G. A. CROWDER AND BOBBYR.
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Acknowledgments. This research was supported by the U. S. Department of the Interior, Office of Saline Water. The authors thank Drs. W. H. RlcCoy and A. B. Gancy for helpful discussions during the course
COOK
of the work and Drs. R. A. Robinson and R. D. Lanier for criticism of the manuscript. A h . Mary L. Meehan assisted in the design of the apparatus and in the preliminary experiments.
Acetonitrile: Far-Infrared Spectra and Chemical Thermodynamic Properties. Discussion of an Entropy Discrepancy
by G. A. Crowder' and Bobby R. Cook Department of Chemistry, West Texas State University, Canyon, Texas
(Received August 51, 1966)
Liquid- and vapor-state infrared spectra in the region 75-650 cm-' were obtained for acetonitrile. The entropy discrepancy a t 298.15"K was shown to result partially from the use of the liquid-state frequency for the skeletal bending vibration. The remaining entropy discrepancy is discussed. A table of the chemical thermodynamic properties of acetonitrile at selected temperatures was prepared.
Introduction The entropy of acetonitrile a t 298.15"K, corrected to the ide:tl gas state at 1 atm, was determined by Putnam, AlcEachern, and Kilpatrick (PMK)2* to be 58.67 f 0.20 cal deg-' mole-'. This value is 0.66 cal larger than the value of 58.01 cal deg-' mole-' calculated by Giinthard and KovatsZbusing the rigid rotatorharmonic oscillator model. This discrepancy suggests an error either in the vibrational assignment or molecular parameters used in the calculation or in the experimental data. The present work was undertaken to examine the discrepancy. The examination consisted of a recalculation of the statistical mechanical entropy using vapor-state wavenumbers and a revised set of molecular parameters and a critical look at the gas imperfection correction and experimental entropy of vaporization.
Experimental Section Far-infrared spectra of acetonitrile were determined at room temperature with a Perkin-Elmer Model 301 spectrophotometer. A stainless steel cell, with path The Journal of Physical Chemistry
length variable in increments of 1-6 m, was used in obtaining the vapor-state spectrum. The sample of acetonitrile was obtained from the Eastman Kodak Co. Infrared spectra in the region 650-4000 cm-' did not show any impurity bands.
Results and Discussion Far-Infrared Spectra. It has been shown that vibrations with a wavenumber lower than about 250 cm-' usually have a lower wavenumber in the vapor than in the liquid statea3 Since the lorn-frequency vibrations contribute the most to the thermodynamic functions, vapor-state values for these vibrational frequencies are necessary in calculations of vapor-state thermodynamic properties. Gunthard and Kovats (1) T o whom all correspondence should be addressed a t Department of Chemistry, West Texas State University, Canyon, Texas 79015. (2) (a) W. E. Putnam, D. M. McEachern, Jr., and J. E. Kilpatrick, J . Chem. Phys., 42, 749 (1965); (b) H. H. Gunthard and E. Kovats, Helv. Chim. Acta, 35, 1190 (1952). (3) W. G. Fateley, I. Matsubara, and R. E. Witkowski, Spectrochim. Acta, 20, 1461 (1964); G. A. Crowder and D. W. Scott, J . Mol. Spectry., 16, 122 (1965).
