2376
CLACS
A. W U L F F
ANI
EDGAR F. W E S T R U M , JR.
discussion of the transition and its apparently large activation energy will be deferred until the thermodynamics of the fusion process have been ascertained. Acknowledgment.-The financial assistance of the Division of Research of the Atomic Energy Commission
Vol. 67
is recognized with gratitude. C. B. thanks the National Science Foundation for an Undergraduate Summer Research Participation Award. The cooperation of Peter Castle and Ray Radebaugh in the calorimetric measurements is acknowledged with thanks.
HEAT CAPACITIES AND THERMODYSAMIC PROPERTIES OF GLOBULAR MOLECULES. VI. SUCCINONITRILE1 BY C L a U S A.
WULFF' APiD EDG.4R
F. WESTRUM, JR.3
Department of Chemistry, University of Michigan, Ann Arbor, Michigan Received M a y 10,1965 The heat capacity of succinonitrile has been determined by adiabatic calorimetry between 5 and 350°K. Crystal I1 is stable below 233"K., at which temperature it undergoes an isothermal transition to solid crystal I with enthalpy and entropy increments of transition of 1482 cal./mole and 6.35 cal./mole-"K. The latter value is in accord with a statistically calculated value of 6.39 cal./mole-OK. Crystal I melts a t 331.3O0K. a t 1 atm. and under its own vapor pressure a t 331.16OK. with enthalpy and entropy increments of fusion of 8% cal./mole and 2.68 cal./mole-OK. An analysis of the heat capacity of crystal I1 permitted evaluation of the spectroscopically unobserved torsional frequency as 136 rt 6 em.-'. The standard entropy of the vapor a t 298.15"K. was computed by a third-law path a3 79.04 cal./mole-"K. and spectroxopically as 79.09 cal./mole-OK.; the agreement constitutes a third-law verification. Thermodynamic functions were evaluated for the condensed phases by integration of the heat capacity data and are, for crystal I at 298.15"1~.,in units of cal./niole-OK.: C, = 34.80, So = 45.79, ( H " - H",)/T = 24.35, and -(F' - H o o ) / T = 21.44.
Introduction Characterization of the plastically crystalline state4 is a topic of current solid-state chemical interest. The distinguishing macroscopic features of compounds exhibiting plastic crystal behavior are : a relatively high melting point, preceded by a transition to the plastically crystalline phase; a high vapor pressure (the triple point is often above one atmosphere); and a low entropy of fusion which is usually less than 5 cal./moleOK. The appearance of the plastic crystal state has been attributed to the onset of molecular "rotation"* in the solid and can be expected for "globular" molecules, ie., molecules of high symmetry such as methane. The previous papers in this series have reported results for such "globular" systems. In this paper the results for a less symmetrical substance, succinonitrile [NC(CH2)2CN],are presented. Comparison of the available data for succinonitrile with the criteria presented previously does not establish conclusively the existence of a plastically crystalline phase. Of the dinitriles in the series NC(CH2),CN, n = 1 to 6, only malonitrile (n = 1) and succinonitrile (n = 2 ) are solids a t room temperature, indicating that their melting points are anomalously high. The sublimation pressure5 is low, however, and the liquid is stable for a 200' range. The entropy of melting, ASm, can be estimated from the enthalpy of melting, AHm, and the melting temperature, Tm. The earliest determination of AHrn,O by a measurement of the cryoscopic constant, gave 940 cal./mole and Tm = 33OoK., leading to ASm = 2.85 cal./mole-OK. This value is well below the arbitrary limit given by Timmermans and indicates that succinonitrile exhibits plastically (1) This uork was supported in part by the Division of Research of the r n i t e d States Atomic Energy Commission. (2) Institute of Science and Technology Fellow. (3) To whom correspondence concerning this paper ehould be addressed. (4) J Timmermans, J . Phys. Chem. Sol.cds, 18, 1 (1961). (6) A L. Woodman W.J hlurbach, and h1. H Kaufman, .J P h y s ( ' h e m , 64, 688 (1960) (6) C, Rruni a n d A LlRnuPIli. A. t,F,ipkLrorhrn~,11, $60 (1905)
