Hydrogen-Bonding Equilibrium in Phenol Analyzed by NMR Spectroscopy Leslie Lessinger Barnard College, New York, NY 10027 Simple NMR measurements plus a n elegant data analysis can determine both the value of n and the equilibrium constant K,, for the hydrogen-bonding equilibrium in CC4 solution:
Physical and Theoretical Background Let P stand for phenol. Assuming that only one associated form, the n-mer, is important in these solutions, we need consider only the equilibrium
The experiment, which monitors the large chemical shift of the hydroxyl proton resonance as a function of concentration (see Dyer ( I ) ) ,is based on the general procedure of Saunders and Hyne (2).An interesting related study of the different hydrogen-bonding equilibrium in the succinimideldimethyl sulfoxide system was reported by Porter and Brey (3).
governed by the equilibrium constant
"OH'
(a1
1
where concentrations of monomer [PI and n-mer [Pal should be expressed in mole fractions.
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REF
Figure 1. Selected proton NMR spectra of CsHsOH in CCb (actual student data). 0.1029 0.2632 0.1363 0.3361 0.4789 X(phenol) 46.8 43.2 +3.7 11.7 v(0H). Hz -7.1 k) (b) Spectrum (a)
0.0619 72.9
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log X
.
log X
F g.re 2 Stepw~sedetermlnat on of parameters ro rep1 cate experimental oata Est mated uncerta~ntes glven for each parameter (a)Exper mental v vs log Xcdrve, usmg all the data llsteo n Flgdre 1 v~ = 167 3 2 Hz from enrapo at on lo X + 0 The s ope of me lnear central region is -1 21.7 i 3 Hz. (b) Three calculated curves, with vt = 167 Hz, tentative v,, = -50 Hz, K, = 1 . Slope of linear central region is -84.2 Hz for n = 2, -128.2 Hz for n 3 , v2 = - l 4 6 . 8 f 8 Hz, va=-39.1 i 6 Hz, v4= +0.8+5 Hf. = 3, -159.0 Hzfor n = 4, so = 4 . 3 8 8 , a=-0.591, ~ 4 ~ 4 . 7 3giving (c) Three calculated curves, with vt = 167 Hz, vn as in (b), Ko = 1 , plus the experimental curve, showing linear central reglons all parallel. - (log aexp] = 0.692 f 0.04 for n = 2, 1.210 i 0.04 for n = 3, 1.402 i 0.04 for n = 4 , so log K2 = 0.692 i 0.04, log 10 = 2.419 Shifts [(log f 0.08, log K4 = 4.205+ 0.12. (d)Calculated curves for n = 2, vt = 167 Hz, vz = -146.8 Hz, Kz = 4.92 f 0.5;for n = 3, vt = 167 Hz, v3 = -39.1 Hz, 10 = 263 i 50;for n = 4, VI = 167 Hz, v4 = +0.8 Hz, 16 = (1.60f 0.5) x lo4:plus experimental data (circled).The fit is clearly best for n = 3.
We also assume that K, is independent of total phenol concentrationX. X = [PI + n[PJ (3) The hydroxyl proton can be in either of two distinct environments: monomer, with NMR absorption frequency vl; o r n-mer, with absorption frequency v,. If t h e r a t e of chemical exchange is fast compared to the frequency separation .1 v. - v..../ between the two absorotions. then onlv one sharp hydroxyl signal is observed, i t a n average frequency weighted by the fraction of the protons in each environment:
,.
For a ~ v e \n \,, and n, all curves ofv vs. IogXfor diflerent K, are parallel and can be supenmposcd simply by shifting alone the loe X a x s : if the curve for K. = 1 is olotcrd. the c& far an; other k mav be obtainea bv translatine the K, = 1cupyealong thglog x -axis by (log K); 1 (n - 1). The central ort ti on at intermediate concentrationsX of anv v vs. log X curve is essentially linear, with a slope dire& proportional to ( v , - v,J. The proportionality constant depends on n, but is independent of Kw
A
The observed v a t any X thus depends on four parameters: vl, v,, K,, and n. All four are determined, one a t a time, such a s to replicate the single curve, v vs. log X, which has the following convenient properties (2):
This one curve displays a large concentration range without compression.
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Journal of Chemical Education
Experimental Caution: Phenol is cawtie and toxic. CC14 is toxic. Use gloves and work in hoods.
The instructor should make up accurately by weight a n almost saturated stock solution, by dissolving, for example, about 45 g of dry phenol in about 75 g of CC4. The stock bottle and all other glassware used must be dry. Solution is very slow, taking 1-2 days because the phenol floats and the process is endothermic. The stock solution is about 5 M. Prepare solutions with approximate molarities of 3 , 2 , 1 , 0.7,0.5,0.4,0.3, 0.2,0.1, 0.07, 0.05, 0.03, 0.02, 0.01, using only approximate volumes but accurate weighings. Transfer solutions with Pas-
teur ~ i ~ e twhich s . serve a s a ~ ~ r o x i m avolume te measures. Use two o r three of the intete&ediate solutions, for example, about 0.7 M and about 0.1 M, a s stock for further dilutions. Ground-glass-stoppered 10-mL and 25-mL volumetric flasks are convenient to use for preparing, weighing, and holding these solutions. Record the proton NMR spectrum of each solution, including the approximately 5 M stock. Measure the shifting hydroxyl proton peak position, using a s a n internal referk the sienal due to the ence anv convenient fixed ~ e a in protons'bn the aromatic ring (see Fig. 1). 6 e hydroxyl freouencies thus measured can be both nositive and neeative. ' Measure the temperature in the NMR probe. 'Ihe splitting of the two proton signals in methanol readily determines this (see Dyer ( 1 ) and Van Geet (4)).
