Article No. jcht.1998.0452Available online at http://www.idealibrary.com on

J. Chem. Thermodynamics1999, 31, 323–337

Thermodynamic properties of themethylpyridines. Part 1. Heat capacitymeasurements for 4-methylpyridine betweenT = 6.4 K and T = 18.6 K, resolution oflow-temperature contributions, and reconciliationof calorimetrically and spectroscopically derivedstandard entropiesa

R. D. Chirico,b,c S. E. Knipmeyer, and W. V. Steeled

Bartlesville Thermodynamics Group, BDM-Petroleum Technologies,P.O. Box 2543, Bartlesville, OK 74005, U.S.A.

Heat capacities and enthalpy increments between the temperatures 6.4 K and 320 K were de-termined for 4-methylpyridine (Chemical Abstract registry number 108-89-4) by adiabaticcalorimetry. Results for temperatures≥ 20 K were found to be in excellent accord with liter-ature values; however, accord forT < 20 K was poor. The new experimental heat capacitiesfor temperatures<20 K are used with results of inelastic neutron scattering (i.n.s.) studiesfrom the literature to resolve the contributions to the heat capacities. Contributions arisingfrom rotation of the methyl group are discussed in detail. Results are interpreted in terms ofa three-fold barrier to rotation in accord with recent i.n.s. studies. Earlier suggestions in theliterature of a six-fold potential are not supported. Revised thermodynamic functions forthe condensed phases of 4-methylpyridine are derived. Revised thermodynamic functionsare corroborated through accord between calorimetric and statistically derived standardentropies. c©1999 Academic Press

KEYWORDS: heat capacity; methyl group rotational barrier; entropy

1. Introduction

The barrier to methyl-group rotation in the solid state for 4-methylpyridine(0.32 kJ·mol−1)

is the smallest known for a molecular crystal.(1) Consequently, 4-methylpyridine is a keycompound in the modeling of molecular rotation, as discussed by Abedet al.(2) In a re-cent review, Daset al.(3) showed that standard entropies1T

0 Som derived independently from

aContribution number 375 from the Bartlesville Thermodynamics Research Group.bTo whom correspondence should be addressed.cPresent address: National Institute of Standards and Technology, 100 Bureau Drive, M.S. 8381, Gaithersburg,

MD 20899-8381, U.S.A. (E-mail: chirico@nist.gov).dPresent address: Oak Ridge National Laboratory, P.O. Box 2008, Building 4501, M. S. 6221, Oak Ridge, TN

37831-6221, U.S.A.

0021–9614/99/030323 + 15 $30.00/0 c© 1999 Academic Press

324 R. D. Chirico, S. E. Knipmeyer, and W. V. Steele

available calorimetric studies and from spectroscopic information are not in accord. Thestandard state is defined as the ideal gas at the pressurep = po = 101.325 kPa. Valuesof 1T

0 Som for 4-methylpyridine derived from assigned vibrational spectra and statistical

mechanics are 0.16 · R(≈0.004·1T0 So

m) larger than those derived from calorimetric stud-ies.(3, 4) These deviations are approximately four times larger than expected based upon theuncertainties associated with each method.

Earlier publications by this research group have shown how accord between calorimetricand spectroscopically derived1T

0 Som values can be exploited to confirm thermodynamic

consistency between many important thermophysical properties including heat capacitiesof all phases, vapor pressures, enthalpies of vaporization, virial coefficients, vibrationalassignments, barriers to internal rotation, and critical properties. Lack of accord indicatesan error in one or more of these properties.(5–7)The purpose of the present paper is to resolvethe discrepancy between the independently derived1T

0 Som values for 4-methylpyridine.

Early inelastic neutron scattering (i.n.s.) studies concluded that the methyl group in4-methylpyridine was hindered by a six-fold potential.(8) More recently, Abedet al.(2)

repeated the i.n.s. studies, showed that the earlier results were in error, and determinedaccurately the barrier to methyl-group rotation in terms of a three-fold potential. The rota-tional barrier determined by Abedet al.(2) is used here together with new heat capacities forthe crystals at low temperature{6 ≤ (T/K) ≤ 20 K} to derive a revised standard entropyincrement120 K

0 Som. This revised increment will be shown to provide very good accord

between the calorimetric and spectroscopically derived1T0 So

m values.

