1208
AARONRIBNERAND EDGAR F. WESTRUM,JR.
Dimethylmalononitrile. Low-Temperature Heat Capacity, Vapor Pressure, Density, and Chemical Thermodynamics of the Crystalline, Liquid, and Gaseous Phases1
by Aaron Ribner2 and Edgar F. Westrum, Jr.8 Department of Chemistry, University of Michigan, Ann Arbor, Michigan &lo4
(Received July 18, 1966)
Heat capacities from 5 to 350°K and entropy increments of transition [7.79 cal/(mole OK) at 302.60°K] and melting [3.15 at 307.47"KI were determined by adiabatic calorimetry. Values of So,(H"- H"o)/T, and -(Go - H"o)/T are 44.92, 21.95, and 22.97 cal/(mole OK) at 298.15"K. The vapor pressure of the liquid from 310 to 370°K is reproduced by log P(atm) = 26.5509 - 3506.24/T - 7.0462 log T. The third-law entropy of the gas at 298.15"K, 83.43 cal/(mole OK), is in good agreement with that calculated from the infrared spectroscopic data taken in the liquid phase (83.55). The density of the liquid (t - 35) g/cc. The mechanism of phase was determined as p = 0.8900 - 11.0 X the plastic crystal transition is discussed.
Introduction Su~cinonitrile,~ NC(CH2)2CN, although composed of molecules deviating considerably from spherical symmetry, possesses typical plastically crystalline with the properties, as formulated by Timmerman~,~ exception of a relatively high fugacity at the triple point. The entropy of melting, for example, is 2.68 cal/(mole OK) at 331.30"K. On the other hand, malononitrile, the prototype member (n = 1) of the homologous series NC (CHZ)%CN,despite greater globularity, has only a small transition with an entropy increment ASt = 1.1 cal/(mole OK) and a relatively normal entropy of melting (8.5).s The third member (n = 3), glutaronitrile, is also normal with no transitions and a ASm = 12.32.7 The greater geometrical similarity of the dimethylmalononitrile [ (CHS)~C(CN)2] molecule to those of plastically crystalline tetrahedral C(CHa)8 and pseudo-tetrahedral (CH& CC12,Qtherefore made it appear likely that this substance would show similar behavior. This expectation is based on indications that nitrile groups on aliphatic molecules do not form sufficiently strong intermolecular bonds to hinder molecular rotation and that (CHa)xCZ4-rtype molecules (Z represents vinyl, halogen, or nitro groups, X 2 2) often form plastic crystals.s The J
O U T of ~
Physicd Chmktry
However, the experimental thermal data on dimethylmalononitrile show that the plastically crystalline region extends only 4.9" below fusion.
Experimental Section Preparation and Characterization of the Sample. Dimethylmalononitrile was synthesized by Hi Laboratories from CHaI and CH2(CN)2,I0fractionally melted, and repeatedly zone-melted. Elemental microanalysis of the sample gave C = 63.95, H = 6.79, and N = (1) This research was supported in part by the U. S. Atomic Energy Commission. (2) Submitted in partial fulfillment of the requirements of the Ph.D. degree at the University of Michigan. (3) To whom correspondence concerning this work should be eddressed. (4) C. A. Wdff and E. F. Westrum, Jr., J . Phys. Chm., 67, 2376 (1963).
(5) J. Timmermans, J . Phye. Chem. Solids, 18, 1 (1961). (6) H.L. Girdhar and E. F. Westrum, Jr., unpublished data. (7) H. L. Clever, C . A. Wdff, and E. F. Westrum, Jr., J . Phys. Chem., 69, 1983 (1966). (8) J. Aston and G. H. Messerly, J . Am. Chem. SOC.,58, 2354 (1936). (9) J. E. Spice, G. A. Harrow, C . R. McGowan, and E. B. Smith, Pure Appl. Chem., 2, 303 (1961). (10) J. J. Bloomfield, J . Org. Chem., 26, 4112 (1961).
