2195
Ind. Eng. Chem. Res. 1991,30, 2195-2200
Kinetics of the Poly(oxymethy1ene)Glycol Formation in Aqueous Formaldehyde Solutions Hans Hasse and Gerd Maurer* Lehrstuhl fiir Technische Thermodynamik, Universitat Kaiserslautern, 6750 Kaiserslautern, Germany
The absorption of gaseous formaldehyde in water is a widely used process. In aqueous solutions formaldehyde is mainly dissolved chemically. Therefore, designing absorption equipment for formaldehyde gas requires not only the knowledge of the vapor-liquid equilibrium but also information on reaction kinetics. While reliable procedures for describing the vapor-liquid equilibrium are available, very little is known on the kinetics of the formation of formaldehyde reaction products, e.g., poly(oxymethy1ene)glycols, in aqueous solutions. In this work rate constants of the formation of poly(oxymethy1ene) glycols are determined by measuring the density changes of formaldehyde solutions after their dilution with water. The measurements cover the temperature range from 275 to 313 K at pH numbers from 1.5 to 6.5. For the interpretation of the data, a simple group contribution model for the density is combined with second-order reaction kinetics. The rate constant K strongly depends on temperature and pH. At room temperature the observed minimal value of l / k is about 8 min; a t 275 K it is 40 min. These numbers are larger than the residence time in typical absorption equipment, which demonstrates that it is crucial to consider reaction kinetics in the design. The data determined in this work allow reasonable estimates of reaction kinetic effects. The results obtained from the density measurements are compared to older, unpublished NMR spectroscopic data. Qualitative agreement is observed.
Introduction Formaldehyde is one of the most important substances of the chemical industry. Due to its high reactivity it is commonly handled in aqueous solutions, where it is predominantly dissolved chemically. The most important chemical reactions in aqueous formaldehyde solutions are the formation of methylene glycol (HO(CH20)H) CHzO + HzO + HO(CH2O)H (1) and the formation of poly(oxymethy1ene) glycols (HO(CH20),H, n 1 2 ) HO(CH2O)H + HO(CH2O)H + HO(CH2O)zH + H2O (11) HO(CHzO),H + HO(CH2O)H HO(CH20),+1H+ HzO n > 2 (111) Data on equilibrium constants of these reactions are available (see refs 1,3,4,6,8,10-15,17,19-23,25-29,31, 32, 34, 35, and 39). These chemical reactions have an important influence on the properties of aqueous formaldehyde solutions, which has to be taken into account in thermodynamic models. (See, e.g., the vapor-liquid equilibrium model for multicomponent formaldehydecontaining mixtures of Maurer (1986)and Hasse et al. (1990).) In many applications, for example, in the absorption of formaldehyde gas in water at low temperatures, reaction kinetics are a key factor for the design of equipment. Even though the importance of reaction kinetics in aqueous formaldehyde solutions has been pointed out by many authors (e.g., by Walker (1964)), data on rate constants are rather limited. Whereas much work has been devoted to methylene glycol formation (see refs 2,5, 7,9,18,27,28, 33,and 38),only a few results are available on the kinetics of poly(oxymethy1ene) glycol formation (Wadano et al., 1934;Skarbal and Leutner, 1937). These older investigations mainly demonstrate that the reaction rate of poly(oxymethy1ene)glycol formation is strongly influenced Author to whom correspondence should be addressed. 0888-5885/91/2630-2195$02.50/0
by the pH (minimum at about pH 3.5) and that poly(oxymethylene) glycol formation is much slower than methylene glycol formation (rate constants differ by about a factor 100-1000). In the present work the rate constants of poly(oxymethylene) glycol formation are determined from dependent density changes observed after the dilution of aqueous formaldehyde solutions with water. The measurements are correlated by combining a simple group contribution model for the density together with a second-order reaction kinetic model. Furthermore, unpublished nuclear magnetic resonance spectroscopic data (Muller and Nonnenmacher, 1970) are evaluated. Results from both investigations agree qualitatively.
