1444
NEIL 5. BERMAN AND JOHN J. PVICKETTA
age adjacent to the side chain rises, ie., less C, more B and D. There is also a small increase in demethanation (more G).
Vol. 66
Acknowledgment.-This work was supported by the Air Force Office of Scientific Research (Directorate of Chemical Sciences).
THE THERMODYNAMIC PROPERTIES OF %BUTANOL BY XEIL S. BERMAN AND JOHN J. MCKETTA Department of Chemical Engineering at The University of Texas, Austin, Texas Received February 17, 1061
Downloaded by UNIV OF SHEFFIELD on September 8, 2015 | http://pubs.acs.org Publication Date: August 1, 1962 | doi: 10.1021/j100814a016
The vapor heat capacity and latent heat of vaporization of 2-butanol have been determined experimentally. A model of an equilibrium mixture of monomers, dimers, and tetramers was used to select constants of an equation of state to fit the heat capacity data and total gas imperfection calculated from the Clapeyron equation. Molecular structure, spectroscopic information, and the vapor heat capacity data were used to evaluate barriers to internal rotation and compute tables of thermodynamic functions.
As part of a program to study the properties of oxygenated hydrocarbons, the vapor heat capacity of 2-butanol has been measured experimentally in a pressure range of one-fourth to five-fourths atmospheres and a temperature raiige of 365.15 to 455.15'K. The heat of vaporization has been determined along with the vapor pressure over the pressure range from one-fourth to five-fourths atmospheres. A model of an equilibrium mixture of monomers, dimers, and tetramers was used to correlate the heat capacity data and the total gas imperfection calculated from the Clapcyron relation. Molecular structure, spectroscopic information from the literature, and vapor heat capacity data were used to evaluate the barriers to internal rotation. Tables of thermodynamic functions for this compound are presented a t selected temperatures from 0 to 1000'K. Experimental Physical Constants and Definitions .-Calculations in this work are based on the 1956 Atomic Weights,' the values of the fundamental physical constants reported by Rossini, et d . , 2 and the definitions: 0°C. = 273.15"Ii. and I cal. = 4.1840 abs. joules. Temperatures are on the defined International Temperature Scale. The Material.-The sample of 2-butanol was supplied by the Celanese Corporation of America. It was purified from Eastman Kodak secondary butyl alcohol by multiple frartional distillation using a 1-in. 90 tray Oldershaw column. Purity by gas chromatography was found to be 99.92%. This material was further distilled in a 1.2-m. column packed with glass rings and vacuum distilled into receivers for introduction into the apparatus. The boiling range of the final distillate was less than 0.005" a t atmospheric pressure. No significant changes in the color or boiling point of the compounds were noted in the course of the determinations reported. The Apparatus.-The apparatus used to measure the vapor heat capacities, heats of vaporization, find vapor pressures was the flow calorimeter used by Pennington, mat hew^,^ and Niclrerson6 and the same type described by Waddington, et ~ l . and , ~ Pitzer? with modifications discussed by Mc(1) E. Wichers, J . Am. Chem. Soc., 78, 3235 (1956). (2) F. D. Rossini, F. T. Guoker, H. L. Johnston, L. Pauling, and G. W. Vinal, ibid., 74, 2699 (1952). (3) R. E. Pennington and K. A. Kobe, ibid., 79, 300 (1957). (4) J. F. Mathews and J. J. McKetta, J . P h w . Chem., 65, 758 (1961). ( 5 ) J. K. Nickerson, K. A. Kobe, and J. J. McKetta, ibid., 65, 1037 (1961). (6) (a) G. Waddington, S. S. Todd, and H. M. Huffman, J . Am. C h e m . Soc., 69, 22 (1947); (b) G. Waddington a n d D. R. Douslin, zbid., 69, 2275 (1947). (7) K. 8. Pitzer, ibid., 63, 2413 (1941).
Cullough, et a1.8 The three-way solenoid valve used in the previous research was replaced with a pair of two-way valves for the heat of vaporization determinations. Vapor Pressure.-Vapor pressures of 2-butanol wore obtained from the flow data a t five pressures bctween onrfourth and five-fourths atmospheres. The valucs shown in Table I are based upon the average of a t least eight cxperimental measurements.
