J . Phys. Chem. 1986, 90, 3213-3217
3213
STATISTICAL MECHANICS AND THERMODYNAMICS Temperature Dependence of the Equilibrium CH,(OH), 4- HS03- = CH,(OH)S03in Aqueous Solution
+ H20
U. Deister, R. Neeb, Institut fur Anorganische und Analytische Chemie, Johannes-Gutenberg- Uniuersitat, Mainz. F.R.G.
G . Helas, and P. Warneck* Max-Planck-Institut fur Chemie, Mainz, F.R.G. (Received: July 25, 1985; In Final Form: February 25, 1986)
Ultraviolet absorption spectrometry was used to measure concentrations of bisulfite in thermal equilibrium with formaldehyde and hydroxymethanesulfonatein deaerated, argon-saturated aqueous solutions. The equilibrium constant of the title reaction was determined as a function of temperature in the range 288-318 K for pH values of 5-6, and at 298 K as a function of pH in the range 4.1-9.7. The temperature dependence (at pH 5-6) is represented by log 1/Kla = (2854 59)/T- (3.0 i 0.2) which leads to values for the reaction enthalpy and entropy of (-54.60 1.10) kJ/mol and (57.6 & 3.7) J/(mol K), respectively. The pH dependence of the equilibrium is shown to result from the equilibrium between sulfite and bisulfite. Finally, the decomposition of hydroxymethanesulfonate was studied at 25 O C . The effective rate coefficient is 1.1 X s-I at pH 5.6. The value is compared with other recent data.
*
Introduction The interaction of formaldehyde and sulfite or bisulfite in aqueous solution leads to the formation of an addition compound whose structure was identified by Raschig and Prahl’ as that of hydroxymethanesulfonate (HMS). At near-ambient temperatures aqueous formaldehyde occurs largely in the form of a diol. The reaction may be written in two ways H2C(OH),
+ HS03- = CH2(0H)SO3- + HzO +
(la)
H,C(OH), S032-= C H 2 ( 0 H ) S 0 3 - + OH(Ib) depending on whether one starts with sulfite or bisulfite. At equilibrium the two reactions are equivalent, because one can derive the former by adding to the latter the reaction HS03OH- = SO?- HzO. Reaction l b shows most directly, however, that the equilibrium is pH-dependent. In the pH range 3-7, where HS03- is the dominant sulfur(1V) species, the adduct H M S is quite stable, whereas raising the pH to values well above 7 causes the equilibrium to shift to the left and H M S decomposes. Owing to this behavior, reaction 1 is widely used in analytical procedures to determine either S(1V) or formaldehyde, or b ~ t h . ~In, ~the following considerations of the equilibrium 1 we denote by S(1V) the sum of all species which derive from HzSO3, namely S032-, HS03-, S2O5’-, and H$03 itself (or physically dissolved SOz) but not HMS. The term “total S(1V)” is used if H M S is to be included. C H 2 ( 0 H ) S 0 3 -is the dominant form of H M S in the pH range considered here.4 The possible importance of reaction 1 in atmospheric chemistry has recently been recogni~ed.~’The formation of H M S enhances the scavenging of SOz (and formaldehyde) by the water droplets
+
+
(1) Raschig, F.; Prahl, W. Liebigs Ann. Chem. 1926, 448, 265-3 12. (2) Dasgupta, P. K.; DeCesare, K.; Ullrey, J. C. Anal. Chem. 1980, 52, 1912-22. (3) Walker, J. F. Formaldehyde; Krieger: Huntington, NY, 1975. (4) Sorensen, P. E.; Andersen, V. S. Acta Chem. Scand. 1970, 24, 1301-06. (5) Warneck, P.; Klippel, W.; Moortgat, G. K. Ber. Bunsenges. Phys. Chem. 1978,82, 1136-42. (6) Munger, J. W.; Jacob, D. J.; Waldman, J. M.; Hoffmann, M. R. J . Geophys. Res. 1983,88, 5109-21. Munger, J. W.; Jacob, D. J.; Hoffmann, M. R. J . Atmos. Chem. 1984, I , 335-59. (7) Richards, L. W.; Anderson, J . A.; Blumenthal, D. L.; McDonald, J. A,; Kok, G. L.; Lazrus, A. L. Atmos. Enuiron. 1983, 17, 911-14.
