T H E JOURNAL OF I N D U S T R I A L A N D ENGINEERING CHEMISTRY
486
SUMMARY
A variation in Professor Hildebrand's method of plotting molal entropy of vaporization is presented which is considered more useful than the original method. A wide range of data is presented to prove the value of the method, and means of determining heats of vaporization are pointed out. SUBSTANCE Sitrogen . . . . . . . . . . . . . . . . . . . . . . Bromine. ..................... Mercury . . . . . . . . . . . . . . . . . . . . . .
c.
1,
-210 08 350 06 46.2 76 57 35 68 30
....
I O
-
80
183 152 101 111 78 61.2 64 7 97.2 98 -33.7 Sulfur dioxide. . . . . . . . . . . . . . . . . . - 1 0 . 1 Hydrogen sulfide.. . . . . . . . . . . . . . 61 34 Ammonia. .................... 1 - 6 52 6
. . . . . . . . . . . . . . . . . . - 192 -73
.................... - 13 . . . . . . . . . . . . . . . . . - 11 . . . . . . . . . . . . . . . . . 4-16 55 .......... (16
aphtlialene
.............
Zinc .......................... Water.
.......................
Dekane ....................... Diisobutyl .................... Diisopropyl .................... Diisopropyl .................... Heptane ...................... Hexane ....................... Hexylene ...................... Octane. Cyclohexane. .................. m-Xylene ..................... $-Xylene, .....................
.......................
199 260 635 757 50 60 80 100 40 107 24 160 90 50 60 90 70 0
120 80 140 138
L/T Abs. 1000 P / T
7,280 12,400 3,790 6,490 7,140 7,270 6,500 6,820 6,180 7 300 10: 200 9,740 8,200 7,990 0,430 7,040 8,568 9 669 7: 500 4,340 6,160 4,497 5,600 .,..
....
.... .... .. .. .. ..
....
.... ....
.... ..... ...
.... .... ..... ... .... .... .... .... 8 600 7'990 6' 708 6: 562 7 790 6: 820 7 800 8: 150 7,293 8 700 8: 600
21.8 22.0 19.9 17.47 20.35 20.45 22.0 21.1 20.0 20.4 20.7 22.4 22.9 21.9 20.8 26.8 21.1 25.4 26.1 20.2 18.1 23.4 21.2 23.5 26.4 28.9 21.8 26.8 26.2 26.8 26.4 27.0 27.6 28.0 26.8 20.3 29.9 31.8 30.5 28.2 26.1 33.2 25.3 35.3 19.85 22.00 20.76 19.73 21.45 19.89 28.57 20.7 20,65 21.05 20.94
2.0 3.0 1.39 2.35 3.13 2.86 3.03 3.25 2.93 2.65 2.84 2.19 0.46 2.62 2.60 2.85 3.00 2.98 2.70 2.70 4.18 3.80 4.73 3.98 1.54 0.69 2.09 0.67 0.51 0.50 0.46 0.40 0.39 0.28 0.24 0.15 0.13 0.38 0.59 1.33 2.68 0.21 3.38 0,098 2.31 1.55 2.38 3.19 2.14 3.02 0.253 2.16 2.76 2.42 2.43
Determination of Heats of Vaporization from Vapor Pressure Data' By W, K. Lewis and H. C. Weber DEPARTMEXT OF CI3EMICAL ENGINEERING, MASSACHUSETTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE, MASS.
I
N the preceding article the authors pointed out a method
for estimating heats of vaporization with a considerable degree of accuracy from the Hildebrand function. I n this paper attention is called to a method for determining the heat of vaporization of any liquid from its vapor pressure curve, and, vice versa, for estimating the vapor pressure curve of a liquid in the neighborhood of one particular point on that curve the data for which are known.
GENERALDISCUSSION The vapor pressure curves of all liquids possess great curvature; consequently where only a few points on a curve are known it is very difficult to interpolate either mathematically or graphically with accuracy. On the other hand, 1 Combined with preceding paper on Meeting program, as "The Calculation of the Heats of Vaporization of Various Liquids, First, b y Means of the Hildebrand Function; Second, from Vapor Pressure Curves."
Vol. 14, No. G
the vapor pressure curves of all liquids are more or less parallel, and it is a fact that if instead of plotting the vapor pressure of a liquid at a given temperature one will plot against the temperature, the temperature a t which some liquid of reference, e. g . , water, exerts the same pressure, one will obtain a curve which is very flat, often sufficiently so to be considered a straight line over quite a wide range of temperature. This fact was first developed by J. Johnston.2 The method of Johnston is of great value in interpolating vapor pressures where only a few points on the vapor pressure curves are available and can be used for extrapolation over fairly large temperature ranges, for instance, 20" to 50" C., with reasonable accuracy. The probable error in drawing a very flat curve through a number of points is much less than in drawing a curve whose curvature is changing rapidly. As Johnston pointed out, the above method of plotting can be utilized not merely for interpolation or extrapolation of vapor pressures, but also-for the calculation of the heat of vaporization of a liquid from its vapor pressure curve. It is, however, equally possible to use it for the construction of a vapor pressure curve from a single point within a reasonable range from that point. The method assumes the gas laws to apply to the vapor and hence should not be used in this form a t pressures much, if any, above one atmosphere. Below one atmosphere the divergence of vapors from the gas laws is almost always slight. The Clausius equation applied to the vaporization of a liquid whose vapor follows the gas laws may be written
This equation obviously applies also t u the liquid of reference
The method of plotting t, against t , given above, is equivalent to placing p = p,, when also dp = dp,. Dividing Equations 2 and 1 gives, therefore, d T w - 1, dT L,
(2)'
(31
The left-hand side of Equation 3 is nothing more than the slope of the T,-T plot mentioned above. Furthermore, when this line is substantially straight this slope may he written AT,/AT, i. e., finite temperature differences may be employed in calculation. In any case the determination of the slope of a curve of slight curvature can easily be made with precision. The following example will serve as an illustration as to how the heat of vaporization may be calculated from vapor pressure data : At 120' C. the vapor pressure of normal octane is 646.4 mm. The temper8ture a t which water has the same vapor pressure is 95.5" C. At this temperature the heat of vaporization of water is 542.6. Upon plotting a T,-T curve for water and octane, it will be found that the slope is 0.825. AT, -
AT
= 0.825 =
I,
(18.02) (542.6) I, = 9170 I, = -9170 _ = 23.3 T (393) lOOOp 1000 (646.4) - = = 2.16 T 393 (760)
2 Z.physik. Chem., 62 (1908), 336, but see also Phil. M a g . , 23 [el (1912). 458; and I b i d . , 23 [5l (1886), 33.
