Table I. Contributions to the Uncertainty in Analysis as Variability of of conditions Pure components Temp. 1 5 X “C Pure components Temp. 1 0 . 0 1 “C Dissolved solute 1 0 . 0 1 M in concentration
of H-D Content Dissolved solutes
Instrument stability
Temperature control
10.013
10.001
...
10.014
Xt0.013
10.024
...
10.037
3Z0.013
3Z0.024
10.1
XtO, 15
of the solution. One further source of error in the method is possible long-term drift of the instrument, quoted (IO) as *O.Olx (3 months). Errors from this source can be eliminated by periodic redetermination of the calibration curve (Figures 2 and 3), or better by using a v - vo calibration, where vo is the sound velocity in the pure solvent, a figure which can easily be checked each day. It should also be noted that if comparison of results with those from other probes or analyzer units is not to be made, the frequency count itself provides a perfectly good basis for a calibration curve. The rapidity with which measurements can be made by this method depends mainly on the time taken for thermal equilibration. Thus, if two or three probes were in use with one pulse generator instrument, and counter, a rate of one determination in five minutes could be achieved. Table I, summarizes the accuracy which can be achieved in analysis of D20-H20mixtures by this method. The sensitivity of the method also makes it suitable for accurate determination of adsorption of substances from solutions, e.g., on high area electrode materials (14). The method, unlike UV spectrophotometry used previously for this purpose (14), is obviously not limited to aromatic molecules and (14) R. G. Barradas and B. E. Conway, J . Electronnal. Chem., 6 , 314 (1963).
Total
can be quite generally employed for any substances, provided previous calibrations are made.
“CONTINUOUS” SAMPLING In practical applications for analysis of H20-D20 or other liquid mixtures, continuous, on-line operation and analysis is usually advantageous. Strictly continuous measurements are not possible owing to the necessity of taking a sample reading over a 10- to 45-second period after thermal equilibration. However, slug-sampling of a liquid flowing in a line could easily be arranged with the probe held in a locally thermostated by-pass section of pipe or tube with admission of samples from the line controlled by a system of two magnetically controlled valves. A suitable mounting manifold for such purposes is available (5).
ACKNOWLEDGMENT The interest of M.C.B. Hotz in this project is acknowledged, as are discussions with W. H. Stevens, Atomic Energy of Canada Ltd. RECEIVED for review December 2, 1971. Accepted January 27, 1972. Support of this and related work on a contract from the Department of Energy, Mines and Resources (Inland Waters Branch), Canada, is gratefully acknowledged.
Apparent Ionization Constants of Water in Aqueous Organic Mixtures and Acid Dissociation Constants of Protonated Co-Solvents in Aqueous Solution Earl M. Woolley Department of Chemistry, Brigham Young Unioersity, Provo, Utah 84601
Loren G. Hepler Department of Chemistry, University of Lethbridge, Lethbridge, Alberta, Canada
WE HAVE RECENTLY described (1) a rapid and convenient method for accurate determination of “apparent” ionization constants of water in aqueous organic mixtures. We have also shown ( 2 ) that these “apparent” ionization constants lead to a convenient method for evaluation of pK, values for ionization of aaueous acids with pKn < 16.
We report here an analogous convenient method for evaluation of pK, values for acid dissociation of protonated aqueous co-solvents with pK, > -2. We have applied this method to the determination of pK, values of protonated aqueous urea, N-methylformamide, and N-methylacetamide.
(1) E. M. Woolley, D. G. Hurkot, and L. G. Hepler, J. Phys. Chem., 74,3908 (1970).
(2) E. M. Woolley, J. Tomkins, and L. G. Hepler, unpublished work, University of Lethbridge. Alberta, Canada, 1970.
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ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JULY 1972
EXPERIMENTAL Potential measurements were made as before ( I , 2) with a variety of wide pH range glass electrodes. The cells were maintained at 25.0 (=+O.l)”Cand potential readings were recorded when they became constant to *O.l mV. Measurements were repeated at least twice with different combinations of electrodes, pH meters, and electrolyte concentrations ranging from 0.0005 to 0.01 molar. Densities of mixtures of water with N-methylformamide and of water with dimethylsulfoxide were measured pycnometrically .
