Correlating Vapor Corn ositions and Related Pro erties of S o h USE OF CRITICAL CONSTARTS DONALD F. OTHNER AND ROGER GILhIOIVTl Polytechnic I n s t i t u t e of B r o o k l y n , B r o o k l y n , S. Y.
A
A method is presented for expressing as a sheaf of data and in some cases elecstraight lines, data for binary solutions representing developed a general trochemical data also could and simple method of corequilibrium conditions o f temperature, pressure, and be worked in t o build up compositions of the liquid and vapor phases. The correlarelating vapor pressures of knowledge sufficient t o give tion is excellent throughout the entire range, including the liquids on a logarithmic plot a working level for engicritical. Lines of constant compositions in the liquid against the vapor prcssures neering purposes and t o check phase are drawn on log paper for a plot of the relative of a reference liquid always the interrelated data obtained volatilities against the ratios for a reference substance of at the same temperature. from different research inthe specific volume of the vapor to the specific volume of The method of plotting was s t r u m e n t s a n d methods the liquid, all at the same value of the reduced temperaas follows: Sclect a sheet of against each other for evaluature. For all binary systems studied, these lines were standard logarithmic paper tion of techniques as wcll and calibrate on the X axis straight; this allows ready interpolation, extrapolation as results. and evaluation of experimental data. Other methods of (against the logarithmic logarithmic plotting with a reference substance are indigraduations) c w n values of CRITICAL CONDITIOYS FOR rated and mal be used in some cases, but do not always give temperatures corresponding A BINARY MIXTC'RE the desired straight-line correlation. to the vapor pressures of a The critical point for a tworeference liquid; erect temphase heterogeneous system oerature ordinates at these in equilibrium is, according to Gibbi, that point a i which the copoints; and plot on these temperat,ure ordinatcs thc rorrespondirig existent phases just disappear and become one and the same values of vapor prefisure data in question on the standard graduaphase. For a pure liquid in equilibrium with its vapor, this point tions indicated on the Y axis. Lines substantially straight is clearly defined as that temperature at which the physical over \Tide ranges were obtained for all types of vapor pressure boundary bet,ween the liquid and vapor just disappears and the data investigat,ed. two phases become one and the same-namely, the gas phase. Later papers shoxed that, by plot,t.itig values of normal vapor In the case of a binary mixture of two pure liquids, the critical pressures ( 2 ) or of reduced pressures ( 6 ) against reduced tempoint becomes a function of composition and is defined in cxact,ly peratures, a better correlation was obtained, particularly in the t>hesame way for a mixture of definite composition. However, region near the critical. The lines so obtained me1 as the vapor composition is different from the liquid composition to the critical; a further advarit,age ( 6 ) \$-asthat all vapor pressure in which it is in equilibrium, tiTo curves rcsult of pressure against lines could be reduced to a sheaf of straight lines through a composition for a given temperature-that, is, one for the vapor common point. and one for the liquid. -It the critical point both compositions The method of plotting also was expanded further ('7) t o express become idcntical. the data for solutions containing two or more volatile components In Figure 1 the pressure against composition curv and to includc vapor compositions, equilibrium constants, activit,y for the liquid and vapor at different temperatures for the system coefficiei:ts, etc. The present study resulted from a desire t o methane-n-pentane (IO). Thc critical point varies with comapply t o the treatment of solutions of liquids the use of critical position; its locus is shon-xi by a dottcd line passing through the constants and to bring to this fic9ld t,he advailtages noted for maximum points of the isotherms. For a given isotherm of pure liquids. Figure 1, the liquid and vapor compositions in equilibrium a t a The methods which have been used previously for expressing given pressure are thc intersect'ions of the horizontal or constant the data a t equilibrium of the four variables P , T , 2 , and y (prespressure line and t,he isotherm; the liquid composition is the left sure, temperature, liquid romposition, and vapor composition) and the vapor composit,ion the right portion of the curve. As the always have required the use of many curved lines aiid surfaces critical point is approached, the vapor and liquid compositions in whatever methods of plotting Tvere used. These methods of approach each ot,her until they become idcntical at. the maximum expression have been greatly complicated by t,he relative awkpoint of the curve. wardness of such plots arid by the large amount of data required Ot,her critical loci also occur, such as the maximum pressure to establish any given system, as interpolation and extrapolation locus and the crit,ical condentherm locus. The maximum presalong sharp curves of unknown shape are impossible. If a method sure locus is readily interpreted by Figure 2, which is a plot of of plotting could be found which would reduce to straight pressure against temperature for lines of constant composition, lines or t o approximately straight lines all data of these fourcalled isosteres. A s the critical locus is defined by those composidimensional systems, considerable advantage n-odd accrue: tions occurring a t maximum pressures for constant temperat,uresin in the evaluation of experimental data; and in the expansion of Figure 1, it becomes the envelope of the isosteres in Figure 2. such data between or beyond themselves with straight lines. Thus, for a constant temperature, the composition which correFinally, because late,nt, heats and heats of solution are related sponds to a maximum pressure lies on this envelope. I n a recipto the slopes of t,he lines on t,hese logarithmic plots, calorimetric rocal manner, the maximum pressure locus is shown in Figure 2 1 Present address, Emil Greiner Company, 161 Sixth .4ve., Xew York, by a dott,ed line t,lirough the maximum pressure points of the N. Y. PREVIOUS paper ( 5 )
2118
November 1948
INDUSTRIAL AND ENGINEERING CHEMISTRY
2119
specific volume of the reference substance in the vapor phase to t h a t of the specific volume of the reference substance in the equilibrium liquid phase; all taken a t the same value of the reduced temperature.