2. Experimental

The sample of 4-methylpyridine used in this research was prepared as part of AmericanPetroleum Institute Research Project 52. A portion of the sample was used previously forstudies of vapor heat capacities and enthalpies of vaporization.(9) The original mole fractionpurity x of the sample was 0.998. This was improved tox = 0.9993 by distillation on aspinning-band still prior to the studies reported here. The purity was determined here byfractional melting.

Molar values are reported in terms of molar massM = 93.1283 g·mol−1 and the gas

constantR = 8.31451 J· K−1 ·mol−1

, adopted by CODATA.(10) The platinum resistancethermometer used was calibrated by comparison with a standard thermometer, whose con-stants were determined at the National Institute of Standards and Technology (NIST). Thecalibration was extended to temperatures belowT = 13.81 K by the method of McCrackinand Chang.(11) All temperatures are in terms of ITS-90.(12, 13)Measurements of mass, time,electrical resistance, and potential difference were made in terms of standards traceable tocalibrations at NIST.

Adiabatic heat capacity and enthalpy measurements were made with a calorimetric systemdescribed previously.(14, 15) The platinum calorimeter (internal volume 62.47 cm3) wasfilled with 46.716 g of 4-methylpyridine and sealed with a gold-gasketed screw-cap closureunder a helium pressure of 11.2 kPa atT = 297 K. Energy measurement procedureswere the same as those described for studies on quinoline.(14) Thermometer resistances

Heat capacities of 4-methylpyridine 325

were measured with a self-balancing alternating-current resistance bridge (H. Tinsley &Co. Ltd.; Model 5840D). The energy increments to the filled platinum calorimeter werecorrected for enthalpy changes in the empty calorimeter and for the helium exchange gas.The ratio of the heat capacity of the sample to that of the empty calorimeter was≈12 nearT = 6 K, and≈5 nearT = 20 K. The maximum correction to the measured energy for thehelium exchange gas was 0.07 per cent atT = 6 K.

3. Results

Crystallization of the 4-methylpyridine sample was initiated by cooling (approximately2 mK · s−1) the liquid sample to≈20 K below the triple-point temperatureTtp. The crystalswere annealed by maintaining the sample under adiabatic conditions in the partially meltedstate (15 per cent to 25 per cent liquid) for approximately 8 h. No spontaneous warming,which would indicate incomplete crystallization or phase conversion, was observed. Thesample was cooled at an effective rate of 1 mK· s−1 to crystallize the remaining liquid. Asa final step, the sample was thermally cycled betweenT < 100 K and within 2 K ofTtp,where it was held for a minimum of 3 h to provide further tempering. All of the solid-phasemeasurements were performed upon crystals pre-treated in this manner.

The Ttp and the mole fraction purity were determined to be(276.826 ± 0.01) K and0.99925, respectively, from the measurement of equilibrium melting temperaturesT(F) asa function of fractionF of the sample in the liquid state.(16) Equilibrium melting tempera-tures were determined by measuring temperatures at approximately 300-s intervals for 1 hto 1.2 h after an energy input and extrapolating to infinite time by assuming an exponen-tial decay toward the equilibrium value. The presence of solid-soluble impurities was notindicated.

Molar heat capacities under vapor saturation pressureCsat,m were determined for thetemperature range 6≤ (T/K) ≤ 320. For all temperatures≥ 20 K these were found to bein excellent accord (within 1· 10−3 ·Csat,m) with those reported previously by Messerlyetal.(4) The average deviation for this temperature range was only 3·10−4 ·Csat,m. The smalldifferences were probably due to differences in purity between the sample used here (molefraction purity 0.99925) and that used by Messerlyet al.(4) (mole fraction purity 0.9997).The triple-point temperatureTtp = (276.826 ± 0.01) K observed here is also in excellentaccord with that reported by Messerlyet al., Ttp = (276.817 ± 0.01) K.(4) Because of thehigher sample purity, the results reported by Messerlyet al.(4) are considered more reliablefor temperatures>20 K. Consequently, no new heat capacity values are reported here forthis temperature region.

