Znd. Eng. Chem. Res. 1994,33, 1022-1029
1022
lH- and 13C-NMR Spectroscopic Study of Chemical Equilibria in Solutions of Formaldehyde in Water, Deuterium Oxide, and Methanol Immanuel Hahnenstein,t Hans Hasse,? Cornelius G. Kreiter,t and Gerd Maurer'J Lehrstuhl fur Technische Thermodynamik and Lehrstuhl fur Anorganische Chemie, Universitht Kaiserslautern, Postfach 3049, 0-67653 Kaiserslautern, Germany
Reliable information on chemical equilibria in formaldehyde solutions is needed for the design of separation process for formaldehyde containing mixtures. Chemical equilibria of the poly(oxymethylene) glycol formation in formaldehyde solutions in water (and deuterium oxide) and of the poly(oxymethy1ene) hemiformal formation in methanolic formaldehyde solutions were studied by lH- and 13C-NMR spectroscopy. Overall formaldehyde mole fraction and temperature range from 0.06-0.19 mol/mol, 275-357 K for solutions in water and 0.17-0.50 mol/mol, 274-317 K for methanolic solutions. Chemical equilibrium constants are determined assuming ideal solution behavior. Results from lH-and 13C-NMR spectroscopy agree well. Chemical equilibria of the poly(oxymethy1ene) glycol formation do not depend on whether water or deuterium oxide is used. The new experimental results confirm only some of the literature data.
Introduction Formaldehyde is one of the most important chemical intermediates. It is highly reactive and therefore commonly handled in aqueous and methanolic solutions, where it forms predominantly adducts with the solvent. In aqueous solutions, methylene glycol (HOCH20H) and poly(oxymethy1ene) glycols (HO(CH,O)iH, i > 1) are formed: CH20 + H,O + HOCH,OH HO(CH20),-,H + HOCH,OH + HO(CH,O),H
+ H,O
(1)
i > 1 (11)
Similarly, in methanolic formaldehyde solutions hemiformal (HOCH20CHd and poly(oxymethy1ene)hemiformals (HO(CHzO)iCH3,i > 1) are formed: CH,O
+ CH,OH
(111)
HOCH,OCH,
+
HO(CH,0)i-lCH3 HOCH,OCH, HO(CH,O),CH, + CH,OH
i > 1 (IV)
Chemical equilibria of these reactions have an essential influence on properties of aqueous and methanolic formaldehyde solutions. They have to be taken into account in thermodynamic models to describe phase equilibria and caloric properties of formaldehyde-containing systems. Such models are needed, e.g., for the design of separation processes for formaldehyde containing mixtures (Hasse et al., 1990;Hasse and Maurer, 1991a; Hahnenstein et al., 1994).
NMR spectroscopy can successfully be applied to investigate the polymerizationreactions I1 and IV, whereas, due to the low concentrations of monomeric formaldehyde, no information on reactions I and I11 is obtained. In previous studies of equilibria of reactions I1 and IV almost exclusively lH-NMR spectroscopy was used (Skell and Suhr, 1961;Ihashi et al., 1965;Hellin et al., 1967;Koberstein et al., 1971; Gorrie et al., 1973; Fiala and Navrhtil, 1974; Dankelman and Daemen, 1976;Kogan, 1979). Only Slonim
* Correspondence should be addressed to this author.
+ Lehrstuhl fur
Technische Thermodynamik. Lehrstuhl fur Anorganische Chemie.