LOW-TEMPERATURE THERMODYNAMICS OF DIMETHYLMALONONITRILE
29.67, as compared with the theoretical C = 63.81, H = 6.43, and N = 29.76. No impurities were detected by high-resolution vapor phase chromatography on a cross-linked diethylene glycol adipate column. After degassing, 67.7835 g (in vacuo) of sample was distilled into the calorimeter and sealed under 30 torr of helium gas. Fractional fusion indicated only 0.0007 mole fraction liquid-soluble, solid-insoluble impurity. Cryogenic Apparatus. Measurements were made in the Mark I11 calorimetric cryostat," provided with an electronic adiabatic shield control consisting of three separate channels of recording circuitry with proportional, rate, and reset actions which maintained a temperature difference of less than a millidegree between the calorimeter and adiabatic shield and reduced thermal exchange to an amount negligible in comparison with other sources of error. The gold-plated calorimeter (laboratory designation W-24) was machined from an OFHC copper rod. It had eight equally spaced horizontal vanes (perforated with six sets of 4.5-mm diameter holes drilled 60" apart) integral with the well to aid in the circulation of liquid and to facilitate thermal equilibration. The cylindrical portion was 3.7 cm in diameter and 7.6 cm long. The circular top carried a cone (for suspending the calorimeter and making thermal contact with the refrigerant tank) and a demountable, gold-gasketed, plug-type valve with a 1.5-mm diameter aperture (for connection to the metal vacuum loading system). The thermometer-heater assembly was in an entrant axial well. The heat capacity of the calorimeter-heaterthermometer assembly approximated 35% of the total and was determined in separate series of measurements with adjustment for the slight differences in the amounts of thermal-conductivity grease and helium used between runs with and without sample. All measurements of time, temperature, potential, resistance, and mass were referred to U.s. National Bureau of Standards calibrations or standardizations. Vapor Pressure Determinations. The vapor pressure was measured in vitro by the isoteniscope method as outlined by Smith and Menzies.12 The sample was distilled into the glass isoteniscope at 70°K. The isoteniscope was then placed in the mineral oil-filled thermostat and connected to an all-metal, vacuum gashandling system by means of flexible copper tubing. The vapor pressure was read with a Wild cathetometer and appropriate adjustments were made for temperature, meniscus co-volume, and gravitational effects. The apparatus was tested by determination of the vapor pressure of water from 43 to 91"; less than 0.1% deviation from literature values was observed.lS
1209
Density Determination. The density was determined at various temperatures using a vacuum-jacketed pycnometer of 25-ml capacity, fitted with a cap to reduce evaporation of the sample from the capillary tube. The effective volume of the pycnometer was determined with distilled water. After the thermostated, sample-filled pycnometer was equilibrated overnight in the thermostat, the pycnometer and sample were weighed and the mass reduced to in vacuo values.
Results and Discussion Thermal Properties. The experimentally determined heat capacity values are presented in Table I in chronological sequence so that temperature increments for individual runs in a series may usually be estimated from the adjacent mean temperatures. Temperature increments for runs in anomalous regions have been included to aid in delineating the nature of the phase transitions. The data are referred to the defined thermochemical calorie equal to 4.1840 joules, an ice point of 273.15"K, and a molecular weight on the carbon-12 scale14 of 94.117 g. The heat capacity values were adjusted for curvature where appropriate, but vaporization correctionswere negligible. Transition. The heat capacity us. temperature plot of Figure 1 shows a single crystal-crystal transition (temperature of maximum C, = 302.60"K) at about 5" below fusion, with ASt = 7.79 cal/(mole OK) and AHt = 2358 cal/mole. The evaluation of the enthalpy of transition is detailed in Table I1 and is based primarily on enthalpy-type runs through the transition. However, because of the proximity of transition and fusion, determinations including both were also made. The entropy increments were evaluated in a similar fashion, except that smooth curves of heat capacity vs. temperature were drawn through the heat capacity points but constrained to the same enthalpy integral as that obtained from the long runs. The entropies were evaluated by appropriate integrals for these curves. Fusion. Details of the evaluation, also summarized in Table 11, indicate that the enthalpy of melting is 969 cal/mole and the corresponding entropy increment, ASm, is 3.15 cal/(mole OK) at the triple-point temperature of 307.47"K. These calculations are made (11) E. F. Westrum, Jr., J. Chem. Educ., 39, 443 (1962). (12) A. Smith and A. W. C. Menzies, J . Am. Chem. Soc., 32, 1412 (1910). (13) A. Ribner, dissertation submitted to the Horace H. Rackham School of Graduate Studies at the University of Michigan (1965); Atomic Energy Commission Report COO-1149-53. Cf. Nuel. Sei. Abatr., 19, 48090 (1965). (14) A. E. Cameron and E. Wichers, J . Am. Chem. SOC.,8 4 , 4175 (1962).