Saturation heat capacitiesCsat,m measured in this research forT ≤ 20 K are listed intable 1. The precision of the heat capacity measurements ranged from approximately 5 percent atT = 6 K, to 1 per cent atT = 10 K, and 0.2 per cent nearT = 20 K.

At temperatures belowT = 20 K, long equilibration associated with the attainment ofthermal equilibrium between the lattice and methyl-group rotations was reported by denAdel et al.(17) and by Beckmannet al.(18) Messerlyet al.(4) did not recognize the existenceof these long equilibration times in their studies. Consequently, their results forT ≤ 20 Kare in error. For nearly all organic compounds, equilibration times for temperatures be-

326 R. D. Chirico, S. E. Knipmeyer, and W. V. Steele

TABLE 1. Molar heat capacitiesCsat,m at vapor saturation pressure for 4-methylpyridine measured

with adiabatic calorimetry(R= 8.31451 J· K−1 ·mol−1)

Na 〈T〉K

1T

K

Csat,m

R

bNa 〈T〉

K

1T

K

Csat,m

R

b

Crystals

5 6.41 0.63 0.476 3 13.37 1.33 1.039

5 7.06 0.82 0.494 3 14.83 1.54 1.178

5 8.11 1.47 0.578 6 15.11 2.97 1.212

5 9.53 1.49 0.690 3 16.46 1.72 1.352

6 10.88 1.40 0.809 3 18.26 1.86 1.548

6 12.60 2.06 0.961 6 18.56 3.90 1.584aAdiabatic series number.bAverage heat capacity for a temperature increment of1T with a mean temperature〈T〉.

TABLE 2. Low-lying energy levelsν of hindered rotors in a three-fold and six-fold potential with

the barrier heights adjusted to make the first excited level 4.2 cm−1

ν

cm−1ga ν

cm−1ga

V3 = 0.32 kJ·mol−1 V6 = 1.5 kJ·mol−1

0 1 0 1

4.2b 2 4.2b 2

25.0 2 15.4c 2

49.4 1 23.8 1

51.1 1 86.7 1

87.2 2 105.6 2

135.0 2 148.2 2

193.5 2 199.9 1

ag is the degeneracy of the energy level.bObserved by Abedet al.(2) and Alefeldet al.(8)

cObservation of this wave number splitting was claimed by Alefeldet al.(8) Abedet al.(2) showed the observationto be in error.

low T = 20 K are less than 60 s. In contrast, equilibration times for 4-methylpyridinefound in this research were≈3000 s forT ≤ 10 K. The equilibration times graduallydecreased to normal values betweenT = 10 K andT = 20 K, and were normal for allhigher temperatures. The change in equilibration time with temperature is reflected in thedeviations of values reported by Messerlyet al.(4) from those given here. The deviationsincrease smoothly with decreasing temperature from near perfect accord nearT = 20 K to0.05 · Csat,m nearT = 13 K, the lowest temperature measured by Messerlyet al.(4)

Heat capacities of 4-methylpyridine 327

TABLE 3. Molar entropies1T0 Sm at low temperatures for crystalline methylpyridinesa

T

K

1T0 Sm (total)

R

1T0 Sm (lattice)

R

1T0 Sm (rot)

R

1T0 Sm (opt)

R

4-methylpyridine

5.0 0.958 0.030 0.928 0.000

10.0 1.332 0.163 1.169 0.000

15.0 1.714 0.368 1.347 0.000

20.0 2.132 0.639 1.493 0.000

a1T0 Sm(total) =1T

0 Sm(lattice)+1T0 Sm (rot) +1T

0 Sm(opt). See text.

4. Discussion

Heat capacitiesCsat,m for the methylpyridines at temperatures<20 K can be representedas a summation of terms:

Csat,m = Clattice,m+ Copt,m+ Crot,m, (1)

whereClattice,m arises from thermal population of intermolecular vibrational energy levels,Copt,m arises from intramolecular vibrational energy levels, andCrot,m stems from energylevels associated with rotation of the methyl group relative to the pyridine ring. For mostorganic materials,Crot,m andCopt,m are very small for temperatures betweenT = 2 K andT = 20 K, and measuredCsat,m values can be extrapolated readily toT → 0 with a sumof Debye functions. This is done typically by near linear extrapolation of a plot ofCsat,m/TagainstT2 for temperatures below 10 K. For 4-methylpyridine,Crot,m is much too large fortemperatures<20 K to use this approach, and an alternative method of extrapolatingCsat,mto T → 0 must be used.

The approach used here was to first calculateCopt,m and Crot,m for the temperaturerange 0≤ (T/K) ≤ 20 with available assigned wave number values(19–21)and the knownrotational barrier,(2) respectively. Values ofClattice,m were then calculated by difference forthe experimental temperature range 6.4 ≤ (T/K) ≤ 18.6 by using equation (1) and themeasured heat capacities given in table 1. Extrapolation of the resulting values ofClattice,m

to T → 0 was then accomplished with the usual plot ofCsat,m/T againstT2.Values ofCopt,m were calculated with the harmonic oscillator approximation for the 35 in-

ternal vibrational modes using available complete assignments(16–18)for 4-methylpyridine.For temperatures<20 K it was found that this contribution was very small and could beignored. TheCopt,m/R was calculated to be only≈1 · 10−4 at T = 20 K and was muchsmaller at lower temperatures.

Calculation ofCrot,m values required the energy levels for the methyl-group rotation.These were calculated from solutions of the torsional wave equation for a rotor with three-fold symmetry:

− F{d29(φ)/dφ2} + {(V3/2) · (1− cos 3φ)}9(φ) = E9(φ), (2)

whereF is the internal rotation constant for the rotor,φ is the rotation angle,V3 is the

328 R. D. Chirico, S. E. Knipmeyer, and W. V. Steele

rotation barrier height, andE represents the rotational energy levels. The value ofF isinversely related to the reduced moment of inertiaIred for the rotor.

F = h2/(8π2 · Ired). (3)

The value ofIred (5.26 · 10−47 kg ·m2) was calculated with an approximate molecularstructure for 4-methylpyridine. The structure was estimated with bond lengths listed byDraeger(22) for the pyridine ring. The C–H bond distances within the methyl group wereassumed equal to those for methane, as reported by Bartellet al.(23) The aromatic-carbonto methyl-carbon distance was estimated from a crystal structure ofp-xylene reported byKoningsveldet al.(24) The method of Lewiset al.(25) was used to calculate the rotationalenergy levels using equation (2), and standard methods of statistical mechanics were usedto calculate the heat capacity arising from their thermal population.

The size of the three-fold rotation barrierV3 was determined with the results of inelasticneutron scattering studies by Abedet al.(2) and Alefeldet al.(8) Alefeld et al.(8) determinedthe splitting(4.19± 0.08) cm−1 between the ground and first excited state for the energylevels associated with rotation of the methyl group in 4-methylpyridine. The magnitude ofthis splitting was later confirmed by Abedet al.(2) Alefeldet al.(8) also reported several veryweak peaks at higher energies in their spectra. The observation of these higher peaks leadthem to postulate a six-fold potential for rotation of the methyl group. The later measure-ments by Abedet al.(2) showed that the higher peaks were not present and that the resultswere well represented by a three-fold potential.

The splitting between the ground and first excited state for the methyl rotation is verysensitive to the size of the three-fold rotation barrierV3. The splitting observed by Alefeldet al.(8) (4.19± 0.08) cm−1 corresponds toV3 = (0.32± 0.02) kJ ·mol−1. The splittingbetween the ground and first excited state for 4-methylpyridine is much larger than thatfor 3-methylpyridine(0.081 cm−1) or 2-methylpyridine(0.013 cm−1).(1, 26) These smallersplittings correspond toV3 values of 3.0 kJ·mol−1 and 4.5 kJ·mol−1, respectively. Thesize ofV3 is inversely related to the magnitude of the splitting.

