WIILIS 13. PERSON AND GEORIXC. PIMENTEL
532 [CONTRIBUTION FROM THE
DEPARTMENT OF CHEafISTRY
AND CHEMICAL
ENGINEERING, UNIVERSITY
Vol. 75 OF CALIFORNIA]
Thermodynamic Properties and the Characteristic CH, Frequencies of n-Parafbs BY WILLISB. PERSON AND GEORGE C. PIMENTEL RECEIVED JULY 22, 1952
A revision of the calculations of Pitzer on the thermodynamic properties of normal paraffins is presented. Reconsideration of the characteristic CH, frequencies has been made. Values of the parameters have been reviewed and, in some cases, revised. Results of the new calculations are compared with the available experimental data. Tables are given which present the calculations of the thermodynamic properties, -( F" Hq"/T),Ha" H;/T, S"and Ci, for normal paraffins from butane through heptane, and a table of increments is given which will permit the calculation of these thermodynamic properties of normal paraffins at least through n-eicosane.
-
-
Several years ago Pitzer' developed an approxiVapor phase heat capacity measurements have mate statistical method for calculating the thermo- also been completed for n-hexane,6 n-heptane7 dynamic properties of the n-parafhs and related and n-octane.8 These values differ from the compounds. In the meantime many precise in- computed values by about 1%, as shown in Table V vestigations have made available more ac- of reference 8. In addition to the new calorimetric curate experimental data. Consequently, a need data, a large amount of spectral data on the nhas arisen to revise Pitzer's calculations12both by paraffins has become available. These spectral the introduction of more precise methods where data are discussed in the following section. feasible, and by the adjustment of parameters to Vibrational Frequencies of the CHBGroup.-In the present best values. Therefore, re-examination view of the abundance of new spectral data of norand revision of the calculations made by Pitzer have mal paraffins, it seemed desirable to investigate the been undertaken, using the same general method of validity of the assignment of fundamental frecalculation, but selecting a more appropriate type quencies used earlier.'U2 Some data have appeared of average in certain cases. Also, the assignment of since the review of the assignment published by vibration frequencies for the infinite paraffin chain Barrowg: e.g., infrared spectra of deuterated derivahas been placed on a more secure basis. tives of propane, l o additional polarization measureNew Data.-Very accurate calorimetric measure- ments of the Raman spectra of n-hexane and nments giving liquid phase standard entropies at 25' heptane," the low temperature infrared spectra of of the normal p a r d n s from C6H14 through C16H34 solid n-pentane, n-hexane and n-heptane,12and the were completed by Huf€man, Waddington, et al., infrared spectra of even-numbered n-paraffins at the Petroleum Experiment Station of the Bureau in solid and liquid states from n-octane to n-tetraof Mines.3 These were coupled with entropies of decane.13 These data were considered in detail vaporization obtained by Osborne and Ginnings4 and they provide basis for minor changes in the and the vapor pressure measurements of the A.P.I. assignments made by Barrow. Disregarding perResearch Project 6b to give reliable values of the mutations among symmetry classes, the present standard entropies a t 25' for the normal paraffins assignment differs from that of Barrow by the subthrough C16H84 in the ideal gas state. These stitution of a frequency a t 1440 cm.-' for one of the values are shown in Table I. The experimental two frequencies Barrow assigned a t 1242 cm.-'. CHaincrement becomes relatively constant a t 9.31 ==! The detailed arguments comparing the several 0.06 cal./deg./mole between successive homo- alternate assignments in the light of the recent logs above C7Hle,whereas the calculated increment data are included in Appendix I. was 9.183 cal./deg./mole. Several attempts to interpret the spectra of long chain hydrocarbons based on calculations by the TABLEI method of Whitcomb, Nielsen and Thomasi4 EXPERIMENTAL ENTROPIES IN CAL./DEC./MOLE OF GASEhave recently appeared.'&'' This method conOUS 12-PARAFFINS AT 298.16"K. sists of calculating the vibrational frequencies of Soaw.tc K. AS/CHa sorm.11 x. AS/CH2 CH, CnHs C& C'Hm CsHii C&Iid CiHls
CsHls
44.50 54.85 64.51 74.10 83.43 92.90 102.26 111.65
10.35 9.66 9.69 9.33 9.47 9.36 9.39
CpHzo CioHzz CuHzr
CuHzs CuHm Cid&o Ci6H32
CIEHM
121.01 130.29 139.57 148.86 158.14 167.51 176.75 186.01
9.36 9.28 9.28 9.29 9.28 9.37 9.24 9.26
(1) K. S. Pitzer, J . Chcm. Phrs., 8 , 711 (1940). hereafter cited as I. (2) The values in reference 1 were revised and extended in (a) K. S. Pitzer, Ind. Eng. Chcm., 86, 829 (1944), and in (b) "Selected Values of Properties of Hydrocarbons," Circular of the National Bureau of Standards C461,U.S. Government Printing Office, Washington, D . C., 1947. (3) Private communication from F. D. Rossini. (4) N. S. Osborne and D. C. Gfnnfngs, J . Rcrsarch Nall. Bur. Sfondards, 89,453 (1947); reference 1. Table 20m. (5) See reference 2b. Table 20k.