TABLE I LATENTH ~ A OTF VAPORIZATION OB' 2-BUTANOL
~ X P E H I M E N T A L VAPOR PRESSbRES A N D
Temp., OK.
339 355 365 372 378
I
91 20 10 49 49
Pressure, mm.
A H v , cal./mo!e
189.78 379.63 568 46 754 70 937.63
log p = 7.14472 -
10824 10350 10014 9753 _ I
1129.08 165.26 t
-____-
+
(1)
Where p is in inin. and t in "C. The accuracy uncertainty of tbis equation is estimated as 1 0 . 5 mm. The norinal boiling point of 99.54" compares favorably with the values of 99.529" by BrunelQand 99.52-99.55' by Parks, et d . ' O The Heat of Vaporization.-Latent heats of Vaporization of 2-butanol were measured a t pressures of l / 4 , z / t , 3/4, and 4/4 atmosphere a t saturation temperatures. The latent heats can be represented by the equation
A H , = 1092.15(225.30 - t)0.4"282 ( 2 ) where AHv is in cal./mole and t in "C. I t is estimated that the accuracy uncertainty of this equation is not greater than +0.15% in the range 66.5 to 100". Experimental results are presented in Table I. The Vapor Heat Capacity.-The vapor heat capacity of 2-butanol was measured at selected pressures from ' / a t o 6 / ~ atmospheres and a t temperatures from 365.15 to 455.15"K. The experimental results are presented in Table 11. The accuracy uncertainty of these data is at least 10.3%. Figure 1 presents a plot of these data and the calculated heat capacities. Direct heat capacity measurements have been made by Sinke and DeVries" from 375 to 437°K. and a pressure of 750 mm. Jatkar and Lakshminarsyanan12deduced the heat (8) J. P. McCollough, D. W.Scott, R. E. Pennington, I. A. Hossenlopp, and G. Waddington, %bid., 76, 4791 (1954). (9) R. F. Brunel, ibid., 46, 1334 (1923). (10) G. S.Parks, S.B. Thomas, and D. W.Light, J . C h e m . Phys., 4,
64 (1936). (11) G. C. Sinke and T. DsVries, J. Am. C h e m . Soc., 76, 1815 (1953). (12) S. K. K. Jatkar a n d D. Lakshminarsyanan, C k e m . Abstr., 41, 1901c (1947); J. I n d z a n I n s t . Sci., 288, 1 (1946).
THERMODYNAMIC PROPERTIES OF
August,, 1962
1445
%BUTANOL
TABLE I1 lTAPOH. HEATCAPACITY OF
2-BCTAXOL IN
c__
383.15
365.15
(7,
atm. a h . ) atrn. abs.) atm. abs.) atm. abs.) atm. abs.)
(6/4
C, (4/4 C,, (a/a C, (z/4 Cp ( I / * A"
a
33.5i 32.23 2,801 Cb 5.312 CpO (exptl.) 31.48 CpO (by equation) 31.47 GPO (calcd.) 31.50 Parameter in eq. 6, cal./mole O K . atm.
CALORIES
Temp., 401.1 5
_ _ _ I _
b
437.15
419.15
35.83 35.48 35.30 35.84 34.43 34.83 35. 60 33.67 34.41 35.38 33.13 34.11 35.22 1.815 1,217 0.842 1,093 0.257 0.068 32.63 33.81 34.95 32.64 33.80 34.95 32.66 33.81 34.94 Parameter in eq. 6, cal./mole "K. atm.a.
