338
INDUSTRIAL AND ENGINEERING CHEMISTRY
mercury isobar is reached. At this piessure the activity coefficients approach unity in the more concentrated region in different directions from those in the less concentrated region. Hence, it may be concluded that st a pressure around 20 mm. of mercury the activity coefficients for one compound at low concentrations are at or near unity and increase to a maximum value, then decrease to unity a t z = 1.0. This may be considered thermodynamically sound and will yield consistent curves showing activity coefficients only less than or greatei than unity when the limiting case of -!= 1.0 when c. = 0.0 is cited. These data show the same trend as those of Ramiussen ( 6 ) wherein the activity coefficients decrease from values greatcJr than unity to values less than unitv as the pressure is decreased. The data in general follow the trend of "thermodynamic consietency" equations based on the Gibbs-Duheni relations. Vapor-liquid equilibrium ratios, K values, were calculated from 2-u data read from the curves on Figure 2 from
(5) Expeiimental K data ale piesenled in 'Fable 111. Smoothed R data are plotted on Figure 5 (tabular data available from American Documentation Instil rite). \o v
m c I, vri 1 HI.
IT = vapoi-liquid eyuilibiium [atio P = vapor pressure, nim. Hg abPohite x = liquid composition, mole fiaction y = vapor composition, molc fraction
Vapor-
activity coefficient
y
=
T
= total pressure in system
riB&O
Vol. 46,No. 2
C.
=
index of refraction at 81 ' 0 .
Subscripts n = naphthalene 6 = tetradecane i = any component LITEEATURE (:ITEU
(1) Dodge, B.F.,"Chemical Engineering Thermodyiiamir.," 1).5 8 2 , New York, McGraw-Hill Book Co., 1944. ( 2 ) Jones, C. A , , Schoenborn, E. M,, and Colburii, A. P., Isn.$hi(;, CHEM.,35,666 (1943). ( 3 ) Jordan, B. T., and Van Winkle, hl., I b i d . , 43, 2903 (1951). (4) Keistler, J. R., and Van Winkle, M., / h i d . , 44,623 (1952). (5) Leeds and Northrup Co., Philadelphia, Pa., "f3tandard ('onvwsion Tables"-Voltage to Temperature, Standard 31031. (6) Rasmussen, R. R., and Van Winkle, kI., Ixn. E m . ~ H I . : > I . ,42, 2121 (1950). (7) Salceanu, C., Comgt. m i d . , 194, 883 (1932). (X) Stull, D. R., IND.Esc,. CHEM.,39, 517 (1947), (9) Ward. 3. H., Ph.D. dissertation, Trniversity of Texas, hustiiI (May 1952). AWF.FTZ:D Septcinber 7, 1953. RECEIVEDfor revie% hZay 2 , 1 Abstracted from thesis submitted i n partial fulfillment of thr rcquivcmenrs for the degree of Master of Science in Chemical En8ineering. 3Iatrrial supplementary to thi? article has been deposited as Document number 4116 with the AD1 Auxiliary Publicationa Project, I'liotoduplication Service, Library of Congress, Tashington 2 5 , I).C. .S. copy may be secured tiy citing t h e Document number and by reniitting 82.60 fur photoprints, or S1.75 for 3:-1nm, microfilm. Advance payment i i required. Mako checks 01' money orders payable to: Chief, i'iiotoduplicatioii Servicr., 1,ibrarg of Congvess.
ui
e
Binary Systems, Naphthalene-n-Tetradecane, Naphthaliene-l-Mexadecexne, n-Tetradecane-1 -Hexadecene; Ternary System, Naphthalene-n-Tetradecane-I -Hexadecene S. H. F-4RD1 AND MATTHEW' VAN TINKLE The t;tiirersity of Texas, lustin 12. Tex.
B
0'113 binary and ternary espevimetital vapor-liquid equi-
librium data were determined on t,he systems composed of the higher boiling hydrocarbons, naphthalene-n-tetradecane1-hexadecene at 200 mm. of mercury prepsure. Correlating equations for equilibrium data are prwented for the binary systems as well as the ternary Pystem. This investigation is part of an over-all study of the vapor-liquid equilibrium characteristics of the higher boiling hydrocarbon mixtures at subatmospheric pressures. Other investigations in this series previously reported concern n-tetradecane-1-hexadecene ( 1 3 , n-dodecane-1-octadecene ( 9 ) , and n-dodecane-1-hexadecene (10). These systems were studicxl a t seven subatmosplierio pressums. M4TFXIALS
The naphthalene was the C.P. grade from t,he ler in Liquid
Vapor-Liquid Equilibrium Diagram for Binary Systems nt 200 Mm. Hg
sure was measured with a mercury manometer. Equilibrium temperatures were indicated by a calibrated iron-constantan thermocouple. The volume of charge to the still was about 40 ml. The period of distillation was 30 to 45 minutes. The length of time depended on the rapidity n-ith which the system approached equilibrium conditions. Equilibrium was assumed established when boiling temperatures were constant for approximatel;\ 15 niiiiutes.