08S8-5885/94/2633-1022$04.50/0
et al. (1975) reported results of 13C-NMR-spectroscopic investigations. Most of the lH-NMR-spectroscopic data on the poly(oxymethy1ene)glycol formation was taken in formaldehyde solutions in deuterium oxide, where the reaction scheme is CH,O
+ D20 + DOCH20D
DO(CH20)i-lD+ DOCH,OD DO(CH,O)iD + D20
(VI
i > 1 (VI)
In aqueous formaldehyde solutions the signals of the protons bound in CHzO groups in poly(oxymethy1ene) glycols are found on the low-field slope of the intense and broad OH signal. That problem is avoided, when the solvent is deuterium oxide. The chemical equilibria of the poly(oxymethy1ene)glycol formation (reaction 11)have also been studied with other methods: freezing point depression (Bezzi and Iliceto, 1951),gel-permeation chromatography (Tsuge et al., 19731, and gas chromatography (Dankelman and Daemen, 1976). The starting point of this work was our interest in reaction kinetics in formaldehyde-containing systems, which strongly influence technical separation processes like absorption (Hasse and Maurer, 1991b; Hahnenstein et al., 1994). During these studies, it turned out, that the NMR equilibrium data obtained at the end of kinetic experiments did not agree satisfactorily with literature data. Therefore, a systematic study of chemical equilibria of the poly(oxymethy1ene) glycol and the poly(oxymethylene) hemiformal formation in aqueous and methanolic formaldehyde solutions was carried out. The Bruker AMX 400 NMR spectrometer, which was used for this purpose, is distinctly more powerful than the instruments used for the investigations reported in the literature. Furthermore, both lH- and 13C-NMRspectroscopy were applied for the investigations.
Experimental Section A Bruker AMX 400 NMR spectrometer (proton resonance frequency of 400.13 MHz) was used for the experiments. Care was taken to get accurate data on temperature. Before starting the experiments, for each temperature and solvent, the temperature was measured inside the spectrometer in a typical sample with a small platinum 0 1994 American Chemical Society
Ind. Eng. Chem. Res., Vol. 33, No. 4, 1994 1023
-
/
ppm
3.67
3.61
3.55
Figure 1. 1H-NMR spectrum of an aqueous formaldehyde solution (standard, TSP).
resistance thermometer, which was immersed in the sample tube. Thus, the conditions during these temperature measurements were identical with those during the experiment, except that the sample tube did not rotate. The platinum resistance thermometer was calibrated with a precision thermometer (accuracy better than 0.02 K). The results of these temperature measurements in the spectrometer were checked by measuring the temperatures of the air, which thermostats the spectrometer, at the inlet and the outlet. The results confirmed the reliability of the method. The overall accuracy of the temperature measurement is better than 0.5 K. The samples were prepared by dissolving paraformaldehyde in the different solvents at elevated temperature and separating solid residues by filtration. Details of the procedure are given by Hasse (1990). Chemicals were purchased in the highest commercially available quality (purities: paraformaldehyde > 0.95 g/g, methanol > 0.998 g/g, deuterium oxide > 0.9995 g/g; suppliers: Merck, Darmstadt or Riedel de Haen, Seelze, Germany). Water was bidistilled at the University of Kaiserslautern. Gas chromatographic analysis of the samples showed only trace amounts of impurities; their estimated totalweight fraction is below 0.002 g/g. For deuterium lock, about 0.05 g/g deuterium oxide was added to aqueous formaldehyde solutions. Similarly, about 0.05 g/g deuterated methanol was added to methanolic formaldehyde solutions. The influence of these small amounts of deuterated species on the results of the measurements can be neglected. Overall formaldehyde mole fractions were determined titrimetrically by the sodium sulfite method (Walker, 1964) with relative errors less than 2 % To ensure equilibration, all samples were kept at the spectrometer temperature in a thermostated bath for several hours before the spectroscopic data were taken.
.