capacity from sonic velocity measurements. These results are presented for comparison in Pig. 2 after correction to zero pressure. Downloaded by UNIV OF SHEFFIELD on September 8, 2015 | http://pubs.acs.org Publication Date: August 1, 1962 | doi: 10.1021/j100814a016
PER MOLEDEGREE
OK.--
4
36.73 36.54 36.38 0.598 0,020 36.08 36.08 36.06
455.15
37.74 37.64 37.56 0.433 0.007 37.20 37.21 37.13
3B,
Correlation of the Effects of Gas Imperfection 37,0 T: 455.15 Hydrogen Bonding in Alcohols.-Thermodynamic and spectroscopic studies of various alcohols 36.OW have shown that two or four molecules tend to associate with the formation of a weak chemical bond. Fox and Martin13 suggested that polymers P 35'0 T=419,15'K with more than four monomer units were unlikely 34.0 T: 383.15'K and that the cyclic tetramer was the major polyd T=401.15°K meric species beyond the dimer. Weltner and Pitzer,14 Kretschmer and Wiebe,16 and Mathew* 33.0 all found that heat capacity could be correlated r / best by assuming an equilibrium mixture of dimers, 8 0 EXPERIMENTAL tetramers, and monomers. Correlation of the (This w o r k ) results of the measurement of the intensity of abBY EQUATION sorption bands in the 2.5 to 3.2 p region of the in31.0k , 2 /I4 3 /I4 4 /I4 5 /1 frared by Goveleled to the same assumptions. 0 l/4 PRESSURE, ATMOSPHERES. Cas Imperfection of Associated Molecules.The model of an equilibrium mixture of monomers, Fig. 1.-Vapor heat capacity of 2-butanol as a function of pressure. dimers, and tetramers can be used to derive an equation of state in the form in Fig. 1. The experimental data can be represented within a maximum deviation of +0,12% V = RT/p 4- B 4- Dp2 (3) by L3 = -b - R T exp(AF2/RT) (4) 282.0 A = exp (2625/T) cal./mole atm. OK. T2 D = -3RT exp(AF4/RT) (5) (9) where effects other than those due to association are grouped in the constant b. From the relationship hetween heat capacity and the equation of C = 1.266 X exp (11559/T) state 7'2 OK
'
-
r
c, c,o =-_.
A
+ Ap + Cp3
AH22 RT2
= -exp(AF2/RT)
(10)
when (7)
AHZ2 exp(AF4/RT) RT2 Equations 6, 7, and 8 were used to correlate the experimental heat capacity data on 2-butanol to give the parameters in Table I1 and the curves
C =
cal./mole atm.3 OK.
(6)
__
(13) J. J. Fox and A. E. Martin, Trans. Faraday Soc., 36, 897 (1940). (14) W. Weltner, Jr , and K. 8. Pitser, J . Am. Chem. Hoc., 73, 2606 (1961). (15) C . R. Kretschmer and R. Wiehe, ibzd., 76, 2579 (1954). (16) J. L. Gove, Ph.D. Dissertation, Pennsylvania State University, 1957.
CPo = 5.533 4- 0.07687T
- 1.598 X
10-5T2
(11) From the constants of eq. 9 and 10 the entropies and heats of forma.tion of the dimers and tetramers are As2
=
21.4 e.u.
AH2 = 5250 cal./mole
AS4 = 74.7 e.u.
AH4 = 23118 cal./mole
Deviations from ideal gaseous behavior (V RT/p) were calculated from the Clapeyroii equation and the vapor pressure and heats of vaporiza-
NEIL S.BERMAX ASD JOHX J. ~ I C K E T T A
1446
38,~
A
Y
3
0
360-
THIS WORK SINKE AND DEVRIES JATKAR AND LAKSHMINARAYAN BY EQUATION
0
I \ -I
34.0-
V OCL
0
32.0-
1
30.0 360
Fig. 2.-Ideal
Downloaded by UNIV OF SHEFFIELD on September 8, 2015 | http://pubs.acs.org Publication Date: August 1, 1962 | doi: 10.1021/j100814a016
2500
I
I
380
1
I
I
400 420 TEMPERATURE, "K.
440
460
vapor heat capacity of 2-butanol.
I
0
FROM DERIVED EQUATION OF STATE 1 320
I 340 360 TE M P E R ATUR E, OK.
I
380
Fig. 3.-Total gas imperfection of 2-butanol for the saturation curve.
B I Fig. 4.-The
Q
m
II
rotational conformations of 2-butanol.
