Heat and the External
orlc of Vaporization of Twenty-two Hydrocarbons J
d
J. E. HAGGENRIACHER C o m m o n w e a l t h Color and Chemical Co., Brooklyn, N . Y ,
A
method is shown for calculating the heat and the external work of vaporization from vapor pressure data. The author's equations for the heat and the external work of vaporization are applied to vapor pressure data on hydrocarbons by the Rational Bureau of Standards.
ROhI an equation of state for saturated fluids (6) there is obtained for the volume difference of a saturated liquid and its vapor a t equilibrium: V0
- VL
= RT
Mp
dY2 T3 per unit mass
where D = Tf/pc Introducing the expression into the Clapeyron-Clausius equation
the heat of vaporization or change in enthalpy ( 6 ) ,per unit mass, becomes:
culstions are given in Table I. The last temperature shown is the normal boiling point as determined by Willingham, Taylor, Pignocco, and Rossini. (The boiling points in the table are rounded to the second decimal, while the calculations were done upon the figures to three decimals as given by the authors). Critieal'data for obtaining the constant D were taken from International Critical Tables and Landolt-B6rnstein Tables. Newer data are specifically stated by reference number after the name of the substance. Equations 2 and 3 are applicable t o the entire range of the liquid phase-that is, from triple point to critical point. Applications are limited only by the availability of exact vapor pressure data and the knowledge of critical pressure and critical temperature. Equation 5 is applicable to the range of the vapor pressure data of Willingham, Taylor, Pignocco, and Rossini. The success of the calculations depends strongly upon the quality of the vapor pressure data and very strongly upon the rate of change of the vapor pressure derived therefrom. The accuracy of the equations may be stated as follows: Comparisons of calculated values and precise measurements show deviations up to a few tenths of 1%. Calculations of the heat and the external work of vaporization! for ethylbenzene from 0" to 14OOC. are given elsewhere (7). NOMENCLATURE
P pe
The external work of vaporization or change in the Helmholtz function A , per unit mass, becomes:
B
-C+t
= absolute temperature, degrees Kelvin (0' C. = 273.16"
re
= critical temperature, O K. = specific volume of saturated vapor, liters per gram = specific volume of saturated liquid, liters per gram
Vi
K.)
R
= ideal gas constant, 1.98647 - 15'' cal. per deg. mole (3)
D
= a constant
1M
With the aid of exact vapor pressure data the heat and the external work of vaporization may be calculated. The National Bureau of Standards has recently published vapor pressure measurements on 52 hydrocarbons (21). The authors correlate their data by an equation of the Antoine type: h p m m= A
T
Vo
(3)
= saturation pressure, atmospheres
= critical pressure, atmospheres
= molecular weight, based on international atomic weights
of 1941, grams
AH = heat of vaporization (change in enthalpy), 15' cal. per
(4)
The equation gives for the rate of change of the vapor pressure (changing from degrees centigrade to degrees Kelvin) :
gram AA = external work of vaporization (change in the Helmholtz function A ) , 15' cal. per gram A , B , C = constants in vapor pressure equation of National Bureau of Standards Conversion factors for thermal units: one 15' cal. per gram = 1.00033def. cal. per gram = 0.99968 I.T. cal. per gram = 1.79942 B.t.u. per pound. LITERATURE CITED
d;o_ dT
2.303 Bp (T $. C - 273.16)'
(1) Aston, J. G., Saasz, G. J., and Fink, H. L., J . A m . C h e m Soc., 65, 1133 (1943). '(2) Beattie, J. A,, and Kay, W. C., Ibid., 59, 1586 (1937) (critical
data).