(6) G. Waddington and D. R. Douslin, THISJOURNAL, 69, 2275 (1947). (7) G. Waddington. S. S. Todd and H. M. Huffman, ibid., 69, 22 (1947). (8) G. Barrow, ibid., 78, 1824 (1951). (9) G. Barrow, J . Ckcm. Phys., lB,34s (1951). (IO) (a) H. L. McMurry, V. Thornton and F. E. Condon, ibid., 17,918 (1949); (b) H. L. McMurry and V. Thornton, ibid., 18, 1515 (1950); (c) H. L. McMurry and V. Thornton, ibid., 19, 1014 (1951). (11) F. F. Cleveland and P. Porcelli, ibid., 18, 1459 (1950). (12) D.W. E. Axford and D. H. Rank,ibid., 18, 51 (1950). (13) J. K. Brown, N. Sheppard and D. M. Simpson, Disc. Faraday SOC., 9, 261 (1950). (14) S. E. Whitcomb, H. H. Nielsen and L. H. Thomas, J . Chcm. Phrs., 8. 143 (1940). (15) L. Kellner, Nafurc, 168, 877 (1949). (16) (a) T.Simanouti and S. Mizushima, J . Chcm. Pkys., 1'7,1102 (1949); (b) T. Simanouti, ibid., 17, 734 (1949). (17) W.E. Deeds and W. H. Shaffer, Vibrational Analysis of Normal Paraffins, presented at the Symposium on Molecular Structure and Spectroscopy, Ohio State University, Columbus, Ohio, June 14, 1961.
Feb. 5, 1953 THERMODYNAMIC PROPERTIES AND CHARACTERISTIC CH2 FREQUENCIES OF PARAFFINS 533 an infinite parailin chain in terms of the motions of individual CH2 groups, each group vibrating with a particular phase relation to adjacent groups. The published normal coordinate analyses based on this method have previously calculated only the frequenaes a t phase angles of X = 0 and T except for the original treatment14 in which the force field seems open to question. Barrow9J8 carried out the analysis for these values of A, substituting a valence force field. We have repeated the analysis of Barrow, extending it to intermediate values of X for several of the symmetry classes. The frequencies a t these intermediate values are important to the present problem, for frequencies a t all values of X contribute to the thermodynamic properties of hydrocarbons. An average frequency for thermodynamic calculations should be weighted in accordance with these intermediate values. In the course of our analysis, two errors were found in the treatment of Barrow: a typographical error and a numerical error which had only a slight d e c t on the calculated frequencies. The interaction force constant, ~ C C , H C C , actually used by Barrow in his calculations had a value of 0.4 X lo6 dynes/cm.lg This interaction force constant enters into the calculation of only one class of frequencies (Big) for X = T. However, it has a value as large as the principal bending force constants used. It was felt that such a large interaction force constant casts significant doubt on the frequency assignment. Good agreement with the calculated frequencies could be obtained with an alternate assignment. The force constants used are given below in units of lo6dynes/cm.
The results of this calculation for X = 0 and r are compared in Table I1 to the proposed assignment and to several earlier assignments. The variation of frequencies as a function of X may be seen in Table I11 for the motions antisymmetric to the plane of the molecule. TABLEI11 FUNCTION OF PHASEANGLEA. DETERMINATION OF THE THERMODYNAMIC FREQUENCIFCS Vibrations antisymmetric to the plane of the moleculeo
FREQUENCIESAS
A
Bp-B,u B;cB;II &-+e “CHJ rock” C-H stretch *‘CHItwist”
Mode
Frequency Observed Frequency Calculated
X =0 x = X
X =0 X = s/4 x = X/2 x = 3u/4 X = X
Average of obs. frequencies A
1135 732 1113 993 911 758 734
2950 2926 2939 2934 2925 2922 2922
1296 1241 1295 1303 1270 1241
933 -21
2938 -2
1268 29
+
Thermodynamic frequency 912 2936 1297 We should like to thank Mr. I. C. Hisatsune for his help in the calculations in this table.