tion found in this work. The results of these calculations are shown in Fig. 3. The smooth curve in this illustration was obtained by setting b equal to 480. Then the parameters B and D in eq. 3 become
B
=
cc./mole D
=
Preliminary steps in this procedure include calculation of the kinetic energy matrix for rotation and assignment of the normal vibrational frequencies. Rotational, Constants.-The 2-butanol molecule CH&H2C"HOHCH3 has an asymmetric carbon atom (marked with the asterisk) and therefore exists as a d and an L-form. Hindered rotation about the C-C* bond results in the three rotational isomers shown in Fig. 4. In this figure the mo!ecules are viewed along the C-C" axis, and it is assumed that these isomers are more stable than the "eclipsed" forms. (That is, the configurations in Fig. 4 correspond to the minima of the potential energy curve as a function of azimuthal angle.) Bernstein and Pederson" have measured the specific rotation of 2-butanol as a function of temperature to determine the equilibrium concentrations of the isomers and the heats of isomerization. Their results in the liquid phase are corrected for association by dilution in a noli-polar solvent, and a solvent correction is derived from rotation measurements in different solvents. This treatment yields an approximation for the gaseous state. They also conclude that I and I1 in Fig. 4 have the lowest energy, each of the same magnitude. hIcCullough, et a1.,'* used a similar assumption in the study of the thermodynamic properties of 2-butanethiol. The product of the principal moments of inertia and the reduced moments of the rotating tops mere calculated for conformation I using the formalized procedure of Kilpatrick and Pitzer.lg The bond distances and angles in 2-butanol were taken to be the same as those of 1-propanol as used by mat hew^.^ Bond lengths for C-H, C-C, C-0, 0-H are 1.09, 1.54>1.43, and 0.96 A , , respectively. Bond angles are tetrahedral except for C-0-H which was taken as 110'. The kinetic energy matrix [ D ]for internal rotation becomes
'Dl
=
I
i
3.0369 0.0299 0.3616 0 1667 0.0299 0.7952 -0.5272 -0 0299 0 3516 -0 5272 18.2320 0 7124 ,0.1567 -0 0299 0 7124 3 0369
If the off diagonal elements are neglected, the reduced moments are 5,043 x g. for TABLE111 SKELETAL BESDINGFREQUENCIES O F 2-BLTa4N0L,
---
-480 - 1,690 X 10-3Texp(262Z/T),
I
cc./mole atm.2 (13) The large deviation a t the lowest temperature may indicate that b should be some function of temperature. PVT data a t low temperatures would be necessary to develop an equation that can be extended outside of the range of this work. Calculation of the Thermodynamic Properties of &Butanol The thermodynamic properties in the ideal gaseous state were calculated from molecular data.
CV-'
Conformation----
I1
(12)
- 1.1738 X 1O-I4T exp(ll5dS/T),
Vol. 66
I11
Obsd
20
467
450
450
500 469
400
43;
435 405 370 230
410
395 370 250
382
274 190
(17) H. J. Bernstein and E. E. Pederson, J . Chem. P h y s . , 17, 885 (1949). (18) J. P. McCullough. H. L. Finke, D. W.Scott, R . E. Pennington. AT. E. Gross, J. F.Nesserly, and G. Waddington, J . A m . Chem. S o c . , 80, 4786 (1958). (18) J. E. Kilpatrick and I ? . S. Pitzer, J . Chem. Phys., 17, 106% (1949).
THERMODYNAMIC PROPERTIES
August, 1962
1447
%BUTANOL
OF
TABLE IV SELECTED SPECTRA AND THE krIBRATIONAL [nfrared, om. -1 Liquid in CCi4 and CSa
ABSIGKMENT
7
I _ _
3682w 2980s 2943s 2891s
3401 2959 2924 2865
1459ni 13941x1
1456 1403 1376
Downloaded by UNIV OF SHEFFIELD on September 8, 2015 | http://pubs.acs.org Publication Date: August 1, 1962 | doi: 10.1021/j100814a016
12411x1
114Sw 11 2 8 ~ 1080lrL 104ovw 1026vw 992m 920m 9OTm 886w
---Raman, 24
Fig.
