3908
E. M. WOOLLEY, D. G. HURKOT,AND L. G. HEPLER
Ionization Constants for Water in Aqueous Organic Mixtures
by Earl M. Woolley, Donald G. Hurkot, and Loren G. Hepler* Department of Chemistry, The University of Lethbridge, Lethbridge, Alberta, Canada
(Received May 14, 19’70)
A potentiometric method is described for determining the equilibrium constants for ionization of water in various aqueous organic mixed solvent systems. The method has been applied t o determination of ionization constants for water in binary mixtures of water with ethanol, 1-propanol, 2-propanol, 2-methyl-2-propano1, ethylene glycol, acetone, and p-dioxane at 25’. In general, pK, values increase with increasing organic concentration, but the opposite is observed for glycol solutions and is discussed in relation to enthalpies and entropies of ionization.
The ionization of water has been investigated‘ by a variety of methods that have led to reasonably accurate equilibrium constants over a wide range of temperature and pressure and a considerable range of dissolved salt concentration. I n spite of evidence2of a small error in the temperature dependence of these K , values, it must be accepted that there are several satisfactory methods for determination of K, in purely aqueous solvent systems. Similar methods have been applied with considerable success to determination of ionization constants for various weak acids in aqueous solution. The status of measurements leading to ionization constants for water and various weak acids in aqueous organic mixed solvent systems is not nearly so satisfactory, in spite of excellent work by Harned, Grunwald, Bates, and o t h e r s . ’ ~ ~ -Experimental ~ methods are difficult and those methods that make use of the hydrogen electrode can only be applied to systems in which there is no complication due to reduction at the hydrogen electrode. Our measurements were undertaken to provide data on the ionization of water in a variety of aqueous organic mixed solvent systems and to establish a convenient and rapid method for determination of ionization constants of various weak acids in these same solvent systems. Method and Calculations We describe the ionization of water in solvent S byl,607
HzO(S) = H+(S)
+ OH-(S)
(1)
Various equilibrium expressions for (1) can be defined on the basis of several reasonable choices of standard states for the various species. One such choice leads to quantities that should be called equilibrium quotients rather than equilibrium constants. I n these expressions we use molar concentrations of H + and OH- and set the activity of water to be unity in all solutions so that we have The Journal of Physical Chemistry, Vol. 74, No. 89,IQ’YO
in which the subscript e l l indicates molar concentrations in the numerator and unit activity in the denominator. We also define an equilibrium constant with activities on the molar scale for H + and OH- and with the activity of water again taken to be unity as Kaii =
CHCOH(Y*)~ = QC/I(Y*)~
(3)
in which yrt is the mean activity coefficient for the solute ions. Still another useful equilibrium expression can be defined with molar activities in the numerator and the activity of water in the denominator set equal to the molarity of water in the solution (subscript ale so that we have
Our last equilibrium constant is one in which we use activities for all species as indicated by
I n principle we have a wide choice of standard states for the activity of water denoted by a,, but in practice the only choice that appears to be useful and for which we have the necessary vapor pressure data for a wide variety of systems is the choice based on Raoult’s lawthat is, the activity of pure water is taken t o be unity. Our investigations of the ionization of water in var-
* To whom correspondence should be addressed. (1) H. S. Harned and B. B. Owen, “The Physical Chemistry of Electrolyte Solutions,” 3rd ed, Reinhold Publishing Corp., New York, N. Y., 1958. (2) J. W. Larson and L. G. Hepler in “Solute-Solvent Interactions,” J. F. Coetzee and C. D. Ritchie, Ed., Marcel Dekker, Inc., New York, N. Y., 1969. (3) H. 8. Harned and L. D. Fallon, J . Amer. Chem. SOC., 61, 2374 (1939). (4) B. Gutbeaahl and E. Grunwald, ibid., 75, 565 (1953). (5) R . G. Bates, “Determination of pH: Theory and Practice,” Wiley, New York, N . Y., 1964. (6) H. 5.Harned and B. B. Owen, Chem. Rev., 2 5 , 31 (1939). (7) E. J. King, “Acid-Base Equilibria,” Pergamon Press, Inc., Oxford, England, 1965.
