "association constant", while clearly quite large, is not specified by these authors. 5. P. J. Antikainen et al. Suomen Kemistalehti B31,255 (1958); !132, 141 (1959). 6. P. H. Hermans, Z. Anorg. Allgem. Chem. 142, 83 (1925), 7. A different form of this equation was used by Brulce, although it is not clear how it was derived. This equation may also be derived as a conditional equilibrium expression according to the method of Inczrdy and Ringbom (J. Inczrdy, Analytical Applications of Complex Equilibria, pp. 51--53) Akadrmiai Kiad6 (Budapest) (1976). 8. R.M. Washburn,E. Levens, C. F. AIbrightand F. A. Billig,Org. Synth. Coll. 4, 68 (1963). 9. H. Zollinger and W. B0chler, Heir. Chim. Acta 34, 591 (1951). 10. J. Heller and G. Schwarzenbach, Heir. Chim. Acta 34, 1876 (1951). 11. Measured in 25% ethanol; B. Bettman et aL, J. Am. Chem. Soc. 56, 1865(1934). 12. W. P. Jencks, cited by Bruice[4b]. 13. D. C. Roberts, Ph.D. Thesis, MIT, 1975; the method of Antikainen[3d] was employed. APPENDIX Derivation of eqn (7) (see text for definitions) Assuming that Beer's Law holds, for I cm cells, at a constant value of A, the component of absorbance due to uncomplexed diol is
Aoiol enL[HL]+ ~L-[L-].
(AI)
=
Since
[ H L ] = C ~ ~ -- -_- ._. C_{ . V and [L-I=
HL \ ' K H ~ - H + ]
J,
(A2) Adio'= c H Lr L ~ H L ~
}
KHL
(A3)
1575
Chemical affinity systems--1 If pH is maintained constant, the expression within brackets remains constant, and is the apparent ~ for the particular mixture of HL and L- present at that pH value. We might call this ~ot,
or o
Ao
Aobs = ~ ( [ H L I
+
t-~HL
SO
[L l) + ~ ( [ H 2 A L ] c . k
+
[HAL 1). (A9)
Adiol = CIqL" eJiol.
(A4)
The value of e~ot may easily be obtained from the absorbance of the pure diol solution A]iot at that pH (i.e. no HA has been added).using eqn (A4). Similarly, the component of absorbance due to complex will be given by
(Note that A~iol and A~omple x refer to values obtained at C.A = 0 and o0 (extrapolated as described in the text), respectively, and not to components of Aob~at intermediate C.A values.) From the definition of CUE, ([HL] + [L-]) = C . L - ([H2AL] + [HAL-])
(AI0)
and this can be substituted into eqn (A9) to obtain Acomple,= EHAL-[HAL-]+ EH2AL[H~AL],
(AS) Aob~' CHL -~ A~ioI(CHL - ([H2AL] + [HAL-])
which reduces similarly to Acomplex = C H L ' ~omplex.
+ A%mp~ex([H~AL]+ [HAL-]). (A6)
The value of e*om¢,~ is obtained from the absorbance of the solution extrapolated to infinite HA concentration (i.e. AOom¢~x) as described in the text, and applying eqn (A6). At intermediate values of C.A,
This simplifies to
Aobs" CnL =
o . _ o Adiol CHL+(A~omplex Adi(~t)
× ([H2AL] + [HAL-]) or
(A7) and, applying eqns (A1), (A4), (A5) and (A6), this reduces to =
(A12)
CHL(Aobs- A~iot) = (A~°omple~- A,%ol)([H2AL] + [HAL ])
Aobs = eHL[HL] + ~L-[L-] + EH2AL[H2AL] + ~HAt-[HAL-]
Aobs ~Jiol([HL] + [L-l) + Ec*o,~plex([H2ALl + [HAL-l)
!All)
(A13) which rearranges to give eqn (7) in the text:
(A8)
C
(Aob~- A~iol)
.L ~ =[H,ALI+[HAL-]. (Acomplex Adiol) -
PergamonPressLtd.,1980. PrintedinGreatBritain
CHEMICAL AFFINITY SYSTEMS--I pH D E P E N D E N C E OF BORONIC ACID--DIOL A F F I N I T Y IN A Q U E O U S SOLUTION PAUL A. SIENKIEWICZtand DAVIDC. ROBERTS* Department of Chemistry, Rutgers, The State University of New Jersey, New Brunswick,NJ 08903,U.S.A. (First received 2 August 1979; received [or publication 20 February 1980)
Abstract--A comprehensivetheory of complexformation between boronic acids (R-B(OH)2)and organic diols is introduced and comparedwith experimental results for two exemplary systems using a direct spectrophotometric method over a wide range of pH values. The complexes of benzeneboronic acid with 4,5-dihydroxynaphthalene2,7-disulfonate (4,5-diol) and with 2,3-dihydroxynaphthalene-6-sulfonate(2,3-diol) were found to dissociate to the extent of one part in 3.39x 104 and 4.37x 104,respectively, at optimal pH values. The conjugate acid form of a complex is observed for the first time in equilibria of this type.
INTRODUCTION
more, the pH dependence of the complexation was not well understood even for the better-characterized systems, and, since it would be necessary to "tune" the complexation equilibrium in order to utilize it conveniently as the basis of a separation method, a full understanding of the nature of this type of equilibrium was sought.
The association of boronic acids with diols has been utilized as the basis for chromatographic separations[l]; it occurred to us that this phenomenon might serve as the basis of a new separation method paralleling the ease and efficiency of biochemical affinity chromatography. Accordingly, we sought examples of boronic acid--diol equilibrium which exhibit a very high degree of association. Although there are several instances of isolation of boronic acid-diol complexes[2], no quantitative studies exist, to our knowledge. We expected the catechols and 1,8-naphthalenediols to favor complex formation most strongly, by analogy to the complexes of boric acid with these species, which were indicated in previous work to be among the most stable of this type[3, 4]. Unfortunately, reliable data concerning the extent of association in these cases were unavailable. Further-
THEORY The most widely-used model, upon which numerous quantitative studies have been based, is one developed by Edwards[3a] and Antikainen[5]; the treatment given here is an extension of their model to account for the ionization of the diol or other chelating species. In accord with the original formulation of Hermans[6], the following species may be postulated to exist in equilibrium upon combining aqueous solutions of a monoalkylboronic acid, R-B(OHh, and a diol:~ capable of forming a cyclic chelate,
*Author for correspondence. tHenry Rutgers Scholar, 1978--79. /-OSAlthough a doubly ionized species X also is possible, ~.Oit is being neglected, since, for the cases studied, its concentration is vanishinglysmall at moderate pH values.