0022-3654/86/2090-3213$01.50/0
present in clouds, thereby increasing the rate of wet deposition of sulfur(1V) over that taking place in the absence of formaldehyde. To assess the magnitude of the effect requires a knowledge of the equilibrium constant for reaction 1 which we define here by K1 = [HMS] / [HCHO] [S(IV)]
(A) A value for the inverse constant 1/K, was originally reported by Kerp.8 H e prepared the sodium salt of H M S and titrated with iodine the amount of S(1V) being present in equilibrium with HMS, assuming that the dissociation rate of the compound is slow, and obtained l/K1 = 1.2 X lo-’ M. Donally9 later reported a similar value. Recently, Dasgupta et aL2 redetermined the equilibrium concentration of S(1V) by means of optical absorption in the ultraviolet spectral region. Working with phosphate buffers to adjust the pH they found l/KI values of 1.17 X lo-* and 2.53 X when the pH equalled 5 and 6, respectively. These results are by 2 orders of magnitude greater than the earlier.ones, raising doubts about the applicability of the titration procedure. In order to resolve the discrepancy we have reinvestigated the reaction system, again by means of spectrophotometry to measure S(1V) concentrations, but working without buffers to preclude possible perturbations. Our results have confirmed the older data. In addition, we were able to study the temperature dependence of the equilibrium which led to a determination of the heat and entropy of the reaction. Experimental Procedures The majority of experiments were conducted with slightly acidic solutions which attained pH values between 5 and 6. The dominant anion then is HS03-. The equilibrium constants for the reactions H2SO3 = HS03- + H+
K2 = 1.7 X
(2)
HS03- = S03z- + H+
K3 = 6.4
(3)
2HS03- = SzO:-
+ H20
X
K4 = 7.2 x
(4)
(8) Kerp, W. Arbeitsberichfe Kaiserliches Gesiindheitsamt 1904, 21, 180-225. (9) Donally, L. H. Ind. Eng. Chem. Anal. Ed. 1933, 5 , 91-92.
0 1986 American Chemical Society
3214 The Journal of Physical Chemistry, Vol. 90, No. 14, 1986
Deister et al.
200
2 20
2LO
-
A/nm Figure 1. Absorption spectra of SO?- and HSOC in aqueous solution at temperatures of 15, 25, 35, and 45 OC.
are known.lOJ1 With the values given (for 25 "C) one finds that are the concentrations of H2S03are negligible and those of SO-: 0.6% of total S(1V) at pH 5 and 6.4% at pH 6. The S20j2concentration rises with the square of the HS03- concentration. The former becomes negligible compared with the latter in solutions containing less than 0.05 M of S(IV). Total S(IV) concentrations employed including sulfur bound to H M S were kept at or below 0.02 M, and HS03- concentrations in equilibrium with M. H M S were observed to be less than 2 X Absorbances of the solutions were measured with a double-beam spectrophotometer. Two identical cylindrical quartz cells of 5 cm length were employed. One contained the solution under study, the other a blank solution. Both cells were provided with jackets through which a thermostated fluid was circulated in order to maintain a constant temperature. The filling ports of the cells were closed with stoppers and the gas volume above the solution was minimized. This prevented losses of sulfur(1V) from the solution. The instrument was adjusted to transmit a wavelength of 205 nm which is close to the lower limit of the accessible spectral region. The resolution was 2 nm at half-width. Hydroxymethanesulfonate shows no noticeable absorption at this wavelength when the absorption of HSO, is suppressed by excess HCHO. We estimate the absorption coefficient for H M S to be 10.5cm M-' at 205 nm. The absorption spectra for HS03- and SO:- are shown in Figure 1. The absorption coefficient for SO:at 205 nm is by a factor of 4 higher than that for HS03-. In determining the concentration of HS03- it thus is necessary to correct for the contribution of S032-to the total absorbance. The correction was made on the basis of the known