A PRESSURE, PS/
I 2400
This last method of plotting, although more complicated, gives lines which are straight for every system tried; it seems t o be the most general method t h a t has becn found.
2000
,600
TOTAL PRES SURE PLOT
800
400
9
Figure 1.
Pressure-Composi tion D i a g r a m of M e t k a n e n-Pentane
isosteres, but it is shown by a n envelope of the isotherms in Figure 1 inasmuch as it is defined as the maximum pressure attainable by a constant composition phase. For this particular system, the maximum pressure occurs for the liquid phase, as the liquid curve is that portion of the isostere t o the left of the critical locus. The critical condentherm locus defines those pressures at which the isotherm reaches a maximum Composition or at which the isostere reaches a maximum temperature. It is interpreted readily by means of Figure 1 as the maximum composition at which condensation will take place if the vapor is compressed isothermally. All three loci coincide, if the pressure-composition diagram yields isotherms in which the vapor and liquid curves meet in points that are maximum compositions as well as maximum pressures. This is the case for the system ethanol-water. I n spite of the complications which occur in the critical region for multicomponent systems, the critical state still retains the definition according t o Gibbs; the calculations of reduced properties in the correlations described in this paper are based on this definition. GEVERAL METHODS OF APPROACH
I t is desirable to obtain a method of plotting of P , T , 2, and y data in a way that will allow their representation on a series of straight lines. Several methods based on the critical state have been attempted and with varying results for different systems. NaturalIy, it is desired to use a plot which is as simple as possible in order to minimize the calculations required. Several methods of plotting (all on logarithmic paper) have been tried:
A reduced piot is made for a binary system for the total res sures; the critical pressure and temperature are taken From known values for each composition. The isosteres are plotted for each desired composition against the reduced vapor pressure of a reference substance a t the same reduced temperature in the same way as has been done for a pure component (6). B plot is made of the relative volatility of the low boiling component in the liquid compared to the other component against the reduced vapor pressure of a reference substance at the same reduced temperature. A lot is made of a pseudo relative volatility against the reduce$ vapor pressure of a reference substance always at the same reduced temperature. The pseudo relative volatility (defined below) is used because the vapor-liquid equilibrium no longer extends over the complete range of composition in the critical region; the upper and lower limits of the compositions are the limiting points where the equilibrium line meets the x = y diagonal on the familiar vapor composition plot. A plot is made of the relative volatility against the ratio of the c
Following the previous technique (6),the logarithm of the reduced total pressure of the binary system at constant composition would be plotted against the logarithm of the reduced pressure of a reference substance (which may be one of the components of the system) ; both reduced pressures would be taken at the same reduced temperature. This would give a series of lines (isosteres) taken at suitable compositions to describe the system completely. All of these lines would pass through the origin, which represents the critical point for each isostere. The slope of each total pressure line in this reduced plot for a binary system would be equal t o the ratio of the reduced latent heat of the mixture in question t o the reduced latent heat of the reference substance. QPR€ssuR€,PS/. I
"
F i g u r e 2.
"
"
"
'
~
'
1
Pressure-Temperature Diagram of M e t h a n e - n - P e n t a n e
T o make this plot, the critical pressure and temperature must be known for the mixture of the composition of each different isostere. Unfortunately, there are very few binary systems for which such information is available experimentally. Moreover, no simple relation exists between these variables and the critical constants for the pure components, a s is apparent from the systems for which data are available. Kay's rule (4)which assumes that t h e critical value for the mixture is the average of those for the pure components weighted according t o mole fraotion, is about as applicable as Raoult's law, of which i t is a specific case.