OH
/---OH
OH
X ~--OH
R~B~ HA
/OH R -- B'-- OH
~OH A-
HL
/---OX
~.--OH L-
1559
f---OH X ~---OH
R - - B ' ° ' - ~X
\o__./
H2AL
HO\ BI_O'-'~X R / \0__/ HAL-
1560
P. A. SIENKIEWICZand D. C. ROBERTS
The case involving a boronic acid is identical to that for boric acid, except that, by virtue of the alkyl group, complexes containing more than one diol molecule are not possible, and the equilibrium is further simplified. The use of a boronic acid also avoids additional equilibria involving polyborate ions, which are sometimes observed in the case of boric acid[4b]. The value of practical interest in such a system is the ratio O/~
E[bound species X-Y] " E[unbound species X] E[unbound species Y]
Direct spectrophotometric measurement of a (1)
which in this case takes on the form [H2AL] + [HAL-] a = ([HAl + [A-])([HL] + [L-l)'
(2)
The model of Edwards and Antikainen is based on the use of the apparent acidity of borate--diol mixtures as a measure of the degree of association. Assuming for the present purposes that [H+] = a~, the experimentally determined "apparent K~" of the mixture, K ~ - [H+][HAL-] [HA]tilL]
(3)
=
can be used to obtain approximate values for a (say, a') by virtue of the approximation [HAL-] ~, [H2AL]; that is; a' =
[HAL-] ([HA] + [A-])([HL] + [L-])"
(4)
By substituting into this expression a rearranged form of eqn (3), and then further simplifying, using the definitions K . A = [H+][A-] KnL= [H+][L-] [HAl ' [HL] we arrive at an expression for a' as a function solely of [H +] and experimentally measurable constants [7]: ~, =
g~ [H +] + K.~, + KHL+ KHLKriA" [H ÷]
(5)
This function will reach a maximum value at [H ÷] = X/KHLK.A (i.e. at a pH intermediate between pKHL and p K , A); if the diol is a considerably weaker acid than boric acid (i.e. K,A>>K,L), the value of a' at the optimal pH reduces to: t O/max
~
Kl KHA"
concerning the pH behavior of all borate--diol association equilibria in which Kt has been experimentally determinedt and the values of /(HA and K,L are known or easily estimated. In general, a plot of (log a') vs pH will exhibit a bell-shaped curve, in which the function will level off at height log ((Kr)/(K.A + KUL)) at pH values intermediate between the pKo's of the boron species and diol, and drop off with slopes of 1 and -1 in the lower and higher pH regions, respectively (see Fig. 1).
(6)
This was undertaken to verify eqn (5) independently and accurately and to assess the contribution of [H2AL] to the overall value of a. The present method is related to that introduced by Bruice[4b] but differs in its experimental approach. Our method involves the observation of the effect of increasing concentrations of boronic acid upon the UV spectrum of a dilute diol solution, while other parameters (volume, pH, temperature, ionic strength) were maintained constant. Since well-defined isosbestic points were obtained in all cases (see Fig. 2), the equilibrium was shown to be well-behaved, and could be treated in much the same way as a simple two-species equilibrium. The following symbols will be used throughout the remainder of this discussion: CHA and Cr~L, total concentration of all boronic acid and diol species, respectively; Aob,, absorbance of experimental boronic aciddiol mixture; A,~o~, absorbance of pure diol solution (in absence of boron species); A~omeex, absorbance of a solution of entirely complexed diol. For each set of curves obtained in a given buffer, a value of wavelength giving maximum AA was chosen, and by plotting (l/Aobs-A~oO vs (I/C.A), an absorbance value at infinite boronic acid concentration (assumed to be A~om¢ox) could be obtained by extrapolation (Fig. 3). The total concentration of complexed species may then be obtained using the expression: A~llol [H2AL] + [HAL-] = C.L(A oA°b~-_-~iol) = X (7) \
complex
(see Appendix for a derivation) and the true value of a for each individual CHA value determined using a modified form of eqn (2): X
a = ( C . L - X)(C.A - X)"
(8)
These values were then averaged, affording an overall a for the pH value used in the experiment. EXPERIMENTAL
Materials. All buffers were prepared using commercialreagent grade chemicals. 4,5-dihydroxynaphthalene-2,7-disulfonic acid disodium salt dihydrate (4,5-diol) was obtained from Aldrich (purity 98%) and 2,3-dihydroxynaphthalene-6-suffonic acid sodium salt (2,3-diol) was obtained from Sigma; both were used as supplied. Benzeneboronic acid was prepared by the procedure of Washburn et al.[8]; it was further purified by dissolving in a minimum volume of hot CCI4 (affording the anhydride plus water, which is removed by filtration through absorbent cotton) tUnder conditions where only a 1:1 complex forms, viz., at and allowing to crystallize upon cooling; filtration and brief air low diol concentration. The same sort of behavior will be obser- drying afforded fluffywhite crystals of the anhydride, m.p. 209212°C (uncorr.; lit[8] 214-216"C), which were stored in a desicved for the process (diol+ l : 1 complex~ I : 2 complex).
This value has been used by Antikainen (as k~) as a means of expressing the extent of borate-diol association in his potentiometric studies; clearly the assumptions used to arrive at such a simple expression for a' are not valid in the context of the present study. The value of eqn (5) is that it affords predictions
Chemical affinity systems--I
1561
'
.\
• (.
,~
\
. /Z
~
~1 0 -I
)\
. "
\
/
.