crystalline behavior prior to melting. Subsequent determinations of AHm,' also by freezing point lowering, led to AXm = 8.3 cal./mole-OK. This value is in accord with entropies of fusion for related mono- and dinitriles8 and has been accepted by handbooks such as that of Beilstein. A still more recent determination is tabulated by Timmermans6 as AHm = 990 cal./mole and ASm = 3.0 cal./mole-OK. Measurements of the dielectric constant9 and the infrared spectrum'O as a fuiiction of temperature indicate a transition between 228 and 235OK. Existence of the transition was further confirmed by single crystal X-ray diffraction methods'l and the structure of the crystal I phase established. Surprisingly, thermal analyses by van de Vloed' did not detect the substantial thermal effect associated with the transition. To clarify the conflicting data on the plastically crystalline nature and to delineate the thermal properties of the substance and its transformation, the low temperature heat capacity of succinonitrile was investigated. Experimental Sample and Calorimetric Apparatus.-The calorimetric sample was purified by two successive vacuum sublimations of Coleman and Bell succinonitrile. Duplicate quantitative microanalyses gave the following results: C, 60.01; H, 5.04; and N, 35.04. The theoretical composition is: C, 59.99; H, 5.03; and K, 34.98. Further evidence of its purity is presented in the fractional fusion data. The calorimeter was loaded in an anhydrous nitrogen atmosphere with a molten sample weighing 88.3200 g. (inoacuo), and after brief evacuation, 135 mm. of helium gas a t 300°K. were added to enhance thermal contact with the sample. The Mark I1 cryostat,'2 a gold-plated copper calorimeter (laboratory designation W-28) with six internal vanes, and R calibrated capsule-type platinum-resistance thermometer (lahora(7) A. van de Vloed, Bull. BOC. chim. Belges, 48, 229 (1939). (8) J. Timmermans, "Lee Constantes Physiques des Compo& Organiques CristallisBs," Mrtsson et Cie., Paris, 1963. (9) A. H. White and S. 0. Norpan, J . Chem. Phys.. 6, 668 (1937). (10) W.E. Fitzgerald and 0. J. Jane, . I . M o l . Speefry., 1, 49 (1457). i l l ) C . R. Peters and C. E. Nordman, personml communication. ( I 7) E. 1.'. W'estnini, Jr., .I. Chem. E d 7 ~ .39, , 443 (1962).
THERMODYNAMIC PROPERTIES OF SUCCINONITRILE
Nov., 1963
TABLEI THEHEATCAPACITY OF SUCCIKONITRILE [Units: cal., mole, OK.] -
T
T
CP
335.32 338.80 343.18 347.63
126 38.48 38.56 38.73
CP
Series I 187.93 196.41 205.46
22.80 23.48 24.37
-
7; "K
0 -
T 79.64 86.52 93.61
2377
CP
13.19 13.99 14.70
100
200
300
50
Crysto/
iT 40
Series V I I I Series VI
Series I1 121.76 128.35 136.50 144.83 153.02
17.25 17.82 18.51 19.20 19.82
Series I11 155.22 163.90 172.42 180.75
20.05 20.76 21.48 22.18
Series I V 205.74 215. a7 224.35 241.38 249.51 258.44 267.78 277.12 286.36 295.48 304.41
24.40 25.32 26.22 32.40 32.62 32.97 33.35 33.74 34.16 34.64 35.15
Series V 303.97 313.20 322.49 328.79 330.87
35.12 35.71 36.38 94. '9 1320
-
T
Series VI1 5.00 5.42 6.00 6.80 7.71 8.67 9.66 10.71 11.81 13.16 14.60 16.22 18.01 20.09 22.51 25.23 28.15 30.73 33.51 37.15 41.34 46.13 47.09 50.85 55.11 60.18 65.83 ;72.56
AT
CP
Transition runs A, 231.056 233.213 233,274 233.303 233.345 236.387
4.293 0.107
.Os1 .060 .lo2 6.113
62.0 f!;'lO 3580 4820 2'850 61.0
Transition runs H' 231.360 232.446 233.008
1.446 0.753 ,372
27.06 37.19 6839
0.026 ,053 .067 .09'7 .16 .26 .36 .48 ,621 ,821 1.081. 1.398 1.780 2 253 2,837 3.515 4,241 4.883 5.558 6.396 7.294 8.251 8.439 9,123 9.837 10.64 11.47 12.33
326.42 328.32 329.60 334.05 337.44 340.82 344.19 347.55
T 233,223 233.280 233,309 234.045
AT
CP
0.068 ,036 ,021 1.451
3520 16100 12700 212
Series I X 341.14
38.56
Series X 227.82 229.70 235.95
26.53 26.74 32.28
Y ,
-al
-0
E
\
0
20
2
u 8'
p
Crystal
- IC
.E
0
IO
20
O
0
1
K
Fig. 1.-The heat capacity of succinonitrile.
