THERMAL PROPERTIES OF GLUTARONITRILE
1983
Glutaronitrile. Calorimetrically Determined Thermal Properties from
5 to 350°K,and Statistical Gaseous Entropy'"
by H. Lawrence Clever, Claw A. Wulff, and Edgar F. Westrum, Jr.lb Department of Chemistry, University of Michigan, Ann Arbor, Michigan
(Received February 8 , 1966)
Heat capacities of solid and liquid glutaronitrile and the enthalpy of fusion have been determined by adiabatic calorimetry. The entropy of fusion a t the triple point, 244.21°K., is 12.32 cal./mole OK. This entropy of fusion and the absence of an enantiomorphic transition indicate that this substance does not possess a plastic crystal phase. Values , Gibbs of the heat capacity (Cp),entropy (E"), enthalpy function [(H" - H o o ) / T ] and energy function [(GO - H"o)/T] are 43.80, 57.23, 32.44, and -24.79 cal./mole OK., respectively, for the liquid at 298°K. For the ideal gas, the entropy at this temperature is 88.1 cal./mole OK. from thermal data. The close accord of this datum with the calculated value, 88.1, evidences lack of residual disorder in the solid at low temperatures.
Introduction Though lacking the high molecular Bymmetry usually associated with plastic crystals, succinonitrile has been shown to possess most of the macroscopic properties characteristic of this state.2 The entropy of transition from normal to plastically crystalline succinonitrile can be quantitatively accounted for in terms of changes in molecular and crystalline symmetry, the onset of hindered internal rotation, and the concomitant volume increment. van de Vloed3 has shown that the homolog, glutaronitrile (GN), on fast cooling goes to a metastable form. Matsubara's416infrared studies indicate that the metastable solid (crystal 11) and the stable solid (crystal I) contain different rotational isomers. This paper reports a study of glutaronitrile in the stable solid and liquid phases; the metastable phase was not formed in the cryostat. Because of the reported phase complexity and the desirability of verifying the absence of residual disorder in the GN crystal phase on which our measurements were performed (presumably the crystal I phase of Matsubara) the entropy of the ideal gaseous state is calculated from spectroscopic data and compared with the experimental value. Experimental Glutaronitrile Sample. The center cut of a GN sample (Eastman Kodak Co.) that had been subjected to
three successive vacuum distillations in a Podbielniak fractionating column was degassed by repeated freezing, evacuation, and melting cycles and was transferred as a liquid into the evacuated calorimeter. Vaporliquid partition chromatography indicated that the distillation procedure virtually eliminated the only detected contaminant. The sample was further characterized by infrared spectroscopy and by fractional fusion as will be discussed later. Anal. Calcd.: C, 63.81; H, 6.42; N, 29.76. Found: C, 63.84; H, 6.43; N,29.74. Cryostat and Calorimeter. Measurements were made by employing a gold-plated copper calorimeter W-246 sealed with a gold-gasketed, demountable valve in the Mark I11 cryostat.' The quasi-adiabatic techniques was used. The scale of the capsule-type platinum resistance thermometer (laboratory designation A-3) is considered to accord with the thermodynamic tem(1) (a) This work was supported in part by the U. S. Atomic Energy Commission; (b) to whom communications should be addressed. (2) C. A. Wulff and E. F. Westrum, Jr., J . Phys. Chem., 67, 2376 (1963). (3) A. van de Vloed, Bull. SOC. chim. Belges, 48, 229 (1939). (4) I. Matsubara, J . Chem. Phys., 35, 373 (1961). Japan, 34, 1719 (1961). (5) I. Matsubara, Bull. Chem. SOC. (6) E. T. Chang and E. F. Westrum, Jr., J . Phys. Chem., in press (7) E. F. Westrum, Jr., J . Chem. Educ., 39, 443 (1962). (8) E. E'. Westrum, Jr., J. B. Hatcher, and D. W. Osborne, J . Chem. Phys., 21, 419 (1953).