Upon substitution, Equation 2 becomes: AH =
M(T
2.303 RBT' C - 273.16)'
+
(3) Birge, R. T., Rev. M o d . Physics, 13, 233 (1941). (4) Fiock, E. F., Ginnings, D. C., and Holton, W. B., J , Research Netl. Bur. Standards, 6, 88 (1931). (5) Haggenmacher, J. E,, J. Am, Chem. SOC.,66, 313 (1944); 68, 1123 (1946). ( 6 ) Ibid., 68, 1633 (1946); P h y s Rev., 69, 242 (1946). (7) Haggenmacher, J. E., J Am. Chem. Soc., 69, 707 (1947). (8) Kay, W. B., Ibid., 68, 1336 (1946) (critical data). (9) Landolt-Bornstein, "Physikalisch-chemisehe Tabellen," Berlin, 5th ed., pp. 14814, J. Springer, 1923. (10) Ibid., 1st suppl., pp. 805-7, 1927. (11) I b i d . , 2nd suppl., pp. 1489-90, 1931. (12) Ibid., 3rd suppl., pp. 2725-9, 1936.
(5)
The heat and the external work of vaporization were calculated for 22 hydrocarbons whose critical pressure and critical temperature are available. The calculations were performed by first calculating the pressure from Equation 4 of Willingham, Taylor, Pignocco, and Rossini for the temperatures chosen. These values vere then used in Equations 3 and 5. The results of the cal-
436
TABLE I. HEATAND EXTERNAL WORKOF VAPORIZATION,
OF CALCULATED AND MEASURED HEATS TABLE 11. COMPARISON
OF
15' CAL.PER GRAM T
~ ~ n-Pentane ~ , , 'C. AH -AA 20 88.07 7.785 30 86.15 7.956 40 84.11 8.102 36.07 84.93 8.048
....
...
2-MethylT ~ ~ ~ butane , , O C . AH -AA 20 82.79 7.703 30 80.77 7.852 27.85 81.22 7.840
.... .
...
,
,
I
88.25 86 60 84.95 83.23 81.46 79.61 79.85
6.664 6.852 7.028 7.187 7.330 7.452 7.438
o-Xylene 60 70 80 BO 100 110 120 130 140 144.41
93.69 92.32 90.99 89.67 88.36 87.04 85.70 84.32 82.90 82.25
5.765 5.926 6.082 6.233 6.377 6,514 6.643 6.762 6.870 6.913
20 30 40 50 60 57.99
,...
,
1.50
160 159.22
85,26 83.97 82.70 81.44 80.19 78.91 77.61 76.28 74,89 75.01
5.797 5.945 6.089 6.226 6.357 6.479 6.593 6.695 6.787 6.781
60 70 80 90 100 110 120 130 140 138.35
30 40 50 60 7n ._ 80 90 100 98,43
:
86 57 85.02 83.48 81.95 80.38 78.78 77.12 75.38 75.64
40 50 60 70 ' 80 90 100 110 110.62 I
60 70 80 90
in0 -..
110 120 130 125.66
... ...
96:64 95.15 93.70 92,25 90.79 89.31 87.79 86.23 36.13
6.904 7.093 7.274 7.446 7.607 7.755 7.890 7.898
20 30 40 50 60 70 80 80.74
94.50 92.88 91.29 89.69 88.07 86.41 84.70 a4.57
...
...
5.733 5.881 6.020 6.150 6,270 6.376 6.468 6 620 6 515
....
6.622 6.797 6.958 7.101 7.225 7.197
...
20 30 40 50 60 63.28
....
6.196 6,366 6.530 ' 6.688 6.838 6.979 7.110 7.229 7.336 7.319
5.637 5.786 5.931 6.070 6.202 6.326 6.441 6.546 6,639 6,659
... ...
.... ..
60 7n 80 90 100 110 120 130 140 139.10
."
40 50 60 70 80 90 100 110 109.10
77:% 75.99 74.62 73.23 71.82 70.38 68.88 67.28 67.45
5:396 5.547 5.690 5.824 5.947 6.059 6,156 6.235 6.231
70 ' 80 90 100 110 120 130 140 150 150.80
....
....
... ..
91.94 BO. 59 89.27 87.96 86.64 85.31 83.95 82.54 81.09 81.22
80.69 79.28 77.89 76,52 75.14 73.73 72.30 70.81 69.26 69.14
.... ....
... ...
n-Pentane
2-Methylbutane (isopentane) 2,2-Dimethylbutane n-Hexane
...