Evaluation of Thermodynamic Properties.-In
the reconsideration of the calculations of the thermodynamic properties of normal paraffins, the terms given in Table IV of paper I must be examined to see which need revision. The revised terms are given in Table VI. The considerations made for those terms which were altered are given below. Further details and further explanation of f ~ = c0.42~ fccc = 0.2 fcc = 3.6 the nomenclature may be obtained by reference to ~ C H = 4.55 ~ H C C 0.61 f c c , ~ c c= 0.15 paper I. TABLEI1 (1) Term in Fo(T).-The only term in the expressions for Fo(T ) which requires consideration is CALCULATED FREQUENCIES OF THE XORMAL VIBRATIONS OF AN INFINITECH2 CHAINFOR X = 0 OR X , AND PROPOSEDthe value of the effective CHZmass, m. This mass should be the geometric mean of the effective CH2 ASSIGNMENTS mass in each degree of freedom. The value used Present calasS. in I, m = 18.6, was obtained by equating the cula- signand B.S. value of the product (M311IzIa) for propane to the Class Description tions ment B.4 M.b S.C value of this product calculated for the carbon Raman active “C-C stretch” 948 890 890 1135 ? A1, “H-C-H bend” 1490 1471 1440 1471 1462 skeleton using point masses of value m a t each 1471 carbon. This gives the geometric mean of the C-H stretch 2837 2878 2862 2846 2846 effective CHZmqss for the translational and rota2878 tional degrees of freedom, but neglects the vibraA2g “CHI twist” 1241 1296 124Zd 978d 7 tional and internal rotational masses. It is difficult 957 1060 1060 1058 1135 Blg “C-Cstretch” 1480 1440 1296 1442 1295 “CHI wag” to estimate the effective CHZ mass for the latter 1113 1135 1135 1295 B:, “CH:rock” ? degrees of freedom. An argument is presented in C-Hstretch 2939 2950 2950 2934 2934 Appendix I1 which gives the same effective CHP 2963 mass, 18.6, an agreement which is fortuitous but Infrared “H-C-H bend” 1459 1467 1475 1475 1462 active which indicates that no major change is needed. AIU C-Hstretch 2847 2853 2853 2853 2853 However, this argument indicates that for short AZU “CH~twist“ 1241 1241d 124Zd 97Sd ? chains the effective CHZmass may be a function of B1u “CH; wag” 1342 1375 1375 1375 1309 the chain length. In calculating the thermoB2U “CHI rock” 734 ’732 728 728 721 C-H stretch 2922 2926 2926 2926 2925 dynamic properties of normal paraffins shorter than “Assignment by Barrow, ref. 9. *Assignment by Si- n-heptane the value of m for these paraffins has been manouti and Mizushima, ref. 16. c Assignment by Brown, adjusted in the ratio of their effective rotational Calculated, but not ob- masses. Sheppard and Simpson, ref. 13. served. (2) Term in C-L,.-The assignment of the (18) G. Barrow, Ph.D. Thesis, University of California, 1951. “C-C stretch” frequencies requires a small change (19) Not 0.2 X 106 dynes/cm. as given in references 9 and 18 Barrow has indicated in a private communication that this value (0.2) in the average frequency from v1 = 1000 em.-’ to VI = 975 cm.-’. The latter value is also used was a misprint.
VOl. 75
WILLIS B. PERSON AND GEORGE C. PIGENTEL
534
in equation 5 of I to evaluate 2 (m/k1)'/2in the term in -(F* - H,?)/T. (3). Term in-C-Cbend.-The only deviation from the earlier calculation is a small adjustment of the value of k:! in accordance with the small change in kl. Pitzer's estimate of the ratio, E = k2/kl, was used in preference to that obtained in the present normal coordinate analysis since kz is not important in any of the modes calculated and hence is not accurately known from the present treatment. (4) Term in CH2.-As mentioned above, the thermodynamic frequency to be used for a given motion in thermodynamic calculations should be a representative average of the frequencies for this motion over all values of A. Such a representative average was obtained by averaging the values of the frequencies calculated a t 0, ~ / 4 ~ , / 2 3a/4 , and T. It was assumed that the calculated frequency variation with phase angle in Table I11 gave a reasonable approximation of the deviation from a linear dependence on A, even when the normal coordinate analysis did not exactly fit the assigned values of the optically active frequencies. The difference, A, between the average of the five calculated frequencies including intermediate values of X, and the average of the two calculated frequencies a t X = 0 and ?r, was then added to the average of the observed frequencies a t X = 0 and T , and the resultant frequency used in the thermodynamic calculations. This is shown in Table 111. Using the thermodynamic frequencies given in the last line of Table 111, or, for frequencies not given in Table 111, the arithmetic average of the values a t X = 0 and T , the contributions to the thermodynamic functions were computed.20 The spectroscopic data available a t present do not permit us to choose between our assignment and that of Barrow. Since the agreement of calculated with experimental thermodynamic quantities was slightly poorer with Barrow's assignment, the present assignment was used. ( 5 ) Term in CH3.-When all the changes mentioned above were made, the calculated entropies were still about 0.1-0.2 entropy unit below the observed values for n-hexane, n-heptane and noctane, although the CH2 increment was correct, and the calculated heat capacities were in agreement with experiment. Therefo:e, attention was given to the term in CHa, a term which does not depend on the chain length. This term is a function of IR, the effective moment of inertia of the CHa group, and Yo,the barrier restricting internal rotation of the methyl group. Pitzer took IR and VOfrom propane, which might not have the same values of these parameters as long chain hydrocarbons. IRis defined by Pitzer and Gwh"' Their equation l a indicates that the value of IR should be a function of chain length. Based on this equation, an approximate expression for IRas a function of the number of carbon atoms, n, ( n greater than six) is __
IR= 5.40(1
-
5.40/30n)10'0
(20) "Contributions to Thermodynamic Functions by a PlanckEinstein Oscillator in One Degree of Freedom," Office of Naval Research, Washington, D. C., July, 1949. (21) K. S. Pitzer and W. D. Gwinn, J . Chem Phys., 7 , 428 (1942).