161.36 169.64 178.44 187.74
20.56 21.26 21.97 22.81
Series XI1 36.94 40.05 71.5 38.32 38.40 38.55 38.67 38.75
Melting runs J 330.27 330.67 330.83 330.92 330.97 331.67
30
Series XI
0.599 ,215 ,105 ,062 ,045 1.359
237 680 1400 2300 4150 133
tory designation A-5) were used in the heat capacity measurements. The quasi-adiabatic technique used has beenpreviouslyde~ c r i b e d . 1The ~ heat capacity of the calorimeter-heater-thermometer assembly was determined by a separate series of measurements with small adjustments applied as needed for the slight differences in the quantities of helium, thermal conductivity grease, and solder between the runs with sample and without. (13) E. F. Westrum, Jr., ,J. P h w , 21, 419 (1953).
-
96.84 15.01 103.93 15.66 110.76 16.28 117.84 16.91 Enthalpy run E AHt run F Enthalpy run G
AHt run B Enthalpy run C AHm run D
H. Hataher, and D. IT. Osborne. J . Chem.
The heat capacity of the samgle amounted to 95% of the total heat capacity a t 10"K., a minimum of 80% a t 12OoK., and 86y0 at 350'K. Manual shield control was used below 50°K. Above this temperature three separate channels of recording electronic circuitry provided with proportional, rate, and reset control actions gave control of the temperature of the adiabatic shield to within approximately a millidegree and thereby reduced the energy exchanged between the calorimeter and surroundings so that it is negligible in comparison with other sources of error. All measurements of temperature, time, potential, resistance, and mass are referred to calibrations or standards of the National Bureau of Standards.
Results and Discussion Heat Capacity.-The experimentally determined heat capacity is depicted in Fig. 1 and presented in Table I in chronological order so that temperature increments across individual runs in a series may be estimated from the adjacent mean temperatures. Since the nature of the phase transition may be deduced from the temperature dependence of the heat capacity in the anomalous regions, apparent heat capacities observed during transition and fusion have been included. The data are stated in terms of the defined thermochemical calorie exactly equal to 4.1840 j., an ice point of 273.15OK.) and a molecular mass of 80.092 g. An analytically determined curvature correction has been applied to the measured values of A H I A T . The vapor pressure is sufficiently low that no error is introduced by equating C, with C,. Corrections for vaporization are also negligibly small. These data are considered to be characterized by a probable error of about 3y0 near 6OK., decreasing to 1% a t 1OOK. and to less than 0.08% above 25OK. Values of the smoothed heat capacity obtained from a digital computer fit accord well with those read from a large-scale plot and are presented in Table 11. A test of the experiment,al heat capacities is provided by the enthalpy-type runs over the crystal I and crystal I1 heat capacity regions as given in Table 111. The agreement of these determinatioiis with the integral
TABLE 111 ENTHALPY INCREMENTS AND ENTHALPY OF TRANSITION [Units: cal., mole, OK.]