IONIZATION CONSTANTS FOR WATER
3909
ious aqueous organic mixed solvent systems are based on the potentials of cells represented by glass electrodelsoln A: HCl(Cl), KN03(C2),in solvent SIAgC1,Ag (A) and glass electrodelsoln B : NaOH(C3), NaCl(Cd), in solvent SIAgC1,Ag (B) A general equation for the potentials of these cells is
E
=
ki
+ k2 log
(6)
(QHaci)
and a specific equation for cell A is
EA
ki
+ k z log (Ci)‘ +
k2
log
(Y*)A~
(7)
A similar specific equation for cell B containing known concentration of hydroxide ion can be given in terms of an equilibrium expression for the ionization of water. It is convenient to do this in terms of Qc/l defined by eq 2, which leads to
EU = ki
+
k2
log (Qc/iC4/Cs)
+ k2 log (y*)n2
(8)
Since solvent compositions are the same and ionic strengths in solutions A and B are low and nearly identical for each pair of measurements, junction potentials, asymmetry potentials, glass electrode responses, and mean activity coefficients may be taken to be equal. Thus we combine (7) and (8) to obtain
EA - EB = kz log (Ci2Ca/C4Qc/i)
(9)
Equation 9 leads directly to
Thus we can calculate Q E / l from t.he two potentials and known concentrations represented by C1, C3, and Cd. This procedure, in which we make use of the difference in two potentials, thereby eliminating the (often unknown) standard potential (kl) from our calculations, was used by Harned and coworkers1*6Jin determining ionization constants for water in aqueous electrolyte systems. For solvent of any particular composition it is possible to determine the equilibrium constant denoted by K,/I by extrapolating values of QCll derived from eq 10 to zero ionic strength, or we can calculate the mean activity coefficient represented by gb by making use of some equation based on the Debye-Huckel theory and then obtain Kul1from eq 3. I n general, we have found that p(K,,l) values obtained in these two ways differ by less than 0.03 and we have therefore treated most of our data with the equationlp7
1%
709.O [p (S)/ 2 (S) ] ‘/‘Pa
=
- 1 -I- 8.876[p(S)/~(S)]’”~I”~ (11)
I n this equation p (S) and E (S) are used to represent the density and dielectric constant of solvent mixture S and I represents the ionic strength, which typically varied from about 0.004 to about 0.015 M . Density and dielectric data were obtained from Tirnmerman~,~ with additional dielectric data for aqueous 2-methyl-2propanol from Brown and Ives.’O The value of k2 to be used in eq 10 for each series of measurements was evaluated by setting pK,,l = 14.001for the entirely aqueous solvent systems. These kt values ranged from 58.3 to 58.9 mV, as compared to 2.303RTIF = 59.16 mV. Calculation of Kaiefrom K,/1 only requires knowledge of the molarity of water in the solution and is easily done from knowledge of solvent composition. Carrying these calculations on to K,,, requires activities of water obtained from a, =
P,/P,O
(12)
in which P, and PO , represent vapor pressures of water over solution S and over pure water, respectively. Vapor pressure data for aqueous 2-methyl-2-propanol solutions have been taken from Brown and Ives.’O Data for aqueous dioxane are from Goates and Sullivan“ and data for all other systems are from Timmermans.e
Experimental Section Potential measurements were made both with an Orion Model 801 digital pH meter and with a Corning Model 12 research pH meter. Glass electrodes used with these meters were the Beckman 39004 pH 0-14 electrode, the Coleman 3-472 pH 0-14 electrode, and the Fisher 13-639-1 pH 0-14 electrode. The AgC1,Ag electrode was prepared from a Beckman 39261 Silver Billet Electrode by electrolysis in chloride s ~ l u t i o n . ~ Most of our measurements began with cell A containing a known volume of purely aqueous solution of HC1 and KN03 of known concentrations represented by CI and CZ. After E A was measured, a known amount of pure organic solvent was added and the new potential measured. This procedure was continued until the solvent composition reached 50-60 wt % organic component. The same procedure was then followed with cell B that initially contained the same known volume of purely aqueous solution with appropriate concentrations of NaOH and NaCl such that C1 CI = Cs C4. These C values ranged between 0.0005 and 0.01 M in the initial solutions and decreased in known fashion as the solutions in the cells were diluted with organic solvent.