With this value of IR, the value of VOwas adjusted until a fit between experimental and calculated entropies for n-heptane was obtained. These calculations, together with those of the following section, were made using the methods presented in reference 21 with graphical interpolation. Agreement was obtained using the reasonable value of VO= 3480 cal./mole. For simplicity in the calculation of the thermodynamic properties of normal paraffins from n-hexane to n-eicosane (C20Hd2) IR = 5.319 X 1040 was used, a weighted average value corresponding roughly to n = 12. (6) Terms in I.Rot. and FSterto.-In these terms the values of Vo', 3260 cal./mole, and a, 500 cal./mole, were chosen to give agreement between the calculated and experimental entropies of n-hexane and n-octane. This value of VO' compares favorably with the earlier estimate of 3300 cal./mole for this potential hindering the rotation of the CH2 group.2 The manner of determining the steric interaction energy, a, causes it to absorb any errors in the approximations made in this calculation. Therefore it is gratifying that this value of a (500 cal./mole) agrees exactly with the value found spectroscopically by Sheppard and Szasz22for n-pentane and n-hexane. The spectroscopic value for butane is 760 cal./mole, but the 500 cal. value was used in the calculation of the thermodynamic properties of butane. Comparison with Experiment.-The comparison of the calculated with the experimental entropies a t 298.16"K. for n-hexane, n-heptane and n-octane is given in Table IV. It is seen that the agreement is very good a t this temperature for these hydrocarbons. Since the calculated increment (9.309) agrees with the average experimental entropy increment (9.31), the calculated and experimental entropies for higher paraffins a t 298.16'K. agree well within experimental error. In Table V the comparison between calculated and experimental heat capacities of the ideal gases, TABLEIV OF CALCULATED AND OBSERVED ENTROPIES IX COMPARISON CAL./DEG./MOLE AT 298.16'K. O F I D E A L GASEOUSnPARAFFINS
so 9 8 , l b 2
Paraffin
Calcd.
Exptl.a
AS/CH2 Calcd. Exptl. b
%-Hexane 92.83 92.90 ... .. n-Heptane 102.24 102.26 9.309 9.31 %-Octane 111.55 111.65 9.309 9.31 Average value of the entropy increa From Table I. ment calculated from the data in Table I.
TABLE V OF CALCULATED AND EXPERIMENTAL HEAT COMPARISON CAPACITIES IN CAL./DEG./MOLE OF IDEAL GASEOUSnPARAFFINS Paraffin
Ci a t 400'K. Calcd. Exptl.
n-Hexane 43.47 43.38" n-Heptane 50.42 50.29* %-Octane 57.36 57.1" a Determined from the equation for in reference 6. b Determined from for n-heptane given in reference 7. values given for C i in reference 8.
C," a t 500'K. Calcd. Exptl.
51.83 52.15" 60.07 60.13* 68.32 68.3' C i for n-hexane given the equation for C,O Interpolated from the
(22) N. Sheppard and G. J. Szasz, ibid., 17, 86 (1949).
Feb. 5, 1953 THERMODYNAMIC PROPERTIES AND CHARACTERISTIC CH2 FREQUENCIES OF 1~-PARAFFINS 535 TABLE VI FORMULAS FOR CALCULATING THERMODYNAMIC FUNCTIONS OF NORMAL PARAFFINS
- (Fa - H ~ ) / T
G
(Ho- H;)/T
64r%v"8ka sin r R +4RlnT hoNo = 4.235 4 R In T R In (2nv1(m/k1)'/2) Ein hvl/kT = 0.689 (hc 975/kT) R In
4R
+ + + Ein R In (2nkm1/2/hkz'/~)+ R In T + s(hv2/kT) 2 -
-
R
4R
Ein hvl/kT vl/c = 975 em.-' R R Z(hvz/kT) ~(hvz/kT)' R
Ein hvl/kT
+
R - -(hvz/KT)' 12
R
24 (hvz/kT)* 413
14,200
413
R[- 1.275
-
R
(T
- 28,40O/P > 250)
( e VL/RT, at ) 1 0 ( T =
(yTO)
170 - (F - Fr) - 0.568 + T
T
R In Q =
=
+ '/z In T + '/z In ( m dsinZy X
= '/z R In T
Q
28,400
="-r+-T*
= -11.296+R1nT+7-T,
R(Q'/Q)
Fe-Ei/kT
Q' =
( a = 500 cal./mole)
-Rlna
=
- Rln2
Z E i n (hvi/kT)
+ R(-
i
,
(g)
Q" =
(Ei)e-Ei/k'F
e-Ei/kT
kT 0
1.275
+ '/z In T +
'/z In IR X 10"
0
T E i n ( & ) + F (Hm ) Vo
c 1E i n g + C ( & )
- In 3)
IR = 5.211 X
Vo = 3480
Ein hvi/kT
Ein hvi/kT
i
Ein hvi/kT
i
1
vi/c = 2936, 2865, 1469, 1407, 1297, 912