Vol. 46, No. 2
ment hetmen the t w o methods mas excellent. Refractive indices were measured against the sodium d i n e nith a J3auscah PE Lomb precision refractometer, used in conjunction with a 450-watC constant temperature heat,ing bath. Because of thr: decreased solubility of the naphthalene at the l o w r tcmporatures, refractive index measurements werc t:tlten a t 81 .O" C. Boiling point measurements were carefully d~termined in t h r z modified Cottrell boiling point appuratus. Ternary System. T h e ternary compositions were tleterniined by measurement of refractive indices a n d boiling point-. The same apparatus w:is employed as wtts used in the study of the binary syatcms. The ternarj- an:ilytical diaprilm is given as Figure 2. Density measurements and chemical analysis nele also colisidered as analytical methods. The density spread between the three components mas quite good. However, calculations assuming additive volumes indicated a probable paralleling of the density and refractive index curves on a triangular anal:-lical diagram. Any such paralleling would invalidate its u w as an analytical method. Because of this possihilit,y and the inconvenience of mea juring densities above the melting point of naphthalene, this method was not considered furt,her. Sonic consideration \vas given to t'he determination of the I-hesadecene in a solution of the three components hy t,he usual methods of determining unsaturation by reaction with halogens. If suoh determinations were reliable, they could be conveniently used in conjunction with a physienl met,hod of analpis Ruch a3 refraclive index mcasurements. It was believed, however, t hat thc possibility of naphthalene undergoing some substitjiltion ( 4 ) anti the gencml inaccuracy of the method? (6) woultl niillif). its usefulncss. EQUI L I B R I U l i DATA
METHOD OF 4\ $LYSIS
Binary Systems. Binary cornpositionq were tletci mined by measurement of refractivc indicee and boiling points I g r e c -
Activity coefficients for binary and ternary systems wvre calculated from esperimcntal data from the relation y = PIv:/Pz. 13ecause of the low prewure of operation (200 mm. of mercury)
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
February 1954
TABLE I. EXPERIMENTAL VAPORPRESSURE DATA Naphthalene Temp., Press.. C. mm,Hg
49.1 73.7 95.2 144.2 200.0 250.9 309.7 397.6 508.9 634.6
145.0 158.5 167.8 175.7 182.6 185.7 186,Q 193.1 196.9 201.9 218.1 221.5 224.1
TABLE111. EXPERIMENTAL TERNARY EQUILIBRIUM DATA
1-Hexadecene Temp., Press., C. mm. H g After heat stabilization
n-Tetradecane T;mp., Prem., C. mm.Hg
21.2 182:l 39.5 206.1 92.9 220.6 160.2 230.4 200.0 238.0 251.4 245.1 304:l Before heat stabilization 231.5 200.0
.. ..,.
...
... ...
...
Detn. NO.
1
3 4 6 7 9 10 11 12 13 14 15 16 17 18
TABLE
11. VAPOR-LIQUID EQUILIBRIUM DATAAT 200 ABSOLUTE
Detn. hro.
MM.HG
-
CIO,Mole % B.P., O c., 200 mm. H g I n vapor I n liquid Naphthalene-n-Tetradecane System 97.4 168.2 168.3 97.2 91.2 170.3 174.9 79 9 180.7 69.4 195.1 32.0 167.9 99 0 15 2 199.7 190.3 47.7 184.4 61.6 172.4 86.0
yi
1.004 1.002 1.014 1.044 1.057 1.108 1.000 1.131 1.114 1.056 1.031
Y%
2.097 2.007 1.612 1.354 1.165 1.008 2.186 0.998 1.009 1.091 1.451
Naphthalene -1-Hexadeoene System 1
2 3
4 5 6 7 8
223.9 212.8 198.9 187.2 179.4 174.1 171.1 168.8
24.7 53.0 73.2 84.4 90.1 94.3 96.7 Nl.0
n-Tetradecane-I-Hexadecene System Cl4,
I n vapor
1 2 3 4
5 6 7 8
9
229.0 226.2 222.2 218.3 215.5 213.6 210.3 207.0 204.1