520
Conformation I designation
om.-’--
Fuiidamentd
260
266
2972 (8) 2928 (10) 2874 (7)
3682 2980 (6) 2943 (2) 2891 (1)
0-H stretch
1450 (5) 1394 1380 (2) 1350 1314 1290 1250
C-H bends COH bend C-H bend CH wag CH wag CH2 twist CH? \vag
1145 1110 I 080
C-C stretch CH, rock CH, rock C-0 stretch CHllrock C-C stretch CH8 rock
C-H stretches
1450 (6)
1537 (0.008) 1445 ( . l ? O )
1350 (1)
1457 ( ,038)
1298 (1)
1299 ( .028)
1108 (3)
1210( ,012) 1155 ( ,026) 1113 ( ,062)
1031 992 969 912
1030 (2) 990 (2)
1034 ( .040) 994 ( ,075)
909 (3)
914 ( .043)
1034 992 970 912
820 794 777
820 (6)
823 ( .087)
820
C-C stretch
780 (4)
779 ( 723 ( 501 ( 435 ( 382 (
.058) .011) ,052) .028) ,017)
780
CH, rock
1314 1290 1250 1147 1116
722w
CCO bend 500 497 500 (5) CCO bend 435 438 437 ( 1 ) CCC bend 382 386 383 ( I ) CCC bend 274 274 b Relative intensities a Relative inteneities are indicated by VTV = very weak, w = weak, m = medium, and s = strong. Absolute intensities are indicated by the scattering coefficients opare indicated by numbers opposite the frequencies. posite the Irequencies.
the CH, tops, 1.320 X g. cm.2 for the OH top, and 30.271 X for the skeletal rotation. The product of the principal moments of inertia g3cm.6. is 7910 X Vibrational Assignment.-Four of the internal degrees of freedom of 2-butanol can be attributed to internal rotations leaving 35 others due to vibrations. As an aid to assigning the skeletal bending frequencies, some infrared data in the range 250-650 cm.-l were obtained from Union Carbide Chemicals Company2O and an analysis of the skeletons of several simpler alcohols was made using the method described for 2-methylbutane21 and the tabulations of Wilson, et ~ 1 Force . ~ constants were selected to give agreement with the observed frequencies of ethanol and propane. The results in Table I11 do not show good agreement with the observed frequencies of 2-butanol; howeyer, they were sufficient to assign the strongest absorptions shown in Fig. 5 to the I conformation. The vibrational assignments along with selected iiifrared20.23s24 and Raman25,26 data are presented in (20) Private communication. (21) D. W. Soott, J. P. MoCullough, K. D. Williamson, and G. Waddington, J . Am. Chem. SOC.,75, 1707 (1951). ( 2 2 ) E . B. Wilson, Jr., J. C . Deoius, and P. C. Cross, “Molecuiar Vibrations,” McCraa-Hi11 Book Co., Inc., New York, N. Y., 1955,
WAVE 100,
‘ I
6o
15
500 I
NUMBER, CM;’.
400 I
250
300 I
7
Room Temperature
20
Fig. 5.--The
25 30 WAVELENGTH, MICRONS,
35
40
infrared spectra of 2-butanol 39.
~Table IV. This assignment is only schematic. The C-C stretches mere assigned by comparing the results from the approximate normal coordinate analysis. The 820, 970, and 1140 ern.-’ lines assigned to 2-butanol appeared in 1-propanol, 971 em.-’, and 2-propanol near 820 and 1140 cm.-l. The various carbon-hydrogen motions were as(231 J. R. Quinan and s. E. Wiberley, Anal. Chem., 26, 1762 (1954). (24) A.P.I. Research Project 44, Catalog of Infrared Spectral D a t a , Serial Numbers 431 and 750. ( 2 5 ) K. W. P. Kohlrausch, “Ramanspektren,” Akademische Verlagesellschaft Becker und Erler, Kom.-Ges.. Leipzig, 1943. (26) W. Braun, D. Spesner, a n d IM. Benske, Anal. Chem., 22, 1074 (1950).
1448
KEIL
8. BERMAX
bSD
JOHN J. MCKETTA
Vol. 66
TABLE V THERMODYNAMIC PROI’ERTIES IS TRE IDEAL Temp., O h .
cal./mole,
OK.
cal./mole,
GASEOKSSTATE^
-
so,
C,O,
OK.
( H T ~ Hoo)/T, - ( F T ~ - Ho’)/T, cal./mole, OK. cal./mole, OK.