TABLE I1 THERXODYSAYIC PROPERTIES FOR SUCCIKONITRILE [Lnits: cal., mole, OK.] T
CP
S"
H o - H'o
T
H'o)/T
5 10 15 20 25
0.047 .382 1.154 2.235 3 I455
Crystal 11 0.016 0 058 .127 .955 ,414 4.629 ,889 13.011 1.518 27.205
0.012 .096 ,309 ,651 1.088
0.004 ,032 ,106 .239 .430
30 35 40 45 50
4,705 5.899 7.010 8.034 8.973
2.258 3.074 3.936 4.821 5.717
47.607 74.153 106.46 144.11 186.7
1.587 2.119 2.662 3.202 3.733
,671 .956 1.274 1.619 1,984
60 70 80 90 100
10.619 12.02 13.23 14.32 15.31
7.503 9.247 10.933 12.556 14.116
284.9 398.2 524.6 662.5 810.7
4.748 5.689 6.558 7.361 8.107
2.755 3.559 4.376 5.195 6.010
110 120 130 140 150
16.23 17.10 17.95 18.78 19.61
15.619 17.069 18,472 19.832 21,156
968.4 1135.1 1310.4 1494.0 1686.0
8.804 9.460 10.080 10,672 11.240
6,815 7.610 8.392 9.160 9.916
160 170 180 190 200
20.44 21.28 22.12 22.97 23.86
22.45 23.71 24.95 26.17 27.37
1886 2095 2312 2537 2771
11.79 12.32 12.84 13.35 13.86
10.66 11.39 12.11 12.82 13.52
210 220 225
24.80 25.78 26.28
28.56 29.74 30.31
3015 3267 3370
14.35 14.135 15.10
14.20 14.89 15.21
235 240 250 273
32.26 32.38 32.66 33. 03 33.39
37.87 38.5.5 30.87 41.16 42.41
Crystal I 5155 5317 5642 5970 6302
21.94 22.15 22.57 22.96 23.34
15.93 16.39 17.31 18.20 19.07
273.15 280 290 298.15 300
33.53 33.84 34.35 34 80 34.91
42.80 43.64 44.83 46.79 46.01
6407 6638 6979 7261 7325
23.46 23,71 24.07 24.35 24.42
19,35 19,93 20,77 21.44 21.59
310 320 325
35,53 36.20 36.56
47.16 48.30 48.86
7677 8036 8218
24.77 25.11 25.20
22.40 23.19 23.58
335 340 350
38.37 38.52 38.81
52.67 53.24 54.36
Liquid 9477 9670 10056
28.29 28.44 28.73
24.38 24.80 25.63
241
Vol. 67
CLAWA. WULFFASD EDGAR F. WESTRUM,JR.
2378
I
Designation
of the heat capacity is excellent and confirms both the validity of the measurement and calculational aspects of the determinations. Thermodynamic Functions.-The molal TTalues of the entropy, enthalpy increment, enthalpy function, and free energy function are also listed in Table I1 at selected temperatures. These values have been obtained by integration of a least-squares-fit polynomial through the data points by means of a high-speed digital computer. Below 5'K. the heat capacity data were extrapolated by means of the Debye limiting law. Kuclear spin and isotope mixing contributions have not been included in the entropy and free energy functions.
Run C Run E Run G
Number of runs
a
HT, - HTI
1
Crystal I1 121.64 227.87
2312.1 2312.5
1 1
Crystal I 238.68 329.94 243.50 324.99
3161.5 3160.6 2787.9 2787.4
I1
Runs A Run B Run F Runs H
Ta
TI
6 1 1
7
-
I Transition
228,909 225.808 227.872 232.069
239.444 238.675 243.504 234.77
1796.4 1855.7 1957.0 1565.3 Average :
AHt 1480.4" 1481.9 1482.4 1481.9" 1481.7f0.6
Corrected for quasi-adiabatic drifts.
The estimated probable error in the thermodynamic functions is less than 0.1% above 100'K. Transition.-Succinonitrile undergoes an essentially isothermal transition between 227 and 233°K. The low-temperature phase, crystal 11, is monoclinic, P21(a, with unit cell parameters a = 9.11 A,,b = 8.60 A,, c = 5.87 A.,and p = 100'36'; the high-temperature phase, crystal I, is body-centered cubic with a density of 1.034 g./cc. a t 25' (pycnometric) and 1.023 a t 4.io.l4 The X-ray diffraction patterns indicate crystal I1 to be completely ordered, whereas crystal I is highly disordered. This disorder is ascribed in part to the onset of rotation about the principal axis passing through the length of the molecule.~4 Similar anomalies in the heat capacities of the correspoiiding dibromoand dichloroethanes have been attributed to the onset of molecular motion of this type.'j The X-ray diffraction datal1 indicate the presence oidy of an equimolal mixture of the enantiomorphic forms of the gauche isomers in an ordered array in the crystal I1 phase, whereas the infrared data show that the crystal I phase consists of a temperature-dependent equilibrium mixture of gauche and trans isomers.1° In the course of the heat capacity measurements four series of runs were made through the transition region with the enthalpy increments shown in Table 111. Although most of the enthalpy of transition, AHt, is concentrated between 233 and 234OK., the apparent heat capacity is anomalously high above 227OK. (but not above 234OK.). From large-scale plots, the best representations of the equilibrium heat capacities were extrapolated into the transition region and integrated to evaluate lattice contributions to the enthalpy increments (exclusive of AHt). Integrations of the excess heat capacities were then performed to evaluate the AHt-values tabulated in Table 111. The temperature increments in runs A and H mere sufficiently small to allow evaluation of the entropy of transition, A S t (corrected for contributions between 227OK. and T I ) . The temperature of transition, T t , was taken as the temperature of niaximuin apparent heat capacity. The average values for ASt and Tt are 6.349 i. 0.002 (14) C. Finback, .4rch. Math. X'nturLidenskab, B42, No. 1,71 (1938); cf. Chem. Abstr., 34, 12 (1940). (15) K. S.Pitzer, J . Am. Chem. Soc., 62, 331 (1940).
