Anal. Chem. 1003, 65, 2294-2299
2204
Autoprotolysis in Aqueous Organic Solvent Mixtures Marti Roses,’ Clara Rdfols, and Elisabeth Bosch* Departament de Qulmica Analltica, Uniuersitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
The primary chemical equilibria which define autoprotolysis in aqueous binary solvents have been elucidated and the constants of these equilibria computed for aqueous solvent mixtures of methanol,ethanol, 1-propanol,2-propanol, 2-methyl-tpropanol, 1,t-ethanediol,l,2-propanediol, 1,3propanediol, l,%,&propanetriol, acetonitrile, acetone, tetrahydrofuran, dimethyl sulfoxide, 1,4dioxane, and formic acid. The values of these constants explain the different behaviors of the diverse binary solvents. From these fundamental constants, the pK,, value at any solvent composition of any of the binary solvents studied can be accurately computed. It is also demonstrated that in most parts of the ranges of solvent compositions of binary solvents, autoprotolysis is mainly performed by proton transfer from water to the organic solvent. INTRODUCTION In various documents the IUPAC has remarked on the importance of the autoprotolysisconstant (K,) in nonaqueous and mixed solvents.1.2 The value of the autoprotolysis constant determines the “normalrange of pH” in each solvent, given as PKap = -log Kap,3and it is needed in order to achieve complete and effective pH standardization in nonaqueous and mixed solvents.’ One of the IUPAC documents2 has defined the autoprotolysis constant for any solvent such as in water and has compiled the pKap values of many nonaqueous solvents, including some solvent mixtures at various compositions. However, the unlimited number of different solvent compositionswhich can be prepared from a particular binary system (e.g., a specific organic solvent and water) prevents determination of the pK,, values in all of the compositions. Therefore, an equation for computation of the PKap value of any solvent composition from some few parameters would be very useful. Although the equation can be empirically proposed and the parameters which best fit it determined, an equation based on the thermodynamics of the chemical autoprotolysis equilibria in a mixed solvent, with parameters having a chemical meaning, would be more desirable. In this paper this equation is derived and applied to 2-propanol/water mixtures. 2-Propanol is a neutral amphiprotic solvent like water, less polar but fully miscible. Therefore, the polarity of the solvent can be easily changed over a large range by changing the ratio 2-propanol/water in the mixture, and for this reason, these mixtures are useful in analytical techniques such as liquid chromatography. Autoprotolysisconstants of 2-propanol/water mixtures up to almost 50% 2-propanol by weight were determined by Woolley et al.‘ Although these authors called the constants (1) Mwini,T.; Covington,A. K.; Longhi, P.; Rondinini, S.Pure Appl. Chem. 1985,57, 865-876. (2) Rondinini, S.; Longhi, P.; Mwini, P. R.; Mussini, T. Pure Appl. Chem. 1987,59, 1693-1702. (3) Bates, R. G. Determination of pH-Theory and Practice, 2nd ed.; Wiley: New York, 1954. 0003-2700/93/0365-2294$04.00/0
obtained “apparent ionization constants for watern,6eein fact they are autoprotolysis constants, since they have been obtained by measuring the overall proton concentration (solvated by water or by the organic solvent) and defined in this way. The data of Woolley et al. have been complemented by determining potentiometrically the PKap values at 50,70,and 90% 2-propanol by weight from the reference potentials in acidic and basic media, following the method described in previous papers.’-g This method can be applied either to solvent mixtures with electrolytescompletely dissociated (50 and 70%)9 or to solvent mixtures of low dielectric constant with acids, bases, and salts only partially dissociated (90% 2-propanol). The good results obtained for the binary solvent studied lead to application of other binary solvent literature data. The IUPAC compilation of pKap values of binary solvent mixtures2 based on the 1iterature,lC-l6 the extensive work of Woolley et a1.,4-eand other data16a has been used. The binary systems studied are mixtures of water with the organic solvents presented in Table I. The results show the applicability of the equation to all these binary systems and lead to the determination of the fundamental constants of the equilibria which affect autoprotolysis in these binary solvents. These constants explain the differences in behavior of the systems studied and allow accurate computation of pKapvalues in the composition range studied.