6.198 6.369 6.534 6.693 6.845 6.986 7,120 7.243 7.350 7.341
5.277 5.415 5,547 5,672 5.789 5.896 5.993 6,078 6.149 6.154
Benzene 20 104.5 102.6 30 100.8 40 99.05 50 97.26 60 95.43 70 93.56 80 80.10 93.54
2,3-Dimethyl- ' butane (diisopropyl) 2-Methylpentane 2,5-Dimethylhexane fdiisobutyl) ' n-Heptane
n-Octane
n-Decane 2,2,4-Trimethylpentane Cyolohexane
30 40 50 60 70 80 90 100 99.24
....
72.94 71.70 70.46 69.20 67.92 66.60 65.23 63.80 63.90
...
5.223 5.374 5.517 5.652 5.777 5.889 5.988 6.072 6.066
...
73.05 71.78 70.53 69.28 68.02 66.76 65.46 64.13 62.75 61.32 61.86
Toluene
20
30 40
50 60 60.27
83.61 81.99 80 33 78.61 76.82 76.77
77.12 75 ..87
77.8 76,35
98 9%35 80.1 120 125 125.3 130 159.86 99.19
75.73 75.66 93.54 73.08 72.24 71.42 68.6 63.97
74.0 76.45 92.4 71.4 71.1 70.8 70.0 60.1 64.87
Young ( 9 ) Mathews, Ramsdell, Thompson (14) Mabery, Goldatein ( 9 ) Pitzer (f7) Wirtr ( 9 ) Young ( 9 ) Mabefy, Goldstein (9) LugInm (9) Young ( 9 ) Luginin ( 9 ) Pitzer (17)
25 29.22
93.68 93.01
94.82 92 .BO
Aston Szasz Fink ( 1 ) de,Kilossow$ky, Alimow
80
84.70
85,62 103.82 102.30 100.71 99.14 104.26 101.05 97.84 104.7 103.0
Mathews, Ramsdell, Thompson (14) Griffiths, Marshall (9) Griffiths, Marshall (9) Griffiths Marshall (9) Griffiths' Marshall ( 9 ) Fletcher' Tyrer (1 1 ) Fletcher' Tyrer (1 1 Fletcher: Tyrer (111 Fauat, Littman ( I O ) de,F2lossowsky, Ahmow
20 40 60 90 100
,
..
,
6.632 6.810 6.972 7.118 7.243 7.246
(13) Lemons, J. F., and Felsing, W. A., J . Am. Chem. Soc., 65, 46 (1943). (14) Mathews, J. K., Ramsdell, G., and Thompson, B. M., Zbid., 48, 562 (1926). (15) Messerly, G. H., and Kennedy, R. M., Ibid., 62,2988(1940).
Young Oshorne, (9)Ginnings (16) Piteer (17) Lemons Felsing (13) Lemons: Felsing (13) Lemons, Felsing ( I 9) Young ( 9 ) Youne (9) TyreT(9) Mahery Goldstein ( 9 ) Lemons,' Felsing (13) Lemons, Felsing (13) Lemons, Felsing (13) Lemons, Felsing (13) Lemons, Felsjng ( 1 8 ) Lemons, Felsing (13) Young (9) Young ( 9 ) '
ll*I
\'=I
50
99.05
99.30
Fiock, Ginnings, Holton
80
93.56
94.16
80.0 80.2 80.35 80.10 42.85
93.56
93.9 94.34 93.45
Ginnings, Holton . Fiock, (4) Nagornow, Rotinjana (9)
,
...
....
93.54 98.21
....
Mathews, Fehlandt (12) Schiff (9)
...........
de,%lossowsky,
86.50
Mathews, Ramsdell, Thompson (10)
Alimow
1131
...........
+Xylene
86.13 82.69
82.89
....
82.25 81.34
82.5 82.5
m-Xylene
144.4 144.6 144.41 138.30
86.23
.... .... ....
(4)
98.5
110 110.2 110.8 110.8 110.62 141.41
.... ....
81.85
....
Nagornow, Rotinjanz (9) Schiff ( 9 ) Marshall, Ramsay ( 9 )
...........
Mathews, Ramsdell, Thompson ( I O ) Brown (9) Nagornow, Rotinjanz (9)
...........