equilibrium constant for reaction 3 as a function of temperature and the measured values of pH and temperature. The correction is minor at pH 5, more substantial but still tolerably small at pH 6. The slight temperature dependence of the absorption coefficients apparent from Figure 1 also was taken into account. Except for the short periods during which measurements were made, the light beam entering the cuvette compartment of the spectrophotometer was blocked in order to prevent any photolysis of the solutions. Trial experiments established that at small concentrations HSOl- was unstable in normal, aerated solutions regardless of whether formaldehyde was added or not. The effect must be ascribed to the well-known autoxidation of S(IV) in the presence of oxygen because the stability of HS03- was greatly improved when oxygen was eliminated from the solutions. Accordingly, the measurements were performed with deaerated, argon-saturated solutions prepared with deionized, doubly distilled water. New solutions were made up every day. Sodium bisulfite solutions with known S(1V) concentrations, needed for the calibration of the spectrophotometer, were prepared from Na2S205(Merck). These solutions attained a pH of 5-6. A linear relationship was observed (10) Wagman, D. D.; Evans, W. H.; Parker, V. B.; Halow, I.; Bailey, S. M. Schumm, R. H. 'Selected Values of Chemical Thermodynamic Properties"; NBS Note 1968, 270-3. (11) Maahs, H. G.AGU Geophys. Monogr. 1982, 26, 187-195.
0
1
1
1
l
i
I
l
I
I
I
I
I
I
I
I
l
.
75
L5
15
t/min Figure 2. Approach of reaction 1 to equilibrium for two different initial experimental conditions: (a) starting with a pure sodium hydroxymethanesulfonate solution; (b) starting with a solution containing an equimolar mixture of formaldehyde and bisulfite. The total S(IV) conM in both cases. centrations were 1 X
TABLE I: Equilibrium Concentrations of Bisulfite in Aqueous Solutions of Hydroxymetbanesdfonate at 15 OC and the Corresponding Values for the Equilibrium ConstanP [HSO,-],, l/Kla, lo-' Kl,, lo6 ~CH2(0H)SO3-10, mol/L pH mol/L mol/L L/mol 5 x 10-3
5.83 f 0.04
8 x 104
5.89 f 0.06
1 x 10-2
5.96 f 0.04
0.015
6.0 f 0.02
0.02
6.1 f 0.02
2.65 2.5 2.45 2.45 2.65 3.7 3.2 3.1 3.22 2.95 3.95 3.52 3.6 3.52 3.4 3.7 4.4 4.35 5.25 5.5
1.41 1.26 1.21 1.21 1.41 1.72, 1.29 1.21 1.3 I .09 1.57, 1.24 1.3 1.24 1.16 1.37 1.29 1.27 1.38 1.52
7.09 7.96 8.29 8.29 7.09 5.81* 7.78 8.29 7.68 9.15 6.38* 8.04 7.69 8.04 8.62 7.28 7.73 7.90 7.24 6.59
a Values indicated with an asterisk are outliers according to Shapiro-Wilk's test16 and were not used in averaging. Average: l / K l a = (1.28 f 0.1) X lo-' mol/L; KIa = (7.82 f 0.62) X IO6 L/mol.
for the rise of (corrected) absorbance with the concentration of HS03- in the range 2 X M. Sodium hydroxymethanesulfonate (Aldrich) was recrystallized from an ethanol/water mixture and then dried at 80 O C . Ion chromatography2,12established the substance to be at least 99% pure. Formaldehyde solutions were obtained by diluting a 38% stock solution (Merck) which contained an additional 10% of methanol as stabilizer. The formaldehyde content of the dilute solution was determined with the analytical procedure described by Nash.13 Results In the pH region 5-6 it took 15-20 min for reaction 1 to reach equilibrium. Figure 2 illustrates the approach to equilibrium for two initial conditions. In one run the solution contained initially an equimolar mixture of formaldehyde and bisulfite, and in the other run the solution was prepared from pure hydroxymethanesulfonate. The total S(1V) concentration was the same in both cases. As Figure 2 shows, the concentrations of HS03observed in the two experiments did not attain the same final level, contrary to expectation. The first procedure generally gave lower HS03- concentrations at equilibrium than the second, indicating (12) Dasgupta, P. K. Atmos. Environ. 1982, 16, 1265-68. (13) Nash, T. Biochem. J . 1953, 55, 416-21.