.\
I
\\
/ 0
/
I
""J(
:•/ t
2
3
4
/
//
~\\',
"
~
6
7
~
8
9
-- -- -- -
11
10
l
1
~\~
12
13
'
~4
pH
Fig. I. Log a' vs. pH for various diols with boric acid ( ): 4,5-diol[4b]; (.......): 2,3-diol[3e]; ( . . . . . ): 4,5-dihydroxy-l,3-benzenedisuifonie acid (R. N/is~.nen et al., Suomen Kemistilehti 33, 111 (1960);( ............ ): 3,4-dihydroxybe~aldehyde[3d]; (. . . . . . . . . ): dl-2,3-bu~anediol[3c]; ( - - ) : ethylene giycol[3c].
,.o '1; iii~
i! :'"
lliii,~ii: !!~I,Ii~ir'
T III ~ I
l i~r'fil
" t
~t~lr*'iii!
iii!
!,, 4 ~i,!Jili
~ ii!
IIil I!i! illi ~
o.~
~'~~ ~ m H 1 1 H ~
11~!i
I.!!I !il,,i tilt
o ~ ilil ~,',!
if!
~H, !' ;hi !"
i!:
:
+lif Li
i!
.~ L.! I!! ;i;i '
!19
o Ii:
:i
3,00
I J: I qii!li i, [:, ~i i I: J ti i,i'i Iti:l 310
B~O
3,$0
34,0
WAVELENGTH,
I
I ;[ 350
I
I
, 360
,
,
.
i:
370
nm
Fig. 2. UV spectra of 4,5-diol solutions containing increasing amounts of benzeneboronic acid; pH = 3.73, [4,5-diol] = 8.75 × 10-5 _M; Curve D is that of pure diol solution; other curves correspond to increasing total boronic acid concentrations up to a maximum of 3.87 × 10-3 _M(Curve C). cator and used directly to prepare solutions of benzeneboronic acid. Apparatus. All pH measurements were performed using an Orion Model 601A pH meter equipped with a combination glass/Ag-AgCI electrode; it was standardized against two of the three Fisher standard buffers (pH 4, 7 or 10) which were closest in value to the pH being measured. UV spectra were recorded at 25*(] on ~qther a Cary 118 or a Cary 17-D spectrophotometer at a sweep speed of 0.2 nm/sec. Absorbance values (vs buffer) were obtainod by careful reading of the chart and corrected for absorbance obtained from a baseline run at the beginning of each set of spectra using buffer in the sample cell.
Preparation of buffers. The buffers shown in Table 1 were prepared, using glass-distilled water, by acidifying a solution of an appropriate salt with its conjugate acid so as to result in INn+] = 0.1 _M in all cases. Arsenite buffers were prepared iby suspending As203 in 0.1 _M NaAsO2 and filtering off the excess upon reaching the desired pH. Two liters were sufficient for erich set of spectra. Preparation of stock solutions. Solutions of 4,5-diol were found to discolor (with change in spectrum) with time and exposure to light, and therefore were prepared immediat~.ly before use by dissolving the solid and diluting to the mark with the desired buffer. Solutions of 2,3-diol appeared to be stable;
1562
P.A. SIENKIEWICZ and D. C. ROBERTS Table 1. Buffers used in experiments (all 0.1 M Na+)
Buffersystem (0.i M HCI) H3PO4-H2PO 4 HCOOH-HCO0-
I.ii 2.12
3.73 4.75
Molar ionicstrength 0.i 0.i 0.i
CH3COOH-CH3C00-
6.24~ 6.49
0.1
/
0.1145 0.1240 0.1564
6.99 7.00
7.24 / 7.97/ 8.00/
9.16~it 9.20
9.85~-~HC0 10.25/
Total
H2P04 _ HF04-< ~
0.1572 0.1776 0.2278 0.2291
~
AsO 2
-
-
3
AsO 2
_ ~ o . 1 0.i
,~0.I166 C03= ~-0.1325
conc.0.05M; restCI for pH 9.85case.
these were prepared by diluting a known volume of a single standard aqueous solution with the appropriate buffer. Benzeneboronic acid solutions were freshly prepared from the anhydride for each set of spectra at a given pH; gentle heating on a steam bath was required to assist solution of the anhydride; the solution was cooled to 20°C before diluting. Preparation and study o[ working solutions. For each set of spectra at a given pH, a single total diol concentration (CnL) was maintained, and a range of boronic acid concentrations (CH^) were employed, as shown in Tables 2 and 3. Each working solution was prepared by transferring 50 mL of stock diol solution via pipette to a 100 mL volumetric flask (the same pipette and flask were used here in all experiments), adding via pipette the appropriate volume of stock boronic acid solution, and diluting to the mark with buffer. The spectrum of each working solution was obtained immediately after preparation (the spectrum was found not to change with time, indicating that equilibration was nearly instantaneous, as previously reported [4b] and the recorder chart caused to wind back automatically prior to.the recording of the next spectrum so that the chart drive and wavelength drive maintained their original engagement. This was repeated until spectra representing a wide range of boronic acid concentrations (and hence, degrees of complex formation) were obtained. The raw data were treated as described in the text of this paper and the a values thus obtained are reported in Tables 2 and 3. Calculations were performed using a programmable hand calculator, and verified using a computer program written in APL. Curve-fitting was performed using a computer program written in BASIC, implemented on a Tektronix 4051 computer equipped with a 4662 digital plotter, upon which plots were prepared. RESULTS The values in Tables 2 and 3 are illustrated graphically in Fig. 4. The expected bell-shaped behavior predicted by eqn (5) is observed in both cases, with a deviation in the low-pH region in the 4,5.diol case. This is to be expected
in certain cases, since our original assumption of [H2AL] ,~ [HAL-] may not be valid at sufficiently low values of pH; the leveling off thus represents the first observation in equilibria of this type of the conjugate acid of the complex. Returning to our original expression for a, eqn (2), we may rewrite it: [H2AL] a = ([HA] + [A-])([HL] + [L-]) + [HAL-] ([HA] + [A-])([HL] + [L-])
(9)
or
[H2AL] ¢X=
KHA
+
K, [H ÷] + K~A + KHL + KHAKHL" [H +1
(10)
Since the equilibrium HA+HLO---H2AL involves no charged species, K/~.2At.,=- ([H2AL]/[HA][HL]) is a true equilibrium constant, and our expression simplifies to 5=
Kt'(H2AL)
KHA
K,
(u)
K.AKHL' [H+] + K~A + KHL + - -
[H +1
The parameters of this equation were adjusted to give
Chemical affinity systems--I
1563
Table 2. Summ~y of data for 4,5~iol-benzeneboronic acid complexes pH
CHL(~)
CHA(max)(~)
log a
std.dev.)