n-hexane, n-heptane and n-octane is given. It is felt that there is enough uncertainty in the experimental values that an adjustment of the calculated values to remove the discrepancies is not justified. NUMERICAL VALUESFOR
gg2J
THE
In particular, the value of the heat capacity of noctane a t 400'K. may be low by as much as 0.10.2 cal./deg./mole just due to the correction for gas imperfection,
TABLE VI1 TERMS IN TABLE VI WHICHCONTRIBUTE TO -(Fa
- Hi)/T
[ F ~ t e r i I* o A IC-CBend 1 KRot.1 [c-cstrl B EHsl 1ce21 0.707 1.252 2.951 4.320 298.16 49.524 1.037 0.882 0.032 .707 1.258 2.960 4.335 300 49.573 1.040 0.898 ,033 .749 1.554 3.444 4.997 1.195 400 51.860 1.399 .118 1.823 3.849 5.425 .813 500 53.634 1.295 1.932 .263 2.065 4.189 5.724 1.365 .890 2.487 .460 600 55.083 2.284 4.482 5.944 .976 700 56.308 1.416 3.055 .698 1.067 2.482 4.736 6.113 800 57.370 1.456 3.630 .965 1.254 1.158 2.663 4.954 6.246 900 58.306 1.487 4.203 1.250 2.830 5.151 6.354 1000 59.143 1.512 4.773 1.557 2.984 5.326 1.340 6.443 1.533 1100 59.901 5.335 1.870 3.128 5.486 60.593 1.428 6.518 1.550 2.189 1200 5.895 3.262 5.625 6.582 2.511 1.514 1.565 6.440 1300 61.229 1.598 3.388 5.753 6.637 2.834 1.578 6.978 1400 61.818 3.506 5.868 6.685 3.156 1.679 1.589 7.503 1500 62.366 For a normal paraffin of N carbon atoms - (Fa - H,O)/T = [Fo(T)] ( N l)[C-CstrI ( N - 2) [C-CBend] ( N - 3)[I.Rot.I [Fsteriol F ( u ) 2[CH31 ( N - ~ ) [ C H Z I F(u) = Rln2 A - (F" - H,"/T) per CHI = [C-cst,] [C-CBend] [I.RotI [B] [CHzl Fo(T ) is decreased by 0.064 for hexane, 0.162 for pentane and 0.195 for butane, for all temperatures. b For heptane and ( N - 7)B; for each of the paraffins, butane, pentane'and hexane, this term was calculated indiabove, [Fsterio]=: A [I.Rot.] was decreased by 0.033 for hexane, 0.054 for pentane, and 0.049 for butane, a t all temperatures. vidually. '
T,O K .
abovea
-
-
+
+
+
++ + +
+
+
+
WILLISB. PERSON AND GEORGE C. PIMENTEL NUMERICAL VALUES FOR
THE
TABLE VI11 TERMS IN TABLE VI WmCH CONTRIBUTE TO (H" H:)/T [Fsterio I"
-
T,OK. [FdT)] [C-CSwl [C-CBsndl 7.949 0.085 0.921 298.16 7.949 .087 0.926 300 7.949 .215 1.132 400 7.949 .359 1.275 500 1.378 600 7.949 -496 700 7.949 .620 1.455 7.949 .730 1.515 800 900 7.949 .825 1.563 7.949 .go9 1000 1.603 7.949 .982 1.635 1100 1200 7.949 1.047 1.663 1.104 7.949 1.686 1300 1.707 1400 7.949 1.155 7.949 1.201 1.'724 1500 For a normal paraffin of iV carbon atoms H" - H,"/T = [ F o ( T ) ]f ( N l)[C-Cst,] 4- ( i !
-
B
A
(I.Rot.1
1.572 1.577 1.766 1.864 1.895 1.896 1.886 1.865 1.835 1.804 1.775 1.743 1.711 1.681
2,524 2.515 2.083 1.762 1.522 1.337 1.191 1.074 0.977 .896 .828 ,769 .718 .673
2)[C-C~end]f ( N
0.592 .589 .487 ,411 .355 .312 ,278 .250 .228 .209 .193 .179 .167 .157
- 3)[I.Rot.) f
[CHaI
[CEL I
1.432 1.443 2.075 2.735 3.382 4.004 4.594 5.147 5.669 6.160 6.621 7.053 7.455 7.825
0.159 ,164 .462 .865 1.315 1.778 2.234 2.672 3.089 3.482 3.851 4.196 4.518 4.819
4-~ [ C H I4I (N - 2)[CHzl
[F~terioI
A ( H o - H,"/T) per CHz group = [C-cstr] f [C-CBend] f [I.Rot.] f [B] f [CHz] a
Vol. 75
See footnote b on Table VII. PU'UMERICAL VALUES FOR THE
T , OK.
[Fo(T)I
[C-CStrl
TABLEI X TERMS I N TABLEVI
[C-CBendl
WHICH
A
II.Rot.1
CONTRIBUTE TO
/Fswriola
7.949 0.406 1.668 298.16 2.334 1.049 1.672 7.949 ,413 2.336 300 1.037 400 7.949 .779 1.810 2.309 0.595 7.949 1.072 1.874 500 2.176 .383 1.284 7.949 1.908 2.010 600 .262 7.949 1.437 1.929 1.858 700 .I96 1.548 7.949 1.943 1.722 .150 800 1.952 7.949 1.629 1.612 900 .119 1.691 7.949 1.959 1000 1.521 ,096 1.964 7.949 1.738 1.446 1100 .079 7.949 1.776 1.967 1.385 1200 .067 1.805 1.970 1.336 1300 7.949 ,057 1400 7 ,949 1.829 1.973 1.292 .049 7.949 1.848 1.975 1.257 1500 ,043 For a normal paraffin of N carbon atoms 3)[I.Rot.I -k Ci = [Fo(T)I (A' - 1)[c-C~trIf (N 2)[C-CBsndl f ( N Ac: per CHI group = [C-cstr] f [C-CriendI f (I.Rot.1 f [ B ]$- [CHI] a See footnote b on Table VII.
