4374
LOWELL M. SCHWARTZ AND LELAND 0. HOWARD
Aqueous Dissociation of Squaric Acid
by Lowell M. Schwartz* and Leland 0. Howard Department of Chemistry, University of Massachusetts, Boston, Massachusetts 08116
(Received August 10, 1970)
The dissociation constants of squaric acid in aqueous solution have been measured by potentiometric titration, The values found at 25" were about 0.6 for pK1 and 3.480 f 0.023 for pK2. The latter value corresponds to a A G O of 4.748 f 0.031 kcal/mol. The dissociation constants were also measured as functions of temperature in order to determine the standard molar enthalpies and entropies of dissociation. The values found for the second dissociation were AH" = -3.028 kcal/mol and AS" = -26.08 cal/mol. Since pK1 was found to be significantly less than previous reported values, it appears that squaric acid is even stronger than previously thought.
Introduction
Experimental Section
The unusual strength of the dibasic acid 1,2-dihydroxycyclobutenedione, commonly known as "squaric acid," has stimulated a number of investigations of its aqueous ionization eq~ilibria.'-~ pK2 values at 25" are reported variously as 2.2,l 2.89 f 0.02,2 3.21 f 0.03,a and 3.48 f .02,4but these differences to some extent reflect differences in ionic strength of the aqueous media used. However, a pK2 value in this range should be readily measurable by pH potentiometric titration and agreement should be expected. On the other hand, the first dissociation, reported as pK1 = 1.7 i 0.03a and 1.2 i 0.2,4is more difficult to determine by this technique. Accuracy in pK1 requires a significant concentration of undissociated squaric acid which in turn requires highly concentrated solutions. Even near the solubility limit of about 0.17 M the acid is largely dissociated and impurities and small errors in pH measurement propagate as large errors in the calculated pK1 values. Also activity coefficients are unknown at these ionic strengths and may be estimated only from semiempirical correlations. I n this work we attempt to verify the thermodynamic pKz value and, in spite of the difficulties just mentioned, to establish pK1 to whatever accuracy that pH potentiometric titration affords. MacDonald4 attempts to analyze the energetics of the aqueous dissociation reactions by comparing pK values of squaric acid with those of oxalic acid. The analysis is highly conjectural and would benefit from additional experimental information. I n particular we measure the dissociation constants as functions of temperature and thereby can determine the standard molar enthalpies and entropies of dissociation via the thermodynamic relations
Squaric acid was purchased from Aldrich Chemical Co. in several lots. After drying at 100" under vacuum, each was titrated with carbonate-free 0.1 M NaOH standardized in the usual way with potassium acid phthalate. Squaric acid samples whose molecular weight analyzed to within 0.4% of the value 114.06 were accepted as sufficiently pure and used in the pK detecminations. Samples of acid were dissolved in conductivity water from a calibrated pipet to make solutions varying in concentration from 0.12 to 0.17 M . Each solution was kept under nitrogen atmosphere from the time of its preparation to the completion of the titration. The titrations were done with 0.2226 M carbonate-free NaOH and pH readings were recorded after each addition of base only when the temperature returned to within 0.05" of the desired value. The pH meter was a Beckman model 76 with Beckman 39303 or Corning 476022 glass electrode and Corning 476002 calomel reference electrode. Since critical pH values for pK1 determination ark in the range l to 2, the pH meter was standardized with 0,1000 M HC1 whose pH is 1.106 at all temperatures covered in this study. In addition we checked the pH meter calibration near 4.0 with 0.05 M potassium acid phthalate5 and between pH 1.1 and 2.5 by measuring the pH of the 0.1000 M HC1 titrated with standardized NaOH. pH values of the HC1-KaC1 solutions were calculated using activity coefficients for HC1 from the Debye-Huckel equation with the "ion size parameter" ai interpolated from the data given by Batess on page 55. These values generally agreed with
d In K - AHo dT RT2 A G O
AG"
-RT In K
(2)
AH" - TAS"
(3)
=
The Journal of Physical Chemistry, Vol. 74, N o . 96,1970
* To whom corresRondence should be addressed. (1) J. D . Park, S. Cohen, and J. R. Lacher, J. Amer. Chem. Soc., 84, 2919 (1962). (2) P. H. Tedesco and H. F. Walton, Inorg. Chem., 8 , 932 (1969). (3) D. T. Ireland and H. F. Walton, J . Phys. Chem., 71, 751 (1967). (4) D. J. MacDonald, J . Org. Chem., 3 3 , 4559 (1968). I n a private communication D. J. MacDonald states that his reported pKi = 1.2 f 0.2 is in error due to a miscalculation and that valid pKi values cannot be obtained from his experiments. (6) R. G. Bates, "Electrornetric pH Determinations," Wiley, New York, N . Y., 1954.
