I
DONALD F. OTHMER, PAUL W. MAURER, CHARLES J. MOLINARY, and RONALD C. KOWALSKI Polytechnic Institute of Brooklyn, Brooklyn, N. Y.
Correlating Vapor Pressures and Other Physical Properties A general equation and nomogram have been designed for conveniently correlating
b b b
Vapor pressures Latent heats Other physical properties
AN
EARLIER article by Othmer (77) described a method of presenting all vapor pressure functions as straight lines. T h e general equation is
Log P = ( L / L ’ ) log P’
+c
where P i s vapor pressure of the material, P’ that of a reference substance such as water; L molar latent heat of the material, L’ that of the reference substance, and C a constant. Values are always taken a t the same temperature. O n standard logarithmic paper, vapor pressures of the material may then be plotted against temperatures from a scale derived from the vapor pressure of a reference compound. T h e steps are:
1. O n the logarithmic paper, the horizontal and vertical scales are calibrated in terms of the desired vapor pressures throughout the intended range. 2. Vapor pressures of a reference compound are taken from standard data a t uniform divisions of temperature; these temperatures are indicated on the horizontal scale at the corresponding pressures. 3. Ordinates are erected a t these temperatures. This gives a coordinate system of pressures on the vertical logarithmic scale versus temperatures on the derived horizontal scale. 4. Points are plotted on this system and lines connecting them are straight, up to the critical range. T h e slope of any line is the ratio of molar latent heat of the material to that of the reference substance a t each temperature. The equation may readily be used directly, and the plot may be converted into a precise, flexible, and readily used nomogram. Because the latent heat function is incorporated, Reprints of this article, with the nomogram on stiff paper, at e available from the Special Publications Dept., American Chemical Society, 1155 Sixteenth St., N. W., Washington 6 , D. C. Single copies, $1.00; in lots of 10 or more, $0.50
both utilizations have advantages (77) in accuracy of construction, generality, and flexibility in use as compared to other equations, such as the Antoine and its modifications, or to other charts (7) empirically prepared from a reciprocal temperature scale, or from the fundamental Duhring relationship using temperature as the coordinates (8, 9 ) rather than the more nearly correct reciprocal temperatures as shown by Perry and Smith (25) and Othmer (77). Thus, the use by Dreisbach and Spencer (3) of the Antoine equation has been shown by Myers and Fenske ( 9 ) to give curves instead of straight lines, as would result if the equation were valid. Myers and Fenske ( 9 ) developed a general plot for hydrocarbons which, because of errors inherent in the usual Duhring plot, also was shown to have deviations which increased as pressures higher or lower than 20 mm. of mercury are considered. Myers (8) used the same system for lower hydrocarbons and found that the deviations, when not at normal boiling point, were usually not greater than 5’ F. As many as six or even seven significant figures are given for the constants in these uses of the Antoine equation, while the experimental data are seldom accurate beyond three significant figures, and the correlations themselves may not be accurate in some ranges beyond two significant figures. Another semitheoretical expression recently developed (27) is considerably more precise than usual forms of the Antoine equation over a wide range. I t requires evaluation of four constants from a t least four known pressures and temperatures and from combinations of vapor pressures, critical properties, and molecular configurations. A straight line plot results only from a complex function of the constants and variables, none of which are directly related to the latent heat. I n the following development, the equation is always as accurate over a wide range as the best experimental data
available; the only other functions used are the vapor pressure and latent heat of water which are known with even greater accuracy. Any relevant precision of expression of the equation and its use are thus possible. T h e graphical expression of the nomogram, however, limits the precision of the values obtained therefrom to a lesser number of significant figures.
Use of the Equation Directly T h e basic equation is of the form, y = mx C, where y = log P and x = log P’. It may be used directly in the ready computation of vapor pressure if the constants are first evaluated. m is equal to L/L’,the slope of the line and it is a useful term. This is equal to MlIM’l’ where M and M’ are the respective molecular weights of the compound and of the reference substance, water, and I and 1’ are the respective latent heats per gram or per pound, at the same temperatures. Since m is a ratio, it is dimensionless and independent of values of temperature or pressure. C, a constant, is the intercept of the line on the usual plot where x = log P’ equals zero or log P’ = log 1. This is a t 100’ C. if pressures are in atmospheres, and if water is the reference substance. C is derived from the same units of pressure as P and P‘. Water is the reference substance used and instead of temperature, the logarithm of its vapor pressure is used in the equation as log P. T o avoid using several sets of tables, logarithms of water vapor pressures in millimeters of mercury and in pounds per square inch are given in Table I against temperatures in both degrees centigrade and Fahrenheit. Similarly, latent heats of water are also given both in calories per gram mole and in B.t.u.’s per poundmole. If another unit of vapor pressure than millimeters of mercury or pounds per square inch is desired, the log of the
+
VOL. 49, NO. 1
JANUARY 1957
125
Table I.
Latent Heats and Logarithms of Water Vapor Pressure
- Temp. O
126
c.
O
F.
Vapor Pressure, Log P' Log: Log mm. ib./sq. inch
Heat of Vaporization B.t.u./lb. Cal./g. mole mole
0 2 4 6 8
32.0 35.6 39.2 42.8 46.4
0.6608 0.7235 0.7851 0.8458 0.9054
- 1.0513 -0.9901 -0.9285 - 0.8677 - 0.8083
10717 10699 10680 10661 10642
19290 19260 19220 19190 19160
10 12 14 16 18
50.0 53.6 57.2 60.8 64.4
0.9640 1.0217 1.0785 1.1346 1.1892
-0.7496 - 0.6919 - 0.6451 -0.5792 - 0.5243
10623 10604 10585 10566 10547
19120 19080 19050 19020 18980
20 22 24 26 28
68.0 71.6 75.2 78.8 82.4
1.2433 1.2965 1.3487 1.4002 1.4510
- 0.4703 -0.4171 - 0.3649 - 0.3134 -0.2647
10528 10510 1049 1 10422 10452
18950 18920 18880 18850 18810
30 32 34 36 38
86.0 89.6 93.2 96.8 100.4
1.5012 1.5254 1.5993 1.6474 1.6947
-0,2124 -0.1630 -0,1142 - 0.0662 - 0.0189
10433 10414 10394 10375 10355
18780 18750 18710 18680 18640
40 42 44 46 48
104.0 107.6 111.2 114.8 118.4
1.7414 1.7855 1.8328 1.8775 1.9217
4-0.0278 +0.0739 +0.1192 $0.1640 +0.2080
10335 10315 10294 10274 10253
18600 18570 18530 18490 18450
50 52 54 56 58
122.0 125.6 129.2 132.8 136.4
1.9652 2.0081 2.0504 2.0920 2.1332
+0.2516 f0.2945 +O. 3367 +0.3784 +0.4195
10232 10212 10191 10171 10151
18411 18380 18340 18300 18270
60 62 64 66 68
140.0 143.6 147.2 150.8 154.4
2.1734 2.2137 2.2532 2.2921 2.3305
0.4602 0.5001 0.5396 0.5785 0.6169
10131 10110 10089 10068 10047
18230 18200 18160 18120 18080
70 72 74 76 78
158.0 161.6 165.2 168.8 172.4
2.3683 2.4057 2,4426 2.4790 2.5148
0.6548 0.6921 0.7290 0.7654 0.8012
10025 10004 9983 9962 9941
18040 18010 17970 17930 17890
80 82 84 86 88
176.0 179.6 183.2 186.8 190.4
2.5404 2.5836 2.6198 2.6540 2.6876
0.8368 0.8718 0.9062 0.9404 0.9740
9919 9898 9876 9854 9832
17850 17820 17780 17740 17700
90 92 94 96 98
194.0 197.6 201.2 204.8 208.4
2.7208 2.7537 2.7860 2.8180 2.8496
1 0072 1.0401 1.0725 1.1044 1.1360
9809 9787 9765 9742 9719
17650 17620 17580 17540 17490
100 102 104 106 108
212.0 215.6 219.2 222.8 226.4
2.8806 2.9116 2.9421 2.9722 3.0019
1.1672 1.1981 1.2285 1.2586 1.2883
9697 9673 965 1 9628 9605
17450 17410 17370 17330 17290
110 112 114 116 118
230.0 233.6 237.2 240.8 244.4
3.0312 3.0602 3.0889 3.1172 3.1452
1.3176 1.3466 1.3753 1.4040 1.4316
9581 9557 9533 9508 9484
17250 17200 17160 17110 17070
120 122 124 126 128
248.0 251.6 255.2 258.8 262.4
3.1790 3.2002 3.2272 3.2540 3.2804
1.4593 1.4866 1.5138 1.5405 1.5668
9460 9436 9410 9385 9360
17030 16980 16940 16890 16850
I
corresponding conversion factor is added or subtracted. If atmospheres are to be used. log 760 = 2.8806 is subtracted from the logarithm of millimeters of mercury in Table I, or log 14.69 = 1.1672 is subtracted from the logarithm of pounds per square inch. Molar latent heats of vaporization for water a t any temperature for which latent heat of the compound is known may be taken for calculating m. Also, if m is obtained from the slope of a line on the reference substance plot, equation, nomogram, or otherwise, latent heat for the compound a t any other temperature may be determined by using the molar latent heat in the last two columns of Table I. Table I1 gives values of m using water as the reference substance. Values of C are also tabulated in units of atmospheres, millimeters of mercury, and pounds per square inch. Over 500 compounds in various classes are listed in the order of increasing number of carbon atoms. Compounds with the same number of carbon atoms follow in the order of the number of hydrogen atoms. Those containing other elements follow by the number of atoms of each element arranged by symbols alphabetically. T h e vapor pressure data utilized are largely from standard handbooks and the works of Doolittle ( Z ) , Jordan (6), and Stull (28). I n most cases, the sources agree; if not, a careful analysis usually showed one set consistent. Selection of preferred values could be made by careful comparison of data points. and against the series lines indicated subsequently for the nomogram. Centrigrade or Fahrenheit temperatures may be used interchangeably in determining the vapor pressure of water, and hence the desired vapor pressure of the compound. Pressures may be in pounds per square inch, millimeters of mercury, or atmospheres, and the corresponding values of C must be used. A simple relationship may be written for C values of any other pressure unit, u. Thus
c,, = Cat,
C,
= C,tm
+ 2.881 (1
- m)
.Also, where w = 14.69 pounds sq. inch per atm. and log 14.69 = 1.167. C,,,
INDUSTRIAL AND ENGINEERING CHEMISTRY
+ (1 - m) log w
Here C,,, is the value of C when atmospheres are used as the pressure unit; C,, is the value of C when another pressure term is used having w units per atmosphere. Thus. where w = 760 mm. of mercury per atm. and log 760 = 2.881
=
Ca+,m
+ 1.167 (1 - m)
Values of C in terms of atmospheres, millimeters of mercury, and pounds per square inch have been calculated (Table 11). In using Table I1 (for use with nomo-
gram, see Figure 1) with the equation, log P = m log P’ C, the desired value of C is selected from the column having the corresponding unit of vapor pressure. The values of the last two columns were calculated for each compound from the relationships,
+
+ (1 - m) log 760 + (1 - m) log 14.696
C,, = Catm and C,,,, = Cstm
The column headed m may be used to give directly the latent heat of the compound a t any temperature, using the relationship 1 = ml’ M ‘ / M or 1 = mL’/M. l’M’ or L‘, the molar latent heat for water, is taken in English or centigrade units from Table I at the desired temperature and inserted along with M , the molecular weight, to solve this relation for 1. Examples for Compounds Listed in Table 11. For example, the vapor pressure of acetic acid at 160 ’ C. may be obtained: 1. The vapor pressure of water, P’,at 160’ C. is 4633 mm. of mercury, and log P’ = 3.6659. These values come from usual tables or from Table I. 2. Values of m = 0.961 and Cmm= - 0.143 for acetic acid come from Table 11. 3. These are substituted in the C,, to equation, log P = m log P’ give log P = 0.961 (3.666) -0.143 = 3.380. 4. The antilog of this, the pressure of acetic acid at 160’ C., P = 2400 mm. of mercury.