+
+
(8) H. 9. Harned and W. J. Hamer, J . Amer. Chem. SOC., 5 5 , 2194 (1933). (9) J. Timmermans, “The Physico-chemical Constants of Binary Systems in Condensed Solutions,” Vol. 4, Interscience Publishers, Inc., New York, N . Y., 1960. (10) A. C. Brown and D. J. G. Ives, J . Chem. SOC., 1608 (1962). (11) J. R. Goates and R. J. Sullivan, J. Phys. Chem., 6 2 , 188 (1958). The Journal of PhysicaZ Chemistry, Vo2. 74>No. 28, 2970
3910
E. M. WOOLLEY, D. G. HURKOT, AND L. G. HEPLER
Table I: Data from a Typical Series of Measurements with Water-Ethanol Mixtures' Wt % EtOH
-log
Ah',
e
P
(PW/PW9
mV
PQCP
PK4ll
0.00 3.77 7.27 10.5 13.5 16.4 21.5 26.0 30.1 33.7 36.9 39.9 42.6 45.1 47.3 49.3 51.3
78.5 76.4 74.3 72.5 70.7 69.1 66.7 63.4 61.0 58.8 56.9 55.0 53.4 51.9 50.5 49.3 48.2
0.9971 0.9902 0.9845 0.9796 0.9754 0.9715 0.9642 0.9573 0.9506 0.9440 0.9377 0.9317 0.9261 0.9208 0.9159 0.9113 0.9069
0.000 0.006 0.012 0 017 0.024 0.031 0.038 0.046 0.053 0.058 0.063 0.067 0.071 0.075 0.079 0.082 0.085
545.8 547.7 550.1 552.1 553.2 554.1 555.3 556.2 556.3 556.1 555.7 555.2 554.5 553.9 553.1 552.5 551.2
13.91 13.99 14.06 14 13 14.19 14.24 14.32 14.38 14.44 14.49 14 52 14 58 14.62 14 65 14.68 14.70 14.74
14.00 14.08 14.16 14.23 14 29 14.34 14.42 14.48 14.54 14.60 14.63 14.69 14.74 14.77 14.80 14.83 14.87
P K ~ I ~
14.00 14.07 14.15 14.21 14.27 14.31 14.38 14.43 14.49 14 54 14.57 14 62 14.67 14.69 14.72 14.75 14.78
PKa/o
15.74 15 80 15.86 15.92 15 96 15.99 16.04 16.07 16.11 16.14 16 14 16.18 16.21 16 22 16 23 16.24 16.26
a 20.00 ml of solution in each cell, with CI = 0.005075 M, Ca = 0.004805 M, Ca = 0.004880 M, and Cd = 0.005000 M; kz = 58.56 mV.
In all cases the cells were maintained at 25.0 (* 0.1)' and the potential readings were recorded when they became constant to AO.1 mV, which was usually within 2 min after each addition of the organic component to the solution in the cell. Measurements were repeated a t least hhree times, using different combinations of pH meters and electrodes. Average deviations in p&,/~and pK,/1 values derived from these independent measurements were always less than 0.06 except for water-dioxane solutions containing more than 40 wt % dioxane, for which some average deviations were as large as0.13.