Figure 1 shows the splitting of the low-lying energy levels for a methyl rotor in amethylpyridine as a function of the restricting potentialV3. Arrows indicate theV3 valuesfor 4-methylpyridine(0.32 kJ·mol−1) and 3-methylpyridine(3.0 kJ·mol−1). The left axis(V3 = 0) corresponds to the energy level distribution for a free rotor. AtV3 = 3.0 kJ·mol−1

the splitting pattern begins to resemble that for a three-fold harmonic oscillator (a series oftriply-degenerate states). The relationship between the barrier height and the distribution ofenergy levels has been discussed in general terms in texts by Pitzer(27) and Davidson.(28)

The methylpyridines provide examples approaching the two limiting cases (the free rotorand the harmonic oscillator) within a single family of compounds.

The change in energy level distribution withV3 has a large effect on theCrot,m valuesbelow T = 20 K, as shown in figure 2. Heat capacities derived withV3 = (0, 0.32, 1,and 3) kJ·mol−1 are shown. Barriers to methyl-group rotation in the solid state for mostorganic materials are larger than 3 kJ·mol−1.(1) Consequently,Crot,m is typically very nearzero in the temperature range 2≤ (T/K) ≤ 12 and only theClattice contribution remains.Extrapolation of measured heat capacities toT → 0 can then be done readily with a plotof Csat,m/T againstT2. This simple approach cannot be used for 4-methylpyridine.

Heat capacities of 4-methylpyridine 329

00

25

50

75

100

1 2 3

V3 / (kJ . mol–1)

Eig

enva

lue

/cm

–1

FIGURE 1. Energy levels derived using equation (2) for a methyl rotor as a function of the restrictingbarrierV3. —, Energy levels with degeneracyg = 1; – – –,energy levels withg = 2. The ground stateis a singlet. The arrows indicate the restricting barriers for 4-methylpyridine(V3 = 0.32 kJ·mol−1)

and 3-methylpyridine(V3 = 3.0 kJ·mol−1).

Figure 3 shows a plot ofCsat,m/T againstT2 for the Csat,m values measured in thisresearch (table 1) for temperatures≤18.6 K. Also shown is a plot ofClattice,m/T againstT2 for 4-methylpyridine derived by subtractingCrot,m values from the measuredCsat,mvalues. TheCrot,m values were calculated withV3 = 0.32 kJ·mol−1.(2) Values ofClattice,mfor temperatures<6.4 K for 4-methylpyridine were obtained by graphical extrapolation, asshown in the figure.

Plots ofClattice,m/T againstT2 for 2-methylpyridine and 3-methylpyridine are includedin figure 3 for comparison. Values ofCrot,m are negligible for 2- and 3-methylpyridine at thetemperatures shown. Consequently, the difference betweenCsat,m andClattice,m for thesematerials is not significant even at the highest temperature (T≈18.7 K) shown in figure 3.

The heat capacities obtained in the present research can be used to provide evidencesupporting the three-fold restricting potential for the methyl rotation determined by Abedet al.(2) rather than the six-fold potential suggested by Alefeldet al.(8) Table 2 lists thelow-lying energy levels for a hindered rotor in a three-fold and six-fold potential with the

330 R. D. Chirico, S. E. Knipmeyer, and W. V. Steele

0 5 10 150.0

0.2

0.4

0.6

0.8

0 0.1 0.2 0.3 0.4 0.50

0.2

0.4

0.6

0.8

T / K

Cro

t,m/R

FIGURE 2. Heat capacitiesCrot,m associated with rotation of the methyl group relative to thepyridine ring for several restricting barriersV3. �, V3 = 0 (free rotation);◦, V3 = 1 kJ·mol−1; O,V3 = 3 kJ·mol−1; - - -, V3 = 0.32 kJ·mol−1 (the restricting barrier for 4-methylpyridine). Thearrow indicates the lower temperature limit of the heat capacities measured in this research.