ETFIANOL-WATER.This is one of the systems for which sufficient data were available t o enable the coristruction of the reduced logarithmic plot. The data of Griswold et al. (3) at higher than atmospheric pressures and of Carey and Lewis ( 1 ) at 1 atmosphere pressure were used. Vapor pressures of pure water and pure ethanol were taken from the handbooks. The method of converting the data t o reduced form is indicated clearly by Table I. A grhph of total pressure was first made against composition from experimental data so that values a t constant compositions could be obtained readily for crossplotting. Thus, for convenient values of x, corresponding values of P and 2' are obtained and given in columns 2 and 3 of Table I with abso-
INDUSTRIAL AND ENGINEERING CHEMISTRY
2120
TABLEI. CALCULATION OF REDUCEDPROPERTIES, WATER-ETHANOL (Component 1: Ethanol)
P, Lh./ 21%
5
10
20
30
40
50
60
io
so
90
100
Sq. In.
14.7 100 293 692 1020 2920 14 7 113 324 756 1120 2660 14.7 125 360 843 1275 2240 14.7 133 384.5 902 1400 1905 14.7 139.5 403 942 1492 1640 14.7 144 416 975 1420 14.7 146.8 422 1000 1240 14.7 147.1 427 1012 1120 14.7 146 8 428 1015 1030 14.7 145 428 970 14.7 22 95 45.6 83.5 142.5 229.5 352 428 510 742 927
Temp.. OC. 91.4 150 200 250 275 357 86.5 150 200 250 275 342 83.3 154 200 250 275 319.5 81.8 150 200 250 275 30 1 80.6 150 200 2 50 275 286 79.9 150 200 2 50 273.5 79.2 150 200 250 264 78.6 150 200 250 257 78.2 150 200 250 251 78.1 150 200 246.5 78.3 90 110 130 150 170 190 200 210 230 243.1
Temp., OK. 364 423 473 523 548 630 359 423 473 523 548 615 356 423 473 523 548 592 354 423 473 523 548 574 353 423 473 523 548 559 352 423 473 523 546 352 423 473 523 537 351 423 473 523 530 351 423 473 523 52 4 351 423 473 519 331 363 383 403 423 443 463 473 483 503 516
~/TR 1.730 1.489 1,331 1.203 1.148 1.o
1.712 1.453 1.300 1.176 1.122 1.0 1.662 1.400 1.252 1.132 1,080 1.o
1.621 1.357 1.213 1.097 1.047 1.0 1.583 1.321 1,181 1.067 1.019 1.0 1,550 1.290 1.153 1.043 1.0 1,524 1.269 1.134 1.027 1 .o 1,509 1.252 1.120 1.013 1.0 1,492 1.238 1,108 1,002' 1.0 1.478 1.227 1.097 1.0 1.470 1 ,420 1.347 1.280 1.220 1.163 1.113 1,091 1.068 1.026 1.0
P'R
PR 0.00503 0.0342 %:&%I I3 ,1002 0.233 0.2367 0.347 0.349 1.o 1.o 0.00341 0,00553 0.0373 0.0425 0.1218 0.115 0,2840 0.283 0.421 0.418 1.o 1 .o 0,00798 0.00656 0.0552 0.0558 0,163 0.1605 0,387 0.376 0.562 0,569 1.o 1.0 0.0109 0.00772 0.0751 0.0698 0.202 0.218 0.498 0.473 0.716 0.734 1. o 1. O 0.0145 0.00896 0.0987 0.0850 0.273 0.246 0.616 0.574 0.874 0.910 1 .o 1.0 0.0184 0.01048 0.123 0.1027 0.297 0.317 0.736 0.696 1.0 1.o 0.0212 0.01183 1.144 0.1183 0.381 0.340 0.806 0,827 1 .o 1.o 0,0248 0.01312 0.163 0.1312 0.422 0.381 0.917 0.904 1.o 1.o 0.0283 0.01427 0,179 0.1425 0.416 0.460 0,986 0,990 1.0 1.0 0.0310 0.01516 0,1496 0,195 0.442 0.498 1.o 1.o 0.0331 0.01582 0.0480 0.02477 0.0815 0.0492 0,133 0.0900 0.1538 0.207 0.311 0.2475 0.446 0.3795 0.462 0 522 0.616 0.560 0.835 0,801 1. o 1 .o (WRter)
0.00472
Ul %
31.9 27.5 22.5 15.9 12.7 5 44.3 37.5 82 .O 25.3 21.3 10 53.0 45.5 41.2 35 .O 30.7 20 57.2 50.4 46.9 41.4 36.7 30 61.2 55.5 52.7 47.8 42.5 40 65.3 60.8 58.8 54.5 50 69.8 66.9 65.7 62.2 60 76.2 73.6 73.0 70.6
io
81.8 81 .O 80.7 80.1 80 89.8 89.6 89.4 90
I
lute values of T in column 4. The critical pressures and temperatures are known ( 3 ) for each value of 2; the reduced temperatures and pressures calculated from these are given in columns 5 and 7 of Table I. The corresponding values of the reduced pressure of the standard substance (water) a t the same Ieduced temperature are given in column 6 . (Figure 3, which is a plot for water of reduced pressure against reciprocal reduced temperature, was drawn from the data of Table I V and was found t o be useful in this connection.) I n Figure 4 the values of the reduced total pressures are plotted against the reduced vapor pressure of water at the same reduced temperature on logarithmic coordinates for each value of x, giving isosteres which are straight lines passing through the origin in a manner similar to the lines obtained before for single component systems ( 6 ) . The constant pressure (1atmosphere) and constant temperature (150°, 200°, and 250' C.) lines are straight as well as the constant composition lines, although they do not pass through the origin as do the latter. The data of Sage and Lacey (9) for PROPANE-WPENTANE. this system also are plotted against water as the reference substance in Figure 5 from data collected and calculated in Table 11.