Kinetic Model The concentration of monomeric formaldehyde in aqueous formaldehyde solutions is always very small. Therefore the formation of methylene glycol from monomeric formaldehyde and water may be disregarded in a kinetic model for the density. By introducing k, and kn*, the rate constants of the reactions leading to longer poly(oxymethy1ene) glycol chains and of the reverse reactions, respectively, and using abbreviations for the compound names, eqs I1 and I11 are rewritten: MG MG,
+ MG
e kl
MG2
+W
+ MG b, kn MG,+1 + W .
(IV)
n 12
(V)
Interpretations of NMR spectroscopic data of chemical equilibria in aqueous formaldehyde solutions (Koberstein et al., 1971;Kogan, 1979b)indicate that a single chemical equilibrium constant is sufficient to describe all reactions given by eqs IV and V. Therefore we assume for the rate constants: k, = k2 = ... = k, = ... k (1) kl* = kz* = ... =. k,* = ... = k* (2) A second-order reaction kinetic model is applied, which leads to the following set of equations: 0 1991 American Chemical Society
m
0
0
30
60
90
t I min
t,
Figure 1. Density changes after diluting an aqueous formaldehyde solution.
dXMG,/dt = ~ X M G X M G-
~*XMG,XW - ~ X M G , X M G + ~*XMG$XW (5)
- ~*XMG,XW - ~XMG,XMG+
~ X M G J =~ ~~X M G , - ~ X M G
~ * X M G , + ~ XnW> 2 (6)
The rate constants k and k* are coupled by the equilibrium constant K K = k/k* (7) The value for K is taken from Koberstein et al. (1971) to be K = 3.77. Thus, only one parameter is left in the kinetic model (either k or k*). In this work k is fitted to the data; k* is then calculated from eq 7. Equations 3-6 describe the transition of a system from an arbitrary initial state x(to) to an equilibrium state in which all derivatives with respect to time are zero. In the present work, the initial state is the situation immediately after the dilution. This initial state x(to)is calculated from the overall formaldehyde concentration in undiluted solution (using K = 3.77) together with the ratio of the mass of the undiluted formaldehyde solution to the mass of water used for dilution. A simple numerical method is then applied to calculate the time evolution of x(t) for a given reaction rate k: When x(t) is known, the derivatives with respect to time are explicitly given by eqs 3-6: dx(t)/dt = f(x(t)) (8) For discrete time steps At eq 8 leads to x(t+At) = x(t) + f(x(t))At
(9) Hence, given x(to) and 12, all x(to+iAt), i E N can be calculated.
Experimental Section Density changes after the dilution of aqueous formaldehyde solutions were measured with a high-resolution vibrating tube densimeter, type DMA 602 HT of Heraeus/Paar. The diluted aqueous formaldehyde solution was filled into the thermostated tube by a syringe. Care was taken to avoid temperature differences between the instrument and the injected solution. The density of the diluted solution was then taken as a function of time at intervals between 1 and 5 min. Aqueous formaldehyde solutions were prepared by dissolving paraformaldehyde (Merck) in water at elevated temperatures. Gas chromatographic analysis of the solutions showed only trace amounts of impurities. The pH of the undiluted formaldehyde solution was adjusted to the desired value by adding either sodium hydroxide, sulfuric acid, or formic acid. The pH of the water used for the dilution was adjusted in the same manner. The pH was measured by an AgCl/KCl electrode with an accuracy better than f0.15 pH. In a typical experiment 5