AQUEOUS DISSOCIATION OF SQUARIC ACID
4375
the pH meter readings to within 0.01 pH unit and since this degree of accuracy was all we could expect with the apparatus, no corrections were made. We experienced sporadic trouble with the p H measuring system in squaric acid solutions of pH 1.5 or less, but not in HC1-NaC1 solutions of similar acidity. The p H reading suddenly began to drop and fluctuate with the rate of stirring. The effect occurred frequently below room temperature and less so above. We localized the trouble in the calomel reference electrode and suspect that undissociated squaric acid was adsorbing into the fiber junction. Since upon washing the tip of the calomel electrode in distilled water the pH system recovered, we adopted the procedure of pipetting 2-ml samples of water onto the electrode tip whenever the trouble occurred, pausing a few minutes, and proceeding with the titration. The calculation method accommodated the solution volume changes due to these small water additions.
Calculations The method of computing the equilibrium constants is basically the same as that used by M a ~ D o n a l d . ~The thermodynamic constants K1 and K Zare defined by (4) and (5) where [H2Sq], [HSq-1, and [Sq-] represent the molar concentrations of the undissociated squaric acid, bisquarate ion, and squarate ion, respectively, yIf:the mean activity coefficient, of the singly charged species, y- = y*4 the activity coefficient for the squarate ion, yo = 10°.” the activity coefficient6for undissociated squaric acid, and I the ionic strength. The ionic activity coefficients were estimated by the semiempirical correlation
developed by Davies’ and reported to represent the activity coefficients of fifty 1:1 electrolytes a t 25” and 0.1 M with an average deviation of 1.6%. The temperature variation of ionic activity coefficients was assumed to be included in the temperature variation’of the Debye-Hiickel coefficient D,whose values were taken from Robinson and Stoked8 Appendix 7.1. After incorporating the usual mass and charge balance relationships, the system of equations is soluble when applied to two solutions, one from before the first equivalence point in the titration (denoted by subscript b), and one from after (denoted by subscript a). I n this form the dissociation constants are computed from
(7) and
where (excluding subscripts b or a)
A = 2C” - [Na+] - [H+]
B
=
(Co- [Na+] - [H+])y=[H+]
C = -([Na+l
+ [H+I)Y~~[H+I~Y=/YO
C” = stoichiometric molar concentration of squaric acid [H+] = 10-pH/y* A digital computer program was written to carry out the calculations. The sodium ion and stoichiometric acid concentrations were calculated at each recorded point in the titration. The volumes of the solutions were assumed additive and to vary with temperature in the same manner as pure water. Calculations were made of K1 and Kz by pairing each reading before with each reading after the first equivalence point. For each pair of readings estimated solution ionic strengths led to values of K1 and Kz calculated according to eq 7 or 8. These equilibrium constants were then used to calculate [HSq-] and [Sq-] in each of the two solutions which permitted more accurate estimates of ionic strength. This iteration continued until pK1 and pKz were each invariant to within 5 X In the course of the computer calculation, it is possible that differences between nearly equal quantities could produce some pK values of questionable validity. These derive from solutions in the immediate vicinity of the first equivalence point and the end point where [HzSq] and [HSq-] are small. Consequently, pK values were rejected if derived from titration volumes within 10% of these points. We have tested the experimental and calculational techniques by titrating Matheson Coleman and Bell reagent ACS grade oxalic acid and found pK1 = 1.31 f 0.06 and pKz = 4.24 f 0.01, which compare favorably with literature values pK1 = 1.2@ and pKz = 4.266.1°
Results Little variation was observed in the several pK1 values calculated by pairing a single reading before the first equivalence point with all the readings after. Sim(6) J. N. Butler, “Ionic Equilibrium,” Addison-Wesley, Reading, Mass., 1964. (7) C. W.Davies, “Ion Associatipn,” Butterworths, London, 1962. (8) R . A. Robinson and R. H. Stokes, “Electrolyte Solutions,” 2nd ed (revised), Butterworths, London, 1959. (9) L.S. Darken, J . Amer. Chem. SOC.,63, 1007 (1941). (10) G. D . Pinching and R. G. Bates, J . Res. Nat. Bur. Stand., Sect. A , 40, 405 (1948). The Journal of Physical Chemistry, Vol. 74, No. 26, 1070
LOWELLM. SCHWARTZ AND LELAND 0. HOWARD
4376 Temp, O C
50
40
30 25 20
Table I: Results of Squario Acid Titrations a t Temperatures from 10 to 50". Nb and N, are the Total Number of Titration Solutions Contributing to the Averages 3 1 and Respectively
10
I
I
z2,
Number of
Temp, OC
10 20 25 30 40 50
1000/T°K.