ACETONITRILE : FAR-INFRARED SPECTRA
used the value 380 cm-' for the doubly degenerate skeletal bending vibration of acetonitrile. This value was taken from the liquid-state Raman spectrum. Although no large frequency shifts have been observed for bands in this region of the spectrum, it was thought that this band might shift to a lower wavenumber in going from liquid to vapor because of the high degree of polarity of the molecule. Figure 1 shows the infrared spectrum of acetonitrile in the region 75-650 cm-'. A shift of the skeletal bend in the right direction is clearly observed, with the vapor-state wavenumber being 360 cm-l. This is 20 cm-' lower than the value used in the previous calculation of the entropy and use of the vapor-state value will result in an increase of 0.17 cal deg-l mole-' in the calculated entropy. The liquid-state infrared value of the skeletal bend is 376 cm-l, so the shift amounts to 16 cm-l. The skeletal bending vibration is the only fundamental vibration with a frequency in the region below 650 cm-l. The acetonitrile molecule has a small moment of inertia about the molecular axis and it may be possible for rotational bands to be observed in the far-infrared region. I n the vapor-state spectrum, the broad band observed at 195 cm-' and the increasing absorption near 75 cm-1 may be superpositions of unresolved rotational bands. Jones and Sheppard4 have given evidence that the acetonitrile molecule has a considerable degree of rotational freedom in the liquid state. The increasing absorption below about 275 cm-l in the liquid-state spectrum may be due to rotational transitions in the liquid state. The weak bands observed a t 418, 510-515, and 575 cm-' may be impurity bands, because no difference combination bands can be assigned to any of these. Calculation of Thermodynamic Functions. The thermodynamic functions of acetonitrile were recalculated, using the vapor-state value for the skeletal bend. The calculations, based on the rigid rotator-harmonic oscillator approximation, were made with the usual formulas of statistical thermodynamics.6 The wavenumbers used in this calculation and their degeneracies are: 360(e), 922(al), 1038(e), 1372(a1), 1443(e), 2262(al), 2941(al), and 3001(e). All these values except for the skeletal bend were taken from ref 6. For the rotational contribution, Gunthard and Kovats used the data of Kessler, et al.' Costain* has redetermined the molecular parameters of acetonitrile and his data were used in the present calculation. The molecular structure constants used were 1.104 A for the C-H distance, 1.458 A for the C-C distance, 1.157 A for the C=N distance, and all C-C-H and H-C-H angles were taken as tetrahedral.
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Figure 1. Far-infrared spectra of acetonitrile: a, vapor a t 83 torr, pathlength indicated on figure; b, liquid, path length indicated on figure or unknown; ordinate given in per cent transmittance.
The moments of inertia were calculated to be I , = 5.441 X 10-qgcm2,1t, = I , = 91.11 X 1 0 - ~ g c m 2 . Gas Imperfection. The total entropy of acetonitrile in the ideal gas state a t 298.15"K and 1 atm was calculated to be 58.20 cal deg-l mole-'. Although significantly higher than the value calculated by Gunthard and Kovats, this value is 0.47 cal deg-l mole-' lower than the experimental value of PMK. Examination of their data shows an unusually large gas imperfection, 0.55 cal. This correction was determined from the rather inaccurate data of Lambert, et ~ l . for , ~ the second virial coefficient as a function of temperature. From a reexamination of Lambert's data, the eq B = -250 - 7.50 exp(2000/T) cc mole-' was fitted to the curve. Extrapolation to 298.15"K gives dB/dT = 138 and from this the gas imperfection is 0.39 cal. Use of this value gives S o o b s d = 58.51 cal deg-' mole-', which is still 0.31 cal deg-' mole-' higher than the calculated value. Enthalpy of Vaporization. Another possibility for error lies in the experimental enthalpy of vaporization. Measurements of enthalpies of vaporization at about room temperature or higher, during which the liquid is distilled from a low-temperature calorimeter and the vapor condensed into a weighed glass sample bulb immersed in liquid air, have been known to be in error. For example, Aston, Finke, and Schumannlo used this type of measurement for cyclopentane and found the ~~
~
~~
~~
(4) W. J. Jones and N. Sheppard, Trans. Faraday SOC., 56, 625 (1960). (5) K. 9.Pitzer, "Quantum Chemistry," Prentice-Hall, Inc., Englewood Cliffs, N. J., 1953. (6) J. C. Evans and G. Y-S. Lo, Spectrochim. Acta, 21, 1033 (1965). (7) M. Kessler, H. Ring, R. Trambarulo, and W. Gordy, Phys. Rev., 79, 54 (1950). (8) C. C. Costain, J . Chem. Phys., 29, 864 (1958). (9) J. D.Lambert, G. A. H. Roberts, J. S. Rowlinson, and V. J. Wilkinson, Proc. Roy. SOC.(London), A196, 113 (1949). (10) J. G.Aston, H. L. Finke, and 8. C. Sohumann, J . A m . Chem. Soc., 65, 341 (1943).