g of aqueous formaldehyde solution was diluted with about 2-5 g of water. Both masses (undiluted formaldehyde solution and water used for the dilution) were determined by weighing with an accuracy of about k0.002 g. For analyzing formaldehyde, the sodium sulfite method (cf. Walker, 1964) was applied (relative errors less than 2%). The temperature was measured with a platinum resistance thermometer with an accuracy better than f0.1 K. Figure 1 shows results of an experiment in which a moderately concentrated aqueous formaldehyde solution (fFA= 0.15 mol/mol) was diluted with water at 293 K. Measured density changes are given as a function of time. Rapid density changes are observed at the beginning, but it takes almost 2 h until constant density is reached. The difference between the initial and the fmal density is about 0.5 g/dm3, which is about 200 times the resolution of the densimeter. The observed density changes may be caused by several phenomena: Small temperature differences between the injected solution and the instrument are important only shortly after the injection. This has been proved in experiments in which water was mixed with water. They show that eff& arising from temperature differences only have to be considered in the first 5 min of the measurement. Furthermore, heats of dilution may lead to density changes. New calorimetric measurements of heats of dilution of aqueous formaldehyde solutions (Hasse, 1990) allow the estimation of these density changes. Only about 0.03 g/dm3 (5% of the total density change) might be due to the heat of dilution. Therefore, the change of density after diluting an aqueous formaldehyde solution is interpreted here solely as an effect of the chemical reactions. Measurements were carried out at temperaturea between 275 and 313 K and pH numbers between 1.5 and 6.5. Initial overall formaldehyde concentration ranged from 0.07 to 0.19 mol/mol. The ratio of the mass of undiluted formaldehyde solution to the mass of water was between 0.5 and 1.0. A complete set of the experimental results is given elsewhere (Hasse, 1990). Correlation To evaluate the experimental results, a model relating density to concentration is needed. A simple group contribution model is developed for this purpose. Aqueous fornialdehyde solutions are considered to consist of three different groups: (1) "freen water molecules (index WF); (2) water "bound" in methylene glycol or poly(oxymethylene) glycols (index WB); (3) CHzO segments in methylene glycol or poly(oxymethy1ene) glycols (index CH20). To each of these groups a constant molar volume (uWF,uWB, uCH 0)is assigned. The volume of the solution is then given by
v = nWF*UWF + nWB*UWB + nCHpO*uCHpO
(10)
Ind. Eng. Chem. Res., Vol. 30,No. 9,1991 2197 At constant temperature the change of volume with time may therefore be expressed as v(t)- v(te) = (nW*(t) - nwE.*(te))UWF+ (nWB*(t) - nWB*(te))UWB + (nCH?O*(t) - nCH20*(te))UCH20 (11) With the balances for the mole numbers of the groups ni* n c H 2 0 * ( t ) = n ~ ~ ~ o *=( tconstant J (12) nwF*(t) + nW*(t)= nm*(te)+ nWB*(te) = constant
0 Exp. pH = 4,2 k = 8,8 ,lo"
--2
c 0,2
ol I
I
0,1
ol
0
(13)
eq 11 can be rewritten as v(t) - v(t&= (nwE.*(t)- nwF*(te))(uWF- VWB)
(14)
S"
I I
t I min Figure 2. Correlation of density changes after diluting an aqueoua formaldehyde solution.
Dividing this by the true total mole number nbt and using the abbreviation AU= UWF - U(15)
100
50
a simple relation between changes in the molar volume of the solution
u = V/n,,
(16)
and changes in the mole fraction of water is obtained:
~ ( t- )~ ( t e ) (xw(t) - XW(te))AUWm An expression for the relative change in density
(17)
7
I"
10
5, \
x
1
is derived from eq 17 by converting the molar volume-u into the (specific) density p using the molecular mass M
OS 2
3
G
5
PH Figure 3. Rate constants of poly(oxymethy1ene)glycol formation obtained from density measurements.
