EQUILIBRIA BETWEEN CYCLIC AND LINEARMOLECULES IN FORMALDEHYDE
2025
Equilibria between Cyclic and Linear Molecules in Aqueous Formaldehyde
by Kurt Moedritzer and John R. Van Wazer Central Research Department, Monsanto Company, St. Louis, Missouri
(Receined January 4, 1966)
When anhydrous formaldehyde is dissolved in deuterium oxide, four to five peaks (plus a generally small resonance due to trace amounts of HzO) appear in the proton nuclear magnetic resonance spectra. From the relative areas of these methylene resonances, one of which is due to trioxane, two equilibrium constants completely describing the system were calculated. One of these equilibrium constants deals with the relative amounts of the variously sized linear polyoxymethylene glycols, and the other relates the cyclic molecule, trioxane, to the linear ones. Rate measurements showed that ring-chain equilibria are established quite slowly whereas chain-chain equilibrations are very fast, with halflives of the order of seconds a t room temperature.
This study is part of a broad quantitative investigation1Z2now being carried out in our laboratory concerning families of compounds in which the kinds and amounts of the various molecular species are determined by thermodynamic rather than kinetic factors. Previous ~ o r k on ~ -aqueous ~ solutions of formaldehyde showed that there is an equilibrium between various linear species, with very little monomeric formaldehyde being present. The one nuclear magnetic resonance (nmr) study4 which has been reported for this system also concluded that there are no cyclic molecules in equilibrium with the linear ones. In this study, quantitative nmr measurements are used to evaluate the equilibrium constants controlling the system.
Experimental Section Reagents. Trioxane, (CHz0)3, from Fisher Scientific, after resublimation gave a single, sharp proton nmr peak immediately upon complete dissolution in water so that any contaminants must represent less than 0.3% of the total hydrogen. Commercial paraformaldehyde, (CHZO), with large n, also from Fisher, was found to contain a considerable amount of methoxyl groups. Paraformaldehyde made by heating the resublimed trioxane with a trace of phosphoric acid in a sealed tube was considerably more pure. However, the nmr spectrum of this product also showed some methoxyl end groups (2-59;’, of the total hydrogen), presumably resulting from a Cannimaro reaction.
The deuterium oxide (99.75%) was purchased from E. Merck A. G., Darmstadt. Analytical Procedure. All analyses were performed by proton nmr, using a Varian A-60 field-sweep spectrometer with a field-frequency lock, running at 60 Mc. A field sweep of 50 cycles was employed with a sweep rate of 0.1 cps. The same nmr peak assignments employed by Skell and Suhr4 for the linear compounds were used in this study. They were in agreement with the various tests we have used in other q701-k~for veri(1) D. W.Matula, L. C. D. Groenweghe, and J. R. Van Waser, J . Chem. Phys., 41, 3105 (1964). (2) K. Aloedritzer and J. R. Van Wazer, J . Am. Chem. SOC.,86, 802 (1964); J. R. Van Wazer, K. Moedritzer, and D. W. hlatula, ibid., 86, 807 (1964) ; &I.D. Rausch, J. R. Vap Waxer, and K. Noedritser, ibid., 86, 814 (1964); D. Grant and J. R. Van Waser, ibid., 86, 3012 (1964) ; H. I. Weingarten and J. R. Van Wazer, ibid., 87, 724 (1965) ; K. Moedritzer and J. R. Van Wazer, ibid., 87, 2360 (1965); J. R. Van Wazer, D. Grant, and C. H. Dungan, ibid., 87, 3333 (1965); J. R. Van Waeer and K. Moedritzer, J . Chem. Phys., 41, 3122 (1964); K. hfoedritzer, J. R. Van Wazer, and C. H. Dungan, ibid., 42,2478 (1965) : J. R. Van Waser, K. Moedritzer, and 11.D. Rausch, ibid., 42, 3302 (1965). (3) J. F. Walker, “Formaldehyde,” 3rd ed, Reinhold Publishing Corp., New York, N. Y., 1964, pp 53-81. (4) P. Skell and H. Suhr, Chem. Ber., 94, 3317 (1961). (5) A. Illiceto, Ann. Chim. (Rome), 39, 703 (1949); 40, 711 (1950); Gazz. Chim. Ital., 81, 786 (1951); 84, 536 (1954); A. Illiceto and S.Bezxi, Ric. S c i . . 19, 999 (1949); Chim. Ind. (Milan), 33, 212 (1951); 42, 728 (1960). (6) A. Illiceto, S. Bemi, N. Dallaporta, and G. Giacommetti, Gazz. Chim. Ital., 81, 915 (1951). (7) J. R. Van Wazer and L. C. D. Groenweghe, “Nuclear Magnetic Resonance in Chemistry,” B. Pesce, Ed., Academic Press Inc., New York, N. Y . , 1965; also see ref 2 .