quantitative interpretation of the spectra becomes difficult. For this reason, the lH-NMR-spectroscopic results on aqueous formaldehyde solutions at 275 and 293 K obtained in this work are less reliable than those for higher temperatures. lH-NMR spectra of formaldehyde solutions in deuterium oxide are-regarding the peaks which result from protons in CH2 groups-similar to those of aqueous solutions, except that the baseline is not disturbed by protons in OH groups. They will not be discussed separately in this section. The assignment of the peaks of protons in different CH:! groups in formaldehyde solutions in water and deuterium oxide is given in Figure 1 in a scheme indicating the positions of the CH2 groups in the formaldehyde reaction products. Each line stands for one reaction product. The number of CH2 groups in the reaction products is given as a subscript. No peak of protons in monomeric formaldehyde is resolved, due to very low concentration. Mo stands for CH2 in methylene glycol, E (end group) stands for CH2 groups at the end of a poly(oxymethy1ene)glycol chain, and Mi (middle group) stands for the other CH2 groups in poly(oxymethy1ene)glycols. The chemical shift of signals of the protons in end groups E and middle groups Mi in poly(oxymethy1ene)glycols is slightly influenced by the next neighbors of these groups. For example, for E2 the next neighbor is another EO,whereas for E3 it is Mi3. However, this influence on the chemical shift is weak and the peaks overlap strongly, so that for the quantitative evaluation no distinction between them is made. It is assumed that the peak areas A are proportional to the mole numbers of the different CH2 groups in the solution. For the results of the investigations of formaldehyde solutions in water or deuterium oxide (index W) with 'H-NMR spectroscopy (index 'H) this leads to 1H,W
1H,W
AM, = k ~ o~ 1H,W
AM,
M G
(1)
1H,W
2CnMGi
=kE
(2)
i=2
(3) Peak area fractions {, are defined as the fraction of the area A, under a given peak j and the sum over the areas Ak of all other peaks k: (4)
JJ
k
NMR Spectra and Data Evaluation Figure 1 shows a typical 'H-NMR spectrum of an aqueous formaldehyde solution taken in this work. All peaks in the spectrum in Figure 1 result from protons bound in CH2 groups in methylene glycol or poly(oxymethylene) glycols. These peaks are found on the low-field slope of an intense and broad peak caused by protons in OH groups. No solvent suppression techniques were used as a common baseline correction normally yielded satisfactory results (cf. flat baseline in Figure 1). Only at low temperatures, where the peak caused by protons in OH groups broadens and its maximum shifts toward the peaks caused by the protons in CH2 groups, problems with the definition of the baseline occur and a
The usual assumption is made, that the proportionality factors k in eqs 1-3 are all equal: 1H,W
1H,W
1H,W
k ~ =, k ~=kMj
(5)
This results in the following relations between peak area fractions { and true mole fractions x :
(7)
1024 Ind. Eng. Chem. Res., Vol. 33, No. 4, 1994
FA J M e 1~~ = 0.495 rnol/rnol
Mo 'H-NMR
where sw stands for
As the true mole fractions can be calculated from chemical equilibrium constants, the peak area fractions can be used to determine these constants. Details on this procedure are given at the end of this section. Figure 2 shows a typical lH-NMR spectrum of a methanolic formaldehyde solution taken in this work. As for aqueous solutions, only peaks resulting from protons in CH2 groups are shown and used for the data evaluation. No peak of protons in monomeric formaldehyde is detected. The influence of the signal of protons in OH groups on the baseline of the CH2 peaks is much weaker in methanolic solutions than in aqueous solutions and can always be easily accounted for in a baseline correction. lH-NMR spectra of methanolic formaldehyde solutions show more peaks than spectra of aqueous formaldehyde solutions. This is mainly due to the asymmetry of the poly(oxymethy1ene) hemiformals, where at one end the next neighbor of the last CH2 group is an OH group, while at the other end it is an OCH3 group. Furthermore, there is a stronger influence of the next neighbors of the CH2 group on the chemical shift. In the peak assignment given in Figure 2, Mo stands for the CH2 group in hemiformal, E for the CH2 groups at the end of poly(oxymethy1ene) hemiformal chains, and Mi for the CH2 groups at other positions in poly(oxymethy1ene)hemiformals. The asymmetry of the poly(oxymethy1ene)hemiformals is accounted for by using superscript primes or double primes. The data evaluation for 'H-NMR spectra of methanolic formaldehyde solutions is similar to that for aqueous solutions. The equations for the peak area fractions are
where S
M stands ~
for m
'Me
= XHF + c i x H F i ~
i=2
Some of the peaks in 'H-NMR spectra of methanolic formaldehyde solutions overlap rather strongly, so that for those peaks the qualitative analysis of the spectra is difficult.
3.67 3.63
-
6
3.65
J
3.51 3.60
3.49
3.51
3.44
ppm
Figure 2. 'H-NMFt spectrum of a methanolic formaldehyde solution (standard, TSP).
El Mi,
6
i
92.3 9 2 . 5 81.8
E2
340
fF*
Mir
= 0.108 rnollmol
n9.o U Y . 2 88.5
84.8
PP"1
Figure 3. W-NMR spectrum of an aqueous formaldehyde solution (standard, TSP).