M = &Mi i
(20)
As the total mole number does not depend on time, the molecular mass is constant and can therefore be calculated from equilibrium concentrations. Density changes after diluting aqueous formaldehyde solutions are hence interpreted here to be caused by transferring free water molecules to water bound in poly(oxymethylene) glycols. The only parameter introduced in this consideration is the difference between the molar volume of "free" and "bound" water, Au-. With eq 19 and the kinetic model described above, time-dependent density changes can be modeled. Two parameters have to be determined from experimental data: rate constant k and volume change A u w A first evaluation showed that the values obtained for A U ~ for B different temperatures, pH numbers, and ratios of the mass of the undiluted formaldehyde solution to the mass of water were always around 1.05 cm3/mol. Therefore this value (which is about 5% of the molar volume of pure water and hence in a physically reasonable order of magnitude) was adopted for all further calculations. With the fixed number for the volume change of water, AUWFB, the density measurements were evaluated to determine the rate constants k of poly(oxymethy1ene) glycol formation. For reasons given above, all densities measured within the first 5 min of an experiment were neglected. A typical result of such an evaluation is given in Figure 2. The correlation of the experimental data is almost within the experimental uncertainty. This holds for most of the measurements, including several series carried out at
Table I. Rate Constants of Poly(oxymethy1ene) Glycol Formation Obtained from Density Measurements T,K pH k , (10-3)l/s T,K pH k, (104)1/8 215.2 1.78 1.39 4.26 2.46 3.14 0.45 4.14 3.38 5.06 1.15 4.94 4.96 6.46 1.42 5.60 9.88 283.2 1.80 5.23 6.12 14.66 3.64 1.54 6.20 33.32 5.65 4.01 6.50 64.36 6.39 19.15 303.2 1.87 23.79 292.8 1.44 28.98 2.47 10.80 1.56 21.35 3.02 1.92 2.09 1.12 4.15 8.17 2.51 5.11 5.10 27.41 3.21 5.08 313.1 1.93 63.15 3.42 3.11 2.41 23.02 3.56 2.61 3.01 18.73 3.15 2.40 3.92 23.14 3.85 2.09 5.02 58.13 4.15 2.14 5.01 11.36
varying initial formaldehyde concentrations and mass ratios. Results The rate constants determined from the density measurements at temperatures between 275 and 313 K in the pH range from 1.5 to 6.5are given in Figure 3 (numerical values, cf. Table I). The rate constants strongly depend on temperature and pH. The observed minimum of the reaction rate at pH 3-4 is in good agreement with the observations of Wadano et al. (1934)and Skarbal and
2198 Ind. Eng. Chem. Res., Vol. 30, No. 9, 1991
444 T s 310 K pH = 5
100
II,, = 0,t mol I mol mFALI mDtO= 1I 9
50
c
v)
5
10
- 5
x
1
0.5 1 min
Figure 4. Influence of temperature on the rate constants of poly(oxymethylene) glycol formation obtained from density measurements (nonlinear scale of the temperature axis, corresponding to a plot of 1/77.
3 min
5 min 30s
Figure 6. H NMR spectra taken after the dilution of formaldehyde/D20 solutions with D20. Mo, signal of protons in DO(CH2O)D;E, signal of pro to^^ in DO(CH,O),D, n 1.2 (CHpO ~ r o u p e at the end of chain); Mi, signal of protons in DO(CH,O),D, n > 2 (CH,O groups not at the end of the chain);OH, signal of protons in OH groups (trace amounts of water).
creases as the average chain length of the poly(oxymethylene) glycol decreases. The spectral dispersion of the 60-MHz spectrometer used for the investigations is comparatively low. Thia gives rise to problems with the quantitative interpretation of the data, 90 peak heights had to be used instead of peak areas
ODG5
0.030
I 60
30
I
90
tlmin Figure 6. Time dependence of mole fractions of the most important formaldehyde reaction products calculated for the dilution experiment shown in Figure 1 (k = 2.46 X l/s).
