ACIDITY MEASUREMENTS WITH INDICATORS IN GLACIAL ACETIC ACID ORLAND W. KOLLING Friends University, Wichita, Kansas
G L A C I A L acetic arid holds considerable interest both as a medium for analytical determinations and as a convenient nonaqneous solvent having several physical similarities to water. However, the low value for the dielectric constant of acetic acid (6.2 at 25°C.) results in very incomplete ionization of solutes for strong acids, babes, and salts, dissolved in this solvent. Ion-pair and ion-multiple association are common. As a result, there is no direct relationship between pH and the color of an indicator in glacial acetic acid, even though hydrogen-ion activity is measurable potentiometrically (I, 5). Yet, the simple experimental measurement of acidity with indicators, as exemplified by the Hamrnett function, as well as the Lewis criteria of acid-base behavior (6) leads investigators to study indicator color reactions in all types of nonaqueous media. Two appropriate questions may be posed, concerning the behavior of indicators in glacial acetic acid. First, to what property of the solution does the indicator respond9 And, second, can a quantitative treatment of indicator reactions be devised that is consistent with the Lewis theory of acids and bases? Let us consider the second question at this point, since the first has been resolved experimentally and will be discussed later. In terms of the general theory proposed by Lewis, the neutralization of an indicator base may be represented by the equation, where I I + RQ e I R + Q e I R + Q(la)
+
is the indicator base, RQ the acid, IR+Q- the neutralization product (salt). The extent to which I R q separates into its ions is governed largely by the dielectric constant of the solvent. By letting [I] = [I.] and [IR+Q-] [IR+] = [I*], representing the base and acid forms of the indicator, respectively, the appropriate equilibrium constant K,TRQis
+
The computed value for this formation constant corresponds to the condition of the half-neutralization of the indicator base by the acid. For this reason, one may avoid ambiguity of terms by introducing K,IRQ
= LL/,
(1~)
t o be called the half-neutralidion number of the indicat.or. Such a notation expresses the strength of the indicator base in a manner consistent with the Lewis theory. In the measurement of acidity in glacial acetic acid solutions of acids as strone as ~erchloric.the color change of a hasic indicator may be used. As has
-
been shown by Kolthoff and Bruckenstein (4) the color of the indicator in acetic acid is not determined by the hydrogen-ion concentration but mther by the stoichiometric concentration of the strong acid. Using the notation and equations of these authors, CHCIO. = [HCIO,] [H+C104-1; IHC104 is the indicator perchlorate, I the indicator base, and K,'HC1o' the formation constant of the indicator salt, we may write
+
By representing [IHCIO,] = [I*] and [I] = [IB] as the acid and base forms of the indicator, respectively, equation (2a) may be rewritten as
where L.1, is the half-neutralization number of the indicator, and in this case is numerically equivalent t o K:HC1o'. We now have in equation (2h) a suitable relation for defining an empirical acidity scale. Without specifying the indicator charge type (requiring only that equntion (2a) be satisfied), this acidity function L
=
-log Cecl",
=
[Is1 - pLv, log -
[I*]
(2c)
Equation (24 is restricted to glacial aretic acid sc+ lutions involving a weakly basic indicator and an acid of strength comparable to HCI04. For the neutralization of weakly basic indicators with acids significantly weaker than perchloric acid, such a simple treatment is inadequate. This neutralization is represented by I+HX=IHtX-=IHt+X-
(3)
in which IH+X- is the ion-pair form and the right-hand terms are the dissociated ions. The apparent strength of the acid HX is dependent upon the indicator used, since the values of the dissociation coustant KnIHX for the indicator ion-pair may differ with the indicator base that is selected. Again the work of Kolthoff and Bruckenstein (4) should be consulted for a detailed discussion of this case. I t was demonstrated that all of the acidic forms of the indicator have identical absorption spectra, and an expression was derived to relate the indicator concentrations to the other variables in the system. I n the equation
Z[IH+] is the sum of the indicator acid forms, CHX the concentration of the acid, KdTHXthe ion-pair dissociation constant, and K:HX the formation JOURNAL O F CHEMICAL EDUCATION
constant for IHfX-. Equation (3a) may be rewritten to correspond to equation (2b):
For the right-hand term let us define a quantity
to be called the ion-pair parameter. Then, the equation
permits a more general definition of the empirical aciditv function [Isl - ~ L I / + L = -log Cax = log , log Yi (3d) [IAI
I t is the contribution of Yi to the computed value of L that could result in the dependency of the acidity scale upon the indicator used. Such a variation has been observed when the Hammett function Ho has been applied to solvents of low dielectric constant (7). It has been recently reported by Fuoss and Kraus (2) that the logarithm of the ion-pair association constant (I/Kd'HX)is a simple linear function of the reciprocal of the dielectric constant. It has been emphasized by Gmnwald (3) that the consistency of any indicator acidity scale must be verified by the use of several indicators having over-
VOLUME 35, NO. 9, SEPTEMBER, 1958
lapping ranges, regardless of the indicator charge type. This is particularly important for solvents of low dielectric constant, especially if the indicator Y i values are unknown. Indicators differing in structure may he used to establish an empirical acidity scale that may be applied to acid-base catalysis in a given solvent system, if the limitations of the usahle acidity range are evaluated. For glacial acetic acid, the suggested L function of equation (3d) provides an acidity measurement compatible with the Lewis theory of acids and bases. Although proton activity in the Bronsted sense has no simple relation to the indicator color in this solvent, the response of the indicator to the coucentration of acid permits its use as the basis for measurement of acid strength and acidity in the more general sense of these terms. LITERATURE CITED (1) BRUCKENSTEIN, S., AND I. M. KOLTHOFF, J. .In.Chem. Sm., 78,2974 (1956)(2) Fuoss, R.,AND C. KRAUS,J . A m . Cheru. Soc., 79, 3304 flOC.7\
(3) GUTBEZAHL, B., AND E. GRUNWALD, J . A m Chen. Soc., 75, 565 (1953). (4) KOLTHOFF, I. M., AND S. BRUCKENSTEIN, J. Am. Chern. Soe., 78, 1-9 (1956). (5) KOLTAOFF, I. M., AND S. BRUCKEXSTEIV, J. A m . Chem. Soc., 79, 1-7 (1957). (6) LUDER,W . F., AND S. ZUFFANTI, "Tho Electronic Theory of ACIDSand Bases," John Wiley & Sons, Ine., New York, 1946, p. 15. (7) PAUL,M., AND F. LONG,Chem. Revs., 57, 25 (1957).