Besides lH-NMR spectroscopy 13C-NMRspectroscopy was applied in this work. The determination of peak areas is more reliable for I3C-NMR spectra than for 'H-NMR spectra, because neither problems with the baseline definition nor problems with overlapping peaks occur. The assumption that the area under peaks in 13C-NMRspectra is proportional to the number of carbon nuclei in the solution is possible here, as the next neighbors of the carbons are identical for all peaks, which were used for the data evaluation. Furthermore, a comparison with 'HNMR data confirms the reliability of the quantitative interpretation. Figure 3 shows a typical example of a broadbanddecoupled I3C-NMR spectrum with full nuclear Overhauser effect enhancement of an aqueous formaldehyde solution taken in this work. There is a strong influence of the neighboring groups on the chemical shift, so that more peaks are resolved than in 'H-NMR spectra. The peak assignment is given in Figure 3 in a scheme for the CH2 groups similar to that in Figure 1. 13C-NMRspectra of formaldehyde solutions in deuterium oxide are very similar to those of aqueous solutions, so they are not treated separately here. The equations relating the peak area fractions to the true mole fractions are
Ind. Eng. Chem. Res., Vol. 33, No. 4,1994 1025 Mo
(18) ?FA = 0.495 mol/mol
13c.w
E2
, E2
9
(21)
(22)
where sw is again given by eq 9. The signals of middle groups Mi in poly(oxymethy1ene) glycols with i > 4 are very weak and were not accounted for in the data evaluation. A typical example of a noise-decoupled 13C-NMR spectrum of a methanolic formaldehyde solution taken in the present work is given in Figure 4. As for 1H-NMR spectra, peaks at the different ends of the poly(oxymethylene) hemiformal chains appear at different chemical shifts. The triangular scheme for the peak assignment is given in Figure 4. This scheme and the equations, which relate the peak area fractions to the true mole fractions, are the same as for 'H-NMR spectroscopy of methanolic formaldehyde solutions (cf. Figure 2 and eqs 10-15). The signals of middle groups Mi in poly(oxymethy1ene)glycols with i > 3 are very weak and were not included in the data evaluation. To derive equations which relate peak area fractions to true mole fractions, it was assumed for both lH- and 13CNMR spectroscopy that the proportionality factors relating the peak areas to the true mole numbers are equal for all peaks (cf. eq 5). It is, however, observed both for 1Hand 13C-NMRspectroscopy that areas under peaks which should be equal according to this assumption (e.g., E'z and E''2), differ. The relative deviations are typically about 10 '7%. In the data evaluation these differences are averaged out, but still this points out that the assumption of equal proportionality factors is an approximation. For the quantitative interpretation of the NMR data, peak area fractions were calculated from true mole fractions, which were determined from overall mole fractions (known from titration) and chemical equilibrium constants. The equilibrium constants were initially estimated, and then determined from a fit to the peak area fraction data. The assumption of ideal solution behavior was made, and mole fractions were used for the definition of the chemical equilibrium constants. For the poly(oxymethy1ene)glycol formation in aqueous formaldehyde solutions this leads to (23)
and for the poly(oxymethy1ene)hemiformal formation in methanolic formaldehyde solutions this leads to (24)
Assumptions for the equilibrium constants KMQ,i = 2, ..., m , and KHF~, i = 2, ..., m , had to be made to reduce
-
95.8
6 / ppm
95.2
88.5 92.2
90.9
88.1
Figure 4. W-NMRspectrum of a methanolic formaldehyde solution (standard,TSP).
the number of model parameters. The following assumptions were tested: 1. All equlibrium constants are equal:
KAi= KAn
i > 1; A = MG, HF
(25)
2. All equilibrium constants are equal, except Kh2:
3. All equilibrium constants are equal, except KA2and
K A ~
Using these three assumptions (referred to as methods 1 , 2 , and 3), the numbers of the equilibrium constants for each system and temperature were determined from a minimization of the absolute deviations between measured and calculated peak area fractions. For aqueous and methanolic solutions the data base for each temperature was four to six peak area data sets from spectra of solutions with different formaldehyde concentrations, while for deuterium oxide there was only one data set for each temperature. Overall formaldehyde mole fractions ranged from 0.06 to 0.19 mol/mol for aqueous solutions and from 0.17 to 0.50 mol/mol for methanolic solutions. The data on formaldehyde solutions in deuterium oxide was taken for an overall formaldehyde mole fraction of 0.19 mol/ mol. Absolute deviations were used rather than relative deviations for the determination of the equilibrium constants, as this results in a weaker influence of peaks with small areas, for which the relative uncertainty in the peak area is larger. It turned out that for the poly(oxymethy1ene) glycol formation methods 2 and 3 gave a better representation of the data than method 1. However, the third parameter introduced in method 3 gives only a marginal improvement over the two-parameter method 2. Hence, method 2 was chosen for the data evaluation for the poly(oxymethy1ene) glycol formation. For the poly(oxymethy1ene)hemiformal formation the comparison of methods 1 , 2 , and 3 showed that the one-parameter model is about as good as the twoand three-parameter models, so that in this case method 1 was preferred.