Leutner (1937). The temperature dependence of the rate constants for fixed pH values is given in Figure 4. The activation energy of the poly(oxymethy1ene) glycol formation is approximately 75 kJ/mol for all pH values. Figures 3 and 4 show that consistent and only moderately scattaring data are obtained. Figure 5 shows mole fractions of the most important formaldehyde reaction products as a function of time after dilution, calculated for the experiment shown in Figure 1.
NMR Spectroscopic Investigations NMR spectroscopy has successfully been applied in the past decades to the investigation of chemical equilibria in formaldehyde solutions (see refs 10-12,15,17,19,21,23, 25,26,31, and 32). However, no NMR spectroscopic data on reaction kinetics in formaldehyde solutions have been published. In the frame of the present work unpublished NMR spectroscopic measurements of DEGUSSA (Miiuer and Nonnenmacher, 1970) on reaction kinetics in formaldehyde/D20 solutions were evaluated. In these measurements formaldehyde/D20solutions were diluted with D20. The diluted solutions were introduced in a Varian A 60 A spectrometer and H NMR spectra were taken at intervals of several minutes. Figure 6 shows typical results. The assignment of the peaks to protons bound in different groups is given in the caption. It can be seen that, after the dilution, the concentration of methylene glycol in-
eqs 21-23 can be reformulated: [Mo = xMG/s [E = ' i i M G i
s i-2
where the abbreviation s stands for (D
To obtain rate constants from NMR data, the kinetic model described above was applied. For the fit of calculated to experimental data, the average molecular mass of the formaldehyde containing molecules was used
As no reliable information on the overall formaldehyde concentration before the dilution and the ratio of the maas of the undiluted solution to the mass of D20 was available, these quantities had to be estimated from NMR spectra taken before and after the dilution (for details see Haese (1990)). The achieved correlation of the experimental data is generally good, as can be seen from the typical example shown in Figure 7. The results of the determination of the rate constants are shown in Figure 8 (numerical values, cf. Table 11). They scatter more than the resulta of the
Ind. Eng. Chem. Res., Vol. 30, No. 9, 1991 2199 IO0 70 50 40
70
1 265
30 . ;
F
T20
60 55
9 \
0
5
10
15
20
t I min
Figure 7. Correlation of NMR measurements. Average molecular mass of the formaldehyde-containingmolecules in formaldehyde/ D20solutions after dilution. Correlation of NMR measurements.
.x 10
I 5
I "'.,,k! 1
Exp.: 0 3:3 K Exp.: 0 310 K
4
Table 11. Rate Constants of Poly(oxymethy1ene)Glycol Formation Obtained from NMR Measurements T.K DH k. (lO-*)l/a T,K DH k, (103l/s 310.1
2.33 2.38 2.81 2.81 3.41 3.50 3.62 4.20 4.33 4.90 4.96
16.2 12.3 5.6 5.0 4.2 4.0 3.8 6.0 6.0 25.0 29.0
323.0
5.08 6.49 2.81 2.87 3.41 3.50 4.20 4.33 4.90 4.96
16.1 51.6 13.9 15.0 9.4 10.0 20.1 19.0 33.8 63.6
density measurements. Again a minimum of the reaction rate at pH 3-4 is observed. The activation energies calculated from the NMR data range between 40 and 80 kJ/mol, which is in fair agreement with the results from the density measurements. However, the numbers for the rate constants obtained from the NMR measurements are lower than those from the density measurements by about a factor 2. The simple model used here is able to correlate the NMR data for the mean molecular weight of the formaldehyde-containing molecules, but the agreement between experimental and correlated data for three relative peak heights (cf. eqs 25-27) is not satisfactory. The application of more sophisticated models (using, e.g., chain length dependent equilibrium constants) does not seem appropriate when only relying on low-resolution NMR or density data. Thus more accurate NMR spectroscopic measurements will be needed to improve the model and reveal the reasons for the discrepancies between the density and the NMR measurements.