-
-
c:
B
[CHI]
[CHI]
0.238 ,235 .135 .087 .058 .045 .034 .027 ,022 .018 .015 .013 .011 .010
3.229 3.253 4.687 6,025 7.212 8.250 9.175 9.998 10.726 11.367 11.931 12.428 12.864 13.247
0.821 0.838 1.908 3.038 4.081 5.007 5.818 6.525 7.140 7.672 8.133 8.532 8.878 9.179
[FsterioI
f ~ [ C H B4-I ( N - ~ ) [ C H I I
Calculation of Thermodynamic Properties.Table X I V the CH2 increments of these thermoTable VI gives the expressions used in calculating dynamic properties are given. The thermodythe thermodynamic properties of normal paraffins, TABLE X with the revised values of the parameters disTHERMODYNAMIC PROPERTKES OF NORMAL BUTANE The terms in Table VI are evalucussed above. ated in Tables VII, VI11 and IX. Using these - 'T T . OK. H;/T) Ho)/T SQ c; tables and the formulas given in them, the thermodynamic properties of any %-paraffinfrom n-butane 298.16 58.54 15.58 74.12 23.29 to n-eicosane may be calculated. Although the 300 58.65 15.63 74.27 23.40 errors will tend to accumulate on extrapolation, the 400 63.51 18.35 81.86 29.60 thermodynamic properties calculated from these 500 67.91 21.19 89.10 35.34 tables should be fairly good approximations for 600 72.01 23.96 95.97 40.30 even longer normal paraffins. For normal paraffins 700 75.91 26.60 102.50 44.55 beyond n-heptane, the average value of Fslcr;c 800 79.63 29.08 108.71 48.23 presented in these tables should be used. For n900 83.18 31.39 114.57 51.44 butane through n-heptane, Fsjericis calculated for 1000 86.60 33.54 120.14 54.22 each molecule using the formulas in Table VI and 1100 89.90 35.53 125.43 56.64 using Table VI of paper I. 1200 93.08 37.39 130.47 58.74 The thermodynamic properties of n-butane, 1300 96.14 39.11 135.25 60.58 n-pentane, n-hexane and n-heptane are presented in 1400 99.09 40.71 139.80 62.17 Tables X, XI, XI1 and X I I I , respectively. In 1500 101.95 42.18 144.13 63.57 (FO
Feb. 5,1953 THERMODYNAMIC PROPERTIES AND CHARACTERISTIC CH2 FREQUENCIES OF %-PARAFFINS 537 TABLE XI THERMODYNAMIC PROPERTIES OF C,P (Ha T , OK. HOP) Ht)/T
- -
298.16 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500
64.52 fM.65 70.57 75.94 80.96 85.74 90.31 94.67 98.87 102.92 106.83 110.58 114.21 117.72
-
18.88 18.94 22.38 25.94 29.38 32.64 35.71 38.55 41.19 43.63 45.91 48.01 49.96 51.75
NORMAL PENTANE S O
83.40 83.58 92.95 101.88 110.34 118.38 126.02 133.23 140.06 146.56 152.74 158.60 164.17 169.47
THE
- (P-
c; 28.73 28.87 36.63 43.58 49.64
54.83 59.30 63.18 66.55 69.48 72.02 74.24 76.16 77.83
TABLE XI1 THERMODYNAMIC PROPERTIES OF NORMAL HEXANE
-
VALUBSOF
TABLE XIV CHr INCREMENT FOR NORMALPARAFFINS
T . OK.
298.16 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500
H:/T,
N 2 7 (H.