Results Typical parameter ranges obtained a t Barnard College for good experiments, using a 60-MHz Varian T-60 N M R spectrometer, with the temperature of the probe a t 34 f 1"C, are given below.
Maximum observable hydroxyl shiR Av = 168 f 4 Hz, over a range ofXof about 0.5-0.001. Experimental v vs. IogXcurve: the slope of the linear central region is -115 f 10 Hz. F r o m calculated curves: e2= 0.385 f 0.015 cg = 0.585 it 0.025 ca = 0.141.0.04.
Data Analysis (Use prepared computer programs or spreadsheet templates.)
Best fit: n = 3. Iv1-v31 =200f %Hz
.
Calculate the total phenol concentration X for each solution in terms of the temperature-independent unit mole fraction. The stock solution should have a total phenol mole fraction X of about 0.5 when it is prepared as directed Plot theohsewed v vs. log Xwee Rg. 2a). Find v, by extrapnlatmn to the constant value of \ approached asX + 0, where only monomer is present. Kn is not large enough to find v, directly by extrapolation at IsrgeX. However, v, can be found indirectly fmm the essentially linear central region of the m e , whose slope is pre portional to (vl - v.). Measure as accurately as possihle the slope of the linear central region of the experimental curve. F i n d the v, that simulates the slope of the experimental curve, as follows. Neither n nor K,, is known at this point. Calculations must therefore be done for all reasonahle values of n, for example, n = 2,3,4. Set K" = 1in each case. For each n, with K, = 1,using the observed vl and any reasonable tentative value v,, calculate and plot a theoretical curve v vs. loe X (see Fie. " 2b). This is easiest when done by choosing an appropriate series of values for 11'1, then finding the corresponding [P,,I. X, and v. ([PImay exceed 1here.) Find the slope of the linear central portion of each theoretical curve and solve far the proportionality constants c, = slope/(vl -v,J. r For each n, using the cn found above, the observed vl, and in each case the measured slope of the experimental v vs. log X curve, solve for the indicated n-mer absorption frequency v, = vl - (slopelc,). Plot v vs. logX for n = 2,3,4, using K, = 1, the observed vl, and the v, found above. The central regions of all three calculated curves now have the same slope and are parallel to that part of the experimental curve (see Fig. 24. For each n, rncasu& the shin ( m e the foll&ing equation, at any point where rhceuwes are pnmllel. Solve for log K,, and then for K,.
.
.
.
F i n d n by seeing which curvev vs. IogXcalculated with vl, v., andK. hest fits all experimental data (see Fig. 2d). Obviously, only data at very high and very low X allow this discrimination, so the stock solution must be as concentrated as possible and the dilutions sufficient. Good experiments show an excellent fit for n = 3. The phenol trimers probably form six-membered (-O-H-I3 hydrogen-bonded rings.
logK3 = 2.45 f 0.25 K3 = 150-500 Aprevious NMR analysis, using less extensive and lower quality data, suggested that the phenol formed dimers (51, but our results agree with those of Saunders and Hyne (21, who found that all the data could be fit only with n = 3. Trimerizatiou of phenol in CCL solution over a similar range of concentration was confirmed from thermodynamic measurements by Woolley e t al. (6). Our results are valid only for the concentration range examined, from saturation down to the sensitivity limit of our NMR spectrometer. The data analysis rests on the assumption that only one n-mer species is present or a t least greatly predominates; it will fail if this no longer holds. Interestingly, recent IR spectroscopic investigation of this hydrogen-bondingsystem showed that, in CCL phenol associates not a s a trimer but a s a diier, with K = 70 5, a t the much lower concentrations (5 x 1PM to 1.6 x 10" M) appropriate to infrared absorption measurements (7). These NMR and IR results are not necessarily contradidory, but perfectly compatible ifthe equilibrium constants for dimerization and trimerization have particular values. Students may want to calculate the concentration ranges over which one particular n-mer predominates and to find the intermediate region where significant concentrations of both dimer and trimer are present. In crystalline phenol there are no separate n-mers, but rather infinite linear hydrogen-bonded chains (8,9).
*
Acknowledgment The author thanks Dorothy Beckett for the data and help in developing this experiment, and Rebecca Wendell for help preparing the figures. Llterature Cited 1. D*, John RApplrootloM ofAbaorptbn Spoclmarom of O w n i c Compounds;Rentie-Hall: Englewmd Cliffs, NJ, 1965:pp 5&97, especially pp 72, 90. 2. Saunders, M,Hyne, J.B. J. Ckem. Phys. 1968,29,1319-1323. 3. Porter,D.M.; Brey, W. S.,Jr.J. Phys. Ckem. 1867,71,37TMT83.
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4. Van G e t . A. LAnol. Chsm lM.40.2227-2229.
Huggina,C.M.:Amentel,G.C.:Shoolery,J. N. J P h y s . Ckem. 1956.60.1311-1314. 6. Woolley, E. M.; h v e r s , J. G.; Emo, B. P:Hepler, L. 0.J Phys. Ckem. 1971, 75, 35913597. 7. Fmhlieh, H. J Ckem. Educ. 1989,7O,A3-A6. 5.
8. Schenhger,C.Z.Xriaf. 1989,119,219-283. 9. Gillie~Pandraud,H. Bull. Soe Chim fiance
1887.1988-1995.
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