+
This calculated value compares favorably with the accepted value, 2409 mm. of mercury and is certainly within the error range of the original experimental determinations. Numerous other examples have been computed, all of which come within 1 or 2y0 of the experimental data used in calculating the constants. The equation is believed to be more accurate than most reported determinations of vapor pressure. Determining Constants for Compounds Not in Table 11. For these compounds, values of C and m may be determined either algebraically or geometrically:
1. By substituting in the basic equation, the known vapor pressure and that of water a t the same temperature. This is repeated for known values a t a second temperature, and the two resulting simultaneous equations are solved for both C and m. However, if latent heat is known at some temperature, m may be calculated from the molecular weight of the compound, the molecular weight of water, and the latent heat of water a t the same temperature. To determine C,this value of m is then substituted in the equation with one value of the vapor pressure of the compound and of water a t the same temperature. The correlation should include several points if available, to minimize the effect of experimental or casual error.
Table 1.
Latent Heats and Logarithms of Water Vapor Pressure (Continued) Vapor Pressure, Log P’ Temp.
Log lb./sq. inch
Heat of Vaporization Cal./g. B.t..u./lb. mole mole
’F.
Log mm
130 132 134 136 138
266.0 269.6 273.2 276.8 280.4
3.3066 3.3324 3.3579 3.3832 3.4082
1.5930 1.6188 1.6443 1.6696 1.6946
9335 9311 9286 9259 9234
16800 16760 16710 16660 16620
140 142 144 146 148
284.0 287.6 291.2 294.8 298.4
3.4329 3.4573 3.4815 3.5054 3.5291
1.7193 1.7437 1.7679 1.7918 1.8155
9207 9182 9155 9128 9101
16570 16530 16480 16430 16380
150 152 154 156 158
302.0 305.6 309.2 312.8 316.4
3.5525 3.5757 3.5986 3.6213 3.6437
1.8389 1.8578 1.8850 1.9076 1.9300
9074 9047 9020 8993 8966
16330 16280 16230 16190 16140
160 162 164 166 168
320.0 323.6 327.2 330.8 334.4
3.6659 3.6769 3.7096 3.7311 3.7524
1.9523 1.9743 1.9960 2.0175 2.0388
8937 8908 8881 8854 8825
16090 16040 15980 15940 15890
170 172 174 176 178
338.0 341.6 345.2 348.8 352.4
3.7736 3.7944 3.8151 3.8356 3.8558
2.0599 2.0808 2.1015 2 * 1220 2,1422
8797 8768 8739 8710 8681
15830 15780 15730 15680 15630
180 182 184 186 188
356.0 359.6 363.2 366.8 370.4
3.8759 3.8958 3.9154 3.9349 3.9542
2.1623 2.1822 2.2018 2.2213 2.2406
865 1 8622 8592 8563 8532
15570 15520 15470 15410 15360
190 192 194 196 198
374.0 377.6 381.2 384.8 388.4
3.9733 3.9922 4.0110 4.0296 4.0480
2.2597 2.2787 2.2974 2.3160 2.3344
8502 8471 8441 8410 8380
15300 15250 15190 15140 15080
200 205 210 215 220
392.0 401.0 410.0 419.0 428.0
4.0662 4.1111 4.1550 4.1980 4,2402
2.3526 2.3975 2.4414 2.4844 2.5267
8348 8270 8191 8110 8029
15030 14890 14740 14600 14450
225 230 235 240 245
437.0 446.0 455.0 464.0 473.0
4.2816 4.3216 4.3636 4.3998 4.4376
2.5680 2.6080 2.6500 2.6862 2.7240
7897 7799 7697 7594 7486
14210 14040 13850 13670 13470
250 255 260 265 270
482.0 491.0 500.0 509.0 518.0
4.4747 4.5110 4.5466 4.5816 4.6158
2.7611 2.7974 2.8330 2.8680 2.8922
7376 7261 7142 7018 6892
13280 13070 12860 12630 12410
275 280 285 290 295
527.0 536.0 545.0 554.0 563.0
4.6495 4.6825 4.7150 4.7469 4.7782
2.9359 2.9689 3.0014 3.0333 3.0646
6761 6627 6485 6340 6190
12170 11930 11670 11410 11140
300 305 310 315 320
572.0 581.0 590.0 599.0 608.0
4.8091 4.8376 4.8693 4.8987 4.9277
3.0955 3.1240 3.1557 3.1851 3.2141
6032 5866 5692 5510 53 14
10860 10560 10250 9920 9570
325 330 335 340 345
617.0 626.0 635.0 644.0 653.0
4.9563 4.9844 5.0122 5.0396 5.0667
3 2327 3.2708 3.2986 3,3261 3.3531
5110 4892 4658 4408 4135
9200 8810 8380 7930 7440
350
662.0
5.0935
3.3799
3834
6900
c.
VOL. 49, NO. 1
JANUARY 1957
127
Figure 1. Nomogram for vapor pressure, latent heat, and other physical properties
7YDROCARBON
\ PETROLEUM' LINE .30
1.54.
\
\',
4,0g
LINE
m and C, found from Table II, or from experimenfal values of vapor pressures at two points or at one point and the value of latent heat, locate a point on the grid, through which a line i s drawn to intersect on the left scale vapor pressure, and on the right scale, the corresponding temperature. Pivot points of all hydrocarbons fall close to the dashed line across the central grid, and only one vapor pressuree.g., the boiling point-or latent heat to give m, is necessary to define the system. Pivat points of all petroleum mixtures, crudes, fractions,or residues fall close to the petroleum mixture line across the central grid. This defines also the equilibrium Rash vaporization relation. To determine Henry's law constant, a temperature within the range shown in Table IV i s located on the temperature scale; a line i s drawn through the pivot point defined by m and C which intersects the left scale. The value from the vapor pressure scale in millimeters of mercury when multiplied by the appropriate power of 10 (last column, Table IV) gives the value of Henrv's law constant, H, in atmospheres per mole fraction of solute.
1 0 s50
% SOz
25
30
5--
5
90
35 4
3
0
3 loo 'lo
45
60
3,000
2,000
1,000 900
75
r" LL
a W
a
400 LL
a ~
140
200
190
240
20
.02
270
10 0
90
2.5'
.30
.010
,006
128
INDUSTRIAL AND ENGINEERING CHEMISTRY
260
2 . By plotting on the logarithmic reference plot indicated previously, all available data. The best straight line is drawn through the points. T h e slope of this line is measured to give the value of m as defined before; the intersection of the ordinate with the vapor pressure of water of 1 atm. or a temperature of 100' C., gives the value of C. If temperatures above or below the Liquid range of water are to be considered the equation may be used with ammonia or mercury, respectively, or with other liquids as reference substances; values of m and C are determined, based on the properties of the particular liquid. In special cases, other reference substances may also be used in order to obtain the higher precision possible when using a reference substance closely related to the compound studied.
latent Heat Variation with Temperature Column m of Table 11also allows direct determination of latent heat, I , at any temperature for the 500 compounds listed, using the ratio of molecular weight, M , to that of water (M' = 18), and the molar latent heat of water, l', per gram mole or per pound-mole taken from Table I at the desired temperature. From the relationship, 1 = ml' M ' / M or I = m L ' / M (molar latent heats are listed in Table I), the needed value may be determined, usually with greater accuracy than those from most calorimetric measurements reported. Relatively few determinations have been reported for latent heats a t pressures other than 1 atm. No other tables are known which give latent heats throughout the entire liquid range for any large Values of latent D number of compounds. heats calculated from these tables check those few determined calorimetrically and given in standard references. As a means of checking the values of rn and hence of the resulting latent heat calculation, the slope of the line drawn to a large scale on the logarithmic reference plot for acetic acid was determined to be 0.963. Seven experimental points of literature data were evaluated by the method of least squares to give a n equation with m = 0.962. The correlated value previously obtained from substitution of values in the equation is 0.961 (Table 11). This agreement may be better than average, for this was the only compound checked in this way. It gives credence to latent heats determined from Table 11, as well as to utilization of the constants in the equation.
A General Nomogram Construction from a Straight-Line Plot. A straight line by any system of plotting on any vertical and horizontal coordinates may be transferred immediately into a nomogram having the same scales as the X and Y axes. The vertical
Table 11.
Vapor Pressures of Some Organic Compounds
Compound Isoprene n-Pentane Benzene Cyclohexane n-Hexane Toluene 2-Heptene Methylcyclohexane n-Heptane Ethylbenzene o-Xylene m-Xylene p-Xylene Ethglcyclohexane 2-Methyl-2-heptene n-Octane a-Methylstyrene @-Methylstyrene 4-Methylstyrene Cumene Nonane Naphthalene Tetralin Butylbenzene Isobutylbenzene p-Cymene d-Limonene Dipentene Myrcene a-Pinene 8-Pinene Terpinolene cis-Decalin tram-Decalin Decane 4-Isopropylstyrene 3-Ethyl cumene 4-Ethyl cumene 1,2-Diisopropylbenzene Triisobutylene Dodecane Heptylbenzene Tetradecane Pentadecane Hexadecane Tribromomethane Chloroform Dibromomethane Methylene chloride Carbon tetrachloride Tetrachloroethylene Trichloroethylene 1,l-Ethylidene chloride
1,1,1,2-Tetrabromoethane 1,1,2,2-Tetrabromoethane 1,1,1,2-Tetrachloroethane l11,2-Trichloroethane 1-Bromo-2-chloroethane 1.2-Dibromoethane 1,2-Dichloroethane Ethyl bromide Ethyl iodide 2,3-Dibromopropane Methyl dichloroacetate 1,2,3-Tribromopropane Epichlorohydrin 1,2,3-Trichloropropane l,l,1-Trichloropropane 1,2-Dibromopropane l,3-Dibromopropane Propylene dichloride 1-Bromopropane 2-Bromopropane 1-Chloropropane 2-Chloropropane 1-Iodopropane 2-Iodopropane 1,2,2-Tribromobutane 1,2,3-Trichlorobutane 1,2-Dibromobutane 1.4-Dibromobutane
Hydrocarbons m 0.6173 0.6274 0.7688 0.7520 0.7263 0.8544 0.8125 0.7992 0.8235 0.9385 0.9597 0.9500 0.9443 0.9006 '0.9330 0.9172 1.0996 1.0830 1.0790 0.9914 0.9810 1.2142 1.1670 1.1180 0.9547 1.1090 1.0700 1.0750 1.0740 0.9863 1.0230 1.231 1.092 0.996 1.092 1.1857 1.140 1.163 1.207 1.060 1.272 1.430 1.401 1.435 1.508
C, Atm.