+
H:)/T
5.979 5.999 7.061 8.043 8.970 9.856 10.705 11.516 12.299 13.053 13.781 .14.477 15.050 15.798
3.330 3.344 4.063 4.774 5.439 6.062 6.643 7.176 7.663 8.112 8.528 8.908 9.258 9.582
S’ 9.309 9.343 11.123 12.817 14.409 15.918 17.348 18.692 19.963 21.165 22.309 23.386 24.409 25.381
cp’ 5.466 7.695 6.941 8.246 9.342 10.276 11.065 11.746 12.333 12.838 13.276 13.657 13.983 14.269
Appendix I
Assignment of Characteristic CH1 Frequencies.-The work of Simanouti and Mizushima on the Raman spectra T,OK. H;/T) H ~ T SO C,” of long chain hydrocarbons1* shows that only a very few 92.83 34.20 70.62 22.21 298.16 Raman lines in n-butane persist through n-hexadecane. It 22.29 93.06 34.37 300 70.77 is reasonable to assign most, if not all, these persisting lines 26.45 104.20 43.47 400 77.75 t o motions of the CHI group on the assumption that the 30.72 114.82 51.83 relative intensities of CHn lines should decrease with respect 500 84.11 t o those of the CHI lines. This assumption is substantiated 58.99 34.82 124.88 90.06 600 in part by the gradual disappearance in the longer chain 38.71 134.43 65.10 700 95.73 hydrocarbons of some of the bands of n-butane (e.g., the 42.35 143.50 70.36 800 101.14 lines at 2950 and 2896 cm.-l in the Raman spectrum and 152.05 74.93 the band at 1340 cm.-l in the infrared spectrum). Also, 106.32 45.73 900 n-hexadecane is probably long enough that no effects due 48.85 160.16 78.89 1000 111.31 t o the odd-even change in selection rules for shorter chains 51.75 167.85 82.32 1100 116.10 are expected. Therefore, the Raman lines in n-hexadecane 54.44 175.18 85.30 1200 120.74 from the data of Simanouti and Mizushima14 were taken t o be the same as the Raman-active CH2 frequencies of the 56.92 182.12 87.89 1300 125.19 infinite chain. The infrared active CH2 frequencies of the 188.71 90.14 129.49 59.22 1400 infinite chain are taken from the infrared active frequencies 194.98 92.10 61.34 1500 133.64 of poIythene*a (which do coincide with those of liquid nhexadecane). It is to be noted that liquid n-hexadecane TABLE XI11 contains a considerable fraction of non-planar molecular configurations. Since polythene is probably in the planar THERMODYNAMIC PROPERTIES OF NORMAL HEPTANE form, it is gratifying that no large spectral differences are -(+FO(Hoobserved between the spectrum of solid polythene and liquid T , OR. H;/T) Ht)/T SO c; n-hexadecane. 102.34 39.67 76.80 25.54 298.16 Except for the present work, all assignments of the “C-C stretch” modes given in Table I1 were made before 102.60 39.86 76.97 25.63 300 the work of McMurry and co-workers on deuteropropane 50.42 30.51 115.42 400 84.91 cast doubt on the conventional assignments of these mo35.49 127.74 60.07 92.25 500 tions. These workers suggest that these modes interact 139.39 68.33 99.13 40.26 600 strongly with other low-frequency rocking motions of the molecule. The presence of the two Raman lines at 890 and 150.45 75.38 105.68 44.77 700 1060 cm.-’ which persist in the spectrum of hexadecane sug160.95 81.43 111.95 49.00 800 gests that this interaction is the same for the series of mole86.68 52.91 170.84 900 117.93 cules from n-hexane through n-hexadecane. Thus one 180.22 91.22 123.70 56.52 1000 “C-C stretch” is assigned a t 890 cm.-l and the other is assigned a t 1060 cm.-l. 59.86 189.11 95.16 1100 129.25 The assignment of the line observed near 1135 cm.-1 in 197.59 98.57 134.62 62.97 1200 the Raman spectra of all normal paraffins presents a di205.59 101.55 139.76 65.83 1300 lemma. Depolarization measurements in the liquid are 213.22 104.12 144.74 68.48 1400 available for two homologs, n-hexane and n-heptane; the measurements were made by Herz, Kahovec and Wagner,*’ 106.37 70.92 220.46 149.54 1500 and later bv Cleveland and Porcelli.ll The deDolarization namic properties for normal p a r a s With more factors obskved by the two groups were 0.57 &d 0.46 for and 0.56 and 0.54 for n-heptane, clearly indicating the n-hexane, thanseven carbons may be by a totally symmetric vibration. In view of the possibility correct number Of CH2 increments to the Of of non-planar forms, there are several possible explanations the properties for heptane. of these measurements. For the planar infinite CHz chain Ac~owle,jgments.-we wish to express our ap- there are dhly three Alg vibrations, one of which is a C-H stretch near 3000 cm.-l, and the other two are composed preciation to the American Petroleum Institute Re- of contributions from the c-c stretch and the CH, symsearch PrOieCt 44 for SUPPOd Of this research. metric deformation. It is expected that the C-C stretch for many We are verj, to D‘’-K* (23) H. W. Thdmpson and P. Torkington. Proc. Roy. SOC.(London), -(+Fa
( H O -
helpful suggestions during the course of this re-
search.
(1g45).
(24) E. He&, L. Kahovec and J. Wagner, Monalsh.. 76, 100 (1946).