METHOD AND CALCULATIONS
__
As before ( I , 2) we describe the ionization of water in a particular solvent system S by
HgO(S)
Hs(S)
+ OH-(S)
(1)
Various equilibrium constant expressions for Reaction 1 can be defined on the basis of several reasonable choices of standard states. We use here the same equilibrium constant expressions, symbols, and choices of standard states we defined and used previously ( I , 2 )to describe Reaction 1 : Qcii =
K,/L Kale
CHCOH
(2)
=
CHCOH(Y+)* = Qc,i(y*)’
(3)
=
C H ~ O Hh)’/Cw (Y = Ka/l/Cw
(4)
=
C~codY *)‘/a,
(5)
Kai1/aw
Our investigations in aqueous organic mixtures are based on the potentials of cells represented by glass electrode 1 soln A : HC1(Cl), KNO~(CZ) in solvent SIAgC1, Ag (A) and
and the corresponding acid dissociation equilibrium constant expression K H , Z = (CHCHZ/CH,Z>(YHYI~Z/YH*Z)(8)
for standard states based on molar concentrations. In solutions of low ionic strength that are also dilute in HZ, we take HZ = 1 and Y H = YH,Z SO that Equation 8 becomes KH?Z= CHCHZ/CH,Z
E
position,
where k z is evaluated from the known ionization constant for pure water and from potentials for cells A and B measured with pure water as solvent. As before, values of Kall were obtained from p(Qell)values by use of an equation based on Debye-Huckel theory or by extrapolation to zero electrolyte concentration. Densities and dielectric constants for aqueous urea mixtures were taken from Timmermans (3). Dielectric constants and densities for aqueous N-methylacetamide and dielectric constants for aqueous N-methylformamide were estimated from data in the literature (2-6). Dielectric constant data for aqueous dimethylsulfoxide were taken from information brochuxes supplied by Crown-Zellerbach. For acid dissociation of a protonated organic co-solvent HiZ+(S) we write
+ HZ(S)
(7)
(3) J. Timmermans, “The Physico-chemical Constants of Binary Systems in Condensed Solutions,” Vol. 4, Interscience, New York, N. Y.,1960. (4) R. A. Hovermale, P. G. Sears, and W. K. Plucknett, J . Chem. Eng. Data, 8,490 (1963). ( 5 ) G. R. Leader and J. F. Gorrnley, J. Amer. Chem. Soc., 73,5731
(1951). (6) T. B. Hoover, J . Phys. Chem., 73,57(1969).
ki
+ kz log
(10)
(aHUc1)
where n~ and ncl represent the number of moles of H+(S) and Cl-(S) in volume V of solution A. For a series of measurements in which ncl is constant we obtain
EA^
- EAHZ= k z x log [nH’(y
Zkw)2(VHZ)2/nHHZ(y hHZ)2(Vw)2](12)
from Equation 11. In Equation 12 we have used superscripts w and H Z to indicate that the potentials, number of moles, mean ionic activity coefficients, and volumes refer to solutions with purely aqueous solvent and with some organic cosolvent HZ added, respectively. From material and charge balance equations we obtain nHPZ
We have previously shown ( I ) that, when Cl + Cz = C3 + C4 and when solutions A and B have the same solvent com-
HzZ+(S) If Hs(S)
=
For Cell A this equation becomes
glass electrodelsoh B: NaOH(C3), NaC1(C4)in solvent SIAgC1, Ag (B)
(9)
We now consider the addition of small increments of the organic co-solvent H Z to an aqueous solution Cl molar in HC1 (Cell A) as a potentiometric titration of a strong acid (HC1) with a (very) weak base (HZ). The potential obtained from Cell A during such a titration can therefore be used for evaluation of the acid dissociation constant KHJ. of the protonated organic co-solvent. A general equation for the potentials of Cells A and B ( I , 2) is given by
+
(13)
nHHZ = n H W
and %HZ)
=
CHZf C H ~ Z
(14)
in which nH,Z and CH%Z represent the number of moles and concentration of HsZi(S), CHZ represents the concentration of HZ(S), and B(HZ) represents the stoichiometric concentration of H Z in Cell A for which we have measured EAHZ. We now express an “apparent” equilibrium constant K * H ? z for dissociation of H2Zs(S),based on Equation 9 as (1 5 )