Conclusions High-resolution density measurements were used to determine rate constanta of chemical reactions in aqueous formaldehyde solutions. A simple group contribution model for the density and a second-order reaction kinetic model were applied for evaluating the data. The rate constants for the formation of poly(oxymethy1ene) glycols obtained from the density measurements under various conditions are consistent. NMR spectroscopy is a suitable method to check these results. Older, unpublished NMR data were evaluated in this work. The results of both investigations agree qualitatively, but further NMR measurements are needed to reveal reasons for quantitative discrepancies. Such investigations (with a 400-MHZ NMR spectrometer) are now being prepared by members of our group. The data provided in this work allow the estimation of the strong influence of the kinetics of the poly(oxymethylene) glycol formation on the absorption of gaseous
3
5
4
6
PH Figure 8. Rate constants of poly(oxymethy1ene)glycol formation obtained from NMR measurements.
formaldehyde in water at low temperatures. Acknowledgment We are indebted to DEGUSSA AG for giving us the opportunity to use unpublished NMR Spectroscopic data. We owe thanks to Prof. Dr. C. Kreiter for his helpful comments on NMR spectroscopy and to I. Hahnenstein for his assistance in performing the density measurements. Nomenclature corr = correlated E = protons bound in DO(CH20),D, n 2 2 (CH20group at the end of the chain) exp = experimental FA = formaldehyde f = operator K = chemical equilibrium constant k = rate constant of poly(oxymethy1ene) glycol formation (reaction leading to longer chains) k* = rate constant of poly(oxymethy1ene) glycol formation (reaction leading to shorter chains) M = average molecular mass MpoVc,= average molecular mass of the formaldehyde-containing molecules in a formaldehyde/D20 solution Mi = molecular mass of component i MG = methylene glycol MG, = poly(oxymethy1ene) glycol with n CH20 groups Mi = protons bound in DO(CH20),D, n > 2 (CH2Ogroups not at the end of the chain) Mo = protons bound in DO(CH,O)D mw = mass of water used for the dilution mbO = mass of D20 used for the dilution mFAL= mass of undiluted formaldehyde solution N = set of natural numbers NMR = nuclear magnetic resonance ni = mole number of component i nbt = total number of moles ni* = mole number of group i p i = height of signal of protons bound in group i T = temperature t = time At = time interval t , = time at the end of the experiment V = volume u = molar volume AuWe = difference between the molar volume of "free" and 'bound" water W = water xi = true mole fraction of component i
2200 Ind. Eng. Chem. Res., Vol. 30,No. 9,1991 x = vector including the mole fractions of all components
Z F =~ overall formaldehyde mole fraction before dilution Greek Symbols
si = relative peak height of the signal of protons bound in p
group i = specific density
Subscripts E = protons bound in DO(CH20),D, n 1 2 (CH20 group at the end of the chain) FA = formaldehyde MG = methylene glycol MG, = poly(oxymethy1ene glycol) with n CHzO groups M i = protons bound in DO(CH,O),D, n > 2 (CH20groups not at the end of the chain) Mo = protons bound in DO(CH,O)D W = water WB = water 'bound" WF = water 'freen Registry No. CH20, 50-00-0; HzO, 7732-18-5;(OCH,),, 9002-81-7.