Figure 1. Results of squaric acid titrations plotted as pK1 and pK2 us. l/T°K. The curve through the pKz values is pK2 = -1937/T 14.25 - 0.014342'.
+
ilarly, the several pKz values corresponding t o a given solution late in the titration were insensitive to points early in the titration. This reflects the fact that the two dissociation constants are sufficiently separated that readings before the first equivalence point largely determine pK1 and readings after determine pKz. Consequently, the several pK values calculated from a single reading were averaged and then treated statistically as follows: (a) averages pKt and pKzwere calculated from the above set of averages (included were data from other titrations at a single temperature if duplicate titrations were done); (b) the standard deviation s = [?PKI
-
""I"
Nb
pKi f a
0.48 f 0 . 0 6 0.61 f 0 . 1 0 0.59k0.09 0.51f0.07 0.61f0.06 0.41~0.01
pKz
2 3 11 13
*
Na
s
3.351 4 0 . 0 1 9 3.444Zt0.019 3.480f0.023 3.511 f 0 . 0 1 0 3.575k0.013 3.6242~0.009
7 6
6 14 13 19
7 6
titrations
1 2 2 3 1 1
that pK1 in the vicinity of room temperature is about 0.55 f 0.15, which is significantly less than other estimated values3l4 indicating that squaric acid is even stronger than previously thought. The availability of the digital computer program makes it convenient to test the sensitivity of the pK values to various uncertainties in the experimental measurements and the calculating equations. The uncertainties which we estimate in this study and the resulting effect on pK1 and pK2 are shown on Table 11. A
Table 11: Computed Effects of Uncertainties on pK Results Approximate effect on pKi PKZ
Estimated uncertainty
pH value Solution volumes Reagent purity (assuming inert impurities ) Temperature Ionic activity coeff correlation eq 6
0.02 unit 0.02 ml 0.4%
0.12 0.01 0.13
0.05' 2y0
Nil
Nil
0.04
0.03
0.02 0.01 0.02
N-1 was calculated; (c) any pK value whose deviation from exceeded 2s was rejected (a total of 2 pK1 and 3 pKz values were rejected in this way) ; (d) in the case of rejection in (c) a new average and standard deviation were calculated. The results are summarized in Table I and plotted in Figure 1. In the table, N b is the number of readings before the first equivalence point utilized in the final calculation of pK1 I s and N , related similarly to S z f s. The pKz values show a clear temperature dependence and can be fitted by the three-parameter function
9
P K ~=
- 1937
+ 14.25 - 0.01434T
(9)
which is the curve in Figure 1. The temperature dependency of pK1 is uncertain. It appears, however, The Journal of Physical Chemistry, Vol. '74, N o . 8.5* 1970
comparison of these results with the standard deviations in Table I shows that the statistical treatment of the data generates uncertainty values that are well within the limits based on our estimates of propagated errors. However, little can be said about inaccuracy in these reported pK values resulting from deviations of the activity coefficients of squaric acid ionic species from Davies' correlation, eq 6. The fitted eq 9 was used to calculate standard molar Gibbs free energy, enthalpy, and entropy of the second dissociation using eq 1, 2, and 3. At 25" these are AGO
=
4.748
f
0.031 kcal/mol
AH" = -3.028 kcal/mol AS" = -26.08 cal/mol-deg
4377
THERMODYNAMICS OF BINARY LIQUIDMIXTURES On the basis of estimated limiting slopes through the 25" pKz value, we conclude that AH" is uncertain t o ' about 15% and AS" to about 6%. The unusual strength of squaric acid, however, is in the first dissociation, and a clearer understanding of this phenomenon awaits more accurate measurements probably by some
other technique. I n this laboratory we are attempting to measure the first ionization conductometrically.