11.4 27.3 45.8 61.6 70. I 75.5 82.4 91.7 98.0
Mole % Inliquid
5.8 16.2 28.4 41.1 50.2 56.1 65.8 80.9 94.7
34 1
ya
Ya
0.954 0.940 0.943 0.973 0.981 0.997 1.014 1.012 1.010
0.980 0.969 0.964 0.938 0.945 0.930 0.953 0.906 0.867
ideal behavior of the vapors could'be assumed with little error. Vapor pressures determined in this work were used in the calculations. Experimental equilibrium data and activity coefficients for the binary systems are recorded in Table 11. These equilibrium data are plotted in Figure 3, and the y-2 curves are given in Figure 4. The equilibrium boiling point diagrams for the binaries are given in Figure 5 . The experimental vapor-liquid equilibrium data for the ternary system are given in Table ITI. EVALUATION OF ERRORS IN EXPERKMENTAL DATA
In order to obtain maximum possible accuracy, all analytical and vapor pressure curves were plotted to a large scale. Re' fractive index curves for the naphthalene binaries could be read to 0.00005 unit and the n-tetradecane-1-hexadecenebinary to 0.00001 unit. Vapor pressure curves could be estimated to the nearest 0.5 mm. of mercury and boiling point curves to a t least 0.05' C. The average error for the naphthalene binaries was estimated to be &0.4% and for the n-tctradecane-1-hexadecene system =l=O.6%. The errors were estimated by the determination of inaccuracies from the various probable sources. The separate source errors were added together without regard to algebraic sign in order to arrive a t the over-all error in the vapor and liquid samples. Although such a procedure does not allow for any cancellation of errors, it will allow somewhat for impurities in
19 20 21 22 23 24 25 26 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 55 56 57 58 59 60 61
62 63 64 65
-
Vapor
ClO 12.1 13.5 2.9 90.1 75.9 4.8 52.3 26.0 28.3 13.3 94.3 36.5 41.3 66.5 36.6 76 5 91.9 46.2 10.7 33.6 20.8 50.8 63.1 96.2 20.8 49.0 50.1 32.6 52.6 32.0 50.0 87.5 49.4 82.5 35.6 7.4 7.0 57.6 25.2 39.4 17.0 6.1 52.8 30.7 59.5 69.3 52.0 57.4 14.7
11.1 95.9 88.0 79.8 69.7 7.1 4.0 5.4 56.4 90.6 68.1 37.9 79.3 69.7 64.8 58.7 64.5 78.3 76.7 77.7 10.9 19.8 70.5 35.1 56.4
%
CIS
65.4 70.5 84.6 6.2 23.0 10.5 27.6 3.9 7.0 26.9 1.6 60.7 57.8 26.0 5.3 13.6 6.3 0.3 83.3 18.1 76.4 34.1 26.1 1.3 69.2 44.3 4.4 43.5 3.8 24.8 33.8 9.9 9.5 14.2 47.1 66.7 61.5 17.7 44.4 20.9 46.2 46.3 17.7 27.1 12.4 9.0 25.8 24.6 30.3 15.3 1.7 4.4 4.4 12.8 9.0 20.3 24.4 30.7 2.5 20.6 49 8 12 8 63 31 I 34 7 28 4 90 16 0 16 2 10 3 14 4 25 6 60 95
Liquid Mole $7, ClO Cl4
2.6 3.5 1.8 73.9 54.9 2.2 20.7 6.5 6.8 4.2 81.9 14.9 19.1 38.4 10.1 45.5 83.7 14.9 3.6 9.6 7.3 20.7 32.4 90.3 7.2 22.1 16.1 10.8 18.2 9.7 21.3 73.7 16.2 63.5 12.4 2.4 2.3 22.4 7.8 12.4 5.3 2.0 19.7 8.9 22.2 32.5 20.4 24.7 4.2 2.4
55.3 62.3 71.3 9.8 40.2 1.9 33.1 0.9 2.1 16.1 4.3 78.5 79.6 40.8 7.2 24.0 11.3 2.2 80.0 13.7 83.5 41.0 38.5 2.4 67.7 59.1 2.5 37.5 3.2 19.5 38.5 18.5 8.3 26.8 49.4 49.2 43.4 20.8 35.2 20.6 82.3 29.8 19.7 18.9 14.3 10.4 28.4 29.3 19.1 7.6 86.3 1 R 65.3 8.9 43.6 5.3 33 7 16.6 1.3 4.5 1.0 11.2 1.0 13.4 25.2 38 7 72.4 4.9 34 2 30.3 14.3 3 5 . 3 51.1 21.0 31.1 6.1 36.9 5 2 . 6 28.6 51.1 33.8 43.1 15.4 44 2 48.8 26 4 49.3 26.9 1.2 6.2 4.1 9.9 42 6 42.6 6.3 I9 4 9,4 20 7
Y
yl
ya
1.448 1.284 0.545 1 012 1.037
0.931 0.967 1.032 1.643 1.315
0.507 0.917 0.939 1,539 1.313
0 : 991
01 864
1 074
...
..,
...
...
:. . .
...
21484 1.342 2.387 1.518
0:999 1.121 1.106 1.022
0 : 969
0 : 998
0:990 ...