Literature Cited (1) Bell, R. P. The Reversible Hydration of Carbonyl Compounds. Adu. Phys. Org. Chem. 1966,4,1-29. (2) Bell, R.P.; Evans, P. G. Kinetics of the Dehydration of Meth1966, A291, ylene Glycol in Aqueous Solution. Roc. R. SOC. 297-323. (3) Bezzi, S.;Iliceto, A. Sul sistema aqua formaldeide I: Constituzione delle soluzioni acquose di formaldeide. Chim. Znd. 1951, 33,212-217. (4) Bezzi, S.;Dallaporta, N.; Giacometti, G.; Iliceto, A. Cinetica di formazione e scissione di macromolecole lineari ed equilibri fra monomer0 e suoi polimeri. Gazz. Chim. Ztal. 1951,81,915-932. (5) Bieber, R.; Triimpler, G. fTber die polarographische Reduktion der aliphatischen Aldehyde I: Das polarographische Verhalten von Formaldehyd. Helu. Chim. Acta 1947a,30,706-733. (6) Bieber, R.; Triimpler, G. Angeniiherte spektrographische Bestimmung der Hydratationsgleichgewichtakonstanten wbsriger Formaldehydlbungen. Helu. Chim. Acta 1947b,30,1860-1865. (7) Boyce, S.D.;Hoffmann, M. R. Kinetics and Mechanism of the Formation of Hydroxymethanesulfonic Acid at Low pH. J. Phys. Chem. 1984,88,4740-4746. (8) Bryant, M.; Thompson, J. B. Chemical Thermodynamics of Polymerization of Formaldehyde in an Aqueous Environment. J. Polym. Sci. Part A-1 1971,9,2523-2540. (9) Burnett, M. G. The Mechanism of the Formaldehyde Clock Reaction. J. Chem. Educ. 1982,59, 160-162. (10) Dankelman, W.; Daemen, J. M. Gas Chromatographic and Nuclear Magnetic Resonance Determination of Linear Formaldehyde Oligomers in Formalin. Anal. Chem. 1976,48,401-404. (11) Fiala, Z.;Navratil, M. NMR Study of Water-Methanol Solutions of Formaldehyde. Collect. Czech. Chem. Commun. 1974,39, 2200-2205. (12) Gorrie, T. M.; Raman, S. K.; Rouette, H. K.; Zollinger, H. NMR-Investigations of the Formaldehyde Addition and Oligomerisation Equilibria in the System Formaldehyde/Water/ Acetic Acid/Hydrochloric Acid. Helv. Chim. Acta 1973,56, 175-195. (13) Gruen, L. C.;McTigue, P. T. Hydration Equilibira of Aliphatic Aldehydes in H,O and DzO. J. Chem. SOC.London 1963, 5217-5229. (14) Hall, M. W.; Piret, E. L. Distillation Principles of Formaldehyde Solutions. Ind. Eng. Chem. 1949,41,1277-1286. (15) Hasee, H. Dampf-Flllssigkeits-Gleichgewichte,Enthalpien und Reaktionskinetik in formaldehydhaltigen Mischungen. Ph.D. Dissertation, UniversitHt Kaiserslautern, 1990. (16) Hasse, H.; Hahnenstein, I.; Maurer, G. Revised Vapor-Liquid Equilibrium Model for Multicomponent Formaldehyde Mixtures. AZChE J. 1990,36,1807-1814.
(17) Hellin, M.; Delmau, J.; Cowemant, F. Etude par rbonance magnhtique nucleaire dea Ctata du formol en solution aquewe, en I'absence et en la presence d'acide sulfurique. Bull. SOC. Chim. Fr. 1967,5,3355-3360. (18) Le Hdnaff, P. Sur la vitesse de la deshydratation du m6thykne-glycol en formald6hyde. C. R. Acad. Sci. Paris 1963, 256, 1752-1754. (19) Ihashi,Y.;Sawa, K.; Morita, S. Studies of the Dissolved Formaldehyde in Deuterium Oxide by the High Resolution Proton Magnetic Resonance. Kogyo Kagaku Zasshi 1965,68,1427-1430. (20) Iliceto, A. Sul sistema acqua-formaldeide. Nota VI. Equilibri delle