The Journal of Physical Chemistry, Vol. 90, No. 14, 1986 3215
Interaction of Formaldehyde and Bisulfite TABLE 11: Equilibrium Concentrations of Bisulfite in Aqueous Solutions of Hydroxymethanesulfonate at 25 OC and the Corresponding Values for the Equilibrium ConstanP [CH2(OH)SOCIo, [HS03-],, l/Kla, Kl,, lo6 pH mol/L mol/L L/mol mol/L 5.7 f 0.02 3.1 3.23 3.1 3 x 10-3 3.13 3.19 3.05 2.85 2.73 3.65 2.9 3.2 3.44 5 x 10-3 5.7 f 0.02 3.8 2.91 3.44 3.6 2.61 3.83 3.5 2.47 4.05 3.6 2.61 3.83 8 x 10-3 5.78 f 0.05 4.7 2.78 3.6 4.55 2.6 3.84 4.7 2.78 3.6 4.55 2.6 3.84 1 x 10-2 5.83 f 0.09 5.05 2.56 3.9 5.35 2.88 3.48 5.2 2.71 3.68 5.1 2.61 3.83
'Values indicated with an asterisk are outliers according to Shapiro-Wilk's testI6 and were not used in averaging. Average: l/K,, = mol/L; K,, = (3.61 f 0.32) X lo6 L/rnol. (2.75 f 0.21) X TABLE 111: Equilibrium Concentrations of Bisulfite in Aqueous Solutions of Hydroxymethanesulfonate at 35 OC and the Corresponding Values for the Equilibrium Constant'
2 x 10-3
5.5 f 0.05
3 x 10-3
5.6 f 0.03
5 x 10-3
5.6 f 0.07
8 x 10-3
5.65 f 0.05
1 x 10-2
5.55 & 0.07
3.2 3.3 3.7 3.5 4.25 4.2 5.0 5.05 4.9 4.8 5.5 6.35 5.9 6.85 7.05 7.05 6.75 7.05 7.4
5.2 5.52 7.19* 6.22 6.11 5.97 5.05 5.15 4.85 4.65 6.12 5.08 4.39* 5.91 5.01 5.01 4.59 5.01 5.52
TABLE IV: Equilibrium Concentrations of Bisulfite in Aqueous Solutions of Hydroxymethanesulfonate at 45 OC and the Corresponding Values for the Equilibrium ConstanP [CH2(0H)S03-10? mol/L
pH
2 x 10-3
5.6 f 0.03
3 x 10-3 5 x 10-3
5.53 f 0.02 5.61 f 0.05
8 x 10-3
5.61 f 0.02
1 x 10-2
5.6 f 0.05
[HSO3-1,, lo-' mol/L
1/K18, 10" mol/L
KI,, 10' L/rnol
4.75 5.05 5.25 5.8 7.45 7.4 7.45 9.15 9.3 10.15 10.3 10.53 11.0
1.15 1.31 1.44* 1.14 1.13 1.11 1.13 1.06 1.09 1.04 1.07 1.12 1.22
8.66 7.66 7.09* 8.75 8.89 9.0 8.89 9.45 9.14 9.62 9.34 8.9 8.17
'Values indicated with an asterisk are outliers according to Shapiro-Wilk's testI6 and were not used in averaging. Average: l / K l a = (1.13 f 0.07) X lod mol/L; K1, = (8.87 f 0.54) X lo5 L/mol. ,
FORMALDEHYOE
-I
l
I
(
l
I
,
BENZALDEHYDE STEWARD 8 DONALLV
log Kid
1.92 1.81 1.39* 1.61 1.64 1.68 1.98 1.94 2.06 2.15 1.63 1.97 2.28* 1.69 2.0 2.0 2.18 2.0 1.81
'Values indicated with an asterisk are outliers according to Shapiro-Wilk's test16 and were not used in averaging. Average: l/K,, = (5.35 f 0.53) X lo-' mol/L; K,, = (1.85 f 0.23) X lo6 L/rnol.