1026 Ind. Eng. Chem. Res., Vol. 33, No. 4, 1994 Table 1. Chemical Equilibrium Constants of Poly(oxymethy1ene) Glycol Formation in Aqueous Formaldehyde Solutions 'H-NMR "C-NMR
T/K 275 293 313 333 353
KMG, 2.81 3.95 3.70 3.45 3.56
KMG? 5.95 4.92 5.87 5.08 5.05
T/K 282 298 317 337 357
KMG? 7.35 6.77 5.91 5.33 4.90
KMG. 4.62 4.20 3.88 3.39 3.35
Table 2. Chemical Equilibrium Constants of Poly(oxymethy1ene) Glycol Formation in Formaldehyde Solutions in Deuterium Oxide
'H-NMR
T/K 293 313 333 353
KMG, 5.96 5.74 4.67 4.71
"C-NMR
KMG, 4.03 4.14 3.17 3.52
KMG, 6.37 5.70 5.67 5.10
KMG. 3.69 3.61 3.59 3.16
Table 3. Chemical Equilibrium Constants of Poly(oxymethy1ene) Hemiformal Formation in Methanolic Formaldehyde Solutions
'H-NMR T/K 274 293 313
KHF. 0.142 0.144 0.160
T/K 279 299 317
L
4
13C-NMR
273
KHF. 0.117 0.130 0.145
The representation of the NMR data with the models is good. Except for very small peak area fractions (l'< 0.031, relative deviations between calculated and measured peak area fractions are typically below 5% and rarely exceed 10%. The deviations show no systematic trends. This holds both for the 13C-NMRand 'H-NMR data and for all systems and temperatures. The fact that no systematic influence of the concentration on the results was found shows that the influence of nonideality on the (apparent)equilibrium constants as defined in eqs 23 and 24 is only weak.
Results Tables 1-3 summarize the results of the NMRspectroscopic investigations of formaldehyde solutions in water, deuterium oxide, and methanol. In Figures 5 and 6 equilibrium constants of the poly(oxymethylene)glycolformation in formaldehyde solutions in water and deuterium oxide, determined by lH- and 13C-NMRspectroscopy,are shown (Figure 5, d a b for KMG,; Figure 6, data for KMG,). The lH- and 13C-NMR data agree favorably at temperatures above 313 K. The lHNMR data on aqueous solutions at lower temperatures are not as reliable, due to the problems arising from signals of protons in OH groups, which were already discussed before. The data for formaldehyde solutions in deuterium oxide scatter more than the data for aqueous solutions, because the data base for formaldehyde solutions in deuterium oxide was much smaller than that for aqueous solutions. Nevertheless, Figures 5 and 6 show that the data for formaldehyde solutions in water and deuterium oxide agree well. It should be remarked that that statement does not hold for reaction kinetics of the poly(oxymethylene) glycol formation, which strongly depend on whether water or deuterium oxide is used as solvent (Hahnenstein et al., 1994). From the considerations on the reliability of the peak area determination given in the previous section and from the smoothness of the results for the equilibrium constants
293
313
333
353
373
T/K Figure 5. Equilibrium constant KMG,of poly(oxymethy1ene) glycol formation in formaldehyde solutions in water and deuterium oxide determined by 'H- and W-NMR spectroscopy.
i...,
rne " "c }FAiJl,O
4 '5
Y=
3 0
273
293
313
333
353
313
T/K Figure 6. Equilibrium constant KMG"of poly(oxymethy1ene) glycol
formation in formaldehyde solutions in water and deuterium oxide determined by 'H- and W-NMR spectroscopy.
at different temperatures, it is concluded that the l3CNMR data are most reliable. They are recommended for further use. These data were correlated using lnK=A+-
B T/K
where B is related to the reaction enthalpy ARh by
A SlOllbXI (1975):
0.30
uc
0
method 3: K, IC,, K. Kogan (1979): 'H method 1: K,
9-
- A This work: "C-NMR 0.25 -
-
6
4 1
.........................
