Heat of Dimerization of Formic Acid by FTIR Giles Henderson Eastern Illinois University, Charleston, IL 61920
Although microcomputers are becoming commonplace in the university, the typical undergraduate physical chemistry laboratory text does not describe experiments that exploit their capability. This paper will describe the determination of the heat of dimerization of formic acid from the temperature dependence of the dimer equilibrium constant. A computer is employed to carry out Fourier transform of IR inter ferograms to transmittance spectra, the conversion of transmittance to absorbance, spectral expansion, the separation of monomer and dimer contributions by spectral multiplication and subtraction, and the determination of vapor composition by spectral integration in addition to least-squares fitting and digital plotting. Although this project was carried out with a Nicolet model 20DXB FTIR using commercial software, the measurement could be easily performed with a conventional dispersion instrument, providing it was interfaced to a microcomputer (1).
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Thermodynamics of Formic Acid Dimer Formation Carboxylic acid molecules are strongly associated, even in the vapor phase. Early electron-diffraction studies (2) reveal that formic acid vapor is rich in a planar dimeric form stabilized by two hydrogen bonds (see Fig. 1). The monomerdimer equilibrium, 2CH202
is characterized by
an
Kn
=
(CHA>2 + heat
(1)
equilibrium constant P(CH20,)2/P2(CH20,)
(2)
where the activity of i is given by the partial pressure, P,. The IR spectrum of the vapor is expected to exhibit a mixture of overlapping monomer and dimer features. It is evident from eq 2 that the dimer concentration will increase quadratically with the partial pressure of the monomer. Thus a change in sample pressure is expected to produce a change in the ratio of monomer to dimer. This suggests the possibility of separating the overlapping monomer and dimer spectra by appropriate data processing. Since heat is evolved in dimer formation, the equilibrium, eq I, is expected to shift to the left, favoring high monomer concentrations and lower dimer concentrations at elevated temperatures. The composition of an equilibrium mixture and the value of the equilibrium constant could be experimentally determined from the IR absorption spectrum, proand dimer features are completely reviding the monomer solved and the appropriate Beer’s law integrated absorption coefficients are known. Assuming the vapor components are ideal, Pi [ijRT. =
Figure
88
1. C2/1
structure of the formic acid dimer.
Journal of Chemical Education
WAVENUMBERS
CCM-1)
Figure 2. FTIR absorption Spectrum of formic acid vapor at 20 °C and approximately 0.01 atm. The spectrum was measured with a 10-cm KBr cell using 20 scans and a 4-cm_1 resolution.
^
_
D
[(CH2Q2)2]
/fl/
where [i] is the molar concentration of i and (D) is the integrated absorption of a completely resolved IR band of the dimer.
Figure 3. A selected portion of the formic acid vapor spectrum. The upper trace was obtained from 20 scans af 0.010 atm and the lower trace was
obtained from 320 scans at 0.0025 atm. The ratios of the integrated absorption of both features are given and permit assignments of the monomer and dimer bands.
CO
Figure 5. The technique described here provides a powerful numerical method for separating overlapping absorption bands. The monomer and dimer components of the absorption between 760 and 530 cm-1 are given in the upper trace and the components of the C=0 stretching mode between 1830 and 1680 cm-1 are given in the lower trace.
WAVENUMBERS
CCM-1)
Figure 4. The absorption spectra of the dimer and monomer are obtained here as "positive and negative residual spectra", respectively, by appropriate linear combinations of high- and low-pressure vapor spectra.
4-cm1-resolution spectrum obtained from the Fourier transform of 20 interferograms. The spectrum was then diluted to approximately 1/4 the original concentration and the spectrum from 320 scans was obtained. The number of scans was increased by a factor of (4)2 to maintain the same signal-tonoise ratio as in the more concentrated sample. This procedure was repeated at five temperatures ranging from room temperature to 45.0 °C and the digitized spectra stored on floppy disk for future data processing. Data Treatment
Figure 3 compares the expansion of a selected portion of the formic acid vapor spectra at two different pressures. Here we note that the integrated absorption of the feature at 1105 cm-1 increased by a factor of 1.66 due to an increase in formic acid pressure while the integrated absorption of the feature at 1218 cm-1 increased by a factor of 2.80 ce (1.66)2. The quadratic pressure dependence of the 1218-cm_1 band allows us to assign this to the dimer and the 1105-cm~’ signal If we now multiply the entire low-pressure to the monomer. spectrum by 1.66 and subtract it from the high pressure spectrum, we expect all of the monomer features to be exactly cancelled and the positive residual absorption will be due to the dimer. Similarly, if we multiply the entire low-pressure spectrum by 2.80 and subtract it from the high-pressure
WAVENUMHERS
CCM-11
Figure 6. The temperature dependence of the IR absorption. The monomer CO stretching band at 1105 cm-1 increases with temperature at the expense of the dimer C-0 stretching band at 1218 ciTT1.
spectrum, all of the dimer contributions will be exactly cancelled. However, in this case, we will over-subtract the monomer contributions and will expect a “negative residual specBoth of these results are depicted in trum” of the monomer. Figure 4. Here we note a very satisfactory separation of the monomer and dimer features, particularly in those regions where the bands are overlapped as illustrated in Figure 5. We can further appreciate the value of this technique when we note how the 2945-cm_1 C-H stretching mode of the is totally obscured by overlapping dimer absorpmonomer tion in Figure 2 and how clearly this weak band is revealed in Volume 64
Number
1
January 1987
89
Table 1.