Volume 71, Number 4 March 1067
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G. A. CROWDER AND BOBBY R. COOK
enthalpy of vaporization to be 6982 f 8 cal mole-'. A more accurate value is 6818 cal mole-'.'' P M K give vapor-pressure data for acetonitrile in the temperature range 280-300°K. They fitted an Antoine equation t o the data and from the Clapeyron equation and the value of dp/dt determined from the Antoine equation they calculated AH,,, = 7865 cal mole-'. Quinn12 determined the vapor pressure for the range 310-378°K and his Antoine equation reproduces the data of P M K as well as their equation. From Quinn's equation, AH,,, was calculated t'o be 7848 cal mole-', in good agreement with the value obtained from the vapor-pressure data of PMK. We fitted a Cox equation to the P M K data by a leastsquares method and found AH,,, to be 7830 cal mole-'. We also fitted a Cox equation to the combined data of PMK and Quinn. The following equation, good in the range 280-38OoK, was obtained. logP(atm) = A ( l - 354.776/T)
(1)
I n eq 1, A is given by logA = 0.772542
- 3.94845
X
+ 4.06868 x
10-4~
10-7~2 (2)
I n eq 1 and 2, T is in OK. From eq 1 and 2, the enthalpy of vaporization was calculated to be 7848 cal mole-', in good agreement with the values given above, but lower than the experimental value of PMK, which is 7941 cal mole-'. We feel that this .is the experimental measurement that is most likely to be in error and prefer the calculated value of 7848 cal mole-'. When this value is used, the calculated and experimental entropies a t 298.15"K are in agreement. Comparison of Experimental and Theoretical Entropies and Table of Thermodynamic Functions. Table I summarizes the experimental entropy tabulation for acetonitrile a t 298.15"K. Table I1 gives the thermodynamic functions, calculated a t selected temperatures for acetonitrile.
The Journal of Physical Chemistry
Table I: The Molal Entropy of Acetonitrile a t 25' (cal deg-1)
Liquid" Vaporization, 7848'/298.15 Gas imperfection" Compression
35.76 f 0.15 26.32 0.39 -4.27
Total experimental entropy Statistical mechanical entropy
5 8 . 2 0 f 0.20 58.20
'
From ref 2a. From vapor-pressure data in ref 2a and 12. From data in ref 9.
Table 11: The Molal Thermodynamic Properties of Acetonitrile in the Ideal Gas State a t I Atm
-
-(P
(NO -
T, OK
HOa)/T, cal/deg
Hoo)/T, cal/deg
273.15 298.15 300 400 500 600 700 800 900 1000
47.65 48.49 48.55 51.48 53.98 56.19 58.22 60.09 61.85 63.50
9,474 9.706 9.724 10.70 11.69 12.67 13.60 14.49 15.31 16.08
Ha
- Nom, kcal
2.588 2.894 2.917 4.278 5.846 7.601 9.521 11.59 13.78 16.08
Sa,
cal/deg
57.12 58.20 58.27 62.18 65.67 68.86 71.82 74.58 77.16 79.58
cos cal/deg
11.99 12.51 12.55 14.66 16.65 18.42 19.97 21.32 22.51 23.55
Acknowledgments. This investigation was supported by Grant 660-A from the Petroleum Research Fund of the American Chemical Society, administered by Oklahoma State University, and was carried out in the Thermodynamics Laboratory of the Bartlesville Petroleum Research Center, Bureau of Mines, U. Department of the Interior, Bartlesville, Okla. The authors are grateful to Dr. Donald W. Scott for discussions of this work.
s.
(11) J. P. McCullough, R. E. Pennington, J. C. Smith, I. A. Hossenlopp, and G. Waddington, J. Ana. Chem. SOC.,81, 5880 (1959). (12) G.L. Quinn, Thesis, University of Wisconsin, 1951.