THERMODYNAMIC PROPERTIES OF SUCCINONITRILE
Nov., 1963
cal./mole-°K. and 233.31 f 0.02' K., respectively, where the umcerta,inties are the probable errors of the mean values. The entropy of transition reflects a disordering process concomitant with the phase change. Three factors influence this process, namely: (a) the change in crystal symmetry, (b) the onset of hindered internal molecular rotation, or of over-all (ie., rigid) rotation about a single axis, and (c) the volunle change. The magnitudes of these contributions will each be estimated below. A. Crystal Symmetry.-Guthrie and NcCullough16 have had some success in correlating transitional entropy increments with the number of orientations allowable by alignment of molecular and crystal symmetry elements. Considering this viewpoint, the following may be envisioned for succinonitrile. The bodycentered cubic structure contains a central molecule and eight others a t the cube corners. Comparison of the longest interatomic distance in the molecule with the intermolecular distance indicates the absence of free over-all rotation about three axes. The existence 01some degree of order can be inferred from the appearance of a diffraction pattern. It is plausible to assume that the principal rotation axis along the length of the molecule will align with one of the four cube diagonals of the unit cell. The entropy increment for this amount of disorder is A S = R In 4 = 2.755 cal./mole- OK. B. Molecular Rotation-For the trans configuration of succinonitrile the axis aligned with a unit cell cube diagonal is a two fold rotation-reflection axis of the molecule. If rotational freedom is alloxred about this axis (but not about either of the other principal axes), two configurations arc apparent, separated by a 180' rigid rotation of the molecule. For a gauche configuration the same rearrangement also gives rise to two different configurations. Thus, for either isomer two additional configurations are available and contribute AS = R In 2 = 1.37:7 cal./mole-OK. to the entropy. The infrared spectralo indicate a gauche-trans equilibrium in crystal I (with the gauche of lower energy by 360 cal./mole in contrast to the presence of only gauche forms in crystal 11, the totally ordered phase. If Xg and Xt are the mole fractions of the gauche and trans isonicrs, respectively, the onset of this geometrical isomerism contributes an entropy of mixing term
Xg/X, = 2 exp (36O/RT) = 4.348
Xt
=
0.1870 Xg = 0.8130
A s = -R(Xt In X t f X , In X, -
xgIn 2 )
= 2.077
cal ./mole- OK. C. Volume Change.-Resolution of the entropy associated with the volume increment from that of the rotation-reorientation process is inherently difficult. Examination of the entropies of order-order transitions in silicon dioxide polymorphs reveals such contributions to be small. Recognition of the effect is provided by estimating the contribution as A S = R In (V2/Vl)and utilizing previously mentioned values for the density of crystal I and lattice parameters for crystal 11. (16) G. B. Guthrie and J. P. MoCullough, J . Phys. Chem. Solzds. 18, 63 (1961).