the Occurrence of S(1V) losses. In addition it was found that the data obtained in this manner were poorly reproducible whereas solutions made up from pure H M S were well-behaved. We do not know the true causes for the difficulties encountered but suspect that our formaldehyde solutions still contained a certain amount of oxidant which converted some S(1V) to sulfate. In view of the superior quality of data obtained with solutions prepared from pure H M S we naturally gave preference to this procedure in determining the equilibrium constant for reaction 1 . The results from a number of such experiments are compiled in Tables I-IV. Measurements were made at four temperatures: 15, 25, 35, and 45 "C. The tables list the equilibrium concentrations [HSOC], observed for various total S(IV) concentrations, the pH values of the solutions, and the equilibrium constants calculated from the relation
3.2
3.7
L 3.2 3.7
10-~
RECIPROCAL TEMPERATURE K-') Figure 3. van't Hoff plots of the inverse equilibrium constant for reaction la. Present results are shown on the left; results for the equivalent reaction of bisulfite with benzaldehyde, taken from Stewart and Donally,15 are shown on the right for comparison to demonstrate that the regression lines have similar slopes.
strength effects are negligible in the concentration range used and it provides further justification for the use of reaction 1 to describe the chemical system under study. It is then possible to average over all individual values obtained for the equilibrium constants at each temperature. The results are given in the tables and they are plotted in Figure 3 on a semilog scale vs. 1 / T . The four data points are found to fall on a straight line as expected. Linear regression analysis yields log ( l / K I a ) = d(28.54 f 5 8 . 9 ) / T (3.01 f 0.19)
+
The equilibrium constant may also be expressed in terms of the enthalpy AH, and the entropy ASR of the reaction In ( l / K L a )= -AHR/RT aR/R
+
(B)
where R = 8.313 J/(mol K) and the chemical thermodynamic properties refer to a hypothetical ideal solution in unit molarity concentration. By comparison of both expressions one finds (with In K = (In 10) log K = 2.303 log K ) AH, = 54.60 f 1.10 kJ/mol (AS', = 57.6 f 3.7 J/(mol K))
where (HMS)o is the initial concentration of hydroxymethanesulfonate. Note that the values derived for the equilibrium constants are independent of total S(1V) concentration. This shows that ionic
The statistical scatter of the data has a magnitude similar to the sum of errors estimated to result from variations in temperature, preparation of solutions, and uncertainties in calibrating and reading the absorbances.
1/Kla = [Hso,-I?/([HMSIo - [HSO3-Ic)
3216 The Journal of Physical Chemistry, Vol. 90, No. 14, 1986
Deister et al.