-AHro, kcal./mole
AFfO,
koal./mole
log KfO
Downloaded by UNIV OF SHEFFIELD on September 8, 2015 | http://pubs.acs.org Publication Date: August 1, 1962 | doi: 10.1021/j100814a016
0 0 0 0 0 62.86 -62.86 Infinite 273.15 24.46 83.66 16.57 67.03 -48.93 39.19 69.35 298.15 2 7 . OS 85.81 17.39 68.42 69.84 -46 ,94 34.46 300.00 27.20 85.98 17.44 68.53 69.87 -46.79 34.14 400 33,70 94.78 20.71 74.07 71.64 -38.29 20.96 500 39.70 103.01 23.92 79.09 73.09 -28.98 12.68 600 44.72 110.74 26.97 83,76 74.25 -19.26 7.04 700 49.02 117.99 29.82 88.17 75.16 - 9.06 2 84 800 52.68 124.80 32.46 92.34 75.83 1.50 -0,40 900 55.88 131.20 34.90 96.33 76.30 12.33 -2.99 -5.11 1000 58.62 137.26 37.14 100.14 76.60 23.39 * To retain internal consistency some of the values in this ta,ble are given to more decimal places than are justified by their absolute accuracy.
signed with the aid of the work on 2-butanethiol by McCullough.lE Although the heat capacities calculated with this vibrational assignment are in agreement with experiment, much controversy exists oil the vibrational modes. ;Ilathews4 summarizes some of the discussion on the 0-H bend and the C-0 stretch, and his conclusions are used in this work. A recent analysis of the infrared spectra of methanol by Falk and Whalley27 also places the 0-H bend in the 1300-1400 cm.-l region. Internal Rotation.-Internal rotational contributions to the thermodynamic properties come from the two methyl rotations, the hydroxyl rotation, and the rotation about the central C-C bond. Simple threefold cosine type barriers to internal rotation were assumed for the methyl and hydroxyl groups. Values of barrier heights selected were 3100 and 4000 cal./mole for the methyl rotations as in 2-butanethiol,18 and 800 cal./mole for the hydroxyl rotation as in other alcohol^.^ 28 The contributions from the rotation about the central bond were calculated as those for a simple t,hreefold barrier of height 2150 cal./mole plus the contribution due to “conversion” of molecules from the I and I1 conformations to the I11 form. The latter values were obtained from a consideration of the equilibrium bptween isomers2gusing Bernstein and Pederson’s17 equation for the equilibrium constant representing the conversion of I to I11 or I1 to I11
K = 1.43 exp(-SO3/RT)
(14)
The restricted rotor contributions to the thermodynamic properties were taken from the tables of Pitzer aiid G~vvinn~~ and the extmsion of these (27) M. Falk and E. Whalley, .I. Chem. Phzls , 34, 1554 (1961). (28) G M Barrow, rbid., 20, 1739 (1952). (29) IC. S. Pitzer, t h z d . , 5, 473 / 3 0 ) K. S. Pitzer and W, n,Gwrnn tbzd , l o , 428 (1942).
(1937).
tables by Li and P i t ~ e r . ~ The ’ barrier height 2150 cal./mole was selected to give the best fit to the experimental heat capacity data. Table I1 presents a comparison between the calculated and experimental heat capacities. The maximum deviation is 0.22% aiid the average deviation 0.09%. Thermodynamic Functions.-The vibrational assignment, product of principal moments of inertia, reduced moments of inertia of internal rotating groups, barriers to internal rotation, and the equilibrium between rotational isomers discussed above were used to compute the values of the thermodynamic functions of 2-butanol a t selected temperatures between 0 and 1000” K., and are presented in Table V. The standard heat, standard free energy, and common logarithm of the equilibrium constant for the formation of 2-butanol from the elements also are tabulated. 4C(graphite)
+ 5112(g) + 1/~02(g)= 2-C4H,O€I(g) (15)
The value of the heat of combustion of 2-butanol reported by Skinner and S n e l ~ o n(635.91 ~~ f 0.22 kcal./mole) and the values of the heats of formation of mater and carbon dioxides3were used to compute the heat of formation of 2-butanol a t 298.15”K. Table V, the heat of formation a t 298.1joE(., and the thermodynamic functions of hydrogen, carbon, and oxygen33 were used to compute the remainder of the table. (1936).
(31) J. C . Li and K. S. Pitzer, J . Phys. Chem., 60, 466 (32) H. A. Skinner and A. Snelson, Trans. Paradag ~ o c . ,66, 1776 (1960). (33) D. D. Wagman, J. E. IEilpatriclt. W. S. Taylor, K. S. Pitzcr and F. D. Rossini, J . Res. Natl. Bur. Std., 34, 143 (1945).