C,Mm. Hg C, Lb./Sq. In.
+0.8110 +0.7743 f0.2526 +0.2392 +0.3898 - 0.1360 +0.0190 -0.0111 +0.0205 -0.4739 - 0.5882 -0,5142 -0.5017 -0.4042 -0.3044 -0.3374 - 0.9246 - 1.0671 - 1.0195 - 0.6937 -0.6534 - 1.6290 - 1.4580 - 1.1471 -0.8576 - 1.0470 -1.0110 -1.0113 - 0.9759 -0.7194 - 0.7841 - 1.2860 - 1.240 - 1.057 - I. 009 - 1.432 -1.279 - 1.334 - 1.529 - 1.044 - 1.670 -2.094 -2.244 -2.509 -2.790
t1.9135 1.8477 +0.9180 $0.9536 1.1784 +O. 2834 +0.5591 +O. 5673 +0.5289 -0.2968 -0.4721 - 0.3702 -0.3413 -0.1179 -0.1114 -0.0989 -1.2115 - 1.3062 - 1.2470 -0.6690 -0.5987 - 2.2461 - 1.9391 -1.487 - 0.7271 - 1.3610 - 1.2126 - 1.2270 - 1.1890 - 0.6804 - 0.8647 -1.951 - 1.505 - 1,045 - 1,275 - 1.967 - 1,684 -1.805 - 2.127 -1.218 -2.454 -3.333 - 3.400 -3.763 -4.255
Halogenated Hydrocarbons 0.972 -0.660 CHBr3 0.720 CHCla +0.489 0.833 4-0.018 CHzBrz 0.668 $0.750 CHzClz 0.754 +0.294 c Cl4 0.891 -0.270 czc14 0.780 CaHCls $0.167 0.711 +0.540 CzH4Clz - 1.798 1.515 CzHzBr4 - 2.089 1.351 CzHzBr4 0.976 -0.608 CzHzC14 0.878 -0.180 CzHaCla 0.858 -0.087 CzHaBrCl 0.919 -0.409 CtH4Brz 0.711 f0.540 CzHaC14 0.641 +0.542 CtHsBr 0.719 +0.336 CzHaI 0.972 -0.550 CaH4Brz 1.065 -0.626 CaHrClzOz 1.239 -1.685 CsHsBra 0.947 -0.248 CsHsCLo 1.066 -0.813 CsHsCla 0.849 -0.104 CaHsCla 0.954 -0.546 C&Brz 1.038 -0.899 CaHeBrz 0.798 4-0.039 CsHeClz 0.729 CaHiBr +0.360 0.694 CaH7Br +0.491 0.674 CaHiCl +0.669 0.604 CaHiCl +0.742 0.809 -0.030 Can71 0.772 CaH7I f0.129 1.197 CaHiBn - 1.565 0.935 -0.824 CaHiCla 1.025 -0.875 CAH8BrZ 1.168 -1,360 C4HsBrz
VOL. 49, NO. 1
+ +
+1.2576 +1.2091 +0.5224 +0.5286 +0.7092 +0.0339 +0.2378 +O. 2232 +0.2264 -0.4022 -0.5412 - 0.4559 - 0.4367 - 0.2883 0.2263 - 0.241 1 - 1.0408 - 1.1639 1.1116 0.6837 0.6313 - 1.8789 1.6528 - 1.285 0.8048 - 1.1742 - 1.0926 - 1.0988 - 1.0622 -0.7035 - 0.8109 - 1.555 - 1.348 - 1.052 -1.117 - 1.649 - 1.443 - 1.525 - 1.771 -1,114 - 1.987 -2.595 -2.712 -3.016 -3.383
-
-
-0.628 +0.816 $0.213 $1.136 $0.580 -0.144 +0.423 $0.877 -2.399 -2.499 -0.581 -0.038 4-0.077 -0.314 +0.877 $1.172 $0.664 -0.518 -0.702 - 1.963 -0.186 -0.891 +0.071 -0.492 -0.943 $0.275 +0.675 f0.848 +1.049 +1.203 +O. 192 +0.395 - 1.795 -0.749 -0.905 - 1.557 (Continued on page I S O ) -0.569 +1.296 4-0.499 f1.704 +1.001 +0.042 $0.799 $1.371 - 3.282 - 3.103 -0.542 +0.169 +0.320 -0.176 +1.371 +1.787 +1.145 -0.471 -0.814 -2.373 -0.096 - 1.006 4-0.329 -0.043 - 1,009 +0.620 +1.139 +1.372 +1.607 +1.881 +0.519 +0.786 -2.134 - 0.638 -0.948 - 1.847
JANUARY 1957
129
Table II.
Vapor Pressures of Some Organic Compounds (Continued) Halogenated Hydrocarbons
Compound
m
C , Atm.
1,2-Dichlorobutane 2,3-Dichlorobutane Dichloroethyl ether 1-Bromobutane Pz-Butyl chloride tert-Butyl chloride 1-Bromo-3-methylbutane Pentachlorobenzene
0.840 0.857 1.148 0.833 0.755 0.649 0.885 1.616 1,262 1.410 1.174 1.175 1.227 1.090 1.108 0.993 0.929 0.786 1.089 1.201 1.064 1.141 1.095 1.012 1.021 1.012 0.8894 0.889 1.164 1.091 1.147 1.203 1.558 1.386 1.336
-0.284 -0.202 - 1.125 -0.020 f0.278 4-0.579 -0.263 -2.868 - 2.049 -2.195 - 1.528 - 1.358 - 1.653 - 1.017 - 1.033 -0.738 -0.421 + O . 195 - 1.176 - 1.226 - 1.078 - 1.177 - 1.139 -0.827 -0.794 -0.819 - 0.209 -0.221 - 1.494 - 1.097 - 1.492 - 1.690 -2.111 -2.514 -2.219
1,2,3,4-Tetrachlorobenzene 1,2,4,5-Tetrachlorobenzene 1,2,4-Trichlorobenzene 1,4-Bromochlorobenzene 1,4-Dibromobenzene 1,4-Dichlorobenzene o-Dichlorobenzene Bromobenzene Chlorobenzene Fluorobenzene Iodobenzene Dichloroisopropyl ether 2-Bromotoluene 3-Bromotoluene 4-Bromotoluene 3-Chlorotoluene o-Chlorotoluene p-Chlorotoluene 3-Fluorotoluene 4-Fluorotoluene 2-Iodotoluene 1-Chloro-3-ethylbenzene 2-Bromoethylcyclohexane 1-Iodo-octane Iodononane 1-Bromonaphthalene 1-Chloronaphthalene
C , Mm. Hg. C, Lb./Sq. In. $0.176 +0.208 - 1.552 $0.458 $0.982 +1.589 +0.066 -4.643 -2.805 -3.376 -2.031 - 1.863 - 2.308 - 1.276 - 1.345 -0.719 -0.218 $0.809 - 1.435 - 1.805 - 1.264 - 1.584 -1.413 -0.862 -0.856 -0.855 +o. 108 $0.095 - 1.967 - 1.359 -1.917 -2.276 - 3.720 -3.628 - 3.188
-0.098 -0.035 +1.298 +O. 173 f0.563 +0.989 -0.129 - 3,587 -2.355 -2.673 - 1.732 - 1.562 - 1.918 - 1.122 - 1,160 -0,730 -0.339 +0.443 -1.281 - 1,461 - 1.153 - 1.341 - 1.250 -0.841 -0.819 - 0.834 +0.080 - 0.093 - 1.685 - 1.203 - 1.664 - 1.927 -2.763 -2.965 -2.611
+0.873 -0,064 f0.407 -3.087 -2.900 +0.228 -0.174 -2.693 - 1.830 -0.399 +0.211
+0.677 -0.511 f0.374 -2.271 -2.273 +0.267 -0.049 - 1.992 - 1.233 -0.238 $0.256 -0,458 -0.086 - 1,960 -1.571 -0.823 -0.477 -0.108 -0.700 -0.824 - 1.199 -0.829 - 1.231 -0.996 -0.996 - 2.899 - 1.651 -2.325 -2.084 -6.111 -2.730 -2.371 -3.536 -2.150 - 2.630 -2.269 -2.669
Alcohols and Polyols 0.885 1.064 0.981 1.476 1.365 1.022 1.078 1.408 1.348 1.093 1.026 1.141 1.081 1.297 1.329 1.175 1.129 1.071 1.167 1.178 1.204 1.162 1.250 1.192 1.192 1.551 1.329 1.384 1.354 2.316 1.411 1.432 1.631 1.323 1.495 1.397 1.466
Methanol 2-Chloroethanol Ethyl alcohol Ethylene glycol 2,3-Dibromo-l-propanol Isopropyl alcohol n-Propyl alcohol Propylene glycol 1-Bromo-2-butanol Isobutyl alcohol tert-Butyl alcohol %-Butyl alcohol sec-Butyl alcohol l,3-Butanediol Furfuryl alcohol %-Amyl alcohol 2-Pentanol tert-amyl alcohol Isoamyl alcohol 3-Pentanol Cyclohexanol &Hexyl alcohol n-Hexyl alcohol 2-Methyl-1-pentanol 2-Methyl-4-pentanol Dipropylene glycol Heptyl alcohol Me thylphenylcarbinol Cyclohexylethanol Tetraethylene glycol Cinnamyl alcohol Nonanol Tripropylene glycol +Terpinol Citronellol 1-Menthol Decyl alcohol
$0.543 -0.434 +0.351 -1.715 - 1.846 +0.293 +0.037 - 1.515 -0.826 -0.129 +0.287 -0.293 +0.008 - 1.613 - 1,187 -0.618 -0.326 -0.024 -0.505 -0,617 -0.960 -0.640 - 0.940 -0.771 -0.771 -2.255 - 1.267 -0.384 - 1.670 -4.575 -2.249 - 1.867 -2.799 - 1.772 -2.051 - 1.805 -2.125
-0.700 -0.226 -2.470 - 2.136 - 1.125
-0.700 -0.230 - 0.986 - 1,130 - 1.550 - 1,107 - 1.660 -1.327 - 1.327 -3.844 -2.216 - 2.984 - 2.692 -8.367 -3.436 -3.112 - 4.618 -2.704 -3.479 -2.951 -3.469
Aldehydes, Ketones, and Ethers Bromal Chloral Chloral hydrate 2-Propenal Acetone Propylene oxide
1 30
C2HBr30 CzHC130 H3ClsOj CtHaO CaHsO C3HsO
1.134 0.802 1.175 0.686 0.729 0.653
INDUSTRIAL AND ENGINEERING CHEMISTRY
- 1.060 +0.028 +0.069 +0.590 +0.567 SO.828
- 1.449 f0.591 -0.437 $1.492 +1.345 +1.827
-1.217 $0.259 -0.135 $0.955 $0.882 $1.232
Figure 2. Diagram illustrating determination of m lines as a function of molar latent heat, between vertical scales
or Y axis is calibrated as for the usual plot. on paper such as ordinary graph paper. The X axis, instead of being placed a t right angles, is drawn parallel to the Y axis a t a convenient distance. I t is calibrated with increasing values, upward if the slope of the line is negative, or downward if the slope is positive. Data previously presented by a straight line on the rectangular coordinates, are now condensed to a single pivot point between the parallel scales. Any line through this point intersects the left scale a t the value corresponding to that of the other variable intersected on the right scale. Thus, the line on the original plot has been condensed on the nomogram to a pivot point; to read what was a point on the original line showing the relationship of the variables, a line is needed on the nomogram between the two scales and through the pivot point. Figure 1 is a nomogram so constructed from the basic vapor pressure plot previously described ( 72) and ( 7 3 ) using the basic equation. T h e vapor pressure scale on the left is calibrated logarithmically in atmospheres. and also in millimeters of mercurv. T h e temperature scale on the right is first calibrated logarithmically from top to bottom with values representing the vapor pressures of water in millimeters of mercury. Centigrade temperatures a t even values are then indicated a t corresponding values of the vapor pressure of water. Calibration of water vapor pressure is then disregarded. and not indicated on the nomo. gram. Calibrations in Fahrenheit degrees are also indicated. For convenience, the point of 1-atm. pressure on the left scale is horizontally opposite the point for 100' C. or 212' F. on the right scale corresponding to the boiling point of water at 1-atm. pressure. To use the nomogram. the pivot
point for each compound must be located between the two scales. For a nomogram wherein hundreds of compounds are to be used, it is impossible to label each pivot point; therefore, a system of coordinates is established to give a grid by which the specific point may be located. The position of the pivot point for each compound is obviously dependent on its values of m and of C in the basic equation. Usually, graphical methods are used in locating the pivot point, but these, however, are not as precise as vapor pressure data. Hence, the following method was devised. It may be used also in other nomographic constructions where precision is desired. Molar Latent-Heat Ratio and Position of m Lines. It can be shown readily that the pivot points for all different compounds having the same coefficient constant, m (and only these points), are on the same vertical line between the two scales. Thus, the relative distance of the pivot point from the two scales is a function only of m. T h e basic equation in the differential form is d log P = md log P’, or in finite differences, m = - A log P A log P’
Figure 2 represents a diagram of the nomogram with the two scales a t a distance, D, apart; the pivot point 0 is a t a distance A from the left scale. T h e distance, A log P,is a change caused by a change in the vapor pressure of the compound; A log P’ is the corresponding change of the vapor pressure of water on the right scale. Two similar triangles are formed, having the common apex 0. The lengths of the sides are proportional.