Volume 71, Number 6 April 1967
1210
AARON
Table I: Experimental Heat Capacity of Dimethylmalononitrilea T
F!
C8
A e r i e s 115.39 82.48 16.56 90.41 17.82 99.94 19.17 110.61 20.44 121.10 21.54 130.59 22.52 139.45 23.48 148.45 24.40 157.50 25.32 166.61 26.20 175.82 27.06 184.77 27.87 193.48 28.68 201.99 29.46 210.53 30.29 219.47 31.15 228.62 32.05 237.63 32.92 246.45 255.37 33.83 264.40 34.75 273.52 35.77 36.93 282.72 AH^ AHm Runs A 320.71 46.15 328.28 46.40
+
A e r i e s IIEnthalpy Run B 276.04 36.01 AHt Run C -Series IIIEnthalpy Run D 282.54 36.89 T
AT
297.55 300.35 301.66 302.22 302.52 302.56 302.50
3.532 2.088 0.599 0.553 0.058 0.024 0.015
.-
T
4
19.60 21.91
2.538 3.147
0.
288.94 37.95 293.94 39.29 AHt -/- A H m Runs E A e r i e s IVAHt Runs F 303.92 45.75 304.50 45.93 305.07 46.06 305.62 47.47 306.04 52.76 Melting Runs G 309.05 45.51 312.68 45.76 A e r i e s V282.53 36.89 AHt Runs H AHm Runs I
A e r i e s VIII18.26 24.44 27.37 30.98 34.69 38.02 41.63 45.74 49.99 54.52 59.50 64.71
2.212 3.825 4.596 5.521 6.439 7.216 8.009 8.879 9.745 10.62 11.55 12.50
83.63
15.57
i::; :::ti
Units: cal, mole,
2 80
290
300
3 10
T , OK.
A e r i e s VI-
--Series
281’98 36‘81 AHt Run J Run
-Series 5.85 7.03 8.27 9.65 10.99 12.68 14.33 15.77 17.53 C.
VII0.065 0.128 0.236 0.416 0.613 0.900 1.248 1.579 2.004 T
IX-
Enthalpy Run L Enthalpy Run M 269.32 35.24 279.01 36.34 AHt Run N AHm Run 0 Aeries
xr
313.60 321.60 329.59 337.79 346.12
45.82 46.11 46.47 46.83 47.20
AT
c:
0.013
24500 7542 60.8 970 4530 270 45.59
+
@
RIBNER AND EDGAR F. WESTRUM,JR.
AHt AHm Runs E 41.84 302.60 49.01 302.63 96.34 304.84 1186 307.11 5738 307.29 13800 307.91 21000 311.15
0.044
4.396 0.338 0.073 1.165 5.334
O K .