No. of points
i.ii*
1.669 x 10 -3
8.28 x 10 -2
1.325
.0062)
5
2.12"
3.687 x 10 -4
5.108 x l0 -2
1.588
.040)
6
3.73
8.750 x 10 -5
3.869 x 10 -3
2.987
.013)
7
4.75
8.140 x 10 -5
3.887 x 10 -3
3.845
.039)
8@
6.24
7.785 x 10 -5
4.152 x 10 -3
4.52
6.99
7.615 x 10 -5
3.915 x 10 -3
4.536
.063)
i0
7.00
8.36 x 10 -5
3.886 x 10 -3
4.524
.071)
io
7.97
7.785 x 10 -5
4.068 x 10 -3
4.070
.098)
8.41
7.440 x 10 -5
3.997 x 10 -3
3.64 (.41)
7
3.41 (.27)
5¢
.i0)
9
7~
9.20
8.200 x 10 -5
8.00 x 10 -3
3.036 (.124)
7
9.85
6.145 x 10 -5
7.843 x 10 -3
2.18
8
(.36)
6#
1.979 (.099)
1 mm cells used in these cases; in all others, 1 cm cells were used. One or two poorly behaved points excluded from averaging (in cases where two points were excluded, average for all points is also given).
Tables 2(a-k). Raw data used to calculate values in Table 2 (note: A~ in these tables refers to A°ornplexas defined in text.) pH = 1.11
CHL = 1.669x10 -3 M
0.1 M HC1 Solution
CHA
Abs.
0
0.675
1.04xi0 -2
0.760
I/A-A~iol
I/CHA
K
log K
11.76
96.15
21.46
1.3317
2.08x10 "2
0.818"
6.99
48.07
21.09
1.3241
4.14xi0 -2
0.895*
4.54
24.15
21.07
1.3236
8.28xi0 -2
0.975*
3.33
12.07
20.73
1,3166
Plot of 1/A-Adiol vs. 1/CHA : A ~ * Points used to extrapolate A ~ Average log K = 1.3248
extrapolated
= 1.152
in Double Reciprocal Plo%
Standard Deviation = 0.0062
over all point~
1564
P.A. SIENKIEWICZand D. C. ROBERTS
Table 2(b). pH = 2.12
CHL = 3.687xi0 -4 M
Sodium Phosphate Buffer
CHA
Abs.
o
O.lO7
° l/A- A diol
I/CHA
K
log K
37.98
1.5795
4.882xlO -3
0.142-
28.57
204.9
9.728x10 -3
o.167"
16.67
lO2,8
37.53
1.5744
1,945x10 -2
0,212
9.52
51.3
45.01
1.6533
3.373x10 -2
0.229
8.20
29.6
34.98
1.5438
5.108x10 -2
0.257*
6.67
19.6
38.82
1.5891
o
Plot of 1/A-Adiol vs. 1/CHA : A oo extrapolated = 0,333 * Points used to extrapolate Ace in Double Reciprocal Plot Average log K = 1.5880
Standard Deviation = 0.0402
over all points
Table 2(c). pH = 3.73
Sodium Formate Buffer
CHA 0
Abs.
1/A-A~iol
CHL = 8.75x10 -5 M 1/CHA
K
log K
0.207
9.708x10-5
0.250
23.26
10300
928.1
2.9676
1,934xi0 "4
0.290
12.05
5170
973.0
2.9881
4.851x10 -4
0.377
5.88
2060
960.9
2.9826
9.708x10 -4
0.475*
3.73
1030
1002.1
3.0009
1.934xi0 -3
0.568*
2.77
517
986.2
2.9939
3,869xi0 -3
0.645*
2.28
258
976,8
2.9898
Plot of 1/A-Adiol vs. I/CHA , Aooextrapolated
= 0.763
* Points used to extrapolate A oo in Double Reciprocal Plot Average log K = 2.9866
Standard Deviation = 0.0126
over all points
Chemical affinity systems--I
1565
Table 2(d). pH = 4.75
CHL = 8.14xi0 -5 M
Sodium Acetate Buffer o
CHA
Abs.
o
0.295
1/A-Adiol
I/CHA
K
log K
1.932xi0 -5
0.352
17.54
51760
11654
4.0664
4.871x10 -5
0.399
9.60
20530
7601
3.8808
9.746xlO -5
0.474
5.58
10260
7443
3.8717
1.942xi0 -4
0.573
3.60
5150
7476
3'8736
4.874x10 -4
0.691-
2.52
2052
7252
3.8604
9.754x10 -4
0.748*
2.20
1025
7029
3.8469
1.943x10 -3
0.779*
2.06
515
6445
3.8092
3.887x10 -3
0.797*
1.99
257
5936
3.7731
o
Plot of ~/A-Adiol vs. I/CHA : A ooextrapolated
= 0.8192
* Points used to extrapolate A~in Double Reciprocal Plot Average log K = 3.8727
Standard Deviation = 0.0864
over all points
Average log K = 3.8451
Standard Deviation = 0.0398
excluding first point
Table 2(e). pH = 6.24
Sodium Phosphate Buffer
CHA
Abs.