Distance D is constant. Thus, for any value of m, A is immediately fixed, and the locus of each value of m is a vertical line drawn at a distance from the left scale equal to the corresponding value of A . As m decreases, its vertical line moves to the left, to coincide with the pressure axis where m equals zero. As m increases, its line moves to the right to coincide with the temperature axis where m equals infinity. Relationship of Constant C or Intercept, and C Lines. Values of C are in any desired units of vapor pressuremost simply in atmospheres. To locate lines representing constant values of C in atmospheres, the relationship for the intercept C alone is obtained when log P = m log 1.0 C. Since log 1 = 0, thus, C = log P when the vapor pressure of water, the reference substance, is 1 atm. (at 100’ C . ) . T h e pivot points corresponding to all values of the basic equation at any one
+
Table II.
Vapor Pressures of Some Organic Compounds (Confinued) Aldehydes, Ketones, and Ethers
Compound 2-Methylpropionyl bromide 1-Bromo-2-butanone Di-2-bromoethyl ether Methyl ethyl ketone Di-chloroethyl ether 1,4-Dioxane Methyl propyl ether Diethyl ether 2-Furfurylaldehyde Tiglaldehyde Levulinaldehyde 3-Pentanone 2-Pentanone 3-Methyl-2-butanone
Formula
m
C , Atm.
C4H7BrO CaH7BrO
1.106 1.085 1.270 0.754 1.148 0.846 0.663 0.660 1.168 0.882 1.180 1.069 1.071 1.054
-0.905 -0.690 - 1.645 +0.255 - 1.125 -0.014 +0.768 4-0.835 -0.940 -0.214 - I . 256 - 0.043 -0.051 + O . 187
-0.935 -2.425 i-0.962 - 1.552 +0.428 +1.738 +1.813 - 1.426 f O . 124 - 1.777 -0.244 -0.256 f0.030
+0.541 - 1.298 + O . 165 +1.161 +1.231 -1.137 -0.077 - 1.467 -0.125 -0.134 + O . 124
1.150
- 1.145
- 1.579
- 1.320
1.151
- 1.303
- 1,740
- 1.480
1.393 0.657 0.990 0.979 1.203 0.809 0.826 1.004 0.778 0.707 0.934 0.761 1.111 1.199 1.243 1.038 1.330 1.303 1.193 1.439 1.171 2.191 0.617
- 1.454
- 1.913
d-0.440 -0.729 -0.418 - 1.229 + O . 123 f0.281 -0.347 + O . 130 +0.396 -0.030 +1.304 - 1.092 -1.381 - 1.721 -0.773 -0.795 -0.878 - 1.442 -2.271 - 1.081 -1.921 -0.614
-2.587 f1.428 -0.702 -0.359 -1.816 +0.671 +0.781 -0.359 f0.769 f1.240 +O. 157 +1.992 - 1.412 - 1.956 -2.423 -0.884 - 1.749 - 1.753 - 2.000 -3.537 - 1,576 -5.352 f0.495
+0.841 -0.718 -0.394 - 1.467 +-0.355 i-0.484 -0.352 f0.389 +-0.738 +0.045 +1.583 - 1.222 - 1.614 -2.005 - 0.818 - 1.181 - 1.233 - 1.668 -2.784 - 1.281 -3.311 -0.165
1.329 1.480 1.146 1.289 1.158 1.233 1.175 1.458 1.497 1.056 1.364 1.244 1.119
-1.914 -2.316 - 1.196 - 1.495 - 1,152 -1.287 - 1.340 -2.360 -2.572 - 1.008 -1.720 - 1.596 -1.039
-2.863 - 3.699 - 1.618 -2.328 - 1.986 - 1.959 - 1.846 -3.679 -4.005 - 1.171 -2.769 -2.301 - 1.384
-2.239 -2.876 - 1.367 -1.833 - 1.714 - 1.559 - 1.545 -2.894 -3.151 - 1.074 -2.145 - 1.881 - 1.179
1.388 1.308 1.723 1.476 1.453
- 1.967 -2.163 -3.275 -2.314 - 2.388
-3.088 -3.052 -5.361 - 3.686 -3.694
-2.421 -2.523 -4.120 -2.870 -2.917
1.529 1.516
-2.510 -2.801
-4.834 -4.290
-3.129 -3.414
- 1.624
- 2.833 -2.480 -2.929 -2.487 -0.1433 - 0.954 -0.926 -2.956 -2.248 -3.923 -3.856 - 1.753 -0.727 - 1.767 -2.867
C , Mm. Hg. C , Lb./Sq. I n ,
- 1.212
- 1.029 - 0.794 - 1.961
2-Chloromethyl-2-chloroisopropyl ether 2-Chloroethyl-2-chloropropyl ether 4-Hydroxy-3-methyl-2-butanone Ethyl propyl ether Cyclohexanone Mesityl oxide Dichlorodiisopropyl ether Allyl propyl ether Allyl isopropyl ether Paraformaldehyde Dipropyl ether Diisopropyl ether Acetal Diethyl Cellosolve Benzaldehyde Salicylaldehyde 4-Bromoanisole Anisole 4-Heptanone Methyl-n-amyl ketone Acetophenone Anisaldehyde 2-Octanone Caprylaldehyde 1,2-Dipropoxyethane Diethylene glycol butyl ether Cinnemal aldehyde Benzyl ethyl ether Phorone Isophorone Azelaldehyde 2-Nonanone Eugenol Isoeugenol Cineole Capraldehyde 2-Decanone Diisoamyl ether Dipropylene glycol monobutyl ether Diphenyl ether I-Acetonaphthalene 2-Dodecanone Lauraldehyde Tripropylene glycol monoisopropyl ether Benzyl phenyl ether
Acids Trichloroacetic acid Dichloroacetic acid Bromoacetic acid Chloroacetic acid Acetic acid Acrylic acid Propionic acid Methoxyacetic acid Succinyl chloride Succinic anhydride Chloroacetic anhydride Metacrylic acid Acetic anhydride Butyric acid Tiglic acid
1.419 1.334 1.404 1.352 0.961 1.113 1.104 1.422 1.283 1.494 1.598 1.260 1.052 1.255 1.424
-1.516 - 1.764 - 1.471 -0.254 - 0.628 -0.625 - 1.739 -1.432 -2.499 - 2.132 - 1.004 -0.575 - 1.032 - 1.645
-2.114 1.906 -2.236 - 1.882 -0.209 -0.760 -0.747 -2.232 - 1.762 -3.076 -2.830 - 1.307 -0.637 -1.330 -2.140 -
(Continued on page 152)
VOL. 49, NO. 1
JANUARY 1957
131
Table II.
Vapor Pressutes of Some Organic Compounds (Continued) Acids
Compound Valeric acid Isovaleric acid Benzenesulfon31 chloride Propionic anhydride Benzoyl chloride Phenylacetic chloride
Formula CaHioOz CaHioOn c6Hjo~ClS CsH1003 CiHjOCl CsH70C1
m
C , Atm.