m a
d 1 2
8.90 7.21 5.52 3.59 2.76
8.90 7.21 6.62 3.80 3.60
7.17 5.40 4.24 3.05 2.44 1.0 4.51 3.34 2.81 2.16 1.77 1.0 3.12 2.37 2.06 1.65 1.35 1.0 2.37 1.87 1.67 1.37 1.11 1.0 1.88 1.55 1.43 1.20 1.o 1.54 1.35 1.28 1.10 1.o 1.30 1.19 1.16 1.03 1.0 1.065 1.065 1.045 1.007 1.0 0.979 0.957 0.937 1.o
7.17 5.40 4.24 3.20 3.15
1.o
..,
...
4.51 3.34 2.81 2.30 2.40
...
3.12 2.37 2.06 1.76 1.98
...
2.37 1.87 1.67 1.48 1.48
,..
1.88 1.55 1.43 1.87
..,
1.54 1.35 1 .S? 1.10
l.. 1.30
1.19 1.16 1.08
...
1.065 1.065 1,045 1.04
...
0,979 0.857 0 937
(Vhh 1560 272 94.4 29.7 17.3 1.0 1370 209 66.4 23.5 13.8 1.0 948 142 45.0 15.5 8.85 1.0 700 103 30.9 10.7 5.58 1. o 530 78.0 24.3 7.55 3.27 1.0 421 61.4 20.2 5.24 1.0 366 51.6 15.8 3.90 1.0 315 45.0 13.7 2.73 1 .o 276 40.4 12.1 1.55 1 .o 252 36.4 10.7 1. 0
Vol. 40, No. 11 For this system the slope of the isosteric lines passes through a minimum. This is an indication that a t a given reduced temperature (or pressure) the reduced latent heat of evaporation of the system as a function of composition passes through a minimum. In the case of the system ethanolwater no such minimum is apparent,. M ~ T I I A S E ~ - I ' B N I . A B ~The ~. t'hird system plotted was from the data reported by Sage et al., (10). The reduced total pressure plot against watcr as the reference substance is shown in Figure 6, plotted from data tabulated in Table 111. (It was found convenient t o use log coordinates for both the pressure and composition in the preliminary pressure-composition diagram, giving lines with little or no curvature; this made isosteric interpolation simple and accurate.) Thc lines of Figure 6 curve as the critical point is approached. However, when there is considered the extreme difference in volatility betmen the components and the fact that t,he vapor-liquid equilibria data arc all in the critical region, the correlation may be considered quite good and should be adequate for most engineering needs. The best straight, lines through the observed points up to the major curvature !%-ere drawn t o show the extent of the deviations. RELATIVE VOLATILITY
PLOT
For the t,hree systems con.,. sidered, when the analogous type of log plot used for the total pressure is applied to reIative volatility (plotting tile logarithm of relat,ive volatility against the logarithm of the reduced pressure of the reference substance a t the same reduced temperature), curvature of the lines occurs in the critical region, although subst antially straight lines are obtained before this region is reached. The equation of these straightline portions is dcrived from thermodynamic considerations similar to those used t o develop the equations for the ordinary log plot of relative volatility ( 7 ) . As the relative volaFigure 3. Plot for Water of tility and the reduced Logarithm of Reduced Prespressure both approach sure against Reciprocal of unit,g at, the critical point, Reduced Temperature
November 1948
INDUSTRIAL AND ENGINEERING CHEMISTRY 60
2121
I
I
I .os
I
0.f
I 0.2 PR’(WAT€R)
Figure 5.