1 i33
1:oie
0 996
0 : 882
i:ii7 1.012 1.021 1.000 1.052 1,048
0 :980
0 : 762
0.914 0.975 1.641 0,972 0.975
2.740 0.894 1,125
1 boo
.: . .
0 : 986
0:905
0 : 970
0:967 1.437
1 058 2,339
0:904 1.004 0.998 0.851 0.967
1:i)iz
0:1b6
0.970
:96s 0 : 984 0.818
...
...
...
1.019
...
:
1 644 0.908 0.862 0.976 0.980 ... 0:778 0:9bJ4
...
0.973 1.016 1.062
...
...
...
0
...
:. . .
1.038 1.313
, . .
:
...
0.896 0.921 1.023 0.928
...
0:8Q6
0.978
... ...
0:87l
0:96l
i:ii2 0.879 1.209
0:998 o:iis 0,944 0.969 0.969 0.943
0:987
1:260 ...
0 : 936
1;
1,042 1.028
1.735
0:990
0:939
...
1 283
0 : 839
0: 925
0:950
1,028 1.055 0.931 1.002 2.575 1.519 1.009 1.143 1.759 ... ... ...
..
i5i
1:961 ..
i:oiz ,..
...
:
1 949 1.131
:
0,814 0.937 ...
materials and any unforeseen or underestimated effects Vapor and liquid samples were analyzed by identical methods so that the average probable error is the same in each The final overall error in the resulting equilibrium data was taken as that of the average probable error in the vapor or liquid samples. Percentage error was taken as the difference between the actual and experimental percentagc composition values on the vieight or mole basis. There is little difference between the two bases in this work, and the method of estimation of accuracy does not warrant any distinction. The procedure used in estimating average errors in the ternary data was similar to that indicated for the binary systems. Examination of the ternary analytical chart shows that accuracy varies somevhat with composition and with the coniponent under consideration. The greatest error of measurement will fall on n-tetradecane and 1-hexadecene because of the tendency of the refractive index and boiling point curves to run
INDUSTRIAL AND ENGINEERING CHEMISTRY
342 ( 0
-::
-w
--
-T-
-
i" 08
z
08
;Os
c
0 4
0 2
a
Vel. 46, No. 2
I O
0 6
04 02
02
04
OP
08
o
(P
Eavi1 br urn Llau 6 Cornpoi Ii:n
I
18
I,
zo
o
02
RE! 0
04
OS
08
Naphthalenen-Tetradecane
JIole % CLO Temp., in Liquid c. Yl ^'2 From ~-~I-'hthalene-n-TetradecaiieCorrelation 203.3 1.128 1.000 0.0 1.097 1.016 20 0 191 7 1.060 1.142 50.0 178.9 1.244 173.4 1.034 60.7 70.0 173.1 1.022 1.380 80.0 171.0 1.011 1.602 93.3 168.G 1.002 2.110 100.0 167.8 1.000 2 530
From Naphthalene-1-Hexadecpne Correlation
100.0
Yl
Y3
0.834 0.894 0.964 0 083 0.997 1.000
1,000
1.038 1.287 1,490 1.950 2.260
From n-TetradnoanF-t-Hexadeccne Correlation Mole % Clr in Liquid ?a "/a 0.0 l5,2 30.0 53.1 80.9 100.0
230.4 226.2 221.7 214.5 207.0 203.3
0.813 0.913 0 962 0.985 0.998 1.000
1.000 0.988 0.963 0.922 0.875 0.846
for the most part in diiections xhich somewhat parallel the l i n ~ s of constant weight % naphthalene. Extreme accuracy in thc analysis of these two components is therefore difficult to obtain. Temperature errors will be greatest with high naphthalene pel eentages where the isothermals ale comparatively widely spaced. However, errors in this region are somewhat offset because her(. the boiling point curves have a tendency t o turn in a directiori at 90' to the index lines. At, low naphthalene percentages.
Figure 7.
4
6
B
20 Equlibrivm L a r d C o m p o s ' o n R o l o
n-Tetradecane-l-Hexadecene
E*aluatioti Plot for Binar? Correlation Constants
TABLE IV. ACTIVITYCOEFFICIEXTS
230.4 212.8 187.2 179.4 171.1 167.8
2
Aaphthalenel-Hexadrcene
Figure 6.
0.0 I8.0 00.0 64.9 88.3
ID
Equ I br vm L 4u d Compor tion R o l o
where the temperature errors are lower, the refractive index errors are slightly greater because of the wider spacing of the index curves. The average probable error in the n-tetradecane and 1-hexadecene is estimated a t &1% and for napht,halene 50.4%.