TABLE 4. Molar enthalpy increments1T0 Hm at low temperatures for crystalline 4-methylpyridinea,b

T /K1T

0 Hm (total)

RT

1T0 Hm (lattice)

RT

1T0 Hm (rot)

RT

1T0 Hm (opt)

RT

5.0 0.480 0.022 0.458 0.000

10.0 0.518 0.114 0.404 0.000

15.0 0.665 0.249 0.416 0.000

20.0 0.865 0.426 0.440 0.000

a1T0 Hm (total) =1T

0 Hm(lattice)+1T0 Hm(rot) +1T

0 Hm (opt). See text.bR= 8.31451 J· K−1 ·mol

−1.

Heat capacities of 4-methylpyridine 331

TABLE 5. Revised molar thermodynamic functions for the condensed phases of4-methylpyridine at vapor saturation pressure(R= 8.31451 J· K−1 ·mol

−1)a,b

T

K

Csat,m

R

1T0 Sm

R

1T0 Hm

RT

T

K

Csat,m

R

1T0 Sm

R

1T0 Hm

RTcr(II) cr(I)

10.00 0.732 1.332 0.519 255.00 13.883 18.295 8.02412.00 0.907 1.481 0.569 257.00 13.942 18.404 8.07014.00 1.097 1.635 0.630 260.00 14.039 18.566 8.13816.00 1.304 1.795 0.702 265.00 14.205 18.835 8.25118.00 1.520 1.961 0.780 270.00 14.376 19.102 8.36320.00 1.740 2.132 0.865 275.00 14.570 19.368 8.47425.00 2.318 2.582 1.098 276.82 14.628 19.464 8.51430.00 2.872 3.055 1.34835.00 3.386 3.537 1.60340.00 3.848 4.020 1.855 liquid45.00 4.261 4.497 2.100 276.82 18.539 24.931 13.98150.00 4.633 4.966 2.335 280.00 18.623 25.143 14.03360.00 5.254 5.868 2.772 290.00 18.897 25.802 14.19670.00 5.773 6.717 3.164 298.15 19.122 26.328 14.32880.00 6.225 7.519 3.520 300.00 19.173 26.447 14.35890.00 6.641 8.276 3.843 310.00 19.461 27.080 14.518

100.00 7.057 8.997 4.144 320.00 19.763 27.703 14.677110.00 7.452 9.688 4.427 330.00 20.077 28.316 14.836120.00 7.840 10.353 4.695 340.00 20.394 28.920 14.994130.00 8.208 10.996 4.951 350.00 20.719 29.516 15.153140.00 8.598 11.618 5.198 360.00 21.047 30.104 15.312150.00 8.993 12.225 5.437 370.00 21.380 30.685 15.472160.00 9.407 12.818 5.673 380.00 21.717 31.260 15.632170.00 9.835 13.401 5.905 390.00 22.077 31.828 15.792180.00 10.288 13.976 6.136 400.00 22.417 32.392 15.954190.00 10.760 14.545 6.366 420.00 23.12 33.50 16.28200.00 11.270 15.110 6.599 440.0 23.84 34.59 16.61210.00 11.817 15.672 6.834 460.0 24.57 35.67 16.94220.00 12.429 16.236 7.074 480.0 25.31 36.73 17.27225.00 12.765 16.519 7.197 500.0 26.06 37.78 17.61230.00 13.135 16.804 7.322 520.0 26.82 38.82 17.95235.00 13.544 17.090 7.450 540.0 27.61 39.84 18.29240.00 13.986 17.380 7.581 560.0 28.45 40.86 18.64242.00 14.194 17.497 7.635244.00 14.416 17.615 7.690246.00 14.650 17.733 7.745248.00 14.941 17.853 7.802250.00 15.328 17.975 7.861252.00 15.878 18.099 7.922254.00 16.824 18.228 7.988255.00 17.453 18.295 8.024

aThe1T0 Sm and1T

0 Hm values include contributions arising from the splitting of the threelowest energy levels associated with the methyl-group rotation. See text.

bValues listed in this table are reported with one digit more than is justified by the experi-mental uncertainty. This avoids round-off errors in calculations based on these results.

