I. 31. KOLTHOPP AND L.s. Guss
2516
Vol. 60
[COXTRIHUTION PROM THE SCHOOL OF CHEMISTRY OF THE INSTITUTE OF TECHNOLOGY OF THE UNIVERSITY OF MINNESOTA 1
Ionization Constants of Acid-Base Indicators in Methanol BY I. M. KOLTHOFF AND L. S. GUSS’
The equilibrium constant in a buffer system containing a small amount of an acid-base indicator is given by the expression
of the indicator can be calculated if the dissociation constant of the acid, KA, is known since PIC1 = PK’ f PKA
Although there are many data in the literature on the acidity constants and concentration ioniin which Q denotes the activity of the component, zation constants of acids in methanol, only few c the concentration, 1b the basic form and I , the studies have been carried out a t sufficiently small acid form of the indicator, A and B the acid and ionic strengths to allow the determination of the basic forms of the buffer, K’ the thermodyiiamic thermodynamic ionization constant. In the presequilibrium constant, while K is the corresponding ent work, the values of Goldschmidt and coand experimentally determinable concentration w o r k e r ~ who , ~ determined the constants by the “constant,” the value of which varies with the conductivity method, have been adopted as the ionic strength of the solution. By extrapolating most reliable values. The constant of veronal, the values of K found at small ionic strengths which is not given in the literature, has been deto an ionic strength of zero, the value of K ’ is termined by the colorimetric procedure described found. This method of evaluation of K’ is simi- in this paper, using the p K , value which has been lar to that used by Guggertheim and Schindler2 found previously in another buffer. In a similar in aqueous solutions. may, the ionization constants of other acids in In sufficiently dilute solution, the limiting methanol have been determined. Debye-Hiickel expression gives the relation beExperimental tween activity coefficient and ionic strength. Reagents.-A good grade of synthetic methanol free of In methanol a t 2j0, this becomes aldehydes was dehydrated by the method of Lund and -logf,,*, =
(2)
.).052d/CL
In the range in which the limiting expression is applicable, equation 1 gives us pK’
= pK -
,og4L!i= p K f:, .(I{
-. .1.11(2,*
- 2,)vG
(3)
where zIa and zA are the charges of the indicator acid and the b d e r acid, respectively. If the values of pK are plotted against the square root of the ionic strength, the slope of the curve should be 4(qa - z A ) in the range where the limiting expression holds. Table I lists values of this slope for various types of indicator and buffer acids. TABLE I VALUES OF
4.0(2Ia
- 2.4)
.Type of buffer acid
Cation Uncharged Anion
Type of indicator acidUncharged Anion Cation
0.u
-4 0
-8.0
4.0 S.!l
0.0 4.0
-4.u 0.0
Having obtained by extrapolation the value of pK, the thermodynamic ionization constant, K I , (1) From the dissertation submitted by L. S. Guss to the Graduate School of the University of Minnesota in partial fulfilment of the requirements for the degree of Doctor of Philosophy. May, 1038. (2) E. A Guggcnhrini :cud ’I‘ I ) S'
.85 .1'
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,651 .2 1.05 -0.35
0.3
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1.55 0.7 - .A52 - ,751 - .3 1.0 -0.46
-
O.513
.I
I
.4 - .45 1.6 1.65 0.85 0.8 - .5 - 62
corresponding univalent anion base), a limiting slope of -4 is obtained. With increasing ionic strength, the pK values decrease less than demanded by the limiting expression. This is to be expected as the latter in methanol will only be valid a t very small ionic strengths. When the
.
.-
0.85
.2
,552 1.45% 0.652 - .72
-
-0.2
-
.55
-1.151
0.75
-
-
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.9z
,951
-
,551
-0.21
0.2 0,4518
0.3
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0.781
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1.452 0.62 - .$59 - ,551
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1.252 1,351 0.351
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1.751 1.51 -1.051 -1.012 -0.15' -0.051 - ,451 - .3' -1.0'2 - ,951 - ,752 0,9512 1 21'
-
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ionic strength has become of the order of 0.06, the
pK values remain practically constant with increasing ionic strength. This behavior is typical of all of the sulfonphthaleins and can be interpreted on the basis of the structures of the sulfonphthaleins as originally proposed by Lund6and supported by the work of Schwarzenbach.' According to Lund, the structural changes of a sulfonphthalein in its various color change intervals is represented by
0.8
7
Acid form
0.8
2 .R,
0.4 0.2 0
0.2 0.4 0.6 0.8 1.0 Square root of ionic strength. Fig. 2.-0, Methyl orange and 0, methyl vellow in trichloroacetate buffer. 0
Yellow form
Alkaline form
Thus, the yellow form is a hybrid ion with one extra negative charge and the alkaline form a hybrid ion with two extra negative charges. Bjerruma postulated that the charges on a hybrid ion are sufficiently displaced that, in a fairly concentrated solution, it behaves as two ions. Giintel(8) H.Lund. J . Chcm. Soc., 1844 (1930). (7) G.Schwarzenbach, Relo. Chim. Acta, SO, 490 (10371, ct (8) N. Bjerrum. Z. ghysik. Clunr., 101, 147 (1923).