Because of the great sensitivity of activity cocfficient values to small errors in equilibrium measurements, especially at low liquid compositions, only trends could be observed when ternary y-values were plotted on' a triangular diagram. The trends agreed reasonably well viith the y-curves determined from the correlations. It is of interest to note that the estimated a.verage error of &0.4% for naphthalene will lead to an average approximate displacement from the true position on a triangular plot of 10 percentage composition units, iyhereas for n-tetradecane and 1-hexadecene, Kith estimated average errors of 1.0%? the comparative displacements are 5 and 6 percentage units, respectively. !Then it is realized that such deviations may be great,ly enhanced if compositions approach intercept condit,ions and that in some determinations thc error is somewhat greater than the average values, it can be deduced that only approximate trends should be obtainable from the plots of experimental activity coefficient,s. The ternary vapor-liquid data would have to be determined with an accuracy considerably greater than the present work allowed before experimental ycurves could be plotted vitli confidence. However, the accuracy is such that vapor-liquid curves can be plotted viith some degree of confidence, and the smoothed experimental equilibrium data agree well with the values derived from the correlations. CORRELATIOK 0 F BINARY D.ITA
The Gibbs-Duhem equation and its mathematical solutions, represented by the van Laar, AIaryules, and Scatchard equations (1, d ) , have been used estrnPively to test for thermodynamic (son-
Activity Coefficients in Ternary System Naphthalene-n-Tetradecane-1-Hexadecene
February 1954
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
sistency and to correlate vapor-liquid data. An examination of the y-x curves for the naphthalene binaries in this work indicated the improbability of checking thermodynamic consistency or correlation by such relations. On the other hand, the ntetradecane-1-hexadecene binary correlates reasonably well by these equations. Rigorous application of the Gibbs-Duhem relation or its solutions to vapor-liquid equilibria has complications. The equations theoretically apply only to constant temperature and constant pressure data. When not applied under such conditions, the equations should be regarded as a limiting condition somewhat analogous to an ideal situation. Difficulties arise when application is made to binary vapor-liquid equilibria. From Gibbs’ phase rule such a system under isobaric and isothermal conditions has zero degrees of variance. It is in a fixed state, and hence composition cannot be varied. If the equations are applied, however, to isobaric or isothermal data, fugacities and activities may require considerable correction. Temperature corrections to isobaric data may be great if the variation in the boiling points of the components is large. Indications of considerable variation in isobaric data for higher boiling hydrocarbons have been noted in work previously cited (9, 15). The shape of the y-x curves in this work indicates that the data would probably correlate by a comparatively simple equation similar to the two-suffix type of van Laar or Margules, if the constants in these equations are not assumed to be identical in both halves of the binary forms. The original van Laar and Margules relations were derived with different constants in each half of the equations ( 7 ) . Only when related by the GibbsDuhem relation do the constants become identical. The present method used to correlate the data was based on that of Li and Coull (12) who presented equations of the van Laar type. These equations are similar to those used by White (16) and those given as l l a , l l b , and 490, to 49c by Wohl ( 1 7 ) although the Li and Coull relations are somewhat different in both form and ronstants. The Li and Cod1 equations are in a somewhat more reasonable form from a theoretical point of view than those of T h i t e . The given equations were slightly modified and for binary 1-2 are
where 6 and k are constants. The sign of k determines whether activity coefficients are greater or less than unity. Combined numbered subscripts on the k-constants refer to the particular binary. The first number refers to the particular binary. The first number refers to the particular component under consideration. The modification involves introduction of such 5; 1 log y, = constants as kzl. Binarv constants are most conveniently evaluated from slopes and intercepts of a plot r , 5: of ( T log y)-1‘2 against the 1 log y’ = ratio of equilibrium liquid compositions. The ( T log y)--1/2 plots are shown in Figure 6. 2: The x-ratio is only plotted from II‘ Dog 7 3 = 0 to less than 2, as the larger values tend to give scattered points. Quantity (Tlog y ) - 1 / 2 becomes more sensitive to measurement and approaches infinity in value as the composition of the mixture approaches that of the pure components. The slopes of the best fitting straight lines were adjusted so that the b-ratios were the same in each particular half of the binary system. Also, since these were to be used in correlating terJ ,
343
nary equilibrium data, it was necessary to adjuet the 6-ratios so that the following relation waR satisfied: (3) The derived equations with estimated average errors are:
Saphthalene-n-Tetradecane (3’ = OK.)
(Y’log
yl)-”’ = (0.1240) (
+ 0.200
(4)
~ 1 / ~ 2 )
Kstimated average error = 1%
( T log
yz)-”’
+ 0.0780
(0.1210) (ZZ/ZI)
(5:
= 1%
Estimated average error
Naphthalcne-1-Hexadecene (3’ = OK.)