TABLE V: Concentrations of HS03- Ions in Equilibrium with Hydroxymethanesulfonate,in the Presence of Methanol
[CH~(OH)SO~-IO,T, mol/L OC 5 x 10-3 15
(&0.05)
Oo
1.2 X IO-’”
5.85 5.85 5.62 5.64 5.95 5.90 5.75 5.60
2.5 3.6 5.1 7.4 3.6 5.2 7.1 10.5
2.4 3.8 5.2 7.1 3.5 5.3 7.2 10.6
25 35 45 15 25 35 45
1 x 10-2
[HSO,-],, lo-’ mol/L
PH
2.5 X 2.4 3.8 5.1 7.6 3.6 5.2 7.6 10.1
i
25’C 0
m
I I
Methanol concentrations, in mol/L. l
,
~
,
01
l
,
l
I
l
7 log
Kl
5
1 1
3
5
9
7 PH
Figure 4. pH dependence of K,. Upper set of data shows the present results; lower set of data was taken from the tables of Stewart and D~nally’~ to show that the pH dependence of the equilibrium constant for the reaction between S(1V) and benzaldehyde is similar. The solid lines were calculated according to the procedure described in the Discussion section. The observation that HS03- equilibrium concentrations in solutions prepared from formaldehyde and bisulfite are lower than those in H M S solutions suggested the possibility that the presence of methanol might interfere with reaction 1. Accordingly, we carried out a number of experiments in which methanol was added to solutions of hydroxymethanesulfonate. The results are shown in Table V. There is no indication for perturbances of the equilibrium in solutions containing methanol/formaldehyde molar ratios of up to unity. The pH dependence of the equilibrium constant was investigated at 25 O C by adding small amounts of either hydrochloric acid or sodium hydroxide to solutions of HMS, keeping its concentrations at M. The relative contributions of HS03- and to the total absorption a t 205 nm were determined from the measured pH and the known equilibrium constants for reaction 2. The results are shown in Figure 4 where the equilibrium constant for reaction 1 is now defined in terms of S(1V) as in eq A. In the pH region 4-6, where HSO; is the dominant ion, the values are independent of pH. In the alkaline pH region the values decline with increasing pH because of decreasing HS03- concentrations. This behavior will be discussed further below. Finally, we report an estimate for the rate coefficients associated with reaction 1. This was determined in H M S solutions by following the rise of HSO; concentration as a function of time until equilibrium was reached, as shown in Figure 5. The rate coefficient for the dissociation step was calculated from the expression Xe
k-, = ( 2 a - x e ) f In
ax,
I/
+ x ( a - x,) a(xe - X)
(c)
which one obtains by integrating the kinetic equations for the decomposition of HMS.I4 Here, x and x, denote the momentary
I
I
I
0 10 20 t / rnin Figure 5. Rise of bisulfite concentration resulting from the dissociation of hydroxymethanesulfonate in a 8 X lo-’ M solution at pH 5.6. Points represent measurements. The solid line is calculated with a rate coefs-’ and K , , = 2.75 X IO-’ M. ficient k-, = 1 X and the final concentrations of HSO), respectively, a is the initial concentration of HMS, and t is the time after dissolving this compound in water. The rate coefficient derived in this manner for the dissociation of H M S at 25 “C and pH 5.6 is k-, = 1.1 X s-l with a statistical uncertainty of about 10%. Combining this value with that for the equilibrium constant, l/Kla = k - ] / k l = 2.75 X leads to kl = 42 M-’ s-I at 25 “C. We were unable to determine with our technique rate coefficients at higher temperatures due to the more rapid rise of HSO), concentrations after preparing the solutions. Neither was it possible to obtain reliable rate coefficients at 15 O C because of an inadequate temperature control during the preparation of the solution. We expect the temperature dependence of K1 to result primarily from the temperature dependence of k-l (dissociation), whereas that of kl (adduct formation) should be slight. It is further known that the rate of H M S decomposition increases with rising pH. This will be discussed later.