Volume 7 0 . Number 0 June 1966
KURTMOEDRITZER AND JOHN R. VANWAZER
2026
fying such assignments. The water (H20) and trioxane resonance assignments were made by addition of these materials to the samples during their final analyses. The chemical shifts, as referenced to trioxane, of the various peaks in the system D20-CH20 are shown at the bottom of Table I along with that due to HzO contamination. As expected, the latter peak is found to shift, depending on the relative proportions of uncombined water to end groups. Reaction Mixtures and Equilibration. The nmr spectra show that trioxane dissolves in deuterated
Table I: Observed and Calculated Nmr Peaks in the Equilibrated System D20 us. CHzO a t 120' 7
RZS D/O
1.977
Trioxane (m-m)3
0.0
u.oa 1.945 1.924 1.893 1.760 1.685 1.638 1.517 1.471 1.445 1.373 1.295 1.263 1.155 1.111
1.073
0.0 0.2 1.0 0.4 1.0 0.6 1.6 1.6 2.2 2.1 2.4 2.4 2.9 3.0 3.2 5.2 3.6 3.3 3.2 3.6 3.5 3.9 3.7 4.1 4.1 4.6 5.4 4.6 4.4 4.7
Nmr chemi- 0.00 cal shifts, PPm
Percentage of total methylenes in Methylene Ends glycol Middles e m p e m-m
0.9 u.2 1.4 0.9 1.1 1.6 2.7 2.7 7.1 8.5 10.0 12.0 11.8 14.2 17.9 19.7 17.2 21.7 18.5 82.8 22.7 25.9 24.1 89.2 26.3 30.6 29.8 34.9 32.4 36.7 33.8 38.2
+0.26
12.2 8.2 19.3 17.1 24.6 11 .8 32.1 27.5 44.2 40.9 44.9 44.6 47.4 46.1 49.7 48.0 52.0 48.3 52.3 48.5 51.9 48.1 51.1 47.6 51.1 47.2 24.9 26.8 18.0 27.6 23.0 26.3 17.8 27.8 22.4 27.4 16.1 28.0 e-me
e-mm
+0.32
f0.33
Values in italics calculated from
The Journal of Physical Chemistry
K1
= 1.0
86.9 91.6 79.3 81.8 73.3 76.2 64.2 69.4 47.1 49.0 42.9 41 .5 38.4 37.3 29.5 29.3 27.6 26.8 25.6 86.6 22.2 12.4 21.3 19.4 18.9 18.3 14.4 14.9 12.6 12.8 12.0 11.1
+0.39
HzO per 100 CHz
60.0 12.0 7.3 8.0 2.3 1.3 1.4 1.5 1.1
0.5 0.5 1.0 0.5 0.5 0.3 0.3
f0.49
and KSO = 4.