Figure 1. Heat capacity of dimethylmalononitrile in the region of the plastic crystal transition and fusion.
points. The extrapolated temperature TI, corresponding to 1/F = 1, is the triple point of the experimental sample; the temperature corresponding to 1/F = 0 is the triple point, TO, of the pure sample. The mole fraction of impurity determined by the van’t Hoff equationI6 is OhOO4. However, the curvature of the T us. 1/F plot is better fit by the treatment of Mastrangelo and Dornte” for solid-soluble, liquid-soluble contaminants. On this basis, the Tovalue is 307.47”K, the mole fraction of impurity is 0.0007, and the ratio of solubilities in the solid and liquid phases is 0.18. Smoothed heat capacities obtained from a least-squares digital-computer polynomial fit through the data points agree well with those read from large-scale plots of the data. Values at selected temperatures are presented in Table IV, together with the entropy, enthalpy increment, and Gibbs energy function. The latter properties were obtained by integrating the resulting functions through the heat capacity regions and incorporating the appropriate entropies of transition and ~
(15) E. F. Westrum.. Jr... and A. Ribner. J . Phm. Chem... 71.. 1216
similarly to those for trimethylacetonitrile.16 The ~ o of s o~~ d - ~ mt l u b l %uid-mluble e, impurity w&5 estimated from a plot of the observed temperature us. the reciprocal Of the fraction F‘ This is tabulated in Table I11 for the eight experimental The Journd of Phy&
Chemidry
(1906). (16) E. F. Westrum, Jr., and J. P. McCullough, “Thermodynamics
of Organic Crystals,” in “Physics and Chemistry of the Organic Solid State,”Vol. I, D. Fox, M. M. Labs, and A. Weissberger, Ed., Interscience Publishers, Inc., New York, N. Y., 1963, p 32. (17) 5. V. R. Mastrangelo and R. W. Dornte, J. Am. Chem. SOC.,77, 6200 (1955).
LOW-TEMPERATURE THERMODYNAMICS OF DIMETHYLMALONONITRILE
1211
Table II : Enthalpy of Transition, Melting, and Pretransition Region of Dimethylmalononitrile" Run designation
Run
No. of runs
Ti
T,
HT;
- H T ~ Hno - Hm
Enthalpy of Transition and Fusion 4565.9 2 287.25 316.89 4234.8 14 285.77 308.49 18 293.59 308.21 3939 309.29 4271.9 3 285.78 4404.1 2 285.24 311.75 4469.0 2 283.81 311.96
A E F+G H+I J +K N+O
4334.4 4332.2 4339 f l o b 4333.2 4333.4 4335.4
[
l I C , d T (smooth curve) for runs E = 4334 Average value Halo - Hasa = 4334
H J N
No. of runs
1 1 1
Ti
TI
HT,
- Hr1
Enthalpy of Transition 3130.8 305.51 285.78 3133.3 285.24 305.13 304.93 3178.9 283.81
HIM
No. of runs
I K 0
TI
HT;
Ta
- Hrsr
2 1 1
AHm = 969 A8m = 3.15 Tmd = 307.47 Run
-
TB
HB HI
Enthalpy Runs in Pretransition Region 231.09 271.34 1344 230 270
1330
designation
3136.3 3136.2 3138.0
AHt = 2358 u t = 7.79 T{ = 302.6
1197.0 1197.3 1197.4
Average value Ha10 - Hws = 1197 Lattice contribution Halo - Ha06 = 228
B
Average value Ha06 - Ha6 = 3137 Lattice contribution Ha06 - Ha6 = 779
- H T ~ HIM- HIM
Enthalpy of Melting 305.50 309.29 1141.1 305.13 311.75 1271.2 311.92 304.94 1290.1
1
Run
designation
deaignation
HT, Ti
TI
HTI
TI
1 1 1 1
[LBCedT = 1332 244.41
D
279.30
1203
245
280
1210
[SABC.dT = 1210 L
85.44
205.71
2766
85
205
2752
[SABC.dT = 2743 M
205.71
264.42
1868
205
265
[s,"CadT
1909
= 1909
a Units: cal, mole, OK. Runs C not included in this table because no equilibrium temperature waa obtained for Te. UnTemperature of maximum Ce. Extrapolated from fractional melting data, certain correction for quasi-adiabatic conditions. see text.