1.399 1.320 1.320 1.171 1.159 1.297
- 1.453 - 1.242 -2.119
- 1.008 - 1.342 - 1.653
C , M m . H g . C , Lb./Sq. In. -2.603 -2.165 -3.041 - 1.503 - 1.805 -2.510
-1.919 -1.616 - 2.493 - 1.209 -1.531 -2.000
4-1.843 -0.812 $1.403 +1.296 -1,0816 -0.490 - 1* 499 - 1.055 -2.433 f0.847 -1.474 +0.832 f0.784 +0.790 - 1.164 f0.389 -0.947 $0.347 +0.278 $0.513 10.640 10.299 4-0.448 4-0.232 $0.497 -0.334 - 2.436 - 1 * 774 - 1.793 -2.160 -2.763 -3.663 -4.780
f1.274 -0.702 10.920 $0.857 -0.893 -0.490 - 1.207 -0.909 -1.931 f0.498 - 1.171 $0.522 4-0.481 f0.476 -0.926 + O . 153 -0.806 $0. 148 f0.093 $0.268 f0.346 4-0.106 f0.195 f0.045 $0.253 -0.352 - 1.933 - 1.445 - 1 .444 - 1.702 - 2.017 -2.839 -3.689 - 0.132 - 0.165 -0.012 -0.246 -0.128 -0.252 - 1.427 -2.117 - 1.985 -2.806 -0.655 - 1.902 - 0.832 -0.477 -0.610 -0.409 -0.642 -0.194 - 0.562 - 0.771 -1.731 - 1.637 - 1.996 -2.171 -2.155 - 2,171 - 1.853 -0.946 -0.875 - 0 * 743 - 0.833 -0.919 - 1.955 - 1.888 -2.393 -2.076 - 2.595 - 1.622 - 1.085 - 1,239 - 1.056 -2.794 -3.607
Esters Methyl formate Methyl dichloroacetate Ethyl formate Methyl acetate Methyl glycolate Ethyl chloroglyoxylate Ethyl trichloroacetate Ethyl dichloroacetate 2-Chloroethyl chloroacetate Methyl acrylate Dimethyl oxalate Ethyl acetate Methyl propionate Propyl formate Ethyl glycolate Ethyl acrylate Isopropyl chloroacetate Ethyl propionate Methyl butyrate Methyl isobutyrate Isopropyl acetate n-Propyl acetate Isobutyl formate Butyl formate sec-Butyl formate Diethyl carbonate Dimethyl maleate Isobutyl dichloroacetate Ethyl acetoacetate Glycol diacetate Diethyl oxalate Dimethyl-2-maleate Dimethyl-d-tartrate Methyl isovalerate Ethyl butyrate Ethyl isobutyrate Propyl propionate Isobutyl acetate Isoamyl formate Jec-Butyl glycolate Dimethyl citraconate trans-Dimethyl mesaconate Dimethyl itaconate Butyl acrylate Diethyl malonate Methyl caproate Ethyl isovalerate Propyl butyrate Propyl isobutyrate Isoamyl acetate Isopropyl isobutyrate Isobutyl propionate Triethyl orthoformate Phenyl acetate Methyl benzoate Methyl salicylate Diethyl maleate Dipropyl oxalate Diethyl fumarate Diisopropyl oxalate Ethyl isocaproate Propyl isovalerate Isobutyl isobutyrate Isobutyl butyrate Amyl isopropionate Benzyl acetate Ethyl benzoate Ethyl salicylate Diethyl itaconate Diethyl glutarate Methyl caprylate Isobutyl isovalerate Isoamyl butyrate Isoamyl isobutyrate Methyl cinnamate Dimethyl phthalate
132
0.668 1.064 0.718 0.743 1.109 1.000 1.170 1.085 1.292 0.796 1.176 0.819 0.823 0.812 1.138
0.862 1.082 0.883 0.892 0.856 0.829 0.887 0.852 0.891 0.857 0,989 1.293 1.192 1.203 1.267 1.435 1.480 1.636 0.919 0.904 0.893 0.947 0.904 0.943 1.214 1.343 1.310 1.640 1.000 1.310 1.0845 0.997 1.015 0.959 1.044 0.928 1.030 1.082 1.251 1.195 1.239 1.327 1.344 1.327 1.316 1.081 1.071 1.054 1.040 1.067 1.263 1.236 1.358 1.252 1.413 1.218 1.100 1.120 1.086 1.388 1.595
INDUSTRIAL A N D ENGINEERING CHEMISTRY
f0.887
-0.627 10.591 $0.558 -0,765 -0.490 - 1.007 - 0.809 - 1,590 +0.260 -0.965 $0.312 f0.274 $0.250 - 0.765 -0.006 -0.709 f0.012 -0.032 fO.lO1
1 0 . 146 -0.024 10.023 -0.081 f0.087
-0.365 - 1.591 -1.221 - 1.207 -1.391 - 1.509 -2.278 -2.947 -0,226 -0.277 -0.135 - 0.308 -0.239 -0.318 - 1.177 -1.717 - 1.623 -2.059 -0.654 - 1.540 -0.734 -0.479 -0.592 -0.455 -0.590 -0,277 -0.527 -0.675 - 1.437 - 1,410 -1.717 - 1.788 - 1.753 - 1.788 - 1.484 -0.851 -0,791 -0.679 -0.786 - 0.840 - 1.647 -1.612 - 1.975 - 1.782 -2.113 - 1.367 -0.967 - 1.098 -0.956 -2.341 -2.912
f0.080
-0.016 f 0 . 169
-0.156 $0.036 -0.155 - 1.794 -2.705 -2.517 - 3.903 -0.657 -2.433 - 0.977 -0.473 -0.635 -0.339 -0.719 -0.072 -0.615 -0.912 -2.162 - 1.972 - 2.406 -2.732 - 2.745 -2.732 -2.394 - 1.085 -0.997 -0.855 - 0.903 - 1.035 - 2.407 -2.294 -3.007 -2.508 -3.303 - 1.996 - 1.257 - 1.445 - 1.205 -3.459 -4.627
value of the intercept, C, will be on a straight line extending from the corresponding value of log P on the left axis to the point a t 100' C., on the righthand scale. For each fixed value of C, the value for pressure on the lefr scale is actually a t the position of log P. T h e constant values of C for these lines are, therefore, obtained directly from the logarithms of the indicated values on the left scale. Thus, where P = 10 atm., C = log P = 1 ; where P = 0.1 atm.: C = log P = - 1 ; where P = 0.01 atm., C = log P = -2, etc. These lines, fixed values of C, are drawn between values of C on the left scale through 100' C. on the right. They are uniformly spaced (Figure 1) cornpared to the left or pressure scale, for the same reason that the divisions on the logarithm scale of a slide rule are uniformly spaced compared to the logarithmic calibration of the C and D scales. This converging point at 100' C. on the nomogram compares on the usual plot with a vertical line at the boiling point of water at 1 atm.-i.e., where log P' = 0. Both this focal point on the nomogram for lines of constant C, and the line on the usual plot represent the same conditions regardless of pressure, P. C e n t r a l Grid for L o c a t i n g Pivot P o i n t s . -4 grid is thus made by the vertical lines, each indicating a constant value of m, and the sheaf of cross lines each indicating a constant value of C. Identification of rn and C for any compound locates its pivot point on this grid, as well as making the basic equation specific for that compound. This grid thus defines for the compound the basic equation, and interrelates temperatures, vapor pressures, molar latent heats, and constant, C. Several methods may be used to locate on the grid the pivot point for any substance :
1. For over 500 compounds, values of C and of m are given in Table 11. (For other compounds they may be determined as described previously.) These values are immediately used to locate the characteristic pivot point for that compound a t the intersection of the corresponding vertical line of rn and the cross line of C. Because these values \yere obtained algebraically by careful insertion in the equation of experimental values which were consistent among themselves, their precision, usually to at least three decimal places, is somewhat greater than may be used in any graphical solution, and somewhat greater than is usually necessary. Thus, the nomogram can never be quite as precise as the equation, although it is within the accuracy of most available data. 2. For other compounds, lines joining the corresponding points on the left and right axis are drawn for vapor pressures at two temperatures to give an intersection which is the pivot point defining
the relation of vapor pressure for all other temperatures. If vapor pressures are known a t more than two temperatures, several such lines may be drawn to check this location of the pivot point, thus casual mistakes are avoided. The values of m and C may be picked off so that the basic equation rather than this nomogram may be used. Latent heat of the compound a t any temperature can thus be determined immediately from the m value of this intersection or pivot point, as indicated previously. 3. If the latent heat per gram or per pound is known for any compound, the molar latent heat is calculated, and that for water a t the same temperature is taken from Table I or elsewhere; the ratio m is thus determined. The normal boiling point (or other single vapor pressure point) must also be known, and a single line connecting the corresponding values on the two scales is drawn. The intersection of this line with the vertical m line a t the determined value gives the pivot point, and if desired, the value of C for use in the equation. 4. If data for two vapor pressures, or for one vapor pressure and the latent heat are known as in the previous paragraphs 2 or 3, values may be substituted in the basic equation, log P = m log P' C, and solved algebraically for the values of the coordinates, m and C, of the pivot point.
+
Use of Nomogram The nomogram gives vapor pressures directly in millimeters of mercury and in atmospheres corresponding to temperatures in degree centigrade or Fahrenheit. It is not convenient to calibrate more than two terms of vapor pressure on the left or pressure scale of Figure 1 ; thus values in other pressure units must be obtained by usual conversion. This may be done by pushing the calibrations up or down by a distance equal to the logarithm of the conversion factor -i.e., an addition or subtraction of logarithms. Values in the last two columns of Table I1 are not for use with the nomogram, but only with the basic equation, as indicated before. Vapor Pressures. As usual, in using a nomogram such as Figure 1 the pivot point is first located from values of m and Cat, in the first two columns of Table I1 or by one of the other methods described previously. To find vapor pressure, a straightedge is laid (or a fine black thread is stretched) from this pivot point to the intersection on the temperature scale in degrees centigrade or Fahrenheit. Extension of this line gives the pressure desired a t the intersection on the left scale in millimeters of mercury or atmospheres. Reversal of the process gives the temperature corresponding to a given pressure. Values have been determined for various points of vapor pressure for different compounds from the nomogram and also by
Table II.
Vapor Pressures of Some Organic Compounds (Continued)
Compound Propyl benzoate Diethyl adipate Diisobutyl oxalate Isoamyl isovalerate Isobutyl benzoate Bornyl formate Geranyl formate Neryl formate Menthyl formate 2-Ethyl hexyl acrylate Octyl acrylate Isoamyl benzoate Geranyl acetate Linalyl acetate Citroneryl acetate Menthyl acetate Dimethyl sebacate Diisoamyl oxylate Bornyl propionate Bornyl butyrate Bornyl isobutyrate Geranyl butyrate Geranyl isobutyrate Formamide Nitromethane Tetranitromethane Acetonitrile Methyl thiocyanate Methyl isothiocyanate Acetamide Acetaldoxime Ethylamine Nitroethane 1,2-Ethanediamine Acrylonitrile Propionitrile Ethyl isothiocyanate 2-Bromo-2-nitrosopropane Ethyl carbamate 1-Nitropropane 2-Nitropropane Propylamine 3-Butene nitrile cis-Crotonitrile trans-Crotonitrile Methacrylonitrile Allyl isothiocyanate Diacetamide Ethyl methyl carbamate Propyl carbamate Diethylamine 3-Bromopyridine 2-Chloropyridine Tiglonitrile Angelonitrile Ethyl cyanoacetate Piperidine Isobutyl carbamate Isoamyl nitrate 2,4,6-Trichloroaniline Nitrobenzene 2-Chloroaniline 3-Chloroaniline 4-Chloroaniline 2-Nitroaniline Aniline 2-Picoline 1,3-Phenylenediamine Phenylhydrazine Benzonitrile Phenyl isocyanide Phenyl isocyanate Phenyl isothiocyanate Benzylamine 2-Toluidine 2-Tolunitrile Phenyl acetonitrile 2-Tolyl isocyanide 4-Ethylaniline 2,4-Xylidine 2,6-Xylidine
Esters rh 1.279 1.659 1.394 1.141 1.380 1.278 1.362 1.336 1.253 1.298 1.379 1.411 1.469 1.312 1.644 1.319 1.740 1.507 1.385 1.437 1.412 1.706 1.659
C, Mm. Hg. C , Lb./Sq. In.