THEORY The IUPAC defines the autoprotolysis equilibria in a solvent RH (single or mixed)
RH + RH +
RH^+ + R-
(la)
(4) Woolley,E. M.; Hurkot, D. G.; Hepler, L. G. J.Phys. Chem. 1970, 74, 3908-3913. (5) Woolley, E. M.; Hepler, L. G. Anal. Chem. 1972,44, 1520-1523. (6) Woolley,E. M.; Tomkins, J.; Hepler, L. G. J. Solution Chem. 1972, 1,341-351. (7) Rmbs, M. Anal. Chim. Acta 1993,276, 211-221. (8) Rosbs, M. Anal. Chim. Acta 1993,276, 223-234. (9) M o b , C.; ROB&,M.; Bosch, E. Anal. Chim. Acta 1993,280,75-83. (10) Rochester, C. H. J. Chem. SOC.,Dalton Trans. 1972,5-8. (11) Parsons,G. H.; Rochester, C. H. J. Chem. SOC.,Faraday Trans. 1 1972,68,523-532. (12) Gutbezahl, B.; Grunwald, E. J. Am. Chem. SOC.1983,75,565-574. (13) Aleksandrov, V. V.; Kireev, A. A. Zh. Fiz. Khim. 1979,53,681684; Chem. Abstr. 1979,90, 1932700. (14) Banerjee, S. K.; Kundu, K. K.; Das, M. N. J. Chem. SOC.A 1967, 166-169. (15) Sastry, V. V.; Kalidas, C. J. Chem. Eng. Data 1984,29,239-242. (16) De Ligny, C. L.; Luykx, P. F. M.; Rehbach, M.; Wieneke, A. A. Red. Trav. Chim. 1960, 79, 713-726. (17) Das, A. K.; Kundu, K. K. J. Chem. SOC.,Faraday Trans. 1 1973, 69.730-736. (18) Fiordiponti, P.; Rallo, F.; Rodante, F. 2.Phys. Chem. (Frankfurt/ Main) 1974,88, 149-159. (19) Baughman, E. H.; Kreevoy, M. M. J.Phys. Chem. 1974,78,421~~
r
422.
(20) Longhi, P.; Mussini,T.; Veleva, M. G. Anal. Quim. 1975,71,10431047. (21) Georgieva, M.; Velinov, G.; Budevsky, 0. Anal. Chim.Acta 1977, 90,83-89. (22) Rochester, C. H.; Sclosa, S. A. J. Chem. SOC.,Faraday Trans. 1 1979, 75, 2781-2797. (23) Barbosa, J.; Sanz-Nebot, V. Anal. Chim.Acta 1991,244,183-191. (24) Harned, H. S.; Fallon, L. D. J. Am. Chem. SOC.1939,61, 23742377.
0 1993 Amerlcan Chemlcal Soclety
ANALYTICAL CHEMISTRY, VOL. 65, NO. 17, SEPTEMBER 1, 1993
Table I. Densities and Autoprotolysis Constants of Pure Single Solvents at 25 solvent P (gem") pKaPm pKapM 1.2141 6.21 formic acid 6.38 0.9970 14.00 14.00 water 1.2582 1,2,3-propanetriol 1.1100 15.84 15.75 1,a-ethanediol 1.0361b 17.21 17.18 1,2-propanediol 1.0597b l,3-propanediol 0.7866 16.77 methanol 16.56 18.94 19.15 ethanol 0.7850 0.7998 19.28 19.47 1-propanol 0.7813 20.74 20.95 2-propanol 0.7812 28.5 28.7 2-methyl-2-propanol 1.0958 32-33 32-33 dimethyl sulfoxide 0.7766 >32.2 >32.4 acetonitrile 0.7844 >32.5 >32.7 acetone 0.8842 tetrahydrofuran 1.0280 1,4-dioxane p from refs 26 and 27. pKapm are averaged values from ref 2. pKapMare computed from pKapmand p. * At 20 O C .