0
0.909
1/A-Adiol
CHL = 7.785x10 -5 M 1/CHA
K
log K
2.075x10 -5
0.770
7.19
~8209
27254
4.4354
5.206x10 -5
0.586
3.09
19206
30606
4.4858
1.041x10 -4
0.380
1.89
9597
34052
4,5321
2.076xi0 -4
0,222
1.45
4816
36875
4.5667
5.206x10 -4
0.132"
1.28
1921
42429
4.6276
1.042x10 -3
0.110"
1.25
960
43534
4.6388
2.076xi0 -3
0.102"
1.24
482
36696
4.5646
4.152xi0 -3
0.100"
1,23
241
22058
4.3435
Plot of i/A-Adiol vs. CHA : Ao~extrapolated
= 0.091
* Points used to extrapolate A oo in Double Reciprocal Plot Average log K = 4.5243
JINC Vol. 42, No. I I---C
Standard Deviation = 0.0995
over all points
1566
P.A. SIENKIEWICZ arid D. C. ROBERTS
Table 2(f). pH = 6.99
Sodium Phosphate Buffer
CHL = 7,615x10 -5 M
o
OHA
Abs.
0
0.950
I/A-Adiol
I/CHA
K
log K
9,760x10 "6
0,871
12.66
102460
35159
4,5460
1.952xi0 ~5
0.789
6,21
51230
41909
4,6223
4,899xi0 -5
0,590
2.78
20410
~0448
4.6069
9.804x10 "5
0,391
1.79
10200
36662
4.5642
1.961x10 "4
0,231"
1.39
5100
35859
4.5546
4.903x10 -4
0,135"
1.23
2040
35630
4.5518
9.810xi0 -4
0.III*
1.19
1020
30212
4.4801
1,962xi0 "3
0.097*
1.17
510
27226
4.4349
3.915xi0 -3
0.088*
1.16
255
29540
4.4706
o
Plot of !/A-Adiol vz, I/CHA : A oo extrapolated = 0,0804 * Points used to extrapolate A oo in Double Reciprocal Plot Average log K = 4.5368
Standard Deviation = 0.0628
over all points
Table 2(g). pH = 7.00
Sodium Phosphate Buffer
CHL = 8.36x10 -5 M
a
CHA
Abs.
0
1.038
I/A-Adiol
1/CHA
K
log K
9.662xi0 -6
0,984
13.51
103930
28142
4.4493
1,932x10 "5
0.915
6.99
51760
27558
4.4402
4,849x10 "5
0,700
2.79
20620
37532
4.5744
9,707x10 ~5
0.463
1,68
10300
39755
4.5994
1.9~Ix10 "4
0,280*
1.28
5152
39569
4,5974
4.855x10 "4
0.183
1,14
2060
35331
4.5481
9.715x10 -4
0.157"
1,11
1029
29057
4.4633
1.943xi0 -3
0,145"
1.09
515
21~12
4.3326
3.886x10 "3
0,135"
1.08
257
18958
4.2778
o
P16t of i/A-Adiol vs. 1/CHA : A co extrapolated = O,1222 *Points used to extrapolate A ~ i n
Double Reciprocal Plot
Average log K = 4.4758
Standard Deviation = 0.1155
over all points
Average log K = 4,5245
Standard Deviation = 0.0712
excluding last 2 points
Chemical affinity systems--I
1567
Table 2(h). pH = 7.97
CHL = 7.785x10 -5 M
Sodium Phosphate Buffer
CHA
Abs.
0
0.950
5.101x10 -5
0.736
1.021xi0 -4 2,034x10 -4
i/A-Adiol °
K
log K
9909
3.9960
1/CHA
4.67
19600
0.584
2.73
9795
10088
4.0038
0.345*
1.65
4916
14382
4.1578
5,101x10 -5
0.188"
1.31
1960
13982
4.1455
1.021xi0 -3
0.124"
1.21
980
14762
4.1691
2.034xi0 -3
0.113"
1.19
492
8894
3.9491
4.068xi0 -3
0,104-
1.18
246
5431
3.7349
o
Plot of 1/A-Adiol vs. 1/CHA : A~extrapolated = .065 * Points used to extrapolate A ~ i n Double Reciprocal Plot A~erage log K = 4.0223
Standard Deviation = 0.1549
over all points
Average log K = 4,0702
Standard Deviation = 0.0976
excluding last point
Table 2(i). pH = 8.41
0-Chlorophenol Buffer CHA
Abs.
0
0.884
CHL = 7.44x10 -5 M
1/A-Adiol
1/CHA
K
log K
1,007x10 -4
0,780
9.61
9930
1745
3.2419
2.0C6xi0 -4
0.725
6.29
4980
1424
3.1537
5,000x10 -4
0.430
2.20
2000
3234
3.5098
1.003x10 -3
0.243
1.56
997
5634
3.7508
1,998xi0 -3
0.152"
1.36
500
12665
4.1026
3,997xi0 -3
0.138"
1.34
250
11881
4.0708
Plot of I/A-A~iol vs. !/CHA : A~extrapolated = 0.122 *Points used to extrapolate A ~ i n
Double Reciprocal Plot
Average log K = 3.6382
Standard Deviation = 0.4058
over all points
Average log K = 3.4140
Standard Deviation = 0.2707
excluding last two points
1568
P.A. SIENKIEWICZand D. C. ROBERTS
Table 2(j). pH = 9.20
CHL = 8.20x10 -5 M
Sodium Arsenate Buffer
CHA
Abs.
0
1.233
1/A-Adiol °
Z/CHA
K
log K
9.857xi0 "5
1.008
4.44
10145
2754
3.4400
1.966x10 -4
0.976
3.89
5086
1542
3.1882
4.916xi0 -4
0.853
2.63
2034
1023
3.0102
1.008x10 -3
0.733*
2.00
992
763
2.8967
1.966x10 -3
0.518"
1.40
510
820
2.9139
3.920x10 -3
0.291"
1.06
255
1081
3.0341
8.000x10 "3
0.157"
0.93
125
1488
3.1727
o
Plot of 1/A-Adiol vs. 1/CHA : A ooeXtrapolated = 0.082 * Points used to extrapolate A oo in Double Reciprocal Plot Average log K = 3.0936
Standard Deviation = 0.1900
over all points
Average log K = 3.0359
Standard Deviation = 0.1239
excluding first point
Table 2(k). pH = 9.85
g CHL = 6.145x10 "~ M
Sodium Carbonate Buffer o
CHA
Abs.