I Q5 --t
Plot for Isosteres of Propane-nPentane System
Logarithm of reduced pressure against logarithm ofreduced pressure of water at same reduced temperature8
Figure 4. Plot for Isosteres of Ethanol-Water System Logarithm vf reduced pressure against logarithm of reduced presnure of wnter a t snme reduced temperntures
TABLE11. XI
% 0
10
20
40
60
80
90
100
CALCULATION O F REDUCED PROPERTIES, PROPANE+&-PENTANE (Component 1: Propane) P , Lb./ Temp., Temp., P’R Sq. In. OF. OR. ~ / T R (water) PR Plt (V/U)P
42 63 93 130 183 246 323 412 494 72 104 141 191 255 328 414 528 532 103 145 193 255 327 411 510 566 166 222 293 377 473 574 619 230 309 400 508 625 654 300 408 530 659 666 337 462 608 651 382 523 622
160 190 220 250 280 310 340 370 392 160 190 220 250 280 310 340 370 378 160 190 220 250 280 310 340 363 160 190 220 250 280 310 329 160 190 220 250 280 293 160 190 220 250 254 160 I90 220 232 160 190 206
620 650 680 710 740 770 800 830 852 620 650 680 710 740 770 800 820 838 620 650 680 710 740 770 800 823 620 650 680 710 740 770 789 620 650 680 710 740 753 620 650 680 710 714 620 650 680 692 620 650 666
1.372 1.309 1.252 1,197 1.150 1,106 1.063 1.026 1.0 1.352 1.289 1.232 1.180 1,132 1.089 4.047 1.010 1 .o 1.327 1.267 1.210 1.160 1.112 1.069 1.028 1 .o 1.272 1.213 1.160 1.112 1.066 1.025 1.0 1.215 1.160 1.108 1.061 1.018 1 .o 1.152 I .099 1.050 1.006 1 .o 1.114 1.062 1.017 1 .o 1.072 1.022 1 .o
0.0680 0,108 0.163 0.242 0.342 0.469 0.637 0.835 1.0 0.0785 0.126 0.188 0.273 0,388 0.530 0.715 0.935 1 .o 0.0940 0.146 0.221 0.317 0.448 0.610 0.815 1 .o 0.141 0.217 0.317 0.448 0.628 0.840 1 .o 0.213 0.317 0.460 0.650 0.880 1.0 0.338 0.492 0.700 0.962 1 .o 0.440 0.645 0.885 1 .o 0.593 0.855 1 .o
0.0851 0.1275 0.1882 0.263 0.371 0.498 0 1653 0.834 1.0 0.135 0.1956 0 265 0.359 0.479 0.617 0.778 0.992 1.0 0.182 0.256 0.341 0.451 0.578 0.726 0.900 1.0 0.268 0.359 0.473 0.608 0.763 0.927 1.0 0.352 0.472 0.612 0.776 0.955 1.0 0.451 0.613 0.796 0.990 1.0 0.518 0.708 0.934 1 .o 0.614 0.841 1 .o
7.24 6.14 5.17 4.24 3.58 3.05 2.66 2.27 1 .o 6.72 5.60 4.67 3.78 3.20 2.73 2.32 1.52 1 .o 6.42 5.22 4.30 3.43 2.86 2.42 1.90 1 .o 6.18 4.78 3.69 2.92 2.32 1.69 1.0 6.00 4.52 3.16 2.38 1.59 1.0 5.82 4.38 2.61 1.26 1.0 5.73 4.32 1.86 1 .o 5.65 4.21 1 .o
73.0 45.7 30.0 19.8 13.7 9.3 5.82 3.10 1 .o 63.5 39.2 25.7 17.3 11.9 7.80 4.66 2.00 1 .o
52.7 33.6 21.7 15.3 9.90 6.25 3.32 1.0 34.9 22.1 15.3 9.90 5.92 3.02 1.0 22.5 15.3 9.5 5.6 2.61 1 .o 14.0 8.9 4.86 1.66 1.0 10.1 5.69 2.56 1.0 6.6 2.96 1.0
the constant of integration drops out; the integrated equation may be expressed as follows:
( I n this discussion only the relative volatility of the more volatile component with respect t o the less volatile component will be considered; b u t i t is obvious that the corresponding relative volatility of the less volatile component to the more volatile could be considered analogously.) An example of this type of plot is shown in Figure 7 for the system propane%-pentane. PSEUDO RELATIVE VOLATILITY PLOT
As the critical region is reached, the vapor-liquid equilibrium no longer extends over the complete range of composition because mixtures relatively high in concentration of either component will have passed beyond their respective critical points. By introducing a modified (pseudo) relative volatility based on the limiting composition for each particular isotherm or isobar, i t is possible to eliminate the curvature of the lines of the log against log PL in the critical region for the system ethanol-water (as shown in Figure 8), but not for the other two systems discussed. If x‘ = y’ defines the lower limit, and x“ = yff the upper limit of the limiting compositions in the critical region, the modified or pseudo relative volatility a’ is defined as follows:
I n the ethanol-water system, r’, = y‘1 = 0 and
this equation reduced to:
INDUSTRIAL AND ENGINEERING CHEMISTRY
2122 ~~
Vol. 40, No. 11
~
T.~BLE 111.