Results and Discussion Data for a typical series of measurements are given in Table 11: Ionization Constants of Water in Aqueous Ethanol Wt % EtOH
pKa/l
PKaia
PKaic
0.00 3.77 7.27 10.5 13.5 16.4 21.5 26.2 30.1 33.7 36.8 39.9 42.6 45.1 47.3 49.3 51.3
14.00 14.10 14.17 14.23 14.29 14.35 14.43 14.49 14.54 14.61 14.65 14.70 14.75 14.79 14.82 14.85 14.89
14.00 14.09 14.16 14.21 14.27 14.32 14.39 14.44 14.49 14.55 14.59 14.63 14.68 14.71 14.74 14.77 14.80
15.74 15.82 15.87 15.92 15.96 16.00 16.05 16.08 16.11 16.16 16.16 16.19 16.22 16.24 16.25 16.26 16 28
The Journal of Physical Chemistry, Vol. 74?No. $8, 1970
-
Table I, in which we have also included the auxiliary data used in our calculations and the results of the calculations. Results of all our pK determinations in mixtures of water with seven organic cosolvents are shown in Tables 11-VIII. Each pK value reported is the mean result of three to five series of measurements. Gutbesahl and Grunwald4 have reported pK,il values for mixtures of water with 20.0, 35.0, and 50.0 wt % ethanol. Their results are in excellent agreement with our pK,/l values at the same solvent compositions obtained by interpolation in Table 11, with differences of 0.06, 0.05, and 0.02. Harned and Fallon3 have reported pK values (molality standard state) that lead to pK,il values for mixtures of water with 20.0 and 45.0
Table 111: Ionization Constants of Water in Aqueous Dioxane
wt % dioxane
pKa/I
PKa/a
~Kaic
0.00 4.90 9.35 13.4 17.1 20.5 26.5 31.7 36.2 40.1 43.2 46.7 49.5 52 0 54 3 56.3
14.00 14.14 14.27 14.38 14.49 14.60 14.79 14.97 15.14 15.31 15.45 15.60 15.76 15.83 15.93 16.01
14.00 14.14 14.26 14.37 14.47 14.58 14.76 14.94 15.10 15.26 15.40 15.54 15.70 15.76 15.86 15.94
16.74 15.86 15.95 16.07 16.16 16.25 16.41 16.56 16.70 16.84 16.96 17.08 17,22 17.27 17.35 17.41
3911
IONIZATION CONSTANTS FOR WATER ~
Table VI: Ionization Constants of Water in Aqueous 2-Propanol
Table IV : Ionization Constants of Water in Aqueous Ethylene Glycol
wt
%
glyool
PK~II
PKa/a
pKa/o
0.00 5.27 10.0 14.3 18.2 21.8 28.0 33.4 38.0 42.0 45.5 48.6 51.4 53.9 56.1 58.12
14.00 13.93 13.88 13.82 13.78 13.73 13.69 13.65 13.61 13.59 13.57 13.55 13.54 12.54 13.54 13.54
14.00 13.92 13.85 13.78 13.71 13.66 13.60 13.55 13.50 13.47 13.44 13.41 13.38 13.37 13.36 13.35
15.74 15.65 15.58 15,50 15.44 15.38 15.30 15.23 15.16 15.12 15.07 15.03 15.00 14.98 14,95 14.93
14.00 14.08 14.17 14.24 14.29 14.35 14.42 14.49 14.55 14.62 14.66 14.73 14.78 14.83 14.87 14.92
14.00 14.08 14.17 14.24 14.29 14.35 14.42 14.48 14.54 14.61 14.65 14.72 14.77 14.81 14.86 14.91
14.00 14.11 14.20 14.30 14.38 14.46 14.58 14.67 14.76 14.84 14.91 14.98 15.04 15.10 15.15 15.22
15.74 15.83 15.90 15.97 16.03 16.09 16.18 16.23 16.29 16.35 16.39 16.44 16.47 16.51 16.54 16.59
14.00 14.11 14.19 14.29 14.36 14.44 14.56 14.64 14.73 14.81 14.87 14.94 15.00 15.05 15.10 15 17
Table VI1 : Ionization Constants of Water in Aqueous 2-Methyl-2-Propanol
Table V : Ionization Constants of Water in Aqueous 1-Propanol
0.00 3.86 7.43 10.7 13.8 16.7 21.9 26.5 30.6 34.3 37.6 40.6 43.3 45.7 48.0 50.1
0.00 3.77 7.26 10.5 13.5 16.4 21.5 26.1 30.1 33.7 37.0 40.0 42.7 45.1 47.4 49.5
PKa/c
Wt % t-BuOH
PKU/I
PKaia
~Ko/c
15.74 15.80 15.88 15.93 15.96 15.98 16.04 16.08 16.11 16.16 16,17 16.22 16.24 16.27 16.29 16.32
0.00 3.76 7.26 10.5 13.5 16.4 21.5 26.0 30.1 33.7 37.0 39.9 42.7 45.1 47.4 49.4
14 00 14.12 14.23 14.32 14.40 14.46 14.61 14.70 14.77 14.86 14.95 15.01 15.09 15.16 18.22 15.29
14.00 14.11 14.21 14.30 14.38 14.44 14.59 14.68 14.74 14.83 14.92 14.98 15.06 15.13 15.19 15,26
15.74 15.84 15.93 16.01 16.07 16.11 16.23 16.29 16.33 16.40 16.46 16.50 16.55 16.60 16.64 16.69