Therefore, the autoprotolysis constant is defined as where a is the activity of the subscript species. Assuming activity coefficientsof the undissociated speciesequal to unity, eq l b can be written as
or
KaP = ([H,qo+lY~~o+[H~S+]YH++)([OH-I~OH~ + [S-IYs-) (7) and replacing eqs 3b-6b in (7), a general expression for the autoprotolysis constant is obtained Kap
KapM= [RH:]
[R-]YRH,+YR-/XRH~
(Id)
Equations ICands I d are the common equations for the autoprotolysisconstant when the concentrations are expressed in molality (superscript m) or molarity (superscript M), respectively. However, in both equations the concentration of the solvent is expressed in mole fraction. Since the standard state of RH species is the pure solvent, its activity agrees with its concentration, which is unity only when it is expressed in mole fraction. Although molality constants are preferred in thermodynamic studies, molarity constants are more used in analytical chemistry and they will be mainlyused in this work. However, the equations derived and the results obtained also apply to molality constants, since both constants are related by means of the equation (2) pKapM= pKapm- 2 log p where p is the density of the solvent RH (single or mixed) in grams per cubic centimeter. The application of the autoprotolysis equilibrium (la) to a water and organic solvent (HS) binary mixture implies four different ionization processes
+ H 2 0 F! H30++ OHH 2 0 + HS F! H30++ SHS + H,O F! H2S++ OHHS + HS s H2S++ S-
H,O
(3a) (4a) (5a)
(6a) However, although equilibria 3a-6a were earlier proposed by Banerjee et a1.14 for l,Pethanediol/water mixtures and accepted by the IUPAC,2as far as we know, their contribution to the overall autoprotolysis has not been elucidated. The constants of these processes can be written as KH,O
In these equations, KH,Oand KHSare the autoionization constants of water and organic solvent, respectively. K d & and &H,O are the acidity and basicity constants of water in reference to the organic solvent or, which is the same, the basicity and acidity constants of the organic solvent in reference to water. The ionization constants have been defined in molarity, as stated above, but the concentrations of the undissociated species (that is to say, of the two solvents) are given in mole fraction ( x ) , in consonance with equation Id, because the standard state is the same (the pure binary solvent). Since in eq Id RH2+ = H30++ HzS+, R- = OH- + S-, and XRH = XH,O + XHS = 1, the overall autoprotolysis constant of the solvent is
= aH80+aOH-/aH20
2
=
[H@+l [OH-]YH~O+~OH-/XH,$ (3b)
= KHzOxHz02 + (KaH,O + KbH,O)XH,OXHS + KHSXH2
Although four constants are used in the definition of the autoprotolysis constant in a binary solvent mixture, it must be noticed that only three are independent because KH,d(HS
= KaH,d(bH,O
(9)
Therefore, only three constants are needed for complete description of autoprotolysis in a specific binary solvent mixture. However, in many solvent compositions two or one of the three terms of eqs 8 can be much smaller than the others, and only one or two constants will be needed to compute KaP. Of course, the values of the constants, as well as mole fractions, change with the solvent composition, and consequently, the relative importance of the terms of eq 8 changes with the solvent composition. In the water-richest compositions, where XH,O >> XHS, the term K H , ~ H is~ o ~ expected to prevail over the other ones (in the limit when XH,O -+ 1 and X H S 0, Kap = KH,O= lO-l4.w,at 25 "C). At , term the other limit, when XHS sufficiently exceeds ~ 4 0the K~g~s2predominates over the others (in the limit when XH,O 0 and XHS 1, Kap= KHS). In intermediate regions, the term (Kd,o + KbH,O)XHQHS may predominate over the other two. This term is composed of two constants K&!O andKbHp, which depend on the specific acidities and basicities of water and the organic solvent. If water is more acidic and less basic than the organic solvent, K ~ , >> o KbH,o, but if the organic solvent is more acidic and less basic than water, K d @ 0 was used
if K ~ H ,