CILCGLATIOS
OF
REDUCED PROPERTIES,
TABLE Iv. SPECL4L PROPERTIES
?%IETHAXE-
??-PENTAYE
Zl%
10
5
3
P , Lb.1 Sq. In. 1090 1230 1320 1330 1115 595 692 774 864 89 2 810 378 452 525 hlb
2
718 685 263 322 390 475
595
1
0
620 142 185 240 326 466 558 15.7 42.6
94.9 188 329 494
Temp.
OF.
100 160 220 280 332 100 160 220 2 80 340 360 100 160 220 280 340 372 100 160 220 280 340 377 100 160 220 280 340 382 100 160 220 280 340 387
(Component 1: Methane) Temp P‘R 1/Tn (vater) O R . 1.412 560 0.0505 620 0.136 1.277 1.163 680 0.309 1.069 0.810 740 792 1 .0 1.0 1,462 0.350560 1 322 620 0.09 1.203 080 0.230 1 , 1 0 8 0.460 740 800 1.023 ,0.852 1 0 1 0 820 560 0.0295 1.486 620 1.341 0,0853 0.202 1.222 680 1,123 0.416 740 0.752 800 1.040 832 1.0 1.0 1.492 0,0282 560 620 1.348 0,081 0.192 1.230 680 1.130 0.394 740 0,727 800 1.044 837 1.0 1.0 560 1 , 5 0 2 0.0262 1,357 0.0755 620 680 1.237 0.182 740 1.137 0.373 800 1 , 0 5 1 0.695 842 1.0 1.0 560 1.510 0.0248 820 1.365 0.0715 0.160 1.254 680 740 1 . 1 4 3 0.360 800 1.058 0 . 6 6 1 1.0 847 1.0
(Ud(5”I = --___
(4 (Y”l
d -
(&(Y
(V/P>)? PR 35.5 99.0 0.977 16.6 36.1 1.103 8.00 15.3 1.183 3.56 6.3 1.192 1 .0 1. 0 1.0 140.0 69.5 0.734 51 . o 32.1 ~0.863 ~ (!.E6 20.8 15.2 7.04 9.5 1.0G6 2.47 2.9 1.111 1 .o 1.0 1.0 95.0 165.0 0.552 43.2 58.5 0.660 20.1 24.0 0.767 9.18 1 0 . 8 0.899 3.57 4.13 1.050 1.0 1.0 1.0 0.424 ll5.0 172.0 0.519 01.2 62.0 23.5 25.2 0.628 10.5 11.6 0.765 4.4 0.959 4.10 1.0 1.0 1.0 185.0 0.2545 1 4 2 . 0 81.2 66.5 0.332 26.7 0,430 27.8 12.3 12.3 0.584 4.9 0.835 4.41 1.0 1.0 1.0 193.0 0 . 0 3 1 8 180.0 74.0 70.1 0,086 29.8 0.192 32.8 14.2 13.1 0.3I6 4.57 5.5 0.66) 1 .0 1.0 1.0 a,!
.
, -
Zl)
-
?A
clll ( y 2 ) ( 5 ” 1
- Yl)
P . Lb./ Temp., Sq. In, F.
1
The lllodified or pseudo relative volatility plot for the system ethanol-i\-ater is shoTn in Figurc 8 in which the lines arc substantially straight but no longer paas through the origin (point 1, 1 on the log paper). It is apparent from the definition of the modified or pseudo relat.ive volatility that it need not approach unity at t,he critical point,.
14 40 100 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000
3200 3206
Temp, 670
717 738 842
381.9 444. 6 480.2 518.2 544.6 ,567 .2 587.1 604, 9 621.0 635.8
003
1 ,740 1.603 1.480 1,384
1.287
0.00437 0.01230 0.0312 0.0625 0.1250 0.1872
1005 1027 1047 1065 1081 1096
1.232 1.192 1.160 1.134 1,113 1.093 1.077 1.063
0.625
, .
...
0.687 0.748
1134
1.027
iii.5
i:o&
ii&
i:ooo
946 975
649.5
662.1 673.9 68S.0 695.4 705 0 705.4
SATURATED
...
0.230 0.312 0.375 0,437 0,500 0.562
0.812 0.873 0.937 0.998 1.000
STEAXl
Y
PR
OR.