2379
Whether total or free volumes are invoked, approximately the same entropy increment, about 0.15 cal./ mole-OK., results. Table IV indicates excellent accord between observed and summarized calculated contributions for the entropy of transition. TABLE IV ANALYSESOF EXTROPY OF TRANSITION [Units: cd./mole-OK.] Factors
Ast
Alignment of axes Rigid rotation of molecule Entropy of mixing isorners Volume change on transition
2.755 1.377 2.077ztO.04 0.15 1 0 . 0 5 6.36 f 0 . 0 9 6.35 1 0 . 0 3
Calcd. : Observed:
Melting.-In the course of the heat capacity measurements, three series of runs were made throuch the region. The process was observed to be isothermal with evidence of premelting above 327'K. From largescale plots, normal heat capacities were extrapolated into the region to determine enthalpy increments exclusive of AHm. The exces~ heat capacities were integrated to evaluate AHm, and the small temperature increments in series T', runs J, permitted evaluation of AXm. The results are presented in Table V, with the A H m value for fusion run C corrected for a contribution of 31.43 cal./mole below TI. TABLE V EWTHALPY AND ENTROPY OF MELTING [Units: c d , mole-'K.] Number of runs
Designation
Series V Run D Runs J
TI
T2
HT?,- HT, A H m
ASm
326.802 333.983 1141.6 885.1 2.676 329.933 334.019 1008.7 885.1 325.437 332.353 1158.0 885.1 2.678
4 1
3
Averages: 885.1 2 677
The amount of liquid-soluble solid-insoluble impurity can be estimated from a plot of the apparent melting temperature, T , against the reciprocal of the fraction melted, 1/F. This quantity is tabulated in Table VI for the six experimental points nearest coinplete melting in runs J and is a linear function of the T-values. The temperature corresponding to 1/F = 1 is the triple point of the calorimetric sample, T I ,and is 330.99OK. The temperature corresponding to 1/F = 0 is the triple point of the pure substance, To, and is 331.16'K. The mole fraction of impurity is given by
AX
=
AHm(To - T,)/RTO2= 0.0007
Extrapolation of the sublimation pressure measurements to the triple point temperature indicates a triple point pressure of ca. 10-4 atm. The normal melting point, Tm, can be approximated by Tm
=
To
+ AVnz/ASnz(l
-PH~)
where A V m = 3.71 ~ m . ASm ~ , = 2.68 cal./mole-°K., ~ 135/760 atm. is the pressure of gas inside and P H = the calorimeter. To this approximation Trn is 331.30'-
CLAWA. WULFFAND EDGAR F. WESTRUM, JR.
2380
K., a value in accord with the latest tabulated results of 331.30-331.35OK.
TABLE VI1 THETHIRD-LAW ENTROPY OF GASEOUS SUCCISONITRILE AT 298.15 OK.
TABLE VI FRACTIOZAL MELTINGDATAo s SUCCISONITRILE
[Units : cal. / r n ~ l e - ~ K . ] T range, OK.
[Units: cal., mole-OK.]
-
0
T
4T
CP
AHsxoesa
1/F
Tfinai
330.27 330.67 330.83 330.92 330.97 331.67
0.599 .215 .lo5 ,062 ,045 1.359
237 682 1393 2297 4150 132
149.8 288.5 431.1 570.7 757.2 885.1
5.908 3.068 2.053 1.551 1.169
330.566 330.781 330.886 330.948 330.993 332.353
C, = 28.583
+ 0.02922T
with a root-mean-square deviation of 0.08%. Analysis of the Heat Capacity of Crystal 11.-The heat capacity is composed of contributions attributable to the lattice vibrations, the internal vibrations, the hindered rotation (torsion a t low temperatures), and the expansion of the lattice. To the harmonic oscillator approximation the lattice vibrationa1 contribution can be given by a Debye function, the internal vibrations by Einstein functions for each of the normal vibrations, the torsional contribution by an additional Einstein function, and the expansion contribution by a n empirical relation1'
Cp - Cv
=
(aClattiee
(17) K. ( Lord, J i , J L 4hlb erg, a n d 13. 5 , 649 (1937). (18) C. A. Wulfl, t b d , 39, ILL7 (10b3).
I-T 4ndreus. I C h r m .
Xt/X,
I'hy\.,
31.23 6.35 8.19 45.79=kOo.03 56.11
--22.86 0.00 79.04 f 0.10
The second value of the vapor phase entropy can be computed from molecular and spectroscopic data. Translational, over-all rotational, and vibrational contributions were computed using the frequency assignments of Fitzgerald and Janz,l0 a gram formula weight of 80.092, and moment of inertia products of 1.758 X g.3 and 1.059 X gS3emu6for the gauche and trans isomers, respectively. The vapor phase consists of an equilibrium mixture of the two forms with the trans of lower energy by 1000 cal./ mole. lo The internal rotational contribution was determined from the tabulated values of Scott and McCulloughlg for the thermodynamic functions for substances possessing rotational isomerism. The barriers chosen, in the notatioii of Scott and McCullough, were 1000 and 2000 cal./mole. These are consistent with the observed energy difference between the trans and gauche forms and with barriers observed in other substituted ethanes. The reduced moment of inertia In addition to was taken20 as 9.403 X 1 0 - 3 9 g. these contributions, an entropy of mixing must be accounted for.