wt % dioxane that differ by 0.03 and 0.14 from the values we obtain at the same solvent compositions by interpolation in Table 111. For solutions that are 10.0, 30.0, and 50.0 wt % ethylene glycol we have pK values (molality standard state) and thence pK,,l values from Banerjee, Kundu, and D a d 2 that differ by 0.03, 0.00, and 0.02 from the values we obtain at the same concentrations by interpolation in Table IV. All of the earlier pK values cited a b ~ v e were ~ ~ ~ derived from measurements with the hydrogen electrode. The good agreement of those results with our results confirms that the glass electrode responds to the same H + (S) species in these aqueous organic solvent systems as does the hydrogen electrode. Results of our pK determinations are displayed graphically in Figures 1, 2, and 3. A simple treatment
I
in which the solvent is regarded as a continuous dielectric medium suggests that a plot of pK vs. l/e(S) should be linear with positive slope.1~6~7 Figure 1 demonstrates once again the well known inadequacies of this approach, especially for water-glycol mixtures for which the slope is negative. Figure 2 was suggested by marsh all'^*^ treatment of “complete” equilibrium constants in relation to ‘(traditional” constants. Ac~cording ’ ~ to this treatment, which was intended to apply only in the case of “inert” cosolvents such as dioxane, the slopes of the lines provide evidence about the difference between “hydration numbers” of H+(S) OH-(S)
+
(12) S. K. Banerjee, K . K. Kundu, and M. N. Das, J. Chem. Soc., A ,
166 (1967). (13) W.L.Marshall, J . Phys. Chem., 74, 346 (1970) I
The Journal of Physical Chemistry, Vol. 74, No. 22, 1970
3912
E. M. WOOLLEY, D. G. HURKOT, AND L. G. HEPLER
Table VIII: Ionization Constants of Water in Aqueous Acet,one
~Ka/c
0.00 3.79 7.30 10.6 13.6 16.5 21.6 26.2 30.2 33.9 37.1 40.1 42.8 45.3 47.5 49.6
14.00 14.11 14.21 14.30 14.42 14.51 14.68 14.84 15.00 15.12 15.24 15.36 15.48 15.58 15.69 15.78
14.00 14.11 14.20 14.29 14.40 14.48 14.64 14.79 14.94 15.05 15.16 15.27 15.38 15.47 15.57 15.66
15.74 15.84 15.92 15.99 16.09 16.17 16.31 16.44 16.57 16.66 16.75 16.85 16.95 17.03 17.12 17.19
17
I.6
I5
I4
109 c w
I
/
Figure 2. Plots of pK,/, us. log C , as suggested by Marshall’s treatrnent.13
16.0
1.5
2.o
2.5
Figure 1. Plots of pK,/, us. I / € aa suggested by the Born theory. 1.0
and H,O(S). The initial slopes of these lines are about -3, f5, f6, f5, f6, f6, and f 7 for mixtures of water with ethylene glycol, ethanol, 1-propanol, 2propanol, 2-methyl-2-propano1, acetone, and dioxane, respectively. Comparison of Figures 1-3 shows the importance of careful consideration of standard states and the basis for classifying or describing solvent composition. For example, in Figure 1 we have pK for water in aqueous acetone always greater than pK for water in aqueous dioxane, whereas just the reverse order is observed in Figures 2 and 3. Possibly the most striking feature of all our results is the qualitative difference between pK values for ionThe Journal of Physical Chemistry, VoL 74, No. 88, 1970
0.9
0.8
0.7
X W
Figure 3. Plot of pK,/, us. mole fraction of water in the solvent,
ization of water in aqueous ethylene glycol and in all of the other systems. The increasing values of pK with increasing organic content in the solvent system is to be expected on the basis of the decreasing dielectric constant of the medium and has been observed before for aqueous ethanol and dioxane13t4in good agreement with our results. Further, the “unexpected” decrease in pK for ionization of water in aqueous ethylene glycol has