( - 2 ‘ log
+ 0.1593
(0.2114) ( z ~ / Q )
yi)-’”
(6)
Estimated average error = 1%
( T log
y3)-”’ = (0.0603) (Xa/xi)
Estirnatcd average error
+ 0.802 =
(7)
1%
n-Tetradecane-1-Hexadecene ( T = OK.) ( - T log y2)-’”
(0.349)
(52/53)
Estimated average error
(-7’ log
ya)-l/z
=
+ 0.1631
(81
1.5%
+
0.0797) ( z z / z ~ ) 0.1703
=
Estimated averagc error
=
(9)
1.5%
Activity coefficients calculated from the correlations are recorded in Table IV and plotted in Figure 7 . CORRELATION O F TERNARY DATA
The Li and Coull method (12) was extended to the ternary data with some success. As in the case of the binary correlations, it was necessary to introduce more k-constants into the relations in a consistent manner. The form of the modified ternary equations is shown by Equations 10, 11, and 12. The constants used in the ternary equations were all obtained from those of the binary correlations. Values which were not obtained directly from the binary correlation slopes and intercepts were found by suitable combination of binary constants. The values that were used to correlate the data are summarized in Table V.
(e)]
DO
(?)I
(11
(?)(?) + (?)(t) z; + [(?)(k) + (2)($+ ($)x2 + ($) (:)(k) + (?)(:) x; + [(t)(k) + (?)(:) [xz + ($) + ($)x3]2 (?)($) + (g)(;).: + + (?)($)- (?)I [x3 + + (2) n]’ [Xl
4
-
52x1
2
2 153 -
21
[(e)(:)
5152
(12
($)XI
The ternary y-equations with estimated average errors are ?’ log y1 = 65.15: - 22.5s: [xi 1.613%
+
- 6.80~2~2
+ 0.755~3]*
Estimated average error = 1%
(13
344
INDUSTRIAL AND ENGINEERING CHEMISTRY
T log
y* =
68.4%: ~
- 5.202;
- %.&i~j
+ 0.62021 + 0.467~31~
[ ~ t
Vol. 46, No. 2
EVALUATION OF ERRORS IN BINARY AVD TERNARY CORRELATIONS
(14)
Estimated average errors in values obtained from the binary and ternary y-coirelations (noted below each equation) were approxiiiialed from the deviations betiveen experimentah 273x2 - 168%; 1O7X122 T log y* = ( 15) smoothed and calculated equilibrium vapor-liquid valuerq. [ ~ 3 1.32521 2 . 1 3 9 ~ 1 ' The aveiage deviations rvere added to llie estimated avcragc errors in the experimental values without rcgard to algebraic Estiniated arcrage error = 1.5% sign to get' estimaied average errors in t,he values from the corwhere T = O K. r e l a h n s . As previously noted such a procedure does not allow for an!; possible cancollation of errors. It. was bclieved, hoaActivity coefficient-composition plots for the three components ever, that the analysis would allow somewhat for unforeseen or are given in Figure 7, and the calculated values that were used to underestimated effents in the determina,tion of the various i n obtain the curves are recorded in Table VI. accuracies. In each binary one of the correlations indicates somew1i:it better accuracy than t,he other. Theore1,ically bot,h reiation~ in a binary system should give identical accuracies. DeviationP TABLEV. CONSTANTS IFOR ACTIVITY C O E P - I ~ I ~ I E S ~ ~ in this work can be traced to the procedure used to evaluate thc CORRELATIONS constant,s in the correlations and t,o possiblc discrepancies in ilic Constant T'aliie Constant T'alrie vapor pressurer;. As previously indicated, ( T log y)-"' is bl hi? plotted against zl/sn or x,/q for values of the 2-ratios froin 0 to 0.620 40 3 br bi less than 2. Thus one plot involves points over thc initial 60 k i l !!! 