C, Atm. - 1.853 -2.520 -2.003 -1,291 -2,065 - 1.673 - 1.963 - 1.868 - 1.694 -1.721 - 1.956 -2.370 -2.268 - 1.785 -2.193 -1.871 -3.284 -2.562 -2.052 -2.257 -2.178 -2.810 -2.655
-2.710 -4.421 - 3.138 - 1.697 -3.161 -2.475 -3.008 -2.839 -2.425 -2.580 -3.050 -3.556 -3.621 - 2.686 -4.048 - 2.791 -5.416 -4.029 - 3.164 -3.516 -3.366 - 4.846 - 4.554
-2.179 -3.290 - 2.462 - 1,456 - 2.509 - 1.998 - 2.386 - 2.262 - 1.990 - 2,069 -2.399 -2.850 -2.816 -2.150 - 2.944 - 2.243 -4.148 -3.154 -2.502 -2.767 -2.659 -3.635 -3.425
.ogen Compobunds 1.687 - 2.158 0.875 -0.015 0.974 -0.357 f0.226 0.760 -0.421 0.914 -0.243 0.879 1.445 - 1.990 1.092 -0.243 0.647 +l.llS 0.917 -0.191 1.019 -0.258 0.731 f0.260 0.830 4-0.037 0.962 -0.422 0.903 $0.252 1.349 -1.396 0.962 - 0.429 0.917 -0.271 0.700 f0.663 -0.250 0.900 -0.103 0.857 -0.296 0.899 0.761 +O. 118 1.032 -0.702 1.491 -2.052 1.234 - 1.102 1.451 - 1.654 +0.569 0.713 1.082 -1.035 1.076 -0.963 0.830 -0.265 0.951 -0,522 1.666 - 2.066 0.858 -0.078 1.463 - 1.814 1.065 -0.685 2.404 -4.037 1.214 - 1.550 1.229 -1.551 1.328 - 1.898 1.339 - 1.932 1.654 -3.028 1.1732 -1.218 0.982 -0.403 1.560 -2.867 1.428 -2.207 1.159 - 1,272 1.066 -0.896 1.049 -0.889 1.252 - 1.687 1.179 -1.226 1.231 -1.457 1.181 -1.457 1.327 - 1.949 1.1395 -1.173 1.319 - 1.764 1.354 -1.741 1.223 - 1.642
-4.139 $0.343 - 0.282 +0.917 -0.173 -0.104 -3.273 -0.511 12.135 $0.046 -0.313 $1.033 4-0.527 -0.328 $0.528 -2.403 -0.312 -0.032 $1.525 $0.035 $0.306 -0.007 +0.803 -0.796 -3.460 - 1.776 -2.954 $1.394 - 1.273 - 1.183 $0.227 -0.385 -3.986 4-0.330 -3.149 -0.875 -8.082 -2.116 -2.211 -2.845 -2.909 -4.914 -1.717 -0.353 -4.483 -3.441 -1.731 -1.088 -1.033 -2.414 - 1.744 -2.124 - 1.981 - 2.891 - 1.575 -2.684 -2.761 -2.287
-2.960 + O . 129 -0.327 +0.504 -0.321 -0.102 -2.510 -0.352 f1.530 -0.095 -0.280 +0.573 +0.235 -0.389 f0.363 - 1.804 -0.385 -0.174 +l.O12 -0.134 +0.062 -0.179 f0.398 -0.740 -2.626 - 1.375 -2.181 +0.903 - 1.132 - 1.052 -0.067 -0.468 -2.843 +0.087 -2.355 -0.762 -5.675 - 1.799 - 1.818 -2.281 -2.328 -3.792 -1.421 -0.383 -3.521 -2.707 -1.458 -0.973 -0.947 - 1.981 -1.436 -1.727 -1.669 -2.331 - 1.336 - 2.137 -2.154 - 1.903
( Continued on p age 134)
VOL. 49, NO. 1
JANUARY 1957
133
Table II.
Vapor Pressures of Some Organic Compounds (Continued)
Compound
Nitrogen Compounds Formula m C , Atin.
C , Mm. Hg. C , Lb./Sq. In.
Tetramethylpiperazine Diisobutylamine Quinoline Isoquinoline 4-Cumidine Triisobutylamine
CsHiENz C~HIYN CQH~N CsH7N CsHi3N CizH2;N
1.069 0.987 1.294 1.348 1.353 1.259
- 1 * 101
- 1.300
-0.539 - 1.942 -2.052 -1.918 - 1.240
-0.503 -2.789 -3.057 -2.936 - 1.988
-2.459 -2.330 - 1.543
2,3,4,6-Tetrachlorophenol
CsHzC140 c sH3C130 CsHsClsO CsHdClzO CeH4C120 CsHsClO CsHaClO CsHsNOs CsHsO CsHsOn C:HsOz CsHioO CBHI~O CsHioO CsHioOz CYHiz0 CsHiZO CsHi20 CIOHI;~ CioHsO CioHsO CioHirO CmHi40 CmHiaO
Phenols 1.641 1.3702 1.480 1.361 1.404 1.037 1.224 1.290 1.258 1.453 1.397 1.297 1.442 1.415 1.294 1.387 1.404 1.467 1.412 1.519 1.522 1.492 1.433 1.328
-2.902 -2.219 -2.317 - 1,734 - 1.910 -0.974 - 1.602 - 1.692 - 1.275 -2.267 - 1.719 - 1.626 - 1,887 - 1.913 - 1.705 - 1.819 - 2.000 -2.094 -2.053 -2.760 -2.820 -2.231 -2.199 - 1.892
-4.751 -3.286 -3.703 -2.774 -3.076 - 1* 081 -2.247 -2.528 -2.020 -3.574 -2.865 - 2.483 -3.161 -3.111 - 2.552 -2.934 -3.165 - 3.441 - 3.240 -4.256 - 4.324 -3.650 -3.447 -2.836
-3.651 -2.651 -2.878 - 2.155 -2.382 - 1.017 - 1.863 -2.031 - 1.577 - 2.796 -2.183 - 1.973 - 2.403 -2.398 - 2.048 -2.271 -2.472 - 2.639 - 2.534 - 3.366 -3.429 - 2.806 - 2.704 - 2.274
$1.685 $1.299 $1.772 $1.848 +0.449 $0.309 $1.129 - 2.400 +1.342 +0.060 t o . 171 $0.466 71.413 $1.655 $1.326 - 1.681 i-0.602 $0.093 -0.330 $1.283 -2.426 $0.659 +0.308 -0.568 $0.399 - 1.828 - 1.383 -0.351 -0.975 -0.328 -0.489 - 2,223 $0.039 +0,852 - 0.700 -2.476 - 1.936 -0.622 + O . 158 - 0.042 -2.336 -1.711 -0.821 - 1.743 - 1,152 - 2.172 - 0.336 -0.626 - 3.899
$1.053 $0.763 +1.121 1.1.239 +O. 163 $0.129 $0.679 - 1.940 4-0.779 -0.117 -0.069 -0.184 $0.880 1.1.066 +0.890 - 1.436 $0. 151 -0.101 -0.383 $0.852 - 1.949 $0.361 $0.050 -0.619 +0.175 - 1.562 - 1.149 +0.148 -0.914 -0.431 -0.556 - 1.842 -0.094 $0.416 -0,586 - 1.902 - 1.643 - 0.607 -0.052 -0.222 -1.981 - 1.462 - 0.801 - 1.423 - 1.023 - 1.668 - 0.438 -0.664 - 3.255
2,5,4-Trichlorophenol 2,4,6-Trichlorophenol 2,4-Dichlorophenol 2,6-Dichlorophenol 2-Chlorophenol 3-Chlorophenol 2-Nitrophenol Phenol Pyrocatechol 2-Methoxyphenol 2-Ethylphenol 3-Ethylphenol 4-Ethylphenol 4,6-Dimethylresorcinol 2-Isopropylphenol 3-Isopropylphenol 4-Isopropylphenol Thymol 1-Naphthol 2-Naphthol 4-Isobutylphenol 4-see-Butylphenol 2-see-Butylphenol
Carbon disulfide Methyl trichlorosilane Methyl dichlorosilane 2-Methyldisilazane Trichloroethoxysilane Trichloroethylsilane Dimethyldichlorosilane Dime thylantimony 2-Ethyldisilazane Allyltrichlorosilane Trichloroisoprop ylsilane Dichloroethoxymethylsilane Trimethylchlorosilane Trimethyldiborane Trime thylgallium Trimethyl phosphate Selenophene Diethylzinc Dichlorodiethylsilane Diethyldifluorosilane Diethyl sulfate Diethyl sulfide Tetramethyllead Allyldichloroethylsilane Trifluorophenylsilane Trichlorophenylsilane Benzenethiol Hexamethyldisiloxane Diallyldichlorosilane Diallyl sulfide Chlorotriethylsilane Triethyl phosphate Diethoxydimethylsilane Trimethylpropylsilane Hexamethylcyclotrisiloxane Benzyldichlorosilane Dichloromethylphenylsilane Triethoxymethylsilane Butyltrimethylsilane Triethylmethylsilane
Dichloroethylphenylsilane Chlorodimethylphenylsilane Dimethylphenylsilane Dibutyl sulfide Tetraethoxysilane Tetraethyllead Amyltrimethylsilane Tetraethylsilane Tetraethylbistibine
1 34
Metal Organic Compounds 0.631 $0.623 0.687 f0.398 0.620 +0.678 0.645 f0.825 0.833 - 0.030 0.894 $0.007 0.737 1.0.373 1.268 - 1.627 0.671 f0.396 0.896 -0.236 0.859 -0.232 0.835 -0,007 0.689 $0.517 0.656 $0.664 0.745 4-0.593 1.143 - 1.269 0.736 - 0.156 0.886 -0.234 0.968 -0.419 0.748 4-0.559 1.278 - 1.624 0.826 t o . 159 0.849 -0.125 0.970 -0,654 0.869 $0.023 1.155 - 1.380 1.136 -0.990 0.881 +0.010 1.035 -0.873 0.939 -0.501 0.9604 -0,603 1.228 - 1.575 0.921 -0.186 0.745 4-0.119 1.066 -0,508 1.335 -1.511 1.171 - 1.443 1.008 -0.598 0.877 - 0.195 0.895 -0.345 1.207 -1.739 1.145 -1.292 1.012 -0.787 1.187 - 1.204 1,073 -0.941 1.293 - 1.326 0.940 -0.507 0.977 -0.691 1.375 -2.817
INDUSTRIAL AND ENGINEERING CHEMISTRY
- 1.181 -0.524
- 2,285
the equation. These values have shown general closeness to literature values and are within the usual variation between different literature sources. Vapor Pressure for Members of Homologous Series. The relationship between lines of vapor pressures for members of homologous series on the usual logarithmic reference plot has been discussed previously ( I 7). From this it follows that a series line is formed by connecting with a straight line the known pivot points or drawing the straight line which best represents the pivot points of more than two members. If the boiling point or other single vapor pressure point is known for some other compounds of the same homologous series, the corresponding line between the two scales \vi11 intersect the series line to give its pivot point and its values of m and C. Similarly, if latent heat is known or calculable by any of the standard methods of approximation, the m line is fixed for the compound ; its intersection wirh the series line gives the desired pivot point and the value of C for use in the equation. By similar triangles it may be shown that any straight line on this grid may be represented by linear equations the same as for standard Cartesian coordinates; henct, the equations may be given for the series lines if desired. For example, a straight line joining two points on the grid-at the top? C = 1 1 . 5 0 and m = 0.800; a t the bottom: C = -2.50 and rn = 1.49-is the locus, within small error, of the pivot points of the normal aliphatic alcohols. Also, the pivot points of the normal primary aliphatic acids such as formic or acetic, fall on the line joining C = +1.50 and m = 0.395 a t the top; and C = -2.50 and m = 1.700 a t the bottom. T h e equarions of these lines are Alcohols C = -5.800m - 3.140 Acids C = - 3 . 0 6 7 ~ ~ 0.290
+
If these expressions for C are substituted in the general equation, the relationship is for alcohols m(log P’ - 5.800) - 3.140
log P
and for acids, log P
=
m(log P’
-
3.067)
+ 0.290
These are general vapor pressure equations for any member in their series. Thus, if a t only one temperature, the vapor pressure or latent heat of a compound is known: the whole range can be calculated. If no data, not even a boiling point, are available for a member of a homologous series: an interpolation or extrapolation to determine the pivot point may be made within reasonable error, since the points for adjacent members fall apart by distances which vary in a regular, although not always strictly proportional, pattern.