Volume 69, Number 6 June 1966
H. L. CLEVER,C. A. WULFF,AND E. F. WESTRUM, JR.
1984
perature scale within 0.03"K. from 10 to 90°K. and within 0.04"K. from 90 to 350°K. The heat capacity of the calorimeter-heater-thermometer assembly was determined by a separate series of measurements with small adjustments applied as needed for slight differences in the quantities of helium and thermal-conductivity grease between the runs with sample and without. Manual shield control was used below 80°K. Above this temperature three separate channels of recording electronic circuitry provided with proportional, rate, and reset control actions maintained the adiabatic shield within approximately a millidegree of the calorimeter temperature. Thus the energy exchange between calorimeter and surroundings was reduced so that it was negligible in comparison with other sources of error. All measurements of temperature, time, potential, resistance, and mass were referred to standardizations or calibrations of the National Bureau of Standards. The degassed sample of glutaronitrile was transferred as a liquid into the calorimeter and 399 torr of helium gas was added to the 8-cc. vapor space to enhance thermal equilibration. The samplehad a mass of 67.923 g. in vacuo. Its heat capacity was a t minimum 64% of the total (i.e., of sample, calorimeter, heater, and thermometer).
Results and Discussion Heat Capacity. The experimental heat capacity measurements are presented in Table I in chronological order so that temperature increments across individual runs in a series may be estimated from adjacent mean temperatures and are shown in Figure 1 as a function of temperature. The data are stated in terms of the defined thermochemical calorie exactly equal to 4.1840 j., an ice point of 273.15"K.,and a gram formula mass of 94.117 g. An analytically determined curvature correction has been applied to the measured values of AHIAT. These data are considered to be characterized by a probable error of about 4% near 10"K., decreasing to 1%at 15°K. and to less than 0.1% above 25°K. Heat Capacity of the Liquid. The vapor pressure is sufficiently I o w , ~13 p a t 303"K., to preclude the need for a vaporization correction. Three heat-capacity determinations in series XI1 were made on the undercooled liquid. These and the heat capacity of the normal liquid are fitted by the least-squares line C, = 0.03170T 34.25 f 0.06%. Thermodynamic Functiens for the Condensed States. The molal values of the heat capacity, entropy, enthalpy increment, and Gibbs energy function are listed in Table I1 a t selected temperatures. Derived thermal
+
The Journal of Physical Chemwtry
Table I : Heat Capacity of Glutaronitrile" 4
T
I
--
-Series 196.74 203.44 212.04 221.23 230.37 237.83 241.68 242.98 243.44 243.64 243.76 243.86 246.79
25.94 26.56 27.85 30.54 34.74 61.29 218.1 708.4 1672.5 3187 4736 4985 64.73
-Series 144.09 151.96 161.22 165.18 174.29 183.19 192.29 201.45 210.43
21.46 22.22 22.98 23.30 24.10 24.86 25.62 26.43 27.57
II-
=--Series 111230.12 34.44 A H m Run A A e r i e s IVA H m Run B A e r i e s V5.55 0.0449 5.88 0.0643 6.82 0.1096 7.75 0.1731 A e r i e s VI6.39 0.0883 7.19 0.1327 8.08 0.2012 9.01 0.2903 10.08 0.4235 11.21 0.5615 12.50 0.7517 13.90 1.013
T
c*
15.45 17.19 19.10 21.15 23.41 26.12
1.335 1.738 2.214 2.765 3.401 4.181
A e r i e s VII24.85 3.816 29.76 5.219 33.32 6.217 37.03 7.214 40.94 8.171 45.22 9.151 49.99 10.16 55.46 11.20 --Series 57.30 64.28 70.97 78.29 86.37 93.86 101.97 120.67
VIII-
-Series 92.37 102.32 111.33 120.38
IX16.46 17.50 18.42 19.31
11.53 12.72 13.68 14.69 15.88 16.64 17.46 19.33
=--Series X130.83 20.29 139.76 21.11 148.67 21.99 157.72 22.77 166.76 23.55 179.97 24.62 206.86 27.90 A H m Runs C -Series XI232.08 36.85 239.06 80.65 242.27 346.0 243.18 1081 243.51 2174
T
CS
243.69 3850 243.79 6394 254.79 108.0 270.61 42.83 278.77 43.08 286.85 43.36 294.78 43.67 302.58 43.94 310.32 44.32 318.00 44.66 325.63 44.94 333.15 45.21 340.62 45.60 346.82 45.86 -Series 234.72 238.51 241.97 245.41 248.84
XII41. 72b 41.81' 41. 95b 42.00 42.06
-Series XIII233.16 37.16 AHm Runs D -Series XIVAHm RunsE
XV-
-Series 209.40 218.03 226.26 233.76 239.25 241.96
27.40 29.42 31.10 37.96 74.51 235.3
-Series
XVI-
A H m Run F 251.15 42.23 257.56 42.43 263.95 42.65 270.31 42.83 276.63 43.02 Enthalpy Run G 329.20 45.07 336.61 45.39 343.97 45.72
a Units are calories, moles, and degrees Kelvin. undercooled liquid.