1.326 -29 8 t,o 65% of the rl-yl curvc and the other over the initial 50 lo ha bi -b? 2 139 65y0 of the zn-2/2curve. Very few, if any, of the points rvill IF -10 90 bs hi common t o both plots. Greater dcoiations in Pxperimentiil 110 8 0.2w equilibrium dat,a in either extremity of the N-y c u r ~ e sn-ill hc - 1 7 54 reficctcd in the calculated act,ivit,y coeffic~ieu 0 .0 i C X scattering of values on one of the ( T log y 96 4 0.159:< tions may be somemtiat~enhanced or cancelled by possible in200 0.0802 accuracies in vapor pressure data used in the determinat,ion oi thepe quantities. It, is quite possible tha,t a curve drann through - 7 3 (1 0.1631 the more scattered points will iiot repreclent, the experirnentd 236 0.1703 data as precisely as t,hc other. Tnaccuraries in the vapor pressure values may once again tend to incream or cancel such discrepancies on recalculation ni' equilibriuin compositions from activity coefficients given h). TABLE 1'1. .'ICTIT.ITY COEFFICIESTS AND EQUILIBRICX T A P O R ~ o 3 I P o S I T I O X SC.4LCl;I..4TED I'ROZT thC cOl:l'elation& Ill t,he pl'erTERXARY CORRCLATIOSS ent .\vork, &ratios W Y C n e w Temp., sarily made identical in earh r 2 NO. CC zz n3 2ir 21 *' I 't 3 Yl u3 2?/ half of the hinai? correlations 191.8 0.333 0.333 0.667 0,234 0.1002 1 0.333 1 ,001 1.016 1.005 1 0 3 by sniall a d j u ~ t ~ r n e noft ~t h e 0.40 2 0.20 0,704 0.237 186.3 0.40 0.0494 1 ,000 1.031 1.073 1 .05; 0.04 0.04' 0.962 3 169.2 0.92 0,0267 0,00944 0.4Y8 1.001 1.966 2.08, best-fitting slopes and intcr224.0 0.06 0.05 0.90 0.189 0.747 4 0,0760 1.012 0.878 0.847 1,002 0.0226 0.10 5 172.1 0.80 0.10 0.912 0.576 1.982 1.002 1 647 1.643 crpts. Such a procedure could 0.10 0.551 217.8 0.341 0.10 0.80 0.131 6 1, 0 2 3 n.914 0,862 1.008 also changc the velatirc a(-0.314 0.30 0.60 0 332 211.7 7 0.10 0.360 1.011 0.985 0.937 0.981 0.30 0.40 0.179 0.10 0.537 8 %06,5 0.296 1.012 1.038 0.912 0 976 curacy of the two equations L) 0.20 0.60 0,ao 0.467 0.483 0.0634 1.013 196.1 1.062 0.946 1.001 202.0 0.04 0.92 0 04 0.114 0.885 0.0140!? 0.862 10 1.013 1.117 1.000 and one n-ill proh:ibly not rc1)11 1Y6.8 0.14 0.82 0.04 0.336 0.646 0.0117 1,101 0.994 0.894 0.990 resent, the experimental data R S 0.20 12 174.1 0.70 0.10 0,849 0.107 0.0211 0.977 1.010 1.414 1.390 0.20 0.25 0 1 la 180., 0.55 0.808 n ,038s I ,006 0.979 13 1 .138 1.255 n-ell as t,he other. 0.60 0.30 0.1223 14 204.5 0 10 0.275 0.613 1.012 1.060 0 926 0.987 0.312 0.40 0 55 0.170 15 213.5 0.05 0.519 1.001 1 .OOi 0.962 0.033 The eatiniatcd averagr x 218.0 0.054 0.246 0.70 0.472 16 0.195 1.015 0.959 0.348 0.981 0.927 curacy of the ternary y-cor0.121 0.150 0.726 0.380 0 181 0 441 17 1.002 213.8 1 008 0.938 0,88.5 221 . 2 0.05 0 80 0.187 0.225 0.603 0.922 0 15 18 1.013 0.895 n.4w relations is A1.170. This fig0.9; 227,6 0.02 0.03 14 0.874 1.000 176.6 20 0.69 0.06 0 26 0:894 0.0289 0 . 06-1.; 0:!287 0'992 11.768 1.525 ure was found from t,hc as21 185.3 0.10 0.40 0.815 0.1113 0.60 0.981 1.250 sumption t,liat errors from the 22 199.7 0.30 0.10 0.60 0.688 0.0811 0.2432 1'013 0.955 0:i01 1 087 23 210.8 0 19 0.05 0.76 0,549 0.0521 0.917 0.12B 1.027 , . . 1 ,039 correlations were of t,ho sarnc 0.36 0,793 24 176.5 0 59 0.06 0.0118 ,.. 1.039 1.221 0.35 25 204.5 0.17 0 48 0 467 ... 0.200 I . noc o.Ym order as those from thr l1inrtry 26 197.2 0.23 0.45 0.32 0.532 ... 0 109 ... 1.034 ... 0.988 correlations arid tire arc'i'ngri 27 0 37 0.55 0.08 0.650 1SL3 . . o.ois1 ... 1 .0%55 ... 1.016 28 193.8 0.20 0.70 0.10 0.447 n. 0284 . . 1 050 0.930 of the l a t k r values. Such es29 181 . U 0 44 0 . a l 0.05 41 214.4 0.1; 0 80 0.:02 ... 1.023 45 179.S3 0.60 0.10 0.30 0.0567 ... ... 1 :io7 ... values within t,be arcrage p r o b able error of measurement. Estimated average error = 1.5%
+
+ +
*
I
I . .
I . .
Fobruuy 1%4
INDUSTUIAL A N D ENGINEERING CHEMISTRY
345
Equilibrium Constants for Naphthalenen-Tetradecane-1-Hexadecene System fidem in some repiow d tbe t e m q vapor-liquid plota. The data -re correlated rvrsonably n-ell by the activity coefficient mrrehtbns. Linea d constant n-tehdecane in the liquid, determined by "oothing crrkul.ted equilibrium valwa, found from tbe Y - C O ~ ~ ~ ~ and O I Mplotted betn-een binary bounduy curvea, appeand to be a re-ably good repreentation of smoothed experimental dnta. The gnoothed experimentd ternary v d w s recoded in TahkR VI1 and \'I11 were 01)tnined from these curves.