Mathews Ramsdell, ThomGson ( I O )
...........
139.10 139.2 139.9
81.22
.... ,...
81.3 82.3
Brown (9) Nagornow, Rotinjanz
137.12
80.85
81.03
.... .... '
81.0 81.1
Mkti;kws, Ramsdell, Thompson (10) Brown ( 9 ) Nagornow, Rotinjanz (9)
138.2 138.5 138.35
2-Methylpentane (8)
Pitzer Sage Evans, ( 1 8 ) Lacey (19) Sage: Evans, Lacey (19) Schuman, Aston, Sagenkahn (20)
90 97.23
60 .~
109.66
p-Xylene
Young ( 9 ) Young ( 9 ) hlesserly, Kennedy (16)
81.4 76.79 73.75 85.9 84.5 80.4 80.8 79.2 81.85 79.4 81.0 78.1 74.9 82.7 80.5 76.5 70.0 68.1
50 20 40 60 20 26.76
.... (.,
Reference
80.77 76.44 72.33 87.43 84.95 81.46 81.46 79.61 80.20 79.99 81.33 78.21 74,85 83.61 80.33 76.84 70.38 68,88
30 25 49,74 25 40 60 60 70 66.88 68 20 40
40
n-Dodecane 130 140 150 160 170 180 190 200 210 220 216.28
VAPORIZATION
T ~ ~ ~ A.H ,, Cal./G. 0 C. Eq. 5 Measured 85.8 86.15 30 84.3 84.11 40 86.80 87.12 25 85.38 84.95 35.94 86.61 86.73 27.94 84.71 84.13 40.17 81.47 81.80 25
20 30
Benzene
2,2,4-Trimethylpentane ( 2 )
n-Decane 100 76.71 5.157 110 75.37 5.275 74: 04 5.387 120 72.71 5.499 130 71.36 5,590 140 69.98 5,677 150 68.57 5.754 160 67.10 ,5.818 170 174.12 66.47 5.841
...
6.645 6.827 6.997 7.141 7.280 7.32
n-Nonane
2,5-Dimethylhexane
....
84.63 83.06 81.46 79.80 78.07 77.48
m-Xylene
Cyclohexane
n-Octane 82.05 80.59 79.15 77.69 76.21 74.67 73.08 71.42 72.15
91.18 89.84 88.53 87.22 85.91 84.57 83.21 81.80 80.34 80.58
84.38 83.05 81.75 80.46 79.18 77.88 76.56 75.21 73.81 73.47
70 80
.... ....
e:iOs
..,
90 100 110 120 130 140 150 152.39
Toluene
....
81.33 79.79 78.21 76.57 74.85 75.16
3-Methylpentane ( 8 )
Isopropylbenzene
%-Heptane
...
...
.. .
p-Xylene
,
n-Propylbenzene 80 90 100 110 120 130 140
...
.. .
2,2-Dimethyl. T ~ butane ~ ~ ( 8 ). 'C.' AH -AA 20 77.23 6.579 30 75.64 6.741 40 74.00 6.886 50 72.29 7.012 49.74 72.33 7.009
2,a-Dimethylbutane (8)
n-Hexane (8) 20 30 40 50 60 70 68.74
437
INDUSTRIAL AND ENGINEERING CHEMISTRY
March 1948
80.58
..,.
17111
......... . .
(16) Osborne, N. S., and Ginnings, D. C., unpublished, quoted in ref. - .1 -7... (17) Piteer, K. S.,J. Am. Chem. Soc., 62,1224 (1940). (18) Ibid., 63,2413 (1941). (19) Sage, - B.H..Evans, H. D., and Lacey. W. N., IND.ENQ.CHEM., 31,763 (1939). (20) Sohuman, 8. C.,Aston, J. G., and Sagenkahn, M., J . Am. Chem. SOC.,64,1939 (1942). (21) Willingham, C. B.,Taylor, W. J., Pignocco, M., and Rossini, F. D., J . Research Natl. Bur. Standards, 35,219 (1945).
__
RECEIVED January 14, 1947.
'