Data on
property values have been calculated with a highspeed digital computer by integration of a least-squares polynomial fitted through the data points. Below 5°K. (9) A. L. Woodman, W. J. Murbach, and M. H. Kaufman, J . Phys. Chem., 64, 658 (1960).
THERMAL PROPERTIES OF GLUTARONITRILE
1985
the heat capacity data were extrapolated by means of the Debye T3 limiting law. Nuclear spin and isotopic mixing contributions have not been included in the entropy and Gibbs energy functions. Estimated probable errors in the thermodynamic functions are less than 0.1% above 100°K.
N2
=
AHm(T0 -
RTo2
)'
=
0.0086
The melting point has previously3~10 been reported as -29.45' (243.70'K.). Attempts to Obtain a Metastable Solid. Matsubara416 reported that the metastable solid is obtained by cooling the liquid rapidly to about 213°K. Two such rapid
7; 'K. 0
Table II : Thermodynamic Properties of Glutaronitrile"
0
I
0
I
I
IO
20 7;
I
lo 30
OK,
Figure 1. The heat capacity of glutaronitrile.
Melting. In the course of heat capacity measure ments seven sets of runs (cf. Table 111) were made through the melting region; two of these, series I and series XV, define purity and melting point. The 1 cal./mole, average enthalpy of melting, 3008 corresponds to an entropy of melting of 12.32 ca1.l mole OK. The GN crystalline phase characterized by these measurements is, therefore, obviously not plastically crystalline. Melting points were taken during runs C and D to confirm that the same crystal phase was present. The amount of liquid-soluble solid-insolubleimpurity can be estimated from a plot of the apparent melting temperature, T , against the fraction melted, 1/F. The temperature (24337°K.) corresponding to 1/F = 1 is the triple point, TI, of the calorimetric sample. That (244.21"K.) corresponding to 1/F = 0 is the triple point, To,of the pure sample. The mole fraction of impurity, Nz, is given by
T
C*
so
5 10 15 20 25 30 35 40 45 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 244.21
0.033 0.399 1.236 2.45 3.86 5.29 6.67 7.94 9.11 10.16 12.00 13.57 14.95 16.18 17.30 18.32 19.28 20.22 21.14 22.06 22.95 23.80 24.60 25.38 26.27
0.011 0.118 0.423 0.938 1.636 2.466 3.387 4.362 5.362 6.381 8.401 10.37 12.28 14.11 15.87 17.57 19.21 20.79 22.32 23.81 25.26 26.68 28.06 29.41 30.74 36.37
244.21 250 260 270 280 290 300 310 320 330 340 350 273.15 298.15
...
...
42.16 42.46 42.79 43.13 43.49 43.87 44.26 44.67 45.10 45.54 46.00 42.90 43.80
Ha
- Hoo
0.042 0.916 4.818 13.92 29.67 52.56 82.50 119.1 161.8 210.0 321.1 449.1 591.9 747.7 915.2 1,093 1,281 1,479 1,686 1,902 2,127 2,361 2,603 2,853 3,111 4,354
Liquid 48.69 49.67 51.33 52.94 54.50 56.02 57.50 58.95 60.36 61.74 63.09 64.42 53.44 57.23
7,362 7,605 8,028 8,455 8,884 9,317 9,754 10,195 10,639 11,088 11,541 11,999 8,590 9,673
-(Go - H o d /
T
0.003 0.027 0.102 0.243 0.449 0.714 1.029 1.385 1.771 2.181 3.050 3.956 4.878 5.802 6.722 7.632 8.528 9.411 10.28 11.13 11.97 12.79 13.60 14.40 15.18 18.54 18.54 19.25 20.45 21.63 22.77 23.89 24.99 26.06 27.11 28.14 29.15 30.14 21.99 24.79
" Units are calories, moles, and degrees Kelvin. (10) J. Timmermans and J. Naveau, BUZZ.soc. chim.Belges, 67, 560
(1958).