332 R. D. Chirico, S. E. Knipmeyer, and W. V. Steele

0 100 200 3000.0

0.2

0.4

0.6

{(Csa

t,m o

r C

latti

ce,m

)/T

}/(J

. K

–2 .

mol

–1)

(T / K)2

FIGURE 3. Plot ofCp,m/T againstT2. ©, Csat,m values for 4-methylpyridine measured in thisresearch;●, Clattice,m for 4-methylpyridine calculated withV3 = 0.32 kJ·mol−1; ¤ , Clattice,m for2-methylpyridine;(31) 4, Clattice,m for 3-methylpyridine.(32) The curves show the extrapolations toT → 0.

barrier heights adjusted to make the first excited level 4.2 cm−1. The first excited state wasobserved by both Alefeldet al.(8) and Abedet al.(2) The excited state at 15.4 cm−1 wasobserved only by Alefeldet al.(8) and led them to postulate a six-fold restricting potential.

Figure 4 showsCrot,m values calculated with the energy levels for the three-fold andsix-fold potentials (table 2). The additional excited state at 15.4 cm−1 results in muchlargerCrot,m values for the six-fold potential in the temperature range 5< (T/K) < 10.TheClattice,m values for 4-methylpyridine derived using equation (1), and theCrot,m valuesderived with the six-fold potential are shown in figure 5. It is seen that these alternativeClattice,m values cannot be extrapolated toT → 0, and become negative forT < 8 K. Weconclude that theCrot,m values derived with the six-fold potential are too large and cannotbe correct.

The restricting potential discussed in this paper arises primarily from intermolecu-lar interactions. The restricting potential arising from intramolecular interactions(V6 =5.6·10−2 kJ ·mol−1) is much smaller. The value for the intramolecular restricting potentialwas determined by Rudolphet al.(29) for the vapor phase with microwave spectroscopy.

Heat capacities of 4-methylpyridine 333

00.0

0.2

0.4

Cro

t,m/R

0.6

0.8

5 10

T / K

15 20

FIGURE 4. Heat capacitiesCrot,m associated with rotation of the methyl group relative to the pyridinering for a three-fold barrierV3 and six-fold barrierV6 adjusted to make the first excited energy levelν = 4.2 cm−1. – – –, V3 = 0.32 kJ·mol−1; ¤ , V6 = 1.5 kJ·mol−1. The arrows indicate thetemperature range of the heat capacities reported in this research.

It is seen in figure 3 that theClattice,m values derived with the three-fold potential for4-methylpyridine are larger than those for the other methylpyridines. Recognition of thisdifference was the key for the attainment of the accord shown later between calorimetricand statistically derived standard entropies. Previous attempts to resolve the contributionsto the heat capacities of 4-methylpyridine by Smith(30) and den Adelet al.(17) were basedon the assumption thatClattice,m was the same, or very nearly the same, for all of themethylpyridines. Figure 3 shows that this assumption is not valid. For 4-methylpyridine120 K

0 Solattice,m = 0.64·R, which is 0.20·Rand 0.14·Rgreater than that for 3-methylpyridine

and 2-methylpyridine, respectively. These differences are much greater than typical exper-imental uncertainties in entropies1T

0 Sm determined by adiabatic calorimetry for the liquid

334 R. D. Chirico, S. E. Knipmeyer, and W. V. Steele

0 100 200 3000.0

0.2

0.4

0.6

{(Csa

t,m o

r C

latti

ce,m

)/T

}/(J

. K–2

. mol

–1)

(T / K)2

FIGURE 5. Plot ofCp,m/T againstT2. ©, Csat,m values for 4-methylpyridine measured in thisresearch;●, Clattice,m for 4-methylpyridine calculated withV3 = 0.32 kJ·mol−1; ✕, Clattice,m for4-methylpyridine calculated withV6 = 1.5 kJ·mol−1. The curves show the extrapolations toT → 0.The dashed curve forClattice,m calculated for 4-methylpyridine withV6 = 1.5 kJ·mol−1 cannot beextrapolated toT → 0. See text.

phase for temperatures betweenT = 300 K andT = 400 K. Uncertainties in1T0 Sm are

near 0.001·1T0 Sm, or roughly±0.04 · R for the temperature range 300≤ (T/K) ≤ 400.