K * H ? z= nHHZCHZ/nH,Z
We use Equations 12-15 and a Debye-Huckel activity coefficient expression ( I ) to obtain K*H,z values from the experimental data. These K * H ? z values apply to a certain Z(HZ). Therefore we must extrapolate K*H,z values to zero Z H Z ) to obtain the usual equilibrium constant K H ~ Z for acid dissociation of the protonated co-solvent as a solute in purely aqueous solution. Another approach to evaluation of K H ~ zwhich , shows clearly the relative importance of dissociation of H2Zi(S) and HzO(S), is developed as follows. Division of Equation 13 by total volume VHZ of solution in Cell A after an increment of H Z has been added leads to nHw/vHz =
+ CH2Z
CHHZ
(16)
Next we multiply both sides of Equation 16 by to obtain
iHz)’
+
nHwCOHHZ(y*HZ)2/VHZ = CHHZCoHHZ(yZkHZ)2 CH,ZCOH~~(Y (17) *~~)~
The term on the left side of Equation 17 is identical to K a / l derived from Equations 3 and 6, in which we did not allow ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JULY 1972
1521
Table I. Apparent Ionization Constants for Water in Aqueous Urea Mass Urea P(Kad6 p(Ka/a) AK=/3 14.00 15.74 0.00 14.00 15.52 13.79 13.79 2.56 4.92 13.62 13.61 15.35 7.06 13.51 13.50 15.23 13.41 15.13 8.84 13.42 15.05 13.34 13.32 10.56 12.11 13.26 13.24 14.96 14.89 13.19 13.17 13.58 13.08 13.06 14.77 16.15 12.96 14.67 18.36 12.99 20.3 12.91 12.88 14.58 12.79 14.49 22.0 12.83 14.43 12.78 12.74 23.4 12.68 14.37 24.8 12.72 12.67 12.63 14.31 26.0 12.55 14.24 27.1 12.60 12.51 14.19 28.0 12.56 12.48 12.43 14.10 30.1
Table IV. Acid Dissociation Constants for Organic Acids in Aqueous Solution Urea NMA NMF P(KH2Z) ; 0.1 ( i O . 1 ) o 0.4(f0.1)” -0.1 (zk0.2p Equation 15 P(KHd; literature 0.17*(21 “C) 0.37 (10.03)f -0.30 0.1@ 0.49 -0.04h (20 “C) 0.13~ 0.8h (20 “C) 0 .05c -0.46’ 0.5d 0.12e 0.18” 0 . 2 to 0.3i (22 “C) ~ ( K H z ) ; 14.3 (i0.3)a ... ... Ref. ( 2 ) , Equation 15 PWHZ); 13.7k literature 13.8l (30 “C) a Our estimates of total uncertainties. bRef. (7). Ref. (8). dRef. (9). “ef. (IO). Ref. (11). Ref. ( 1 2 ) ; corrected to aqueous solution. Ref. (13). ’Ref. (14). 3 Ref. (15). Ref. (16). Ref. ( 1 7 ) .
z
Table 11. Apparent Ionization Constants for Water in Aqueous N-Methylacetamide Mass NMA P(Ka/l)s p(Ka/J p(Ka/c) 0.00 14.00 14.00 15.74 4.28 14.01 14.01 15.73 8.19 14.02 14.01 15.72 11.8 14.02 14.01 15.71 15.1 14.03 14.01 15.69 18.1 14.05 14.03 15.70 20.9 14.07 14.04 15.70 23.5 14.08 14.05 15.70 28.2 14.12 14.08 15.70 32.3 14.15 14.10 15.70 14.16 35.9 14.11 15.69 39.1 14.18 14.11 15.68 42.0 14.18 14.11 15.66 44.5 14.18 14.10 15.64 ~
~~
~
~
~~~
~
~~~~
~
“apparent” equilibrium constant for acid dissociation of H2Z+(S) which we represent by KH2z;+. Equation 17 thus becomes (&/1)6
~
Table 111. Ionization Constants for Water in Aqueous Dimethylsulfoxide Mass DMSO P(K~IJ~ P(Ka/a) P(Ko/c) 0.00 14.00 14.00 15.74 5.21 14.11 14.11 15.83 9.90 14.22 14.21 15.92 14.1 14.31 14.30 15.99 18.0 14.41 14.39 16.07 21.5 14.51 14,48 16.17 24.8 14.60 14.56 16.23 27.8 14.69 14.64 16.31 33.1 14.88 14.82 16.47 37.7 15.05 14.98 16.61 41.7 15.23 15.15 16.76 45.2 15.40 15.31 16.91 48.3 15.57 15.47 17.05 51.1 15.72 15.61 17.18 53.6 15.87 15.75 17.31 55.8 16.03 15.91 17.45 57.9 16.18 16.05 17.58 62.2 16.49 16.35 17.85
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ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JULY 1972
(Ka/Jcorr
+ CHZ[(Ku,l)oorr/KH2Z*l
(18)