Volume 69. Number 6 June 1966
1986
H. L. CLEVER,C. A. WULFF,AND E. F. WESTRUM, JR.
Table 111: Enthalpy of Melting of Glutaronitrile"
Table IV: The Thermal Entropy of GN (Ideal Gas) at 298.15"K."
Designation
Number of runs
( H Z Q- Haso)
Excess ( H S Q h'z~o)~
-
AHm
Series I AHm Run A AHm Run B AHmRunsC
Temp., OK.
9 1 1 2
3624 3624.0 3623.7 3623.9
2962 2961 2961 2961
3009 3008 3008 3008
0-5 5-Tm 243.87 T,-298. 15
Series XV AHmRunsD AHm Run E
8 2 1
3623 3625.7 3625.3
2960 2963 2962 Av.
3007 3010 3009 3008 f 1
'
Units are calories, moles, and degrees Kelvin. I.e., enthalpy above the extrapolated normal lattice curve. The excess ( H23a - HzW)is 47 cal./mole for each set of runs. a
cooling experiments were tried in which the sample was cooled from 315 to 225°K. at rates of 1.7 f O.l"K./min. This is the maximum cooling rate obtainable even with exchange gas in the cryostat. Heat capacity determinations and equilibrium melting temperatures at the same fraction melted on the rapidly cooled samples (series XIV and XV) did not differ from values found for the more slowly cooled solid. The presence (or absence) of certain impurities or inadequate quenching rates may account for failure to obtain the metastable solid phase.
Entropy of the Gas In view of the phase behavior recorded previously for glutaronitrile, it is desirable to verify that the sample used for heat capacity measurements contains no residual disorder. The thermodynamic state function most applicable to this end is the entropy, which is capable both of elucidating the existence of disorder and of providing a quantitative estimate of its extent. The usual schema, to be applied here, is a comparison of the measured thermal entropy (invoking the third law postulate) with an entropy computed from the energetics of the system as derived from structural and spectroscopic data. However, the computational difficulties involved limit such a comparison to the ideal gas standard state. Experimental Entropy of the Gas. The low temperature thermal data on the condensed phases augmented by vapor pressure data of Woodman, et a l l 9on liquid GN permit an estimate of the entropy of ideal gaseous glutaronitrile. Details of the calculation are shown in Table IV. Calculated Entropy of the Gas. Description of the position, spatial alignment, and internuclear separations of an n-atom molecule requires specification of positional coordinates for the 3n degrees of freedom. The Journal of Physical Chemistry
298.15
AS
Debye T* extrapolation Numerical integration of C,dT/T aHm/T,, melting Numerical integration of C,dT/T AHv/298.15, vaporization* R In p , compression to 1 atm.' Ideal gas correction" Thermal entropy of GN (ideal gas)
0.01 36.36 12.32 8.54 53.6 -22.7 0.00 86.1
a Units are calories, moles, and degrees Kelvin. 'See ref. 9. Negligible since vapor pressure of GN is only 1.075 X atm. a t 298°K.