538
WILLISB . PERSON AND GEORGE C. PIMENTEX,
will dominate one of these motions and that it will be lower in frequency than in ethane ( L e . , 993 cm.-’). The remaining vibration is expected to be characteristic of the CHs group, and the totally symmetric CH2 deformations of several molecules are found near 146Q cm.-’. To assign the 1135 cm.-’line t o the At, class required a choice between two undesirable alternatives: t o omit the polarized and persisting line at 800 cm.-’ and assign the 1135 cm.-’ line as the “C-C stretch,” or to omit the persistent (but not highly polarized) line at 1470 cm.-l and assign 1135 cm.-1 as the “CH2 deformation.” Simanouti and Mizucihima select the first alternative which merely shifts the difficulty to the assignment 6f the 890 cm.-l l h e and adds the problem of justification of an assignment which departs from predictions made from simpler molecules. The other alternative appears equally undesirable in view of conventional assignments. If this line arises from a planar farm, a possible explanation for the polarization properties of the 1135 cm.-* line in n-hexane and n-heptane is that two vibrations are coincident at this frequency, one a totally symmetric CHc motion which causes the line t o be polarized in the lower members of the series and the other a Bza CH2 motion which accotmts for the persistence of this line iti the Raman spectra of normal paraffins through hexadecane. Further polarization data are needed in the Raman spectra of higher normal paraffins or of polythene to check this assignment, since any GHs contributions should become relatively less intense. Another explanation for the polarization properties of this line which suggests itself is that the CHa frequencies are still quite intense in n-hexadecane, and that either the $90 or the 1135 cm.” line is a line due t o a motion of the CHCgroup. However, on the basis of existing data it seems that the 1135 cin.-l line should be assigned to a Bz C!H* motion, and the 890 cm.‘‘ line is assigned to an Alg kH2 motion, in agreement with Barrow. There has been some criticism’3 of the choice of 1375 cm. -l as a CH2 fundamental. This band is one of the most intense in the infrared spectrum of n-hexadecanezb and the ratio of the intensity of the 1375 cm.-l band to that of the 1470 cm.” band in n-hexadecane is roughly the same as the ratio in 72-hexane. If this band were due to a CHs deformation entirely, as claimed by Brown, Sheppard and Simpson, it seems that the relative intensity should drop off between n-hexane and n-hexadecane. The polarized infrared s ectrum of poIythenez6 is consistent with the assignment of t&s band as a “CHz wag,” with the dipole moment change parallel to the chain. 111polytherie itself this band is very much more intense than any absorption near 1310 c1n-l which Brown, Sheppard and Simpson assign to the “CH2 wag. I ’ I t seems likely that the assignment of the 1375 cm.-’ band as a BI, fundamental is correct. (See SimanoutilGb for further discussion in favor of this assignment.) Since the fine a t 1296 cm.-’ remains as one of the stronger Raman fines in the spectrum of n-hexadecane and falls close to the value calculated for the Azg “CH,twist,” it is so assigned in preference to the earlier assignments of unobserved frequencies. The assignment of the AN “CHZtwist” a t 1241 cm.-l was selected to fit the normal coordinate analysis, since this fre(29) Catalog af Infrared Spectral Data, Issued by the American Petroleum Institate Reqearch Project 44 at the Nations1 Bureau of Standards. (26) h.BIllolt, K J ht1l~JIf)sed11d:1 I3 ’1 erllple, J ( &??+I PhYS , 18, 877 (1948)
Vol. 7;
quency should be inactive. This choice is consistent with the assignment of the analogous Atg motion a t 1296 cm.-’. The assimment of the B1, “CH2 wag” a t 1440“L-l was made on the basis of the normal coijrdinate analysis, as discussed above. The several assignments agree in the selection of the remaining frequencies. Without reference t o classes, our assignment differs from that of Barrow only by the replacement of a frequency at 1242 cm.-‘ by one a t 1440 cm.-’. The present assignment seems t o be consistent with all the data available at present, except for the polarization of the Raman line at 1135 cm.-’. It is possible that the assignment of this h e may be changed in the future, when more experimental data are available. In spite of this possibility and the hncertainty in the assignment of the “C-C stretch” fundamentals, this assignment seems to be a satisfactory basis for thermodynamic calculations. The assignment includes every Raman line in the spectrum of nhexadecane except for two C-H stretching frequencies and one line which is approaching zero frequency as chain length increases. It also includes every band in the infrared spectrum of polythene except for onc branch of the unexplained doublet a t 1732 cm.-l.
Appendix I1 The Effective CH2 Mass.-Considering the mass of the CHZgroup to be concentrated a t a point, then for a normal paraffin with n of these points, the degrees of freedom may be divided among 3 translations, 3 rotations, n 1 stretching vibrations, and 2% - 5 bending vibrations and internal rotations. Asai ing an effective CHI mass to each of these degrees of freegm, the complete expression defining m, the average effective CHZmass, should be m3n = ( m t r ) s ( ” 3 t ) 3 ( m e t ) n‘(mbend)2nThe translational mass, ml,, is 14.0. The rotational mass, mrot,of the CHZ group in a long chain has been evaluated by equating the exact product of inertia, (111218) to this product calculated using point masses a t the carbons, and solving for the value of the mass needed to make these products equal. This was done for the setie3: CznHdn+ 8 ; for n from 2 to 6. For long chains the value of mrotapproaches 18.5. The value of the stretching vibrational mass, m.$,is estimated to be close to that of a pure C-C stretching mode, 14.0. The value Of the bending vibrational mass, Mbend, is expected to be higher because of the large contribution of the hydrogen atoms to the moments of inertia involved in the bending motions. Since the bending modes may be considered to be local rotations with moments of inertia close to those of the group CHZ-CHZ,two CH2 units of the chain, %end may be approximated by equating the exact product of inertia (11IaIe) for CHpCHz to that product calculated using point masses a t the carbons. In this manner, mbend is estimated to be 21.5. Thus mYn= (14.0)3(18.5)3(14.0)n-1 (21.5)2n-6 and for large n m = 18.6 While the argument given above is certainly not conclusive, and the exact agreement with the earlier choice is fortuitous, the argument does justify the empirical choice of ;it = 18.6 as a reasonable value.
-
BhRKEI.&P, CALIF.