bC,nternad2T
The heat capacity of crystal I1 can be fitted, with a mean deviation of 10.4%, between 30 and 140°K. by the following parameters: OD = 148'K., eE = 200'K., a = 0.0070, b = 0.0024, and characteristic Einstein parameters corresponding to the observed normal vibrational frequencies. The $E corresponds to the spectroscopically unobserved frequency for the torsional oscillation. The frequency (derived by a method fully discussed elsewhere18), 136 =t 6 cm.-l, is of the same magnitude as those for the corresponding ethylene dibrornide and dichloride.15 The Entropy of Gaseous Succinonitrile Vapor.- Two routes are available for the evaluation of the entropy of the vapor, and agreeinelit would constitute a third-law test for this substance. Such a verification is important for succinonitrile in view of the fact that crystal I1 has been assumed to be perfectly ordered in calculating the entropy of transitioii. The third-lam entropy of the vapor can be computed from the thermal data plus the enthalpy of sublimation and the sublimation p r e ~ s u r e . ~The third-law calculation for 298.15'K. is presented in Table ITI.
4si
0.02
298.15 Sublimation 16,730/298.15 298.15 Compression t o 1 atm. 298.15 Ideal gas correction Entropy of the gas: 298.15
331.16
The low value of AXm indicates that succinonitrile is a plastic crystal below fusion. The sum of A s t and ASm is 9.03 cal./mole-OK. and is comparable to ASm for malonitrile 7.9, glutaronitrile 9.4, and acetonitrile 9.3. Heat Capacity of the Liquid.-The heat capacity data points for the liquid region were fitted (by least squares) to the straight line
Contribution
Debye extrapolation 5 Numerical integration crystal (11) 233.31 Transition 1482/233.31 233.31-298.15 Numerical integration crystal ( I ) 298.15 Entropy of crystal I: - 5 -233.31
Triple point temperature of sample: 330.99 Triple point of pure succinonitrile:
Vol. 67
Xt
S
=
=
- R ( X t ln X t
=
exp (1000/RT)
0.7301 X ,
=
0.2699
+ X , In X , - X , In 2) = 1.53 cal./ mole-OK.
The contributions to the spectroscopic entropy are tabulated for the equilibrium gauche-trans mixture in Table T'III. TABLE VI11 SPECTROSCOPIC ENTROPY OF GASEOCS SUCCINONITRILE AT 298.13"K." [Units: cal./mole-"E(.] Contribution
'j
41SI
Translation and rotation 63 97 Vibration 8 52 5 07 Internal rotation Entropy of mixing iwniers 1.53 Entropy of the gati. 79.09 f 0 10 The values are for the equilibrium mixture of isomers.
The agreement between the third-lam and the spectroscopic entropies is an indication of the absence of (19) D. \? i o o t t and .J P JIcCuIlouph, Bureau of hlines Report, H I 8930, 1982. ( 2 0 ) G. J Jallr, ~ J C l S o l l d lL ~ I l l U l U i l l L ~ t l ~ l l
Nov., 1963
TRANSITION AND FUSIOX OF TRIETHYLENEDIAMINE
residual disorder in crystal I1 and justifies assumptions made in the entropy of transition calculation. Summary From the evidence presented, we conclude that the transition from crystal I1 to crystal I is from an ordered phase to a plastically crystalline phase. The analysis of the entropy and transition shows that some freedom of molecula,r rotational reorientation must be allowed to account for the observed entropy increment. This conclusion is supported by the low value for the entropy of melting, which indicates crystal I to be highly disordered. Comparison of the measured enthalpy of melting with this value obtained by van de T'loed7 from freezing point depressions indicates that care must be taken in the interpretation of data obtained by that method. If relatively large amounts of the second component are used, the formation of a solid solution coulcl lead t o a crystal structure other than that of the plastic crystal phase and a resulting enthalpy of melting corresponding to the melting of an ordered phase. The existence of an ordered phase by solid solution formation is supported by the accord between the entropy of melting, from freezing point depressions, 8.5 cal./mole-°K., and the sum of the observed entropies of transition and melting, 9.0 cal./ mole-OK. The postulated molecular rotational reorientation in crystal I is supported by dielectric dispersion data of Clemett aiid DaviesZ1who conclude (21) C . Clemett and