water rapidly upon gentle heating with no reaction, whereas the more lengthy dissolution of paraformaldehyde, a process which must be effected by heating, apparently involves some chain scission since more nonmethoxyl end groups show up in the methylene region of the nmr spectrum than can be accounted for by the phosphoric acid added and the formic acid formed in its preparation. Since the H2O nmr peak lies in the same region as the methylene peaks, it was necessary to use the purest possible deuterium oxide in order that a quantitative measure of the various methylene peaks could be obtained. Equilibration was achieved by heating the chosen proportions of trioxane and deuterium oxide with a trace amount of phosphorus pentoxide as catalyst in sealed 5-mm 0.d. thin-walled precision nmr tubes (the pH of the solutions was always in the range of 0.5 to 1.5 as measured by a glass electrode). I n all cases, more than half of the tube was filled with liquid so that at elevated temperatures the relative amount of material in the gas phase would be small. The reported equilibrium data correspond to heating the sealed tubes at 120" for 43 hr and then quenching them at room temperature. Pilot runs a t several different ratios of CH20/D20showed that equilibrium was achieved in less than 26 hr at this temperature. Kinetic runs were made on single samples in sealed nmr tubes by heating for the desired length of time, quenching, and measuring the nmr pattern, and then reheating for the next desired interval of time. I n applying the formal treatment that we have devised' for equilibrium-controlled families of compound to the linear and cyclic polymethylene oxide structures, we may consider either the methylene groups or the oxygen atoms as the central moiety. I n the first case, methylene glycol, DOCHzOD, is the neso compound, and DOCH201/,- and -01/,CH201,,- are the end and middle groups, respectively. I n the latter case which was employed, since an extra equilibrium constant is then not needed to describe the reaction with the free water (D20),the neso compound is D20 while the end and middle groups correspond to DO(CH2)1/,- and -(CHz)l/,0(CH2)l/z-,respectively. I n the situation employed herein, where oxygen is the chosen central atom, the usual parameter, R, describing the over-all composition is seen to be equal to the deuterium/oxygen atom ratio. With oxygen as central atom and the methylene groups being analytically determined, the methylene nmr peaks must be assigned to bridging groups so that trioxane is formally represented' as (m-m)3, methylene glycol as e-e, and the groupings DOCHz0(CH2)1/z-and -(CHz)1~,0CH20(CHz)1~zas
EQUILIBRIA BETWEEN CYCLIC AND LINEARMOLECULES IN FORMALDEHYDE
e-m and m-m,respectively, where n, e, and m stand for neso, end, and middle groups. The end-group resonance which is shown as e-m in Table I appears as a doublet for R 5 1.7. However, the relative areas of this close-lying pair of peaks could only be approximately estimated, except in the case of the last three entries in Table I. For these entries, the m n resonance is broken up into m e and e-", which corresponds to the dioxymethylene glycol molecule, DOCH20CHZ0D, and the DOCHZOCHZO(CH2)l/z- structure, respectively.
Results and Conclusions Equilibrium Measurements. The lowest ratio of D/O which could be achieved in the D20-CHZO system without immediate precipitation of paraformaldehyde polymers upon quenching to room temperature was in the neighborhood of 1.0. However, for D/O ratios less than 1.3, paraformaldehyde precipitation was seen to occur in a few hours at 25". Because of the very slow rates of the ring-chain equilibration at room temperature and the negligible temperature dependence of the chain-chain equilibria, the data reported in Table I are believed to correspond well to 120", the temperature of equilibration. I n Table I, the experimentally measured nmr peak areas are presented in Roman type. From these data it is apparent that, as infinite dilution is approached, all of the hydroxyl, (OD) terminated species are to be found in the form of methylene glycol, with no trioxane being present. As the water (DzO) content is reduced, the resonance due to trioxane is observed to appear and then grow and the polymethylene glycols are seen to become progressively longer. Assuming a reorganization heat order' of unity and no monomeric formaldehyde, the entire system can be defined by the following two equilibrium constants