Acknowledgment. We thank Professor Robert I. Gelb for his many helpful discussions and the Research Corporation for partially supporting this work.
Thermodynamics of Binary Liquid Mixtures by Total Intensity Rayleigh Light Scattering. I1 by Harvie H. Lewis, Raymond L. Schmidt, and H. Lawrence Clever* Chemistry Department, Emory University, Atlanta, Georgia 90922 (Received March 26, 1970)
Rayleigh scattering and depolarization were measured for benzene-methanol, benzene-propanol-2, and benzene-n-dodecane solutions. The gradient of the concentration dependence of refractive index, An/ AX, was directly measured as a function of composition for the solutions by differential refractometry. The measurements were combined with total intensity light scattering and depolarization data to obtain activity coefficients and excess Gibbs free energies of mixing which were compared with results from vapor pressure measurements for the alcohol-containing solutions. The excess free energy of mixing from light scattering at 0.5 mole fraction was 4% below the accepted vapor pressure value for benzene-methanol and 16% below for benzene-propanol-2. The benzene-n-dodecane solutions appear to have a negative excess free energy of mixing over part of the composition range. The light scattering method, a t best, can give only approximate thermodynamic values for solutions with a negative excess free energy of mixing.
Rayleigh scattering from liquids and liquid solutions is an active field of study with a constant reevaluation of the theoretical equations as they apply t o liquids.l-* Over the past several years there have been several studies of Rayleigh scattering from binary nonelectrolyte solutions of small molecules. I n these studies either the Rayleigh scattering and depolarization measured for the solution were treated to obtain activity coefficients of the components and excess Gibbs free energy of mixing6-' or properties of the solutions were used to calculate a predicted Rayleigh scattering which was compared with experiment.*bg Studies of the second type have also been carried out on aqueous electrolyte solutions.10 This work is a further study of the relationship between Rayleigh scattering and the thermodynamic properties of binary nonelectrolyte solutions, with particular attention to the contribution of the gradient of t h e concentration dependence of refractive index t o the relationship. The total Rayleigh scattering, RgO, can be separated into an isotropic contribution, Ris, and an anisotropic contribution, R,,, by the Cabannes relation. In pure liquids the isotropic scattering is due to density fluctua-
tions, Rd. I n solutions two further terms contribute to the isotropic scattering, a concentration fluctuation, R,, and a density-concentration fluctuation cross term, R#. The total isotropic Rayleigh scattering from a solution is the sum R i s = Rd R, R#with
+ +
Rd
=
(a2/2b4)k TKt [N(be/bN)t 1'
(1)
* T o whom correspondence should be addressed. (1) D. J. Coumou, E. L. Mackor, and J. Hijmans, Trans. Faraday Soc., 60, 1539 (1964).
(2) A. Litan, J . Chem. Phys., 48, 1052, 1058 (1968). (3) M . Kerker, "The Scattering of Light and Other Electromagnetic Radiation," Academic Press, New York, N. Y., 1969. (4) D. McIntyre and J. V. Sengers in "Physics of Simple Liquids," H. N. V. Temperley, J. 5. Rowlinson, and G. S. Rushbrooke, Ed., North-Holland Publishing Co., Amsterdam, 1968, Chapter 11. (5) D. J. Coumou and E . L. Mackor, Trans. Faraday Soc., 60, 1726 (1964). (6) R. L. Schmidt and H. L. Clever, J . Phys. Chem., 72, 1529 (1968). (7) R. 6 . Myers and H . L. Clever, J . Chem. Thermodynamics, 2, 53 (1970). (8) G. D. Parfitt and J. A . Wood, Trans. Faraday SOC.,64, 805 2081 (1968). (9) M. 6. Malmberg and E. R . Lippincott, J . CoZZoid Interface Sci., 27, 591 (1968). (10) B. A. Pethica and C. Smart, Trans. Faraday Soc., 62, 1890 (1966).
The Journal of Physical Chemistry, Vol. 74, N o . 26, 1970