fusion. Below 5OK, the values of the functions were estimated from the Debye Ta limiting law and from plots of C,/T us. T2. The heat capacity data are considered to be characterized by a probable error of less than 0.1% above 25°K and to have a precision index gradually increasing to 1% at lOoK and to 5% at 5°K. The thermodynamic functions are believed to have a probable error of less than 0.1% above 100°K. Nuclear spin and isotopic mixing effects have been neglected in the evaluation of the entropy and Gibbs energy function. Vapor Pressure. The vapor pressure data in Table V were fitted by digital computer to the Rankine equation log P(atm) = 26.5509
- 3506.24/T -
7.0462 log T
Although the data in Table V are listed in sequence of increasing temperatures, the series designations indicate
Table ILI: Fractional Melting of
Dimethylmalononitrile" T
AT
306.96 307.18 307.23 307.27 307.29 307.32 307.33 307.34 307.78
0.369 0.064
0.036 0.036 0.021 0.020 0.015 0.009 0.859
9 545.9 1606 2893 2836 4900 5129 6719 12120 105.87
ZAH
Trinal
190.77 294.56 398.35 501.93 605.47 708.91 812.39 915.80 1019.34
307.15 307.21 307.25 307.28 307.31 307.33 307.34 307.35 308.21
-Triple
Van't Hoff equation Solid solution equation
' Units:
cal, mole,
O K .
1/F
4.680 3.116 2.335 1.868 1.557 1.335 1.168 1.038
...
point-
Mole
Pure
fraction
Sample
compd
impurity
307.35 307.35
307.43 307.47
0,0004 0.0007
Baaed on melting runs G. ~
~~
Volume 71, Number 6 April 1887
1212
AARONRIBNERAND EDGAR F.WESTRUM,JR.
Table IV:
Thermodynamic Functions of Dimethylmalononitrile" T
C.
5 10 15 20 25
0.048 0.449 1.398 2.637 3.973
30 35 40 45 50
5.283 6.506 7.652 8.730 9.750
S O
Crystal I1 0.012 0.128 0.476 1.043 1.775 2.616 3.523 4.468 5.432 6.405
Ho
- H'o
-(a"
-
HOo)/T
0.995 5.443 15.457 31.975
0.003 0.029 0.113 0.271 0.496
55.141 84.647 120.08 161.06 207.3
0.778 1.105 1.466 1.853 2.259
0.044
60 70 80 90 100
11.65 13.39 14.99 16.48 17.85
8.353 10.281 12.175 14.027 15.835
314.4 439.7 581.7 739.1 910.9
3.113 3.999 4.903 5.815 6.727
110 120 130 140 150
19.12 20.32 21.46 22.56 23.63
17.597 19.313 20.99 22.62 24.21
1095.8 1293.1 1502.1 1722.2 1953.2
7.635 8.537 9.431 10.314 11.19
160 170 180 190 200
24.66 25.65 26.62 27.56 28.48
25.77 27.29 28.79 30.25 31.69
2195 2446 2708 2978 3259
12.05 12.90 13.74 14.57 15.39
210 220 230 240 250
29.40 30.34 31.30 32.28 33.28
33.10 34.49 35.86 37.21 38.55
3548 3847 4155 4473 4801
16.20 17.00 17.79 18.57 19.35
260 270 280 302. Sob
34.29 35.36 36.56 (34.37)
39.87 41.19 42.50 45.45
5139 5487 5846 6704
20.11 20.87 21.62 23.30
302. Sob 307.47=
(45.31) (45.51)
Crystal I 53.24 53.97
9061 9282
23.30 23.78
(45.51) 45.65 46.07 46.50 46.93
Liquid 57.12 57.48 58.93 60.36 61.75
10251 10364 10823 11286 11753
23.78 24.04 25.11 26.16 27.18
307. 47c 310 320 330 340
their source and, within series, runs were made in sequences of both increasing and decreasing temperatures. In the course of the first four series of runs (omitted from the table), the sample was taken to temperatures as high as 440°K. This sample turned dark brown in color, suggesting condensed phase polymerization. Moreover, the calculated ACv. term was also positive in this region, suggesting possible reversible gas phase polymerization. A new sample was therefore introduced and measurements were restricted to temperatures below 413°K. These are the values in Table V, and, as noted in the last column, the data are well fit and have a mean-square deviation of 0.08 torr and a ACv, of -14.1 cal/(mole OK). This is in good accord with the difference between the calculated ideal C.