Ki
=
[nl[m*I/[e12
(1)
and
where n stands for DzO,m" and m* stand for -(CHZ)I/,O(CHz)l/z- in ring and chain structures, respectively, and e is for the DO(CHZ)~/,-group. VO and VZrefer, respectively, to the molar volumes in liters/mole of D20 and CHzO and r to the ring size (r = 3 for trioxane). By use of our computer program,'** the equilibrium constants corresponding to eq 1 and 2, which give the best fit to the experimental data shown in the first five columns of Table I, were determined. I n this calculation, the ring-chain equilibrium constant was
2027
obtained by two independent procedures. I n one, the observed amount of trioxane was used to calculate Ka" and, in the other, the value of this constant which gave the best fit to the experimental data for the m-m, m, and e-e resonances was calculated. The values of both K1 and K3" thus obtained were within experimental error for the two procedures. These values for 120" are K I = 1.0 and K3' = 4.0, with standard errors of 0.06 and 0.7, respectively. The calculated values for the nmr peak areas shown in italics in Table I were computed from these two constants. The enthalpy for the reaction whereby the various chains equilibrate with water must be small since K1 = 1.0 is not very far from the random value of 0.25. By assuming that the entropy of the reaction corresponding to eq 1 is exactly equal to that calculated for the statistically random case, the enthalpy of this reaction is found to be 0.04 kcal. The temperature dependence, assumed to be due solely to the enthalpy, of the ring-chain interconversion represented by eq 2, was obtained by measuring the equilibria corresponding to 100 and 150" for a composition exhibiting a D/O mole ratio of 1.123. Analysis of these measure0.1 and -3.0 kea1 for the reacments gave AH = tions described by the constants of eq 1 and 2, respectively. From the enthalpies given in the preceding paragraph, it is possible to extrapolate the equilibrium constants to 30°, at which temperature there is data on the equilibrium concentration of monomeric f~rmaldehyde.~ From this operation, we obtain the following set of three constants (where K1" represents the equilibrium between monomeric formaldehyde and the system of linear polyoxymethylene glycols) describing the system at 30": K1 = 1.0, K3" = 1.3, and K1" = 4.0 X with standard errors of 0.06, 0.4, and 2.0 X respectively. From these constants, the concentrations of the different molecules present in equilibrated formaldehyde solutions at room temperature have been calculated and are given in Table 11. Data similar to those listed in Table I1 have also been calculated by Illiceto and B e z ~ i . ~These ~ ~ ~ authors *~ based their calculations on the values for the methylene glycol concentration (determined by the "bisulfite" method) and the average molecular weight of the polymeric glycols in equilibrated aqueous formaldehyde solutions. Fairly good agreement of the data in Table I1 with the equivalent values listed by these
+
(8) L. C. D. Groenweghe, J. R. Van Wazer, and A. W. Dickinson, Anal. Chem., 36, 303 (1964). (9) A. E.F. Chadwick, reported on p 61 of ref 3. (IO) See ref 3, p 64.
Volume YO, Number 6 June 1966
KURTMOEDRITZER AND JOHN R. VAN WAZER
2028
Table 11: Percentage of [CHZO]in Various Molecules in Equilibrated Aqueous (DzO) Solutions as Calculated from the Constants KI, Kl", and K3' for 30" CHzO conon, wt
%
2 5 10 15 20 25 30 35 40 45 50 55 60
DO[CHsOInD
R ES D/O
CHzO
(CHz0)8
n = 1
n = 2
n = 3
n - 4
n = 5
n=6
n - 7
n = 8
n = Q n=lOn>ll
1.9731 1.9322 1.8620 1.7893 1.7141 1.6362 1.5533 1.4714 1.3843 1.2938 1.1997 1.1017 0.9996
0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.01
0.02 0.10 0.28 0.47 0.64
90.24 78.46 63.70 52.77 44.29 37.46 31.68 27.04 22.95 19.41 16.30 13.55 11.10
9.00 17.83 25.56 28.68 29.43 28.88 27.53 25.80 23.78 21.60 19.34 17.04 14.74
0.68 3.05 7.70 11.70 14.67 16.70 17.94 18.47 18.48 18.03 17.21 16.08 14.69
0.04 0.46 2.06 4.24 6.50 8.58 10.38 11.74 12.76 13.38 13.62 13.48 13.00
0.00 0.08 0.53 1.45 2.70 4.13 5.65 7.00 8.25 9.30 10.10 10.60 10.80
0.00 0.00 0.12 0.48 1.08 1.92 2.94 4.02 5.13 6.21 7.20 8.01 8.61
0.00 0.00 0.03 0.14 0.42 0.88 1.51 2.24 3.12 4.03 4.97 5.88 6.65
0.00 0.00 0.00 0.04 0.16 0.36 0.76 1.20 1.84 2.56 3.36 4.24 5.04
0.00 0.00 0.00 0.00 0.05 0.18 0.36 0.68 1.08 1.62 2.23 2.97 3.78
0.80 0.94
1.07 1.20 1.32 1.44 1.55 1.67
1.0J..
0.01 o
ai
LI
na
oippm
I 20
.