Kogan (1 979): 'H-NMR
This work: 'H-NMR
I..,,
ms work %/'H method 2: K,, K,
............................
VK
0.10
273
293
313
333
353
373
TiK Figure 7. Comparison of equilibrium constants of poly(oxymethylene) glycol formation taken in this work with literature data. Table 4. Correlations for Chemical Equilibrium Constants of Poly(oxymethy1ene) Glycol and Poly(oxymethy1ene) Hemiformal Formation: In K = A B / ( T / K ) A B
+
~~~~
~
KMG~ KMG. KHF.
1.449 X 1k2 -1.084 x lo-' -3.476 X lo-'
5.609 X lo2 4.604 X lo2 -5.032 X lo2
The correlation functions for KMG,and KMG,are shown in Figures 5 and 6; parameters are given in Table 4. In Figure 7 these correlations for the equilibrium constants KMGof the poly(oxymethy1ene)glycol formation are compared to literature data. In the literature different methods for the data evaluation were used. The nomenclature used in Figure 7 follows the one used to explain the different correlation methods in the previous section. The subscript MG is not used in Figure 7 to avoid a tooprofused picture. Although a comparison between results of different correlation methods is difficult, it can be seen from Figure 7 that the equilibrium constants obtained in this work are generally larger than the numbers reported in the literature, but that there are also considerable discrepancies between literature data. The agreement between the results obtained in this work and the results of Slonim et al. (1975), who also used W-NMR spectroscopy, is fairly good. For methanolic formaldehyde solutions, the new data are shown in Figure 8. The 'H-NMR data give slightly higher numbers for the chemical equilibrium constants of the poly(oxymethy1ene) hemiformal formation than the 13C-NMR data. As the determination of areas under the peaks in 'H-NMR spectra is difficult, also here the 13CNMR data are considered to be more reliable and used for the correlation (cf. Table 4). For a comparison with literature data only one source is available (Kogan, 1979) for methanolic formaldehyde solutions. The literature data are also shown in Figure 8. The data taken in this work and the data of Kogan (1979) only agree at temperatures around 313 K and deviate strongly both at higher and lower temperatures. From
273
293
313
333
353
373
T/K Figure 8. Equilibrium constant K w . of poly(oxymethy1ene) hemiformal formation in methanolic formaldehyde solutions.
the temperature dependence of the data of Kogan (1979), the poly(oxymethy1ene)hemiformal formation should be exothermal, while the results from this work (both lH and 13C) indicate an endothermal reaction. That the poly(oxymethylene) hemiformal formation is endothermal is confirmed by calorimetric data on heats of dilution reported recently by Hasse and Maurer (1992). I t should, however, be remarked t h a t both for the poly(oxymethylene) glycol and the poly(oxymethy1ene)hemiformal formation the temperature dependence of the chemical equilibrium constants is rather weak and reaction enthalpies are below 5 kJ/mol. Figure 9 shows some results obtained from the correlations for the chemical equilibrium constants of the poly(oxymethylene) glycol and poly(oxymethy1ene) hemiformal formation given in Table 4. For 293 and 373 K, the average number i of CHzO groups in the formaldehyde reaction products with water and methanol OD
Chi 1=1
cA=-*
, A=MG,HF
(30)
r=l
is shown as a function of the overall formaldehyde concentration. It can be seen that, for the same overall formaldehyde concentration, the mean chain length of the formaldehyde reaction products in aqueous solutions is much larger than that in methanolic solutions. This explains why the precipitation of solids (long-chain poly(oxymethy1enes)) occurs at lower overall formaldehyde concentration in aqueous solutions than in methanolic solutions and why solid precipitation from aqueous formaldehyde solutions can be avoided by adding methanol. Furthermore, it can be seen that in aqueous solutions, with increasing temperature, the average chain length decreases, whereas in methanolic formaldehyde solutions temperature has only