0
0.828
1/A-Adiol
1/CHA
K
log K
1.928x10 "4
0.813
66.67
5185
99.83
1.9992
4.837x10 "4
0.784*
22.73
2067
121.33
2.0839
9.679x10 "4
0.780
20.83
1033
66.29
1.8214
1.928x10 "3
0.684
6.94
518
114.69
2.0295
3.857x10 "3
0.621-
4.83
259
91.03
1.9591
6.775x10 -3
0.234*
1.68
148
430.58
2.6340
7.843x10 -3
0.176"
1.53
128
569.16
2.7552
o Plot of I/A-Adiol vs. 1/CHA , A~extrapolated = 0.0982
* Points used %o extrapolate A ~ i n
Double Reciprocal Plot
Average log K = 2.1831
Standard Deviation = 0.3602
over all points
Average log K = 1.9786
Standard Deviation = 0.0989
first five points
Chemical affinity systems--I
1569
Table 3. Summ~y of data for 2,3-diol-benzeneboronic acid complexes pH
CHL(M)
CHA(max)(~)
log a (std. dev.)
No. of points
4.75
1.924 x l0 -4
5.852 x I0 -2
1.6735 (0093)
6.49
4.062 x 10 -4
2.288 x 10 -3
3.601 ( 034)
6#
7.24
4.812 x l0 -5
2.153 x i0 r3
4.269 ( 065)
9
8.00
4.812 x l0 -5
3.082 x 10 -3
4.647 ( 095)
9
9.16
4.812 x I0 -5
7.995 x 10 -3
3.700 ( :359)
8
10.25
9.623 x 10 -5
1.566 x i0 -2
3.537 ( 024)
l0 #
I0
One poorly behaved point excluded from averaging.
Tables 3(a-f). Raw data used to calculate values in Table 3 (note: As in these tables refers to A°ora~,lexas defined in
text.) pH
=
4,75
CHL
Sodium Acetate Buffer
CHA
Abs,
0
0,215
1,924x10-4. M
=
1/A-Adiol °
1/CHA
K
log K
1,302xi0 "3
0,276
16,40
768,0
46,92
1,6713
2,605xi0 -3
0,336
8.25
383,7
49,46
1,6942
5,191xi0 -3
0,425
4,75
192,6
47,49
1,6766
7,339xi0 -3
0,484
3,70
136,2
46,17
1,6644
1,038x10 -2
0,568*
2,85
96,3
47,85
1,6799
1,468xi0 -2
0,648*
2,30
68,0
46,69
1,6693
2,202x10 -2
0,758*
1,85
45,4
47,18
1,6737
2,926x10 -2
0,830*
1,60
34,2
46,57
1,6681
5,852x10 -2
0,994*
1,28
17,0
46,17
1,6643
Plot of i/A-Adiol vs, 1/CHA : A~extrapolated * Points used to extrapolate A ~ i n Average log K = 1,6735
= 1,283
Double Reciprocal Plot
Standard Deviation = 0,0093
over all points
1570
P.A. SIENKIEWlCZ and D. C. ROBERTS
Table 3(b). pH = 6.49
CHL - 4.062x10 -4 M
Sodium Phosphate Buffer o
CHA
Abs.
0
0.042
I/A-Adiol
I/CHA
K
log K
2,870xi0 "5
0.062
50.00
34750
4423
3.6458
1.147x10 -4
0.102
16.66
8~10
48986
4.6900
2.869x10 "4
0.156"
8.77
3480
4071
3.6097
5,740xi0 "4
0,297
6.45
1740
4133
3.6163
1.144xi0 -3
0.224*
5.49
875
3739
3.5728
2,288xi0 "3
0,244-
4,95
437
3641
3.5613
Plot of
1
o /A-Adiol vs • I/CHA : A ~
extrapolated : 0.269
• Points used to extrapolate A~o in Double Reciprocal Plot Average log K = 3,?826
Standard Deviation = 0.4402
over all points
Average log K - 3.6012
Standard Deviation = 0.0342
excluding second point
Table 3(c). pH = 7.24
CHL = 4.8115x10 "5 M
Sodium Phosphate Buffer
CHA
Abs.
o
0.078
I/A~A~iol
1/OHA
K
log K
1.350x10 -5
0.111
30.30
74060
24914
4.3964
2.700x10 "5
0,134
17.85
3?000
20679
4.3155
5.380x10 -5
0.169
10.98
18575
18478
4.2666
1.076x10 -4
0.217
7.19
9287
18973
4.2781
2.700x10 -4
0.262
5.43
3700
16534
4.2183
5.~00x10 -4
0.286*
4.80
1850
17442
4.2416
1.076x10 -3
0,298*
4.54
928
17792
4.2502
2.153x10 -3
0,303*
4.44
464
15260
4.1835
o
Plot of 1/A-Adiol vs. 1/CHA : A ~ * Points used to extrapolate A ~ i n Average log K = 4.2687
extrapolated = 0.310 Double Reciprocal Plot
Standard Deviation = 0.0648
Chemical affinity systems--I
1571
Table 3(d). pH = 8.00
Sodium Phosphate Buffer
CHA
Abs.
o
o.150
CHL = 4.8115x10 -5 M"
l/A-Adiol
I/CHA
K
log K
1.937xi0 -5
0.188
26.31
51624
62081
4.7929
3.876x10 -5
0.212
16.13
25796
47587
4.6774
7.724xi0 -5
0.241-
ii.00
12947
42541
4.6288
7.758x10 -5
0.243
10.75
12890
45768
4.6605
1.545xi0 -4
0.268
8.47
6469
52047
4.7163
7.736xi0 -4
0.283
7.52
1293
36577
4.5632
1.541xi0 -3
0.285*
7.40
649
30121
4.4788
3.082xi0 -3
0.287*
7.29
324
45151
4.6546
Plot of
1
o /A-Adiol vs. I/CHA : A oo extrapolated = 0.288
* Points used to extrapolate A oo in Double Reciprocal Plot Average log K = 4,6465
Standard Deviation = 0.0946
over all points
Table 3(e). pH = 9.16
Sodium Arsenate Buffer
CHA 0
Abs.