209.6 267.3 327.8
OF
1
D
1680 Fl3 250 124.4 60.2 38.3 27.2 20.6, 16.2 13 . 0 10.67 8.82 7.31 c.07 J .03 4.12 3.29 2.48 1.303 1.000
7.7
of the molal vapor volumc, V , to u t,he molal liquid volume, u , was a useful criterion for corresponding states; he pointed out, in addition, that its use does not require a knowledge of critical data, Rased on this ratio of the molal volumes, a nex, met,hod of plotting was developed lvhich gives a dil’ferent function of temperature as the reference plotting along the X axis. Instead of using the reduced pressure of a reference substance along the X axis as a means of set’tingup a scale against which to plot relative V volatilities, it m s replaced by the ratio of areference substance at the same reducec]temperature, This in lines, t,hat the ratio
-
Unfortunately, the use of the pseudo relative volatility does
especiall), in the critical region, for all t,hree systems considered. The system ethanol-n.ater is plotted in Figure 9 against arater as the reference substance; the system propane%-pentane is plotted in Figure 10 against n-pentane as the reference substance; and, finally, the system methane-n-pentane is plotted in Figure 11 against n-pentane as the reference substance. The method Of malcinffthis plot is as fol*oiTs:
not always eliminate curvature of the lines in the reduced log Plot, so that a more genera’ type Of ‘Ought. By means of a statistical mechanical analysis, Pitzer (8) showed
The values of V / v for n-ate? are obtained from data in thc steam tables throughout an entire range of temperatures (which are then expressed also as reduced pressure a t the same reduced tempera-
RATIO O F MOLAR VAPOR VOLUME TO MOLAR LIQUID VOLUME
v
05
Ol
Figure 7 . Plot for lsosteres of Propane-nFigure 6.
Plot for Isosteres
of
Vethane-mPentane System
Pentane System Logucithm of relative volatilitiee of propane with respect
Logarithm of reduced pressure ngainst logarithm of reduced pressure of water a t same reduced temperatures
to pentane agilinst logarithm of reduced pressure of water a t same reduced temperatures
November 1948
INDUSTRIAL AND ENGINEERING CHEMISTRY
a!,
f
t
2123
a/z
y (C"/AT€R) Figure 9.
--C
Plot for Isosteres of Ethanol-Water System
Logarithms of relative volatilities of propane with respert to water against logarithms of ratio of vapor to liquid volume of water at same values of the reduced temperature
IV). This may be done for any arbitrary standard substance for tures). -4logarithm plot of P ' R against V / v for water is given in Figure 12 for convenience in obtaining the value of V / o from the reduced pressure of the standard substance (water) a t the same reduced temperature (data for making this plot are given in Table
which the data are available. The values of the relative volatilities at the different concentrations are calculated, and the temperatures and reduced temperatures noted. These values are plotted vertically on a standard sheet of logarithmic paper against values of V / v for water (the reference material) a t the same value of the reduced temperature. SAMPLE CALCULATION
.
T o illustrate the use of these charts in interpw lation of the data a representative example is worked : PRoBLmr. What is the total pressure and vapor composition of a water-ethanol mixture at 100" C. containing 25 mole % of ethanol? Thus, T = 100" C. and XI = 25%. From a graph of the critical conditions against composition, the critical pressure and temperature are obtained for the mixture
T, = 310" C. and P,
=
2060 pounds per square inch Therefore,
Figure 10.
Plot for Isosteres of Propane-n-Pentane System
Logarithms of relative volatilities of propane with respect to npentane against logarithms of ratio of vapor ta liquid volume of npentane a t same values of the reduced temperaturea
-
Figure 11. Plot
for Isosteres of Methane-n-Pentane System
Logarithms of relative volatilities of methane with respect to npentane agninst logarithms of ratio of vapor to liquid volume of n-pentane at same values of the reduced temperature
From Figure 3, P'R = 0.0168 From Figure 4, PR
=
0.0142
Therefore P = 0.0142 X 2060 = 29.3 pounds per square inch
Figure 12. Logarithmic Plot for peference Substances Reduced Pressure against the Ratio Of 'pecific vO1U ~ E of S Vapor and Liquid
Of
INDUSTRIAL AND ENGINEERING CHEMISTRY
2124
This value of the total pressure may be compared with the experimental data by interpolating with the Clausius-Clapeyron equation a t 2, = 25%. Temp., OC.
P , Lb./
Sq. In.
160
129
loo
82.5
1417
log P
l/Temp.,OK.
log P
2.110
0.00236 0.00268 0.00282
i:&
1:iC.s
...
P , Lh. / Sq. I n .
...
28.6
...
Similarly, for the vapor composition:
pseudo relative volatility and shows the phenomenon in v, hich all three critical loci coincide, it may be found that, in general, those systems in which the three critical loci coincide give straight-line correlations in the pseudo relative volatility plot. NOMEYCLATURE
L
=
= =
n =
v/v = 459 a12 =
= molal latent heat of compound
L’ LR L‘R
From Figure 12, the ratio of volumes for the standard substance a t the same reduced temperature is obtained from P’R = 0.0168: From Figure 9,
R
P
3.8
= =
=
= =
=
This may be compared with the experimental data by logarithmic interpolation. P , Lb./Sq. In 14.7 28.5 129
yi
70
log
ai
55.3
1.743
48:l
1:&2
log P
log
1,167 1.455 2,110
1: i i 4
~9
...
ti I
53:o
..