Vapor Pressure a n d Latent Heat of Hydrocarbons. The pivot points for all hydrocarbons (straight-chain, branched, or cyclic) fall very near a straight line, as would be expected (29). This, the hydrocarbon line, falls across the center grid from the point on the top where m = 0.445 and C = 1.50 to the point on the bottom where m = 1.45 and C = -2.50. The equation of this line on the coordinates of the central grid is C = -3.980 m 3.270, Thus, for any hydrocarbon, only vapor pressure-eg., the normal boiling point -is necessary, since its line between the scales will intersect the hydrocarbon line at its pivot point. A single latent heat value giving the m line will also indicate the pivot point for the compound by its intersection with the hydrocarbon line. Conversely, the latent heat a t any temperature for the hydrocarbon is determined, using only a single vapor pressure, by taking the m value of the pivot point. As for the other series lines, substituting the equation for the hydrocarbon line into the general equation yields
+
log
P
=
m (log P'
-
+ 3.08
If the boiling (bubble) point a t any pressure of any petroleum mixture is known, the line between the temperature and pressure scales will intersect this petroleum mixture line to give a pivot point. This pivot point may then be used the same as for a pure compound. As for the series lines, the equation of the petroleum mixture line may be substituted in the general equation to yield finally log P
m(log P' - 3.87)
+ 3.08
This, therefore, is the general vapor pressure equation for any petroleum mixture; only one vapor pressure or bubble point must be known to determine the entire range. Equilibrium Flash Vaporization. The boiling temperature of a petroleum crude or fraction in a continuous still a t a k e d pressure depends on the percentage of the total which is continually vaporiz-
Vapor Pressures of Some Organic Compounds (Continued) Metal Organic Compounds Formula m C , Atm.
Compound
C, Mm. Hg. C, Lb./Sq. In.
1,3-Diethoxytetramethyldisiloxane
CsHtzOsSiz
1.160
-0.884
-1.219
-1,020
CsHzaClzO&4 CsH2404Si4
1.307 1.078
- 1.798
- 2.684
- 2.157
-0.727
-0.953
-0.818
CsH~aO4Sia
1.157
- 1.048
-1.502
-1.232
CgHlaClOSi CeHzlSi CsHzzSi CioHzzS C10H24Si CloHzaSi
1.238 1.019 1.079 1.238 1.107 1,129
- 1.603
-2.290 -0.891 - 1.224 -2.329 - 1.453 -1.629
-1.881 -0.857 - 1,089 - 1.920 -1,270 - 1.407
1,7-Dichloroctamethyltetrasiloxane Octamethoxytrisiloxane
Octamethylcyclotetrasiloxane
Chloroethoxymethylphenylsilane Hexyltrimethylsilane Triethylpropylsilane Diisoamyl sulfide Heptyltrimethylsilane Butyltriethylsilane
-0.834 -0.997 - 1.642 - 1.145 - 1.256
Decamethylcyclopentasiloxane Decamethyltetrasiloxane
CloH8006Si5 CioH~oO3Si4 Diethoxymethylphenylsilane CllH1802Si Trimethyloctylsilane CIIHZBS~ Amyltriethylsilane C11HzeSi Difluorodiphenylsilane ClzHloFzSi Tetraethoxyphenylsilane ClzHzoOsSi Triethylhexylsilane C12HzsSi 1,7-Diethoxyoctamethyltetrasiloxane Dodecamethylpentasiloxane ClzH&&is Dodecamethylcyclohexasiloxane C12H360 6si 6
+ 3.270
3.980)
This is the general vapor pressure equation for any hydrocarbon. I t can be solved if only one vapor pressure point or one latent heat is known. Vapor Pressure a n d Latent Heat of Petroleum Mixtures. Vapor pressures and latent heats of all petroleum mixtures, whether crudes, distillates, side streams, or bottoms, may also be correlated with a straight line o p the nomogram. This, the petroleum mixture line, intersects the hydrocarbon line and both give values which are nearly the same throughout much of their usable lengths. The petroleum mixture line extends from a point where m = 0.408 and C = i-l.50 to a point where m = 1.44 and C = -2.50. Its equation is Catrn= -3.87m
Table II.
Table 111.
Mole %, 5 10 15 20 25
"3
0.733 0.746 0.735 0.717 0.693
-1,351 -1.815 - 1.524 - 1.573 -2.178 -2.147 - 1.813
-2.369 - 1.926 -2.865 -2.286 -2.226 -3.190 -3.477 -2.556
-1.917 - 1.584 - 2.240 - 1.833 -1.837 -2.588 -2.588 -2.114
1.443 1.345
-2.050 -1.831
-3.327 -2.825
-2.567 -2.234
1.394
-2.074
-3.209
-2.534
Partial Pressure of Some Gases in Liquids
HC1
Wt.3 % HC1 10 20 30 40
- 1.609
Aqueous Ammonia Partial Pressure Hz0 Cat, m Cat, -0.070 0.999 -0.025 +0.216 1.000 -0.050 f0.432 1.001 -0.077 -I-0.619 1.002 -0.106 i-0.790 1.004 -0.134
m
3"
1.263 1.199 1.364 1.264 1.226 1.351 1.461 1.258
m
Cstm
0.840 0.812 0.778 0.746 0.715
+0.256 1-0.405 f0.551 f0.695 f0.840
Aqueous Hydrochloric Acid Partial Pressure HzO -2.43 -1.2 $0.04 +l.O
Total Pressure
m
Cat,
m
Cstm
1.01 1.02 1.06 1.16
-0.05 -0.18 -0.39 -0.68
1.14 1.06 1.13 0.82
-0.04 -0.14 +0.17 +1.06
cat,
1.78 1.48 1.15 0.79
Total Pressure
m
Aqueous Nitric Acid Partial Pressure
Wt. %, "01 30 40 50
60 70 80 90 100
G. SOz/ 100 G. Hs0 1 2 4 6
"01
HzO
~
m 1.6 1.45 1.31 1.19 1.05 0.98 (0.91) (0.86)
Cat, -2.1 -1.7 -1.34 - 1.04 -0.70 -0.35 (-0.05) (+0.2 1)
so2 m
10 20 30 40 50 60
...
C*tm -0.12 -0.21 -0.29 -0.43 -0.60 -0.85 - 1.34
...
Total Pressure m Catm 1.03 -0.11 1.04 -0.18 1.04 -0.28 1.05 -0.34 1.02 -0.37 1.01 -0.24 (0.90) (- 0.03) (0.86) (fO.21)
Aqueous Sulfur Dioxide Partial Pressure Hz0 Catrn
0.59 0.60 0.60 0.60
m 1.03 1.04 1.05 1.04 1.04 1.03 1.03
-0.13 +o. 19 +0.51 $0.70
m
Cat,
Total Pressure m
0.00 0.74 0.00 0.68 0.00 0.63 0.00 0.61 Fuming Sulfuric Acid Partial Pressure 80s m Cat, 102.25 1.800 -1.00 104.50 1.680 -0.745 106.75 1.400 -0.100 109.00 1.090 +0.300 111.25 1.020 +0.580 113.50 1,010 f0.795 1.0 1.0 1.0 1.0
VOL. 49, NO. 1
C*tm +0.21. f0.38 f0.59 +0.75
JANUARY 1957
135
Table IV.
Henry’s Law Constant for Gases Temp. Jiange,
Gas
Formula C2Hz Brz
Acetylene Bromine Carbon dioxide Carbon dioxide Carbon monoxide Ethane Ethylene Hydrogen sulfide Nitrous oxide Propylene
coz co COY
5-55
C~HG CzHd HsS Nz0 CaHs
Table V.
c.
0-30 0-50 0-30 30-60 5-50 0-30 0-55 5-35 2-18
m
C
0.35 0.72 0.47 0.39 0.23 0.41 0.41 0.37
-1.22 $0.06 -0.95 -1.06 -1.77 -1.8 -0.20 $0.41 -0.77 -0.29
0.50
0.49
H Atm./;LIol. Frac., Mm. Hg Times 100 1
100 100 10,000 10,000 100 1 100 100
Partial Pressures of Adsorbed Vapors on Charcoal
Compound
Concn., G./G. Char c o SI
m
C
Acetone
CnH60
0.10 0.20 0.30 0.40
1.00 0.95 1.01 0.93
-1.77 -1.12 -0.52 +0.35
Methyl ethyl ketone
CdHsO
0.10 0.20 0.30 0.40 0.50
1.13
-2.54
1.10 1.07 1.01 1.28 1.23 0.40 0.74 0.86 0.95 1.01 0.85 0.77 0.91 0.70 0.77 0.83 0.87 0.90
-1.42 -0.77 $0.05 -2.80 -1.84 -1.55 -1.08 -0.94 -0.68 -0.32 -1.64 -1.60 -0.38 -1.83 -1.42 -1.09 -0.82 -0.45
Formula
Methyl isobutyl ketone
CjHizO
Methanol
CH30H
Diethyl ether
ClHioO
Carbon disulfide
CS?
ing. A common plot at constant pressures is of boiling temperatures versus per cent vaporized. ,4 corresponding cross plot (29)on logarithmic paper for a constant percentage vaporized of total pressures against a temperature scale derived from the vapor pressure of a reference substance gives straight lines which intersect in a common point. For a certain fixed amount of vaporization such as 50c;F, a line between the temperature and pressure scales will intersect the petroleum mixture line, Catm = -3.87m 3.08, to give a pivot point. Other lines through this point give all other values of equilibrium temperatures and pressures when 50% of the original mixture is being vaporized. These values suffice for most design work, since they have a probable accuracy better than that of usual experimental data. The entire range of boiling points at any fixed pressure of different percentages vaporization may be found similarly from the petroleum mixture line if there are known the temperatures of distillation after any given amount of vaporization at one experimental pressure; usually atmospheric. For any mixture known to consist entirely of hydrocarbons, the locus of
+
1 36
0.20
0.30 0.02 0.04 0.06 0.10 0.20 0.10 0.20 0.30 0.10 0.20 0.30 0.40 0.50
...