CHL = 4.8115x10 -5 M
i/A-A~iol
1/CHA
K
log K
0.157
4.020x10 -5
0.133
41.70
24900
6543
3.8158
1.005xlO -4
0.114
23.25
9950
5231
3.7186
2.012xi0 -4
0.089*
14.70
4970
5390
3.7316
4.008x10 -4
0.066*
11.00
2500
5133
3.7104
8.017xi0 -4
0.049
9.25
1250
4558
3.6587
2.006x10 -3
0.032*
8.00
500
4549
3.6579
3.997xi0 -3
0.025*
7.57
250
4772
3.6787
7.995xi0 -3
0.022*
7.40
125
4246
3.6280
Plot of i/k-A~iol vs. I/CHA : A ~
extrapolated = 0.018
* ~oints used to extrapolate A co in Double Reciprocal Plot Average log K = 3.6999
Standard Deviation = 0.0585
over all points
1572
P. A. SIENKIEWICZ and D. C. ROBERTS Table 3(f). pH = 10.25
Sodium Carbonate Buffer
CHA
Abs.
0
0.527
CHL = 9.623x10 -5 M
1/A-A~iol
i/CHA
K
log K
3.951xlo -5
0.480
21.27
25309
37o6
3.5689
7.907xiO "5
0.443
11.90
12646
3506
3.5488
1.575xlO -4
0.379
6.75
6347
3600
3.5563
3.150xlO -4
0.302
4.44
3173
3399
3.5314
3.940xlO -4
0.272
3.92
2537
3452
3.5382
7.885xlO -4
o.192-
2.98
1268
3420
3.5341
1.571x10 -3
0.141-
2.59
636
3043
3.4833
3.929xlo -3
0.089*
2.28
254
3456
3.5386
7.862xlo -3
0.073*
2.20
127
3437
3.5362
1.566xlo -2
0.069*
2.18
64
2263
3.3547
Plot of 1/A-A~iol vs. 1/CHA : A ooextrapolated
= 0.056
* Points used to extrapolate A oo in Double Reciprocal Plot Average log K = 3.5191
Standard Deviation = 0.0618
over all points
Average log K = 3-5373
Standard Deviation = 0.0236
excluding last point
the best visual fit for both the 4,5-diol and the 2,3-diol data; the resulting theoretical curves are displayed in Fig. 4 along with the experimentally determined points. The parameters giving the best fit are collected in Table 4 along with available literature values for comparison. The determination of glf{'H2Ag) further allowed the first measurement of the true acid dissociation constant of the complex: K _ [H+][HAL-] g~ (12) ~('~L) = [I2I~ALi.....Kf(H'--~AL) in equilibria of this general class. Interestingly, no complex formation whatsoever could be observed at pH 2 in the 2,3-
\/
~'OH2
o B .o
I
reported values was in the apparent PKHA for the 4,5diol case, which is at least 1.15 units lower than expected. Neither of two possible explanations, viz., covalent interaction of the buffer species with the diol or boronic acid ("buffer competition") and incorporation of the buffer species into the complex itself (substitution of OH by the buffer anion in the HAL- structure), seem plausible, since the averaged a values would have to be low by the same factor to correlate so well with eqn (11), and this is unlikely given the wide variety of buffer anions used. The optimal log a values reported here of 4.52 (for 4,5-diol) and 4.65 (for 2,3-diol) represent the largest degrees of association ever observed in 1:1 complexes of this type, and, for reasons previously mentioned, the values are more reliable than those obtained by potentiometric methods. The spectrophotometric observation of H2AL for the 4,5-diol case allows a tentative conclusion to be drawn concerning its structure. As can be seen in Table 5, little change occurs in the spectrum of HL in the presence of high HA concentrations, on passing from pH 7 (complex entirely in the HAL- form) to pH l.ll (complex at least 90% in H2AL form). This may be interpreted as suggesting a water-coordinated species, I, as the structure of H2AL rather than II, since Ph
Ph
I
I +o B\o
II
1573
Chemical affinity systems--I E+l 2 $0
2.0~
o &
1 +5B
J
o \
J
1 OB
e. 5 g
B.BB
B.PB
B.4B
+.6B
B Be
I .00
|/CHA
Fig. 3. Double reciprocal plot: 4,5-diol, pH 3.73.
Table 4. Equilibrium constants from curve fitting of spectrophotometric data using eqn (l 1) 4,5-Dioi
2,3-Dioi
-o
Fit
Lit.
Fit
Lit.
PK I
0.84
1.3 [13]*
3.o0
P~L
5.45
5.36 [12]
8.12
8.12 [3e]
8.70
8.7 [13]
p~
7.55
5.53
[9]
5.33
[4a,lO]
8.7 [13] 9.71 [ii]
log Kf(H2AL )
1.30
pKa(H2AL )
2.14
pK I for H3BO 3 + 4,5-dioi:
#pK I for H3BO 3 + 2+3-dioi:
9.71 [ii]
1.55 [4a]
3.89 (extrap. to I = O.i) [3e]
Table 5. pH dependence of UV spectral data for complexed 4,5-diol __
1 max
max E
pH
i.ii
pH
7.00
332.5
336.5
8027
9796
347.5
351.5
9249
11093
1574
P. A. SIENKIEWICZ and D. C. ROBERTS r
l
o
2 o
.J /
\ \
II
~" ~-~i
//
L~ ~..~ , , / / / / v . . . 0
1
2
3
/ , 4
5
~__, 6
7
,
~_
__
8
9
18
, II
, 12
13
14
pH Fig. 4. Log a vs pH for 4,5-diol and 2,3-diol.