The assumption that120 K0 So

lattice,m is equal for all of the methylpyridines results in an errorthree to five times larger.

Entropy and enthalpy increments for 4-methylpyridine between the temperaturesT → 0andT = 20 K were calculated by summation of lattice, methyl rotation, and internal vibra-tional contributions, by analogy with equation (1). Values of the individual contributionsare given in tables 3 and 4. The methyl rotation contribution is seen to be the largest for alltemperatures≤20 K. Enthalpy and entropy increments for the temperature rangeT → 0to T = 400 K were obtained by combining these results with those given previously byMesserlyet al.(4) for the condensed phases in the range 20≤ (T/K) ≤ 400 K. Revised ther-modynamic functions for 4-methylpyridine are given in table 5. It is important to recognizethat the revised thermodynamic functions include contributions arising from the splitting of

Heat capacities of 4-methylpyridine 335

280–0.2

–0.1

0

0.1

360 440 520

T / K

{1T

S°(

cal)

–1

TS

°(st

at)}

/R0

m0

moo

FIGURE 6. Comparison of calorimetric1T0 So

m (cal) and spectroscopic1T0 So

m (stat) standard entropies

for 4-methylpyridine. For values represented by the filled symbols1T0 So

m (cal) was calculated usingrevised entropies for the condensed phases determined in this research. For values represented by theunfilled symbols1T

0 Som (cal) was calculated using values reported by Messerlyet al.(4) The1T

0 Som

(stat) values were calculated using the vibrational assignments reported by:(¥,¤), Lambaet al.;(19)

(M, N), Greenet al.;(20) (•,◦), Draeger and Scott.(21) For all1T0 So

m (stat) calculations, the wave

number values below 700 cm−1 reported by Draeger and Scott(21) for the vapor phase were used.

the three lowest energy levels associated with the methyl-group rotation. This contributionoccurs belowT = 2 K for 2-methylpyridine and 3-methylpyridine and is not included inthe usual tabulations of the thermodynamic functions for the condensed phases.(31, 32)

Corroboration of the revised entropies for the condensed phases is provided by compar-isons of standard entropies1T

0 Som (cal) derived with the calorimetric results and standard

entropies1T0 So

m (stat) derived with assigned vibrational spectra for the vapor phase and themethods of statistical mechanics. The standard state is defined as the ideal gas at pressurep = po = 101.325 kPa. Details of the calculation of1T

0 Som (cal) and1T

0 Som (stat) values

for the methylpyridines are described fully in an adjoining paper.(33)

Figure 6 shows comparisons of1T0 So

m (cal) and1T0 So

m (stat) values for 4-methylpyridinein which 1T

0 Som (cal) was derived with entropies for the condensed phases published

336 R. D. Chirico, S. E. Knipmeyer, and W. V. Steele

originally by Messerlyet al.,(4) and with the revised values derived here (table 5). The1T

0 Som (stat) values were calculated with three slightly different vibrational wave number

assignments.(19–21) A definitive assignment for 4-methylpyridine is not available, but dif-ferences between the1T

0 Som (stat) values derived with the alternative assignments is small.

Standard entropies derived with the results of Messerlyet al.(4) are clearly low, as seen infigure 6. Accord between the1T

0 Som (cal) and1T

0 Som (stat) values is achieved with use of

the revised entropies derived here.

The authors acknowledge the financial support of the Office of Fossil Energy of the U.S.Department of Energy. This research was funded within the Processing Research and Down-stream Operations section of the Oil Technology program. The research was completedunder the Management and Operation Contract DE-AC22-94PC91008.

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(Received 19 June 1998; in final form 28 September 1998)

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