= = = = =
= = = =
CONCLUSIONS
I n applying the above plots t o the correlation of vapor-liquid equilibria data of binary systems, no particular difficulty arises in the use of the total pressure plot. However, in the application of the relative volatility plot some choice must be made between either the plot against the reduced pressure of the reference substance or t h a t against volunie ratio of the reference substance (in either case a t the same reduced temperature). I t is recommended that the plot of the logarithm of relative volatility against the logarithm of total pressure of a reference substance a t the same reduced temperature be tried first. If curvature in the critical region is pronounced, then it is suggested that the pseudo relative volatility plot be tlied next. Should this second method fail to eliminate excessive curvature in the critical region, application of the volume ratlo plot can be expected to give a straight-line correlation, as it has in all cases studied. As the system ethanol-water correlates very \yell using the
Vol. 40, No. 11
=
-
molal latent heat of reference substance ( L / T , ) = reducedmolallatent heat (L’/‘T’c) = reduced molal latent heat of refwencr sub. . stance (LI/T,) = reduced molal latent heat of component 1 from solution (L2/T,) = reduced molal latent heat of coniponc~nl 2 from solution total pressure a,t given temperature critical pressure of compound or rnixt,ure total pressure of reference substance ( P / P c ) reduced pressure a t given temperatmure (P’/P‘J = reduced pressure of reference iiubstanw at the same reduced temperature absolute temperature critical t,emperature of compound or mistui~: critical temperature of referenee substance (T/T,) = reduced temperature molal volume of liquid molal volume of vapor mole TOof component 1 in liquid mole of component 2 in liquid mole % of component 1 in vapor mole YOof component 2 in vapor y z z = relative volatility of component 1 (tht. ninre volatile) compared to component 2 zly, 3
LITERATURE CITED
s.,
C a r e y , J. a n d Lewis, IT.K., IXD. P h G . C H E M . , 24, 882 (1932). G o r d o n , D. H., Ibid., 35, 8 5 1 (1943). Griswold, J., Haney, J. D.. a n d Klein, V.A . ,I b i d . , 35, 701 (1943). K a y , W.B., I b i d . , 28, 1014 (1936). Othmer, D. I?.. I b i d . , 32, 841 (1940). Ibid., 34, 1072 (1942). Othmer, D. F., and Gilmont, R . , I b i d . , 3 6 , 8 5 8 (1944). Pitzer, K. S., J . Chem. P h y s . , 7 , 5 8 3 (1939). Sage, B. H., a n d Lacey, IT’. N., Isn. ENG.CHERI., 32,992 (1940). Sage, B. H., R e a m e r , 11. H., Olds, E. H., a n d Lacey, W.N., I b i d . , 34, 1108 (1942). RECEIVED March 31, 1047. Presented before the Division of Industrial and Engineering Chemistry at t h a 111th Meeting of %heAXSRICAXCHEMICAL SOCIETY, Atlantic City, N. J. Previoiis articles of this series have appeared in ISDUWrRI.4L A X D E S C I S i % ~ R I K OC H h h l I S T l t Y : 1940 (P. 841); 1942 (pp. 952 and 1072); 1943 (p. 1269): 1944 ( p p 669 and 858); 1945 (p. 1112); 1046 (pp. 111 and 408); and 1948 (pp. 723, 883, a n d 886).
Action of Antifouling Paints EFFECT OF NONTOXIC PIGMENTS ON THE PERFORMANCE OF AXTIFOULING PAINTS BOSTWICII; H. ICETCHUNI AND JOHN C. AYERS Woods Hole Oceanographic Institution, F’oods Hole, Muss.
REVIOUS papers of this series (3-6) have discussed the properties of toxic pigments and of paint matrices which are important in formulating antifouling paints. The effects of adding nontoxic pigments to paints formulated both with soluble and insoluble matrices are described here. The use of a nontoxic pigment introduces a third related variable in the paint tomposition. Any variation in one of the components, matrix, toxic pigment, or nontoxic pigment, must be compensated by a related variation of one or both of the other components. For expqrimental purposes it is convenient to maintain either the weight or the volume occupied by the toxic pigment constant so that comparisons between paints may be
made. The nontoxic pigment is, then, substituted for an equal weight or volume of the matrix. I t has been shown by Young, Schneider, and Seagreri (8) that the substitution of a nontoxic pigment for an equal weight of vehicle improves the antifouling effectiveness of a copper paint. This effect was attributed to an increase in the permeability of the paint film. The authors of the present paper found results with paint3 compounded with insoluble matrices confirm these observations. However, the increase in the availability of toxic is attributed to the increase in the volume which it occupies in the paint film when the nontoxic pigment is substituted in this u-ay. As has been shown by Ferry and Ketchum ( d ) , the