After delineation of the translational and rotational coordinates, the remaining (3n - 6) degrees of freedom 1 :1 are assigned to correspondence with the (3n - 6) fundamental vibrations deduced by normal coordinate analysis. Upon the assumption of (a) separability of the 3n degrees of freedom, (b) rigid rotation about the center of mass, and (c) harmonic oscillator behavior for the (3n - 6) normal vibrations, high-temperature limits for the 3n partition functions in terms of the molecular mass, equilibrium internuclear separations, and the normal vibrational frequencies and resultant thermodynamic state functions may be evaluated. However, calculation is complicated by the necessity for using two of the normal vibrational degrees of freedom to describe the internal rotational degrees of freedom and by the concomitant rotational isomerism. Internal rotation results in nine configurations grouped into four enantiomorphic pairsll (TG, G T , GG, and GG') and one unpaired configuration'l ( T T ) . The entropy calculation is simplified in the manner adopted for succinonitrile12i.e., an entropy is computed for each conformation that exists in GN vapor; these contributions together with the entropy of isomer mixing are summed to obtain the molal entropy, S o , of GN (ideal gas). 9
So =
i=l
Xi
(j:l
)
9
S, - R x X z l n X i
A . Translation. The high-temperature, limiting, translational, partition function is dependent only on the molecular mass and is, therefore, identical for all rotational isomers. Taking the gram formula mass to be 94.117, the entropy of translation is given by12 (11) For the nomenclature of rotational isomerism see S. Mizushima, "Structure of Molecules and Internal Rotation," Academic Press, Inc., New York, N. Y., 1954.
THERMAL PROPERTIES OF GLUTARONITRILE
Sot, = R(3/2In M
+
5/2
1987
In T) 2.315 = 39.541 cal./mole
OK.
B. Over-aZE Rotation. The high-temperature rigidrotor limit of the partition function is dependent on the value of the moment of inertia determinant, D, and upon the rotational symmetry number, u. Of the rotational conformations listed previously the GG’ is absent in GNF5and the TG and GT are spectroscopically and rotationally equivalent. For C-C, T=N, and C-H bond lengths of 1.542,1.149, and 1.071 A., and for C, N, and H atomic masses of 12.01, 14.008, and 1.008, respectively, the evaluation of the moment of inertia determinants yields the values given in Table V. which Values of u and of the rotational entropy, SorJX2 is given by Sor= R[l/2 In (D X lo1’’)
+
”2
In T - In u]
also are presented in the same table. Table V : Rotational, Vibrational, and Conformational Entropy Contribution8 for GN” -ConformationContribution or quantity
Inertial determinant, D X 10113, g.3 cm.6 Symmetry number, u
so, so, Mole fractions Coniigurations 8 ‘298.16 a
TT
TG,GT
GQ
6.28 2 26.555 11.156 0.43 1 84.71
6.21 1 27.923 10.234 0.50
5.01 2 26.331 9.939 0.07 2 83.27
na‘ively as rotations about the two C-C bonds. An exact treatment involving the calculation of appropriate energy levels is prohibitively difficult, necessitating the adoption of some approximate treatment. As has been indicated,14since the entropy is not very sensitive to assumed potential energy function, even a severely strained potential model might provide a suitable value for this entropy contribution. One approximate treatment is provided by the entropy tabulations of Pitzer and Gwinn15 for hindered rotation of groups attached to a rigid framework. If the central methylene group in GN is considered as the rigid framework, the reduced moment of inertia, Ir,6.83 X lo-” g. cm.2, is computed using the atomic masses and bond lengths given previously. A cosine potential of the form V = ‘/zV0(l - cos 4) is assumed with Vo,the maximum barrier height, ranging between 3000 and 3600 cal./mole, these values being consistent with those for a number of substituted alkanes. The internal rotation symmetry number, n, is taken as 3 and will be discussed later. The high-temperature limit of the partition function12 is 2.7935(10381,T)1’2/ n = 4.203. The entropy contribution consists of three terms and is for both internal rotators. S’ir
4
85.16
Entropies are in calories per mole degree Kelvin.