I
40
authors is generally observed. However, the latter data calculated for a temperature of 35" are based on the assumption of the exclusive presence of linear molecules at equilibrium. Kinetic Measurements. When the temperature of an equilibrated or partially equilibrated mixture containing catalytic amounts of phosphoric acid (DIPOJ is raised above ca. 50°, noticeable broadening of the nmr resonances corresponding to the methylene groups in the chain molecules is observed. This broadening increases with increasing temperature, and at ca. 100" the e-e, m,and m-m resonances have coalesced The Journal of Physical Chemistry
0.00 0.00 0.00 0.01 0.05 0.04 0.14 0.38 0.80 1.53 2.72 4.49 7.11
.
I
60
I
80
I
100
\ I
TEMPERATURE,'C
Figure 1. Proton nmr spectra of an equilibrated sample in the system [CHzO] us. DzO for the composition R 3 D/O = 1.506 a t various temperatures.
0.00 0.00 0.00 0.00 0.00 0.05 0.15 0.35 0.60 1.00 1.50 2.10 2.80
I
I
b
I
I
I
180 220 (on UTabs scale)
140
Figure 2. Average lifetimes, 7,in equilibrated samples in the system [CHZO]us, DzO for various compositions a t various temperatures. The solutions are 0.2 M in DaP04. D/O = 1.883; The circles represent the composition R the triangles, R = 1.506, and the squares, R = 1.064. I n each composition, the open symbols denote data obtained from line broadening of the m-m and m-e resonances, and the filled symbols data from the e-e and e-m resonances. The symbols with a dot in the center were obtained from saddleshaped spectra. The pH was ca. 1.0.
so that no valleys are seen between them. As shown in the spectra of Figure 1, the trioxane ring structures exhibit little or no line broadening at these elevated temperatures, indicating that it apparently does not readily exchange methylene groups with the chain
EQUILIBRIA BETWEEN CYCLIC AND LINEARMOLECULES IN FORMALDEHYDE
Figure 3. Kinetic curves for the equilibration of trioxane with D20 a t a pH of ca. 1.0 (0.2 M in DaP04)a t 100' for various compositions: (A) R 3 D/O = 1.883, (B) R = 1.506, (C) R = 1.064.
structures. Application of the proper equationsl1J2 to the data gives the variation of average lifetimes for exchange of methylene groups between the various chain molecules shown in Figure 2. The rate of exchange is a function of the over-all composition, being faster with decreasing R values up to ca. 80" a t which temperature a reversal of this order is observed. The slopes of the curves in Figure 2 correspond t o the following activation energies for the exchange process: 16 kcal for R = 1.883, 10 kcal for R = 1.506, and 7 kcal for R = 1.065, with standard errors of 4.5, 1.0, and 1.1 kcal, respectively. In spite of the fact that the chain molecules exchange parts with each other quite readily a t 100°, the equilibration of mixtures of trioxane with water (D20) in the presence of phosphoric acid (D3P04)as catalyst takes several days to reach equilibrium.
2029
Typical rate curves are given in Figure 3 for the same three over-all compositions employed in obtaining the data of Figure 2. Comparison of the times involved in these two figures indicates that the rate-determining step in the hydrolysis of trioxane involves the attack of the cyclic structures by the water (D20)or the linear polymethylene glycols. Indeed, calculations show that the chain molecules are in a dynamic equilibrium with each other throughout the rate processes shown in Figure 3, since the relative areas of the e-e, e m , and m-m signals are in accord with the equilibrium of eq 1 a t all times during the runs presented in this figure. A similar situation is found in the halogen-terminated polydimethylgerm~xanes~~ in which the cyclic trimeric and tetrameric dimethylgermanium oxides show up in the proton nmr spectra as sharp peaks at concentrations where considerable coalescence is observed for the resonances corresponding to the chain structures.
Acknowledgment. We are grateful to Dr. Leo C. D. Groenweghe for use of his computer programs and general advice. We also wish to thank Raymond E. Miller for nmr measurements and for experimental assistance. (11)K.Moedritzer and J. R. Van Warer, Inorg. Chem., 4,893 (1965). (12) J. A. Pople, W. G. Schneider, and H. J. Bernstein, "High Resolution Nuclear Magnetic Resonance," McGraw-Hill Book Co., New York, N.Y., 1959,pp 220-225. (13) K. Moedritzer and J. R. Van Wazer, Inorg. Chem., 4, 1753 (1965).
Volume 70,Number 6 June 1966