We note that the term [ ( K u , ~ ) c o r r / K ~represents 2z*] an “apparent” base dissociation constant for H2ZOH, similar to for “?OH. the traditional Kb = 1.8 X In those cases where HzZ+(S) is significantly more acidic than water, we can obtain significant data from Cells A and B only when C H Zis sufficiently large that (Ku,JCorr+ 1.0 X In these cases it is necessary ( 2 ) to obtain estimates of 5s. C H Zfrom the equathe initial slope So of a plot of (Ka,l)corr tion SO = -5.1
z
for formation of H2Z+(S) from H+(S) and HZ(S). We now call this left-hand term (KU,J6. The first term on the right side of Equation 17 is a n equilibrium constant expression for ionization of water in the mixed solvent system [with proper allowance made for formation of H2Z+(S)]that we now designate (Ku,l)corr. The second term on the right side of Equation 17 is equal to CHZtimes (Ku,~)corr divided by another
=
X lo-’*
lim
CHZ
+
0
[d(l/e)/dC~~]
(19)
in which e represents the bulk dielectric constant of the solvent system. The derivation leading to Equation 18 considers only the basicity of the organic co-solvent described by Equation 7. In a previous treatment (2), we derived an expression similar to Equation 18 in which we considered only the acidity of the organic co-solvent according to the reaction (71 J . Bell, W. A. Gillespie, and D. B. Taylor, Tram. Faraday Soc., 39,137 (1943). (8) N. F. Hall. J . Amer. Chem. Soc.. 52,5115 (1930). (9j H. Lemaire and H. J. Lucas, ibid., 73,5198 (1951). (10) D. D. Perrin, “Dissociation Constants of Organic Bases in Aqueous Solution,” Butterworth, London, 1965,p 450. (11) J. Koskikallio and S . Syrjaepalo, Soumen Kemi, 37B, 120 (1964); Chem. Absrr.,63,14139d(1965). (12) T. Higuchi, C. H. Barnstein, H. Ghassemi, and W. E. Perez, ANAL.CHEM., 34,400 (1962). (13) R. Huisagen and H. Brade, Chem. Ber., 90,1432 (1957). (14) A. R. Goldfarb. A. Mele, and N. Gutstein, J. Amer. Chem. Soc., 77,6194 (1955). (15) D. L. Hunston and I. M. Klotz. J . Phvs. Chem., 75, 2123 (1971). (16) G. Charlot and B. Trimillon, “Chemical Reactions in Solvents and Melts,” translated by P. J. J. Harvey, Pergamon Press, New York, N.Y., 1969,p 83. (17) H. B. Bull, K. Breese, G. L. Ferguson, and C. A. Swenson, Arch. Biochem. Biophys., 104,297 (1964). ~
HZ(S) J _ H+(S)
+ Z-6)
(20)
and the corresponding acid ionization equilibrium constant expression K Hz
=
CHCZ(Yh H Z ) ’/ CHZ
(21)
An equation that allows for both co-solvent acidity and cosolvent basicity (Equations 7 and 20) is
+
+
(KQ/i)6= ( K U / i ) c m CHZ[KHZ* ( K Q ~ i ) ~ o r r / K ~(22) 2z*]
RESULTS AND DISCUSSION Tables I, 11, and I11 contain “apparent” ionization constants p(Kuil)e for water in aqueous urea, N-methylacetamide, and dimethylsulfoxide, respectively. We do not give p(K,,J6 values for water ionization in aqueous N-methylformamide because potential readings in Cell B for this solvent system were unstable and not reproducible. In Table IV we list ~ ( K H zand ) p ( K ~ , z values ) that refer to acid dissociation of HZ(aq) and H2Z+(aq)as derived from the
method described previously ( 2 ) and from Equations 12-15. We also give corresponding pK, values from the literature. Our value for p ( K ~ , zfor ) aqueous protonated urea is in excellent agreement with results of previous investigations. Our p ( K ~ , z )values for aqueous protonated N-methylacetamide and N-methylformamide are also in good agreement with results of previous work. We also note that, according to Equations 19 and 22, the limiting slope of a plot of (KQ& 6s. C H Z leads top[KHZ 1.0 x 10-14/KH2Z]= 13.9 (ho.1) for aqueous urea, in good agreement with ~ [ K H z 1.0 x KHZ] = 13.8 (*o.l) from the K H Zand K H ~values Z in Table IV for aqueous urea. Dimethylsulfoxide was found to be neither appreciably acidic ( ~ K H>z 16) nor basic ( ~ K H ,