M. Davies, J . C h e n . Phgs., 3%,316 (1960).
2381
that rotation in the solid involves the entire molecule and is a cooperative phenomenon involving adjacent molecules. Future studies suggesl ed by this research concern the heat capacities of malo- and glutaronitriles which contain one less and one more CH2 group, respectively. Malonitrile is a solid a t room temperature having the mechaiiical properties associated with a plastic crystal. Glutaronitrile exists in two solid modifications, a inetastable phase (formed by rapid cooling to -60') which undergoes an irreversible transition t o a stable form a t -40°.22 The dimorphism has also been noted by van de Vloed7 who reported melting temperatures and entropies of melting derived from cryoscopic constants. Thermal measurements on glutaronitrile are presently in progress. Acknowledgment.-The authors thank Professor C. E. Nordmaii for making accessible unpublished X-ray diffraction data aiid Professor G. J. Janz of Rensselaer Polytechnic Institute for unpublished preliminary results on the gas phase thermodynamic functions of succinonitrile and Dr. Elfreda Chang for assistance in the evaluation of the data. C. A. W. acknowledges the support of the Institute of Science and Technology of the University of Michigan in the form of a postdoctoral fellowship. The partial financial support of the U. S. Atomic Energy Commission Division of Research is greatly appreciated. (22) I. Matusbara, zbzd., 35, 373 (1961).
HEAT CAPACITIES AND THERMODYNAMIC PROPERTIES OF GLOBULAR MOLECULES. VII. TRANSITION AND FUSION OF TRIIETHYLENEDIAMINE~ BY JOHX C. TROWBRIDGE AXD EDGAR F. WESTRUM, JR.~ Department of Chemistry, University of Michigan, A r m ArboP, Michigan Received M a y 23, 1963 The heat capacity of 1,4-diazabicyclo[2,2,2]octane has been determined from 300 to 450°K. by adiabatic calorimetry. A sharp transition a t 351.08'K. associated with the transformation to the plastically crystalline phase involves an entropy increment of 7.19 cal./(mole OK.). The triple point occurs a t 433.1"K. with an entropy increment 4.10 cal./(mole OK.) and thus confirms the classification of this substance as a plastic crystal. Thermodynamic functions have been computed from the primary thermal data.
Introduction I n a previous paper of this series3.the low temperature heat capacity of triethylenediamine, l14-diazabicyclo[2,2,2]octane, was reported, revealing the onset of a transition just beyond the high temperature limit (350'K.) of the cryotkat. This investigation coiiceriis studies on the same material a t higher temperat'ures and presents evidence coiicerning the nature of the "rotator" or as designated by Timmermans4the "plastically-crystalline" phase. Experimental Preparation of Sample.-The triethylengdiaiiiirie saniyle used in t,his investigation was that previously used in t,he low tempera-.
(1) This work w a s supported i n part by the Division of Research of the United States Atomic Energy Commission. submitted by J. C. T. in partial fulfillment of the requirements for the Ph.D. degree of the Horace H, Reckham School of Graduate Studies of the University of Michigan. ( 2 ) To whom correspondence concerning this paper should be directed. (3) 8. 8 . Chang and Z. F. Westrum, Jr., J . Phys. Cham., 64, 1551 (1960). ($1 J . Timmevmans, J . c h i w . ph~/.s., 36, 331 (1938); I d chinr. B e l g c , 16, 178 (1951); cf. J . P h y s . Chem. Solids, 18, 53 (1961).
ture measurement^.^ Because of the hygroscopicity of the sample, the calorimeter was loaded in the anhydrous nitrogen atmosphere of a drybox. Although crystals used for the calorimetry were in the form of transparent hexagonal platelets approximately 1 cm. in diameter, they were fused in the process of these measurements. The fractional melting experiments reported later in this paper give a further indication of the high purity of this material. Microchemical analysis of the triethylenediamine sample indicated the following composition: C, 64.39; H, 10.81; and X , 24.75 icalcd.: C, 64.24; H, 10.78; and N, 24.96, for
CsHizNz). Silver Calorimeter.-The calorimeter used in this study (laboratory designation W-22) is machined from two solid silver cylinders and shown in Fig. 1 . It is provided with an entrant, axial well ( G ) rontaining the 2.50-ohm Karma wire heater and J,eeds and Northrup capsule-type resistance thermometer (H). The t,herniometer is gripped in a threaded beryllium-copper collet arrangement tightened by being forced into the slightly conical bore of the heater sleeve. The heater sleeve is itself conical and is held in a mating hole within the well of the calorimeter by means of a fine screw thread. The thermal equilibration spool (1) ensures that the leads achieve the surface temperature of the calorinieter. Six vertical radial vanes machined as an integral piece of the thermometer well portion facilitated thermal equili-