C. Vibration. Of the 3n = 39 degrees of freedom for the molecule we have assigned 6 for translation and over-all rotation and 2 for the internal rotations. The remaining 31 degrees of freedom correspond to the fundamental vibrations of the molecule and differ for the spectroscopically distinguishable conformations. An analysis of the infrared spectrum of GN between 4000 and 400 cm.-l has been reported by Mataubarad and a complete set of fundamental, skeletal vibrations based upon force constants derived from the observed spectrum has been given for each conformation existent in GN. Summations of the entropy contributions for each set of 31 frequenciesare made by utilizbg tabulated harmonic oscillator f~ncti0ns.l~These sums are in Table V also. D. ~~~~~~~l ~ ~The potential ~ energy ~ func~ tion describing the hindered internal rotation in GN is a function of two angles which can be thought of
= 2R(’/2
+ In 4.203) - 2(St - S) + R In g
The first of these terms is the contribution calculated on the basis of free internal rotation, i.e., V o= 0. The second is the effect of the nonzero V oand can be evaluated using the tables of Pitzer and Gwinn15 where (Sr - S) is tabulated as a function of I , and Vo. The third term is related to the rotational symmetry number n. The parameter g is the number of distinct conformations produced by complete rotations about the two axes of internal rotation. As stated above, nine configurations are grouped into five distinct conformations. Since only four of these contribute to the partition functions of GN, g = 4 and the entropy contribution is R In 4. An alternate approach to evaluating the effect of rotational isomerism involves inclusion of all five conformations in 9, but restriction of the integration of the potential energy to regions that do not include the GG’ configurations. For the analogous, but simpler, system-succinonitrile-both methods were employed and gave results which differed in entropy (12) G. N. Lewis and M. Randall, “Thermodynamics,” 2nd Ed., revised by K. S. Pitzer and L. Brewer, McGraw-Hill Book Co., Inc., New York, N.Y.,1961. (13) J. Hilsenrath and G. G. Ziegler, “Tables of Einstein Functions,” U. S. National Bureau of Standards, Monograph 59, U. S. Governi Printing ~ ~ ment O5ce, Washington, D.. C., 1962. (14) C . A. wUlff, J . them. phV8., s9, 1227 (1963). (15) K.s. Pitzer and w. D. Gwinn, ibid., io, 428 (1942).
Volume 69, Number 6 June 1966
1988
H. L. CLEVER,C. A. WULFF,AND E. F. WESTRVM, JR.
by 0.15 cal.,/mole OK. Because of the approximations already made here, use of the alternate method was not warranted. The entropy is computed as
pentane.I7 This differs little from that for similar compounds" and has been adopted for GN. Mole fractions of X T T = 0.43, XT,,GT = 0.50, and XGG = 0.07 yield an entropy of mixing of 3.30 cal./mole OK. F. Entropy of GN (Ideal Gas) at 298.15"K. From the composition and the conformational entropies summarized in Table V the entropy of GN (ideal gas) is 88.1 f 0.6 cal./mole OK. Comparison of Calculated and Thermal Entropies. The agreement between the thermal (88.1 f 0.1 cal./ mole OK.) and calculated (88.1 f 0.6 cal./mole OK.) values for the entropy of GN (ideal gas) indicates a lack of residual disorder a t low temperatures in the crystalline phase characterized by these thermal measurements. However, because of the assumptions made in obtaining the calculated value, the thermal value is preferred for chemical thermodynamic use.
SOir
= 2R('/z
+ In 4.203) - 2(1.49 R In 4
f 0.12)
+
= 7.46 =k 0.25 cal./mole
OK.
and the precision index is determined by the range of
vo. A second route is available to the evaluation of (Sf - S) through the work of Scott and McCdough,l6 who considered the effect of rotational isomerism upon thermodynamic functions. Their tabulations of (St S) are dependent on two barrier heights that characterize a synthesized potential energy function. Assigning values of Vz = 1000 f 200 cal./mole and VI = 2000 f 200 cal./mole (notation of Scott and McCullough) a value of 7.84 f 0.25 cal./mole OK. is obtained for Soir. The numerical values assigned to the two barrier heights are those used for succinonitrile2and are consistent with barriers observed in substituted alkanes. A mean value of 7.83 f 0.40 cal./mole OK. has been adopted for Soirand is the same for each of the conformations. E. Entropy of Mixing. No data exist for the vapor phase energy separations of the configurations contributing to GN. A conformeric distribution is available for the symmetrically substituted analog, n-
The Journal of P h y W Chemistry
Acknowledgment. C. A. W. thanks the Institute of Science and Technology of the University of Michigan for assistance in the form of a postdoctoral fellowship. The partial financial support of the U. S. Atomic Energy Commission is greatly appreciated. (16) D. W. Scott and J. P. McCullough, Bureau of Mines Report of Investigation RI 5930, U. S. Government Printing Office, Washington, D. C., 1962. (17) F. A. Momany, R. A. Bonham, and W. H. McCoy, J. Am.
Chem. Soc., 85, 3077 (1963).