(g) and the experimental value for C,(1) of -14.0. DensitlJ. The density was determined at three temperatures between 35 and 45°K with a probable error of 0.01%. Over this range, the density (in g/cc) Table V : Vapor Pressure of Dimethylmalononitrile" Seriea designation
T
Pobd
9 11 11 11 11
322.24 329.76 333.90 337.29 340.88
7.50 11.35 14.14 16.77 19.97
7.55 11.36 14.09 16.73 19.98
0.05 0.01 -0.05 -0.04 0.01
11 11 11 11 11
344.10 346.67 351.22 354.33 359.69
23.49 26.26 32.41 37.92 47.08
23.34 26.36 32.51 37.38 47.23
-0.15 -0.10 0.10
11 11 11 11 10
360.59 367.31 371.05 357.38 863.04
49.01 64.62 75.46 43.14 54.15
49.08 64.90 75.42 42.75 54.42
0.07 0.28 -0.04 -0.39 0.27
10 10 7 7 5
369.17 373.19 384.08 391.46 393 * 94
69.47 81.76 123.31 161.06 175.56
69.97 82.05 123.72 160.81 175.13
0.50 0.29 0.41 -0.25 -0.43
405.19 405.47 405.95 407.16 409.44
253.38 255.62 260.28 270.60 290.02
253.70 255.96 259.88 269.99 289.87
0.32 0.34 -0.40 -0.61 -0.15
412.63
319.74
319.64
-0.10
350
47.35
63.12
12224
28.18
273.15
35.72
41.60
5599
21.10
8 8 8 6 6
298.15
42.90
44.92
6544
22.96
6
'
Units: cal, mole, OK. Assuming transition to be truly isothermal. e L u m h g melting to be &.dy isothermal.
The Journal of Phyaieal Chemietry
-
Pcslcdb
Pcslod pobad
-0.54
0.15
= "Units: torr. OK. Based on the eauation loe - P(atm) I , 26.5509 - 3506:24/T - 7.0462 log T.
LOW-TEMPERATURE THERMODYNAMICS OF DIMETHYLMALONONITRILE
1213
is well represented by the empirical equation p = 0.9285 - 0.0011t. Third Law. The standard entropy of ideal gaseous dimethylmalonodde was calculated from the thermal and vaporization data already presented, as indicated in Table VI, leading to a value of 83.42 cal/(mole OK). Table VI: Experimental Third-Law Entropy of Dimethylmalononitrile at 298.15'K" Temp,
Contribution
OK
0-5 -298.15 298.15 298.15-302.60
0.01 44.91
So,crystal I1
44.92 0.53
298.15 298.15
So, gas
307 * 47 307.47-3 10 310 310 310-298.15
+
Units: call mole,
I
I
3000
2000
Entropy
Debye extrapolation Numerical integration, crystal I1 Numerical integration, crystal I1 (lattice) Transition (2358/302.60) Numerical integration, crystal I (lattice) Melting (969/307.47) Numerical integration, liquid Vaporization (11702/310) Compression, 4.43 torr to 1 atm Integration, C.(liq) d In T AC, d In T Adjustment to ideal gas
302.60 302.60-307.47
01
-
7.79 0.73 3.15 0.36 37.75 -10.59 -1.22
83.42 f0.2
OK.
Raman and Infrared Spectra. The infrared spectrum of the liquid at 35", shown in Figure 2, was observed on a recording Beckman IR-12, with a polyethylene cell for the spectral region between 200 and 700 cm-l and an NaCl cell from 600 to 4000 cm-l. The frequency assignments were made by analogy with those frequencies of propane1* [ (CHa)2CH2], malononitrilel* [(CN)2CH21, and dichlorodifluoromethane20 [C12F2C] which, from structural considerations, are expected to have values similar to those of dimethylmalononitrile. The Raman spectrum of the liquid was also taken on the spectrograph described by Vidale and Taylor21 for observation of the C-CN deformation frequency (