scq.
IONIZATION CONSTANTS OF ACID-BASE INDICATORS IN METHANOL
Oct., 1938
2519
1.2
1.0
0.8
3 I 0.6
% 0.4
0.2
0
0 0.2 0.4 0.6 0.8 Square root of ionic strength. Fig. 3.-Methyl red in 0 , benzoate and 0 . trichloroacetate buffers.
I
berg and Schiodtg showed that the behavior of methyl orange with varying ionic strength could be explained by such a hypothesis. The same reasoning should apply to any highly charged ion, with widely displaced charges. Thus, we might assume that a t higher ionic strengths the electrical work required to build up n individual charges will be n times as great as that required to build up a single charge. In the yellow form of the sulfonphthaleins, n is equal to 3 and in the alkaline form, equal to 4. At high ionic strengths, we then may write the following relation for thr activity coefficient _- log f n = -
?I
log j ,
(4)
in which fi is the activity coefficient of a univalent ion. For univalent ions in fairly concentrated solutions, the Debye-Huckel expression might be written - l o g h = /(fi) H (3)
+
where B is some function of the ionic strength. It seems fair to assume that B will be of the m e magnitude for ions of a conjugate acid-base system. Applying the above to the sulfonphthaleins in buffers af the type A-B- a t higher ionic strength, we find pK = pK" - logf; = pK" - 3 logf,
+ logf; - log!,
4- logfo
+ 4 logf1 - logf, = PK"
((i)
(9) E.Ciintrlberg and R. Schiodt, 2 . physik. Ci.~nr.191,393 (19%).
I
I
I
0.4 Square root of ionic strength. Fig. 4.-Thymolbenzein in 0 , veronalate, and 8, trichloroacetate and @, thymol blue in trichloroacetate. 0
0.2
in which pK" is not the true thermodynamic constant since the relation in equation 4 will not permit extrapolation down to infinite dilution. According to the above interpretation, pK becomes constant a t relatively high ionic strengths, which is in agreement with experimental results. The above considerations are also of practical importance. If the pK values of sulfonphthaleins in various alcohols are determined in b d e r solutions of the type A-€3- with an ionic strength of about 0.1, the result of a 5- to 10-fold dilution will be a very small effect upon the pK measured. Extrapolation of those data to an ionic strength of zero, however, would lead to an erroneous result. Kolthoff,lo who investigated the sulfonphthaleins in ethanol, has applied such an extrapolation. From this discussion, it is clear that his data need correction. In buffers of the type A--B=, the pK values of the sulfonphthaleins should become constant and independent of the ionic strength when the latter is very small. Actually, this was found to be the case with brom cresol green in bitartratetartrate buffers at ionic strengths below 0.001. When the ionic strength becomes greater than (IO) I M. KolthoR. J Phys
CkPni
, 96, 2732 (1081)
I. M. KOLTHOPF AND L. S. Guss
25%
this, the PK values increase. This is in agreement with the above considerations. The tremendous effect of the ionic strength upon the ilk' values in buffers of the type A+-B is also in agreement with the predictions based on the above discussion. At low ionic strengths, the curve has the slope of -8 required by equation 3 (we Fig. 1). At higher ionic strengths, the theory of individual charges seems again applicable. The behavior of thymol blue in its acid range is ill agreement with the structure proposed by L ~ i i d . The pK values found in trichloroacetate buffer were found to be constant up to an ionic strength of 0.1. 2. In connection with what has been said of the sulfonphthaleins, the behavior of thymolbenzein in its two color changes is of interest. On the basis of the work of Lund and Schwarzenbach, the structural changes may be represented by
Y-ellow form
Acid f o r m
Alkaline form
In its acid range, in a buffer of the type A-B-, we would have pK
=
PI