1028 Ind. Eng. Chem. Res., Vol. 33, No. 4, 1994
HO(CH,O),H
/sy
293 - 373 K
1.oo
0.2 0.3 0.4 0.5 / (mol/mol) Figure 9. Average number of CH20 groups in poly(oxymethy1ene) glycols in aqueous formaldehyde solutions and poly(oxymethy1ene) hemiformals in methanolic formaldehyde solutions. 0.0
0.1
-x,
a very small influence on the chain length, which cannot be resolved in the representation in Figure 9. Conclusion Data on the equilibrium constants of the poly(oxymethylene) glycol formation in formaldehyde solutions in water and deuterium oxide and on the poly(oxymethy1ene) hemiformal formation in formaldehyde solutions in methanol were taken with a Bruker AMX 400NMR spectrometer using *H- and 13C spectroscopy. Temperatures ranged between 275 and 357 K. A broad concentration range was covered. For the correlation of the data, chemical equilibrium constants are defined assuming ideality. The results from 'H- and 13C-NMRspectroscopy are in good agreement, except for low temperatures, where the 13CNMR data are more reliable. Within experimental uncertainty the equilibrium constants determined in this work show no concentration dependence. Chemical equilibria of the poly(oxymethy1ene) glycol formation do not depend on whether water or deuterium oxide is used. For the poly(oxymethy1ene) glycol formation, the equilibrium constants reported in this work are slightly higher than those reported in the literature. For the poly(oxymethylene) hemiformal formation, where only one literature source is available, the equilibrium constants reported here differ significantly from the literature data. However, a comparison with calorimetric data confirms that the new results are reliable. Acknowledgment We gratefully acknowledge financial support for this work by BASF AG, Ludwigshafen am Rhein, Bundesminister fur Forschung und Technologie, Bonn, and Degussa AG, Wolfgang bei Hanau, Germany. Nomenclature A = peak area or adjustable parameter B = adjustable parameter
E = CH2 group at the end of a poly(oxymethy1ene)glycol or poly(oxymethy1ene)hemiformal FA = formaldehyde Agh = reaction enthalpy i = number of CHzO groups in poly(oxymethy1ene)glycols or poly(oxymethy1ene)hemiformals i = average number of CHzO groups in formaldehydereaction products K = chemicalequilibriumconstant, defined assumingideality and using mole fractions k = proportionality factor Me = methanol Mi = CH2 group not at the end of a poly(oxymethy1ene) glycol or poly(oxymethy1ene)hemiformal Mo = CH2 group in methylene glycol or hemiformal n = mole number NMR = nuclear magnetic resonance R = universal gas constant s = sum, defined in eqs 9 and 15 T = temperature TSP = 3-(trimethylsily1)propionic acid-dd sodium salt W = water 3c = true mole fraction 3 = overall mole fraction Greek Symbols 6 = chemical shift from TSP
t = peak area fraction
Subscripts
E = peak resulting from a CHZgroup at the end of a poly(oxymethylene)glycol or poly(oxymethy1ene)hemiformal FA = formaldehyde HF = without subscript, hemiformal, with subscript, poly(oxymethylene) hemiformal i = number of CHzO groups in poly(oxymethy1ene)glycols or poly(oxymethy1ene)hemiformals j , k = peak indices Me = methanol MG = without subscript, methylene glycol; with subscript; poly(oxymethy1ene)glycol Mi = peak resulting from a CHZgroup not at the end of a poly(oxymethy1ene)glycol or poly(oxymethy1ene)hemiformal Mo = peak resulting from a CHZgroup in methylene glycol or hemiformal W = water 1,2,3,4,5 = numbers of CH2 groups in poly(oxymethy1ene) glycols or poly(oxymethy1ene)hemiformals A = MG or HF Superscripts 13C = 13C-NMRspectroscopy lH = 'H-NMR spectroscopy Me = solvent methanol W = solvents water or deuterium oxide r rr = different ends of a poly(oxymethy1ene)hemiformal
,
chain
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Received for review August 26, 1993 Revised nanwcript received December 1, 1993 Accepted December 21, 1993. 0 Abstract published in Advance ACS Abstracts, February 15,1994.