IONIZATION CONSTANTS FOR WATER also been observed before,12 again in good agreement with our results. It thus appears that neither the "normal" behavior of water in most of the systems nor the "abnormal" behavior in aqueous ethylene glycol can be attributed to experimental error. Banerjee, Kundu, and D a d 2 have previously discussed the decrease in pK for ionization of water in aqueous ethylene glycol in terms of the idea that ethylene glycol is more acidic and less basic than water. Since further understanding along this line requires more data about the acid-base properties of the organic solvents that appear to lead to "normal" behavior of water in their aqueous mixtures, we presently turn to another approach. Earlier calorimetric measurement^'^ have led to AH" values for reaction 1 in aqueous ethanol mixtures. We also have AH" values for reaction 1in aqueous ethylene glycol from the pK values at several temperatures as calculated by Banerjee, Kundu, and Das.12 Both sets of positive AH" values decrease with increasing organic content, which corresponds to decreasing (positive) AGO of ionization and thence to decreasing pK values as observed for water in ethylene glycol, but opposite to the observed trend for ionization of water in aqueous ethanol. It is therefore required that the trend in TAX" with increasing organic content must be dominant in determining the trend in pK for ionization of water in aqueous ethanol. As previously noted, the choice of standard states can have important bearing on conclusions drawn from comparisons of equilibrium constants, and also on AGO and AS" values derived from these equilibrium constants. For present purposes it appears to be most useful to calculate AGO from pK,/, values and then to combine these AGO values with the AH" values cited above to obtain T A S " values. I n order to display the results of these calculations in convenient form, we define the quantity 6AG" in terms of the difference between pK values in solvent S and for pure water as 6AG"
=
2.303RT(pKa/,8 - pK,/,W)
(13) in which superscripts s and w indicate pK values referring to solvent system S and to pure water. We similarly define 6AH" as 6AH" = AH," - AH,"
(14) in which subscripts s and w indicate AH" of ionization values referring to solvent system S and to pure water. We also have T6AS" = 6AH"
- 6AG"
(15) Values of 6AGo,6 A H " , and T6AS" for ionization of water in aqueous ethanol and in aqueous ethylene
3913
I 1.0
0.8
0.9
0.7
x w
Figure 4. Thermodynamics of ionization of water in aqueous ethanol and ethylene glycol.
glycol are displayed in Figure 4. We see that there is partial compensation of 6AH" values by T6AS" values so that changes in 6AG" values are smaller than the increments in either enthalpy or entropy with changes in the chemical system under consideration. This sort of compensation has been observed many times before2!' for other ionization reactions and also for other reactions in solution. The magnitude of 6AH" for ionization of water in aqueous ethylene glycol is always larger than the corresponding T6A.S" value and thus establishes the trend in 6AG" that accounts for the "unusual" decrease in pK with increasing glycol concentration. Except a t very small ethanol concentration, the situation is just the reverse for aqueous ethanol, where the magnitude of TGAS" is greater than that of the corresponding 6AH". It is therefore T6AS" that largely accounts for the "normal" trend in 6AG" for ionization of water in aqueous ethanol, and we might expect to find the same situation for other ''normal" solutions. Further data are necessary to determine whether T6AS" values are in fact larger than 6AH" values for these other systems.
Acknowledgment. We are grateful to the National Research Council of Canada for support of this research. (14) G. L. Bertrand, F. J. Millero, C. H. Wu, and L. G. Hepler, J. Phys. Chem., 70, 699 (1966).
The Journal of Physical Chemistry, Vol. 74, No. 8.8, 1970