in going from HAL- to structure II we would expect a substantial change in the UV spectrum, rather than the almost negligible pH effect observed (expected for simple protonation). In view of the fact that the aryloxy groups in II are quite electron-withdrawing, it seems quite plausible that II would prove to be a sufficiently strong Lewis acid to form a stable adduct with water. Further studies of these systems in our laboratory are presently focusing on the use of diol-functionalized solid supports, in conjunction with boronic acids, in new separation methods. Acknowledgements--Acknowledgement is made to the donors of The Petroleum Research Fund, administered by the ACS, for partial support of this research. Additional financialsupport from the Rutgers Research Council and the Rutgers Biomedical Research Support Grant Program (funded by NIH) is gratefully acknowledged. REFERENCES 1. H. L. Weith, J. L. Wiebers and P. T. Gilham, Biochemistry 9, 4396 (1970); H. Schott, E. Rudloff, P. Schmidt, R. Roychoudhury and H. Krssel, Biochemistry 12, 932 (1973) and Refs. therein. 2. I. M. Pailer and W. Fenzl, Monatsh. 92, 1294 (1961); W. Kliegel, Organometal. Chem. Rev. AS, 153 (1972); O. C. Musgrave and T. O. Park, Chem. Ind. (London) 1552(1955). 3. For catechol itself, see (a) G. L. Roy, A. L. Laferriere and J. O. Edwards, £ lnorg. Nucl. Chem. 4, 106 (1957); (b) P. J. Antikainen and A. Kauppila, Suomen Kemistilehti !132, 141 (1959); (c) J. M. Conner and V. C. Bulgrin, J. Inorg. Nucl. Chem. 29, 1953 (1967); for relevant catechol derivatives, see (d) P. J. Antikainen and H. Oksanerl, Acta Chem. Scand. 22, 2867 (1968) and Refs. therein; (e) R. N~is~inen,P. Tilus and P. Helander, Suomen Kemistilehti I~3, 331 (1970). Values in the range of 103-105are reported for the "association constants" in these papers, using potentiometric methods, although, as pointed out by Conner and Bulgrin, the method of calculation used in these cases incorrectly assumes that the diol component is less acidic than boric acid, and is, to this extent, inaccurate. 4. The association of 4,5-dihydroxynaphthalene-2,7-disulfonate
(chromotropic acid) with boric acid has been studied potentiometrically: (a) M. Bartugek and L, Havelkovfi, Coll. Czechoslov. Chem. Commun. 32, 3853 (1967)--and qualitatively by spectrophotometric methods: (b) D. W. Tanner and T. C. Bruice, J. Am. Chem. Soc. 89, 6954 (1967); however, an actual "association constant", while clearly quite large, is not specified by these authors. 5. P. J. Antikainen et al. Suomen Kemistalehti B31,255 (1958); !132, 141 (1959). 6. P. H. Hermans, Z. Anorg. Allgem. Chem. 142, 83 (1925), 7. A different form of this equation was used by Brulce, although it is not clear how it was derived. This equation may also be derived as a conditional equilibrium expression according to the method of Inczrdy and Ringbom (J. Inczrdy, Analytical Applications of Complex Equilibria, pp. 51--53) Akadrmiai Kiad6 (Budapest) (1976). 8. R.M. Washburn,E. Levens, C. F. AIbrightand F. A. Billig,Org. Synth. Coll. 4, 68 (1963). 9. H. Zollinger and W. B0chler, Heir. Chim. Acta 34, 591 (1951). 10. J. Heller and G. Schwarzenbach, Heir. Chim. Acta 34, 1876 (1951). 11. Measured in 25% ethanol; B. Bettman et aL, J. Am. Chem. Soc. 56, 1865(1934). 12. W. P. Jencks, cited by Bruice[4b]. 13. D. C. Roberts, Ph.D. Thesis, MIT, 1975; the method of Antikainen[3d] was employed. APPENDIX Derivation of eqn (7) (see text for definitions) Assuming that Beer's Law holds, for I cm cells, at a constant value of A, the component of absorbance due to uncomplexed diol is
Aoiol enL[HL]+ ~L-[L-].
(AI)
=
Since
[ H L ] = C ~ ~ -- -_- ._. C_{ . V and [L-I=
HL \ ' K H ~ - H + ]
J,
(A2) Adio'= c H Lr L ~ H L ~
}
KHL
(A3)
1575
Chemical affinity systems--1 If pH is maintained constant, the expression within brackets remains constant, and is the apparent ~ for the particular mixture of HL and L- present at that pH value. We might call this ~ot,
or o
Ao
Aobs = ~ ( [ H L I
+
t-~HL
SO
[L l) + ~ ( [ H 2 A L ] c . k
+
[HAL 1). (A9)
Adiol = CIqL" eJiol.
(A4)
The value of e~ot may easily be obtained from the absorbance of the pure diol solution A]iot at that pH (i.e. no HA has been added).using eqn (A4). Similarly, the component of absorbance due to complex will be given by
(Note that A~iol and A~omple x refer to values obtained at C.A = 0 and o0 (extrapolated as described in the text), respectively, and not to components of Aob~at intermediate C.A values.) From the definition of CUE, ([HL] + [L-]) = C . L - ([H2AL] + [HAL-])
(AI0)
and this can be substituted into eqn (A9) to obtain Acomple,= EHAL-[HAL-]+ EH2AL[H~AL],
(AS) Aob~' CHL -~ A~ioI(CHL - ([H2AL] + [HAL-])
which reduces similarly to Acomplex = C H L ' ~omplex.
+ A%mp~ex([H~AL]+ [HAL-]). (A6)
The value of e*om¢,~ is obtained from the absorbance of the solution extrapolated to infinite HA concentration (i.e. AOom¢~x) as described in the text, and applying eqn (A6). At intermediate values of C.A,
This simplifies to
Aobs" CnL =
o . _ o Adiol CHL+(A~omplex Adi(~t)
× ([H2AL] + [HAL-]) or
(A7) and, applying eqns (A1), (A4), (A5) and (A6), this reduces to =
(A12)
CHL(Aobs- A~iot) = (A~°omple~- A,%ol)([H2AL] + [HAL ])
Aobs = eHL[HL] + ~L-[L-] + EH2AL[H2AL] + ~HAt-[HAL-]
Aobs ~Jiol([HL] + [L-l) + Ec*o,~plex([H2ALl + [HAL-l)
!All)
(A13) which rearranges to give eqn (7) in the text:
(A8)
C
(Aob~- A~iol)
.L ~ =[H,ALI+[HAL-]. (Acomplex Adiol) -