Discussion The equilibrium constant obtained for reaction 1 at 25 O C is in good accord with the earlier values of Kerp’ and Donally.8 The reasons for the grossly different values reported by Dasgupta et aL2 are not entirely obvious, but we suspect that the origin of the discrepancy lies in their use of buffers. We noticed that the addition of phosphate buffer raises the absorbance of the solution sufficiently to cause appreciable errors in determining the additional contribution of HS03- to total absorbance. Kok et al.I7 have recently determined the effective forward and reverse rate coefficients of reaction 1 at pH 4 and 5 . Their values give equilibrium constants at 25 O C of K, = 4.0 X lo6 and 3.6 X lo6 M, respectively, which are in excellent agreement with the present value (3.61 f 0.33) X lo6. Dong and Dasgupta18 also have reinvestigated the equilibrium from vapor concentrations above formaldehyde-S(1V) solutions. Their value at 20 O C is 8.5 X lo6 M which agrees reasonably well with 5.5 X lo6 M obtained by interpolation of the present data. The temperature dependence of K,is reported here for the first time. Stewart and DonallyI5 had previously studied the temperature dependence of the similar equilibrium between benzaldehyde, bisulfite, and the corresponding adduct, using the titration procedure. The results at pH 5.2, obtained in the presence of acetate buffer, are shown in Figure 3b for comparison with our own data. The slopes of the two van’t Hoff plots are almost the same, indicating similar heats of reaction. Indeed, by linear regression analysis we find AHR = 51.3 2.2 kJ/mol for the dissociation energy of the benzaldehyde-bisulfite complex versus
*
(14) See, for example: Frost, A. A,; Pearson, R. G . Kinetics ond Mechonisms, 2nd ed.; Wiley: New York, 1961; p 187. (15) Stewart, T. D.; Donally, L.H. J . Am. Chem. SOC.1932,54,3555-58. (16) Shapiro, S.S.;Wilk, A. B. Biometriko 1965, 52, 591-611. (17) Kok, G. W.; Githin, S.N.; Lazrus, A. L. J . Geophys. Res., in press. (18) Dong, S . ; Dasgupta, P. K., preprint.
J . Phys. Chem. 1986, 90, 3217-3220 54.6 kJ/mol for that of HMS. The difference in the equilibrium constants is determined by the entropy term for which we find ASR = 98.2 f 7.6 J/(mol K-I) in the case of benzaldehyde. Comparison with our value of 57.6 for the formaldehyde-bisulfite system shows that the former is greater by a factor of about 1.7. The reason presumably is steric hindrance by the larger benzene ring. The pH dependence of the equilibrium constant is obtained by combining the equilibria 2 and 3 with eq A to express the total concentration of S(1V) species in terms of the concentrations of HS03- and hydrogen ions:
+ [HS03-] + [SOj2-]
[S(IV)] = [H2SO3] = [HS03-]([H+]/K2
+ 1 + K,/[H+])
= [HS03-]/f
(D)
As before, we denote by KIa the equilibrium constant in the pH range 3-6 where HS03- is the dominant S(1V) ion. In this manner, K1 can be calculated from KIaand the prevailing hydrogen ion concentration. The results are shown in Figure 4 by the solid line. The experimental data points (at 25 "C) follow the calculated line quite closely, indicating that eq D represents the formaldehyde-S(1V) equilibrium reasonably well. Figure 4 includes a similar calculation for the equilibrium involving S(IV) and benzaldehyde. The rate constant for the decomposition of HMS as determined here is an effective rate constant for the sum of reactions l a and lb
k-1 = k-ia
+ k-,b[OH-]
Skrabal and SkrabalIg and Sorensen and Andersen4 have previously studied the decomposition of H M S in the alkaline pH range and found k-lb = 8.5 X lo3 M-' s-I each. At pH 5.6 one M so that kqb[OH-] = 3.4 X This has [OH-] = 4 X value has the same magnitude as the effective rate constant ob-
3217