The Temperature Dependence of the Formic Acid Absorption8
Table 2. Method
t(° C)
pi
(D)lJ18
29.1 29.1
h
22.4j
33.0 33.0 37.0 37.0 41.0 41.0 45.0 45.0
h
I
I
h I
h 1
h 1
8.01a
,10s
16.5,
9.95,
30.5, 9.90,
21.72 12.38
30.6o 9.37s
24.4S 13.5s
27.3S
25.7,
8.30, 33.35
14.32 31.55
10.2,
17.6,
-8.21 -8.23 -8.46 -8.46 -8.71 -8.71 -8.94 -8.96 -9.16 -9.17
o CM
Figure 7. AFib is obtained from the slope of the least-squares fit of eq 5 to the observed data. Flere Q = (D) / (M)2T.
Figure 4. The curious student might wish to compare these observed vibrational frequencies with values calculated from recent normal coordinate analyses of both the monomer (3) and dimer (4). Now that we have a simple method of exactly separating the monomer and dimer absorption, we can investigate the
effect of temperature on the equilibrium composition. Figure 6 shows the C-0 stretching bands for both the dimer (1105 cm-1) at five tempera(1128 cm-1) and the monomer tures. We note that the monomer absorption increases at the expense of dimer absorption, as expected for an exothermic reaction. The integrated absorption of these features are summarized in Table I. These results were then employed in eq 5 to obtain the heat of dimerization. A plot of In[(D) / ((M)2T)] versus T~l is given in Figure 7. The least-squares slope, (5.76 ± 0.5) X 103, multiplied by —R gives AH°n = —47.9 ± 0.4 kJ/mol. This result is compared with other literature values in Table 2. Discussion
It is evident from Table 2 that there is a wide disagreement in the value of A Ho for formic acid. The very careful vapor .density measurements by Coolidge (5) give a higher experimental result than the absorption measurements. Perhaps the discrepancy of these methods is real and caused by the fact that the vapor density method includes all types of associations whereas the absorption methods do not. Herman (6') reports a Aslightly higher than the results deter-
Journal of Chemical Education
Date
Source
ln«D>/(M>27)
M (D) and (M) correspond to the integrated absorption of the v, dimer band at 1216 cm-1 (4} and the monomer band at 1105 cm-1 (3), respectively. 6h and I represent approximately 0.010 and 0.0025 atm ot formic acid vapor.
90
Heat of Dimerization ol Formic Acid AFfc(kJ/mol)
Vapor density IB absorption LCAO-MO-SCF Min-Basis-STO-SCF optimized structure Double zeta SCF with distortion energy
1928 1940 1971 1976
Coolidge (5) Flerman (6) Clementi et al. (8) Del Bene et al. (9)
-59 -52 ± 3 -67.8 -63.2
1978
Smit et al. (10)
-49.4
FTIR
this work
-48.9 ± 0,4
mined here. However, this discrepancy may be due to Herman using absorption values at Amax rather than integrated absorption values. As the temperature changes, the corresponding Boltzman population of rotational levels change resulting in a different band shape. This phenomenon could cause the apparent absorption coefficient at Amax to vary with changes in temperature and introduce a systematic error in the slope of In K versus 1/T. This difficulty is clearly avoided by integrating the absorption over all of the observed rotational envelope. Clague and Bernstein (7) have compared both methods and also observe a 4-kJ/mol decrease in AHn when using band areas rather than peak height. We also note large discrepancies in the theoretical ab initio values (8-10). However, with continued refinements in basis sets and optimized geometries, these calculations are converging with the experimental spectroscopic values. It is evident from eq 5 that AS^ could be determined to three significant figures from the intercept of Figure 7, providing accurate values of the integrated absorption coefficients were known. This would require accurate sample concentrations or making pressure measurements with an order of magnitude greater precision than possible with a simple mercury manometer. Another alternative would be to measure the spectra at a sufficiently high temperature that the sample would be virtually 100% dissociated, permitting a direct determination of (cm) from Beer’s law. Here we estimate AS°n as —180 ± 50 J/mol deg, based on the leastsquares intercept (—27.3 ± 0.2) and reasonable limits on the absorption coefficients. The sign of AS confirms a decrease in entropy or disorder upon dimer formation. In summary, this FTIR measurement seems well suited to the modern undergraduate physical chemistry laboratory. It exploits the capability of the microcomputer to carry out what would otherwise be prohibitive calculations and simultaneously illustrates fundamental thermodynamic equilibrium principles. The exercise can be easily completed in two 3h laboratory periods. Perhaps the most efficient use of the equipment is realized by collecting one set of data during the first period, storing all of the spectra on floppy disk, and then scheduling individual students (pairs) for a second keyboard session to carry out the data treatment.
Acknowledgment The author wishes to convey his appreciation for finanical support of this project by the Eastern Illinois University Council for Faculty Research. Literature Cited (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Mattson, B. M.; Shepherd, T. R.; Solsky, J. F. J. Chem. Educ. 1985,62,690. Karl. -J.; Brockway, L. J. Amer. Chem. Sac. 1944,66,574. Redington, R. J. Mol. Spectrosc. 1977, 65,171. Hagen, I.; Cyvin, S. J. Mol. Struct. 1971,8,159. Coolidge, A. J. Amer. Chem. Soc. 1928,50, 2166. Herman, R. J. Chem. Phys. 1940,8, 252. Clague, A.; Bernstein, H. Spectrochim. Acta 1969,25A, 593. Clementi, E.; Mehl, J.; von Niessen, W. J. Chem. Phys. 1971,54, 508. Del Bene, J.; Kochenour, W. J. Amer. Chem. Soc. 1976, 98, 2041. Smit, P.; Derissen, J.; van Duijneveldt, F. J. Chem. Phys. 1978,69,4241.