...
the pivot points determining thc vapor pressure-temperature relationship, either initially or after any percentage vaporization, is the hydrocarbon line giving slightly different values from the petroleum mixture line. I n either case, the effective molar latent heat of any petroleum mixture or after any percentage of vaporization may be picked off immediately from the value of m corresponding to the pivot point. An average or effective molecular weight may be estimated to convert this to the latent heat per pound, either from other considerations or by taking the molecular weight of a known hydrocarbon which may be used as typical for the mixture: and which has a pivot point a t about the same point on the petroleum mixtures line, or the hydrocarbon line. Such a simple determination is of the same order of accuracy and more readily done than the approximations by much more involved means. Gas Solubilities. Data for gases dissolved in liquids are available ( 7 ) . Such data are best presented as partial pressures at various temperatures of fixed concentrations, rather than as isotherms in varying concentrations. Partial pressures of gas not in solution may be cor-
INDUSTRIAL AND ENGINEERING CHEMISTRY
related just as are other vapor pressures (70, 13, 24). Therefore, the partial pressure for a fixed concentration of gas can be determined at any temperature from a pivot point located in the %rid on the nomogram (Figure 1). Here, the value of m relates to molar heat of dissolution (or escape) of the gas from the solution; the relations above considered for m and C are applicable. Different pivot points for each concrntration of gas in the solution form a line in the center grid, which is not necessarily straight. I n cases of major abnormalities from hydration or othcr compound formation, there may- be sharp curves in the line defining the location or the pivot point. For convenience, values of m and C are given in Table I11 for solution of various gases at several different concentrations, and iniermediate concentrations \vi11 have pivot points between them. Here, as for other physical properties discussed hereinafter, the original data were usually considered not \vel1 enough established to warrant values of m and C closer than tiuo decimal points. Here again. the corrclation is believed to be capable of greater precision when better data are available. Similarly, values of the Henry’s l a ~ v constant, which correlate gas solubilities, have a relation with temperature following the basic equation (24). Henry‘s laiv constants may be determined by taking values from the left or vapor pressure scale which is calibrated in millimeters. These values must then be multiplied by a factor, individual for each gas as given in Table IV. Temperature ranges of the pivot points for the various gases are indicated lor which the correlation holds: since this “constant” actually changes its relation with temperature for some gases. This is indicated bv two or more straight sections of a broken line on the usual logarithmic plot (24),or by two different pivot points on the nomogram for different temperature ranges. Gas Adsorption. The adsorption equilibria of solvent vapors on solid adsorbents also may be regarded as a vapor pressure function of temperature for a fixed concentration of solvent vapor (adsorbate) on the solid adsorbent (20). The coordinates of pivot points are listed in Table V for various vapors adsorbed on activated carbon ( 2 6 ) . Each fixed concentrarion exerts i t s corresponding vapor pressurejust as if it were a separate compound. The molar heat ol adsorption controls m and is determinable therefrom. A line which may not be straight, is formed on the center grid by the pivot points for different concentrations of any adsorbate on any adsorbent. An intermediate concentration may be interpolated to obtain the corresponding pivot point. Solutions of Nonvolatile Solutes. Vapor pressures for solvents out of solutions containing nonvolatile soiutes may
Table VI. Concn.,
Vapor Pressures of Aqueous Solutions of Solids
Molality
m
C,,
Cam
Cpsia
Sodium Hydroxide Solutions in Water -0.014 -0.028 -0.051 -0.081 -0.111 -0.147 -0.201 -0.253 -0.289 -0.360 -0.433 -0.513 -0.613 -0.705 -0.757 -0,826 -0.921
-0.016 -0.031 -0.051 -0.075 -0.101 -0.134 - 0.168 -0.208 -0.232 -0.280 -0.327 -0.376 -0,449 -0.504 -0.539 -0.592 - 0.652
Sodium Chloride Solutions i n Water 1.003 0.000 0.000 -0,023 1.001 -0.021 -0.004 0.991 -0.030 - 0.040 0.999 -0.044 -0.057 -0.057 1.000 1.003 -0.071 -0.079 1.007 -0.086 -0.106 1.011 -0.132 -0.101 -0.177 1.021 -0.117
0.000 -0.022 -0.020 -0.043 -0.057 -0.074 -0.094 -0.114 -0.142
0.999 0.998 1.000 1.004 1.006 1.008 1.019 1.026 1.033 1.047 1.062 1.080 1.096 1.117 1.127 1.137 1.157
1
2 3 4 5 6
7 8 9 10 11 12 13 14 15 16 17 0.684 1.369 2.050 2.765 3.435 4.100 4.785 5.465 6.155
-0.017 -0.034 -0.051 -0.070 -0.094 -0.125 -0.146 -0.178 -0.194 -0.225 -0.255 -0,283 -0.337 -0.368 -0.391 -0,432 -0.469
Peterson, Robert A. Gere, and David Zudkevitch for their help in drafting, compiling tables, and plotting, and to the Esso Education Foundation for its grant of funds for supporting part of this and related projects in this field. Acknowledgment is due to Interscience Encyclopedia Inc., for the original draft of the nomogram which appeared in an earlier form in the Encyclopedia of Chemical Technology.
References Chemical Engineers’ Handbook (J. H. Perry, editor), 3rd ed., McGrawHill, New York, 1950. Doolittle, A. K., “Technology of Solvents and Plasticizers,” Wiley, New York, 1954. Dreisbach, R. R., Spencer, R. S., IND.ENG.CHEM.41, 176 (1949). Gilmont, R., Weinman, E. A . , Kramer, F., Miller, E., Hashmall, F., Othmer, D. F., Zbid., 42, 120 (1950).
Jenkins, A. G., Chambers, G. F., Zbid.,46, 2367 (1954). Jordan, .T. E., “Vapor Pressure of Organic Compounds,” Interscience, New York, 1954. Killeffer, D. H., IND. ENG. CHEM. 30, 565 (1938).
Sucrose Solutions in Water
Mvers. H. S.. Zbid.. 47. 1659 (1955) MGers; H. S . , Fenskd, M. R . , Zbid.,
Concn., Wt. % (” Brix) 25 30 45 60 75.2 80.4
1.000 1.001 1.001 1.003 1.006 1.011
- 0.006 -0.009 - 0.022 -0.046 -0.120 -0,146
also be obtained from this nomogram. Each different concentration will have a pivot point which is characterized as before, describing the entire vapor pressuretemperature relationship for each specific solute concentration. These points may be connected by a line not necessarily straight, that enables interpolation for points of intermediate concentration. m and C values, calculated from accepted experimental data (24),are listed in Table V I to serve as examples. The partial heat of solution (70, 75) at any concentration may be calculated from
-
H = - L ( 1 -rn)
5
J
where is partial heat of solution of the solvent-water (positive for heat evolved) and L is molal latent heat of pure solvent, water, a t the same temperature. These L values may be obtained from Table I. Functions Related to Vapor Pressure. The same or a modified nomogram can be used immediately for a large number of other functions related to vapor pressures. I t is only necessary to observe the applicable units and range requirements on the left or property scale. T h e pivot point may always be determined by plotting intersections of lines for two or more sets of data or otherwise, as before. Functions for which the nomogram may be used include dehydration and similar reaction
-0.006 -0.010 -0.026 - 0.055 -0.121 - 0.178
47, 1652 (1955).
-0.006 -0.009 -0.023 -0.050 -0.126 -0.159
pressures ( 7 7, 79), vapor compositions ( 7 7)) vapor-liquid equilibrium constants (72)) and relative volatilities and activities (4, 76). Functions of azeotropic mixtures may also be indicated, including partial pressures, total pressures, vapor compositions, and activities (27). Properties such as heats of reaction, solution, and vaporization are always related and determinable as from the original plots. Other Functions. Other functions which also are immediately correlated by and usable with the nomogram include solubilities and liquid-liquid distribution coefficients (ZZ), diffusivities in liquids (23), chemical equilibrium and reaction rate constants (79), viscosities of liquids (74) and gases (78))permeabilities of plastic membranes (75) and paper. Many additional tables could be developed for m and C values for all the different functions related to vapor pressure and other functions which give straight lines on a logarithmic plot on a temperature scale derived from the vapor pressure of water; such values of m and C may be obtained readily for each function and each system. I n many cases, Table I will help in evaluating heat functions peculiar to the relationship concerned.
Acknowledgment Thanks are expressed to Marvin A.
Othmer, D. F., Chem. Met. Eng. 47, 551 (1940).
Othmer, D. F.. IND. END. CHEM. 32, 841 (1940):
Zbid.. 36.669 f1944) Othmer; D. F., Benenati, R. F., Zbid., 36, 375 (1944). Othmer, D. F., Conwell, J. W., Zbid., \
,
37,1112 (1945).
Othmer, D. F., Frohlich, G. J., Zbid.. 47. 1034 (1955). Othmer, D. F.,‘ Gilmont, R., Zbid., 36, 858 (1944). Othmer, D. F., Gilmont, R., Petrolcum Refiner 30, Ibid., 111 (1951); 31, 107 (1952). Othmer, D. F., Josefowitz, S.,IND. ENG.CHEM.38,111 (1946). Othmer, D. F., Luley, A. H., Zbid., 38,408 (1946).
Othmer, D. F., Sawyer, F. G., Zbid., 35,1269 (1943).
Othmer, D. F., Ten Eyck, E. H., Zbid.,41, 2897 (1949). Othmer, D. F., Thakar, M. S., Zbid.,44,1654 (1952). Zbid., 45, 589 (1953). Othmer, D. F., White, R. E., Zbid., 34, 952 (1942).
Perry, J. H . , Smith, E. R., Ibid., 25, 195 (1933).
Sawyer, F. G., Othmer, D. F., Zbid., 36, 894 (1944).
Sondak. N. E.. Thodos. George. A Z C h E J. 2, 347 (1956). ’ Stull, D. R., Ibid.,39, 517 (1947). Ten Eyck, E. H., Othmer, D. F., Petroleum Rejner 10, 151 (1953). V
I
RECEIVED for review December 8, 1954 ACCEPTED April 7, 1956 Previous articles in this series have appeared in IND.ENG.CHEM.during 1940, 1942-46, 1948-51, 1953, 1955; Chem. Met. Eng., 1940; Chimie @ Industrie (Paris), 1948; Euclides (Madrid), 1948; Sugar 1948 ; Petroleum Refiner, 1951-53 ; World Petroleum Congr. Proc., 3d Congr., Hague, 1951; Proc. Inter. Congr. Pure and Appl. Chem., 11th Congr., London, 1947.
VOL. 49, NO. 1
JANUARY 1957
137