served here, Ll = 1.1 X S-I, indicating that at pH 5.6 the decomposition of H M S still proceeds primarily via reaction 1b. Kok et al.,17who studied the decomposition of H M S at pH 4 and 5, reported the effective rate coefficients at 25 "C to be 4.8 X and 3.5 X 10" S-I, respectively. Their values agree within a factor of 2 with the rate coefficients expected if reaction 1 b were rate determining. If one assumes that may be ignored at pH L 4, one finds from the data given by Kok et aL17 and from our own value at pH 5.6 an average k-lb = (3.7 f 1) X lo3. This is by a factor of 2.3 lower than the values of Skrabal and SkrabalIg and of Sorensen and A n d e r ~ e n but , ~ otherwise self-consistent. Accordingly, we conclude that in the pH range greater than pH 4 reaction 1 b is dominant. If we have reported our equilibrium constants in terms of HS03-, it was mainly because this is the major S(1V) species in the pH range 3-6 and because it is the species that was measured. Boyce and HoffmannZohave studied the rate of formation of HMS from formaldehyde and S(1V) in the pH region C-3.4. They found bisulfite to be the principal reactant at pH C 2, whereas above this value sulfite had to be included as a reactant. According to their data the formation of HMS occurs at about the same rate via both channels of reaction 1 when the pH is near 2.7. In this situation, and assuming equilibrium, the equal rates should also occur for the two reverse reactions. At pH 2.7 the concentrations M. We thus estimate kla k-lb, 5 X of OH- is 5 X = 1.9 X s-l and kla = Klak-,, = 0.07 M-' s-'. Boyce and Hoffmann20 reported kla = 0.43 M-' s-' which is by a factor of 6 greater. However, Kok et al.I7 noted that their own results at pH 4 for the effective forward rate coefficient k , was by a factor of 4 lower than that of Boyce and Hoffmann20 when extrapolated from pH 3.4 to pH 4. Thus, it appears that the rate constant values of Boyce and Hoffmann near pH 3 are slightly too high. Nevertheless, the data of Boyce and Hoffmann,20 Kok et al.,17 and the present results combined now provide a consistent understanding of the formaldehyde-S(1V) system over a wide range of pH.
+
Registry No. HMS, 75-92-3; HCHO, 50-00-0; HSOC, 15181-46-1. ~~
~~
~
(20) Boyce, S. D.; Hoffmann, M. R. J . Phys. Chem. 1984,88,4740-46.
(19) Skrabal, A.; Skrabal, R. Monatsh. Chem. 1936, 69, 11-41.
Effect of Solvent upon Anlon Radical Solvation Enthalpies Gerald R. Stevenson* and Ramli Tamby Hashim Department of Chemistry, Illinois State University, Normal, Illinois 61 761 (Received: September 24, 1985; In Final Form: February 19, 1986)
A new calorimetric technique is described for the direct measurement of relative solution electron affinities. This technique involves the measurement of the heat of reaction of the solvated anion radical with a solution of Iz in the same solvent that is hosting the anion radical [A'-,Na+(solv) + 1/212(solv) A(solv) + Na+,I-(solv)]. The enthalpy of this reaction has been placed into a thermochemical cycle to yield both the enthalpy of solvation [A'-(g) + Na+(g) A'-,Na+(solv)] and the enthalpy of generation [Na(s) A(solv) A'-,Na+(solv)] of the naphthalene anion radical in several solvent systems. It was found that the solvation enthalpy only varies by about 11 kcal/mol, going from the best solvents (hexamethylphosphoramide and = -1 79 kcal/mol), which yield unassociated ions and loose ion pairs, to the poorest solvent dimethoxyethane, AHosOlv (tetrahydropyran, AHosolv = -168 kcal/mol), which hosts only very tight ion pairs. The heats of generation (AHogen) vary (AP,, = -23 kcal/mol by the same amount, but this 11 kcal/mol difference is a much more significant percentage of in hexamethylphosphoramide). The benzophenone ketyl has a heat of solvation that is almost identical with that of the naphthalene anion radical system in tetrahydrofuran. However, it has a much more exothermic generation (-22 kcal/mol as compared to -14 kcal/mol in tetrahydrofuran), which is due primarily to the larger electron affinity of benzophenone.
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Introduction The gas-phase alkali metal salts of organic anion radicals are inherently unstable relative to the metal and hydrocarbon in their standard States. For example, the heat of generation of W-Phase sodium naphthalenide from the metal and the hydrocarbon in their 0022-3654/86/2090-3217$01.50/0
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standard states can be calculated from the two heats of sublimation,' the ionization potential of Na,2 and the electron affinity (1) (a) Hicks, W. T. J . Chem. Phys. 1963, 38, 1873. (b) Cox, J. D.; Pilcher, G . Thermochemistry of Organic and Organometallic Compounds; Academic: New York, 1970.
0 1986 American Chemical Society