fasi liquida e gassosa. Gazz. Chim. Ztal. 1954,84,536-552. (21) Koberstein, E.;Miiller, K. P.; Nonnenmacher, G. Molekulargewichtsverteilung von Formaldehyd in wbsrigen h u n g e n . Ber. Bunsen-Ges. Phys. Chem. 1971,75,549-553. (22) Kogan, L. V. State of the Vapor Phase above Solutions of Formaldehyde in Water and Methanol. Zh. Prikl. Khim. 1979% 52,2722-2725. (23) Kogan, L. V. NMR-Study of the State of Aqueous Methanol Solutions of Formaldehyde. Zh. Prikl. Khim. 197913, 52, 2725-2730. (24) Maurer, G.Vapor-Liquid Equilibrium of Formaldehyde- and Water-Containing Multicomponent Mixtures. AIChE J. 1986,32, 932-948. (25) Moedritzer, K.; Van Wazer, J. R. Equilibria between Cyclic and Linear Molecules in Aqueous Formaldehyde. J. Phys. Chem. 1966,70, 2025-2029. (26) Miiller, K. P.; Nonnenmacher, G. "Molekulargewichtaverteilung, Polymerisations-, Depolymerisationskinetik, Dampfdruck und Destillationsverhalten wbsriger Formaldehydlbungen"; Internal Report; DEGUSSA AG, Fachbereich Chemie Physikalisch Wolfgang bei Hanau, 1970. (27) Rudnev, A. V.;Kalyazin, E. P.; Kalugin, K. S.; Kovalev, G. V. Formaldehyde. 11. Kinetics of the Desolvation of Formaldehyde in Aqueous and Methanolic Solutions. Russ. J.Phys. Chem. 1977, 51, 1519-1521. (28) Schecker, H. G.; Schulz, G. Untersuchungen zur Hydratationskinetik von Formaldehyd in wbsriger Lbung. 2.Phys. Chem. 1965,65,221-224. (29) Siling, M. I.; Akselrod, B. Ya. Spectrophotometric Determination of Equilibrium Constanta of the Hydration and Protonation of Formaldehyde. Russ. 4. Phys. Chem. 1968, 42, 1479-1482. (30) Skarbal, A.; Leutner, R. Uber den Depolymerisierungsvorgang in Formaldehydlbungen. Oesterr. Chem. 2. 1937,40,235-236. (31) Skell, P.;Suhr, H. Untersuchungen an wbsrigen Formaldehydlosungen. Chem. Ber. 1961,94,3317-3327. (32) Slomin, I. Ya.; Aleksejeva, S.G.; Akselrod, B. Ya.; Urman, Ya. G. W N M R Spectroscopic Investigation of the Molecular Weight Distribution of Polyoxymethylene Glycols in Aqueous Formaldehyde Solutions. Vysokomol. Soedin., Ser. B 1976, 17, 919-922. (33) Sutton, H. C.; Downes, T. M. Rate of Hydration of Formaldehyde in Aqueous Solution. J. Chem. SOC.,Chem. Commun. 1972,1-2. (34) Tsuge, M.; Miyabayashi, T.; Tanaka, S. Characterization of Polymethylene Oxide Oligomers Involved in Aqueous Formaldehyde Solutions by Gel Permeation Chromatography. Nihon Kagaku Kaishi 1973,5,958-962. (35) Valenta, P. Oszillographische Strom-Spannungs-Kurven 111. Untersuchung des Formaldehyde in gepuffertem Milieu. Collect. Czech. Chem. Commun. 1960,25,853-861. (36) Wadano, M.; Trogus, C.; Hem, K. Kinetische Untersuchungen an wbsrigen Formaldehydltbungen. Chem. Ber. 1934, 67, 174-190. (37) Walker, J. F.Formaldehyde, 3rd ed.; ACS Monograph Series; Reinhold New York, 1964. (38) Warneck, P.The Formaldehyde-Sulfite Clock Reaction Revisited. J. Chem. Educ. 1989,66,334-335. (39) Zavitsas, A. A.; Coffiner, M.; Wiseman, T.; Zavitaas, L. R. The Reversible Hydration of Formaldehyde. Thermodynamic Parameters. J. Phys. Chem. 1970,74,2746-2750. Receioed for review October 31, 1990 Accepted June 4, 1991