30-
LO
-+I
fI
3
---
----.
-
INDUSTRIAL AND ENGINEERING CHEMISTRY
February 1954 T.4BLE
VII.
EQUILIBRICM CONSTASTS FROM CORRELATIONS AND FROM SMOOTHED EXPERIYENTAL
PLOTS
Temp., 0
r.
53
X2
XI
Ki
71
Exptl.
Kz
Ys
Exptl.
Ks Expt.
71
Clo-Clr Binary
397.9 377.1 354.0 347.7 343.6 339.8 335.5 334,O 446.7 415.0 369,O
364,9 340.0 334.0
0,000 1.000 0.200 0.800 0.500 0.600 0.607 0.393 0.700 0.300 0.800 0.200 0.933 0.067 1 .a00 0,000 0.000 0,180 0.500 0.649 0.883 1.a00
446.7 439.0 431,l 418.1 404.6 397,9
...
397.9 387.7 368.4 380.8 342.9 342.0 339.1 338.0 337.3 334.0
0.000 0.092 0.302 0.550 0.720 0.740 0.821
446.7 437.2 428.2 403 .o 381 . O 363.4 351.3 342.0 334,O
0.000
... ,
.
. .
...
... ... , . .
... ...
0.000 0.152 0.300 0.531 0.809 1.000
, . .
...
. .
... , . .
. . ,..
.,.
2.970 2.150 1.453 1.290 1.190 1.112
1.027 1.000
0,908
0.698 0.450 0.280 0.260 0.179 0.150 0.850 0.870 0.130 1.000 0.000
2.130 1,446 1.288 1.194 1.112 1.028 1,002
2.890 2.160 1.450 1.300 1,202 1.116 1.028 1.000
1.000 4.120 4,150 4.790 0.820 2.980 2.960 2.820 1.688 1 663 1.687 0.500 0.351 1.384 1.374 1.389 0.117 1.098 1.099 1.095 0,000 1,000 1.002 1.000 CII-CI~Binary 1,000 0,848 0,700 0,469 0,191 0,000 K3
1.000
2.950
1.000 0.709 0 . 520 0.504 0.511 0.549 0.659 0.773
0.980 0.698 0.519 0.502 0.527 0.557 0.674 0.786
1.800
1.782 1.722 1.589 1.340 1.091 0.980
3,110 1.789 0.603 1.368 1.133 1.000
0.993 0.593 0.306 0.266 0.253 0.256
1.000 0.573 0.312 0.282 0.274 0.280
1.000 0.993 1,000 0.872 0.863 0.889 0.744 0.731 0.742 0.567 0.567 0.683 0.422 0.413 0.440 0.360 0,352 0,360
Intercept Values on Cio-Ci&Binary
0.360 0.304 0.225 0.189 0,193 0.197 0.207 0.211 0.216 0.253
... ,..
. . ,..
...
... . .
...
0.352 0.208 0.225 0.188
0.lYO
0.192 0.202 0.208 0.211 0.256
Kz Intercept Values on Cio-Cia Binary 0.050
0.100 0.250 0,400 0.550 0.700
0.850 1.000
,
.
. . . .
. . . .
...
1.796 1.506 1.296 0 889 0,682 0,594
1.000 0.950 0.900 0,780
0.600 0.450
0.595
1.778
1.493 1.279 0.869 0,670 0.586
0.597 0.663 0.667 0.773 0.785
0,300 0.150 0.000
EQUILIBRIUM CONSTAKT CORRELATIONS
The ycorrelations, derived by the modified method of Li and Coull (f2), were used to give K-correlations by simple substitution. Vapor pressure equations of the form log Pi = A / T
1,000 0.605 0.306 0.268 0.559 0.253
1.744 1.606 1.364 1 118 1,000
347
...
...
...
...
...
...
. . .. .., , .
+B
were determined for each component over the temperature range of interest from a linear plot of 1/T w. log Pi by use of experimental vapor pressure data. Thus activity coefficient equations were expressed in terms of log K as a fupction of equilibrium temperature and mole fractions by substitution for values of log P,, as determined from the linear logarithmic vapor pressure plots, and for the total pressure, 200 mm. of mercury absolute. The vapor pressure equations are
...
...
...
Iiaphthalene
, . .
... , . . . ...
log Pi = -444612'
+ 7.903 (16)
K1 Intercept Values on Cl4-Cl6 Binary
...
...
...
...
... ... ... ...
0.000 1,000 4.13 0.150 0.8FO 4.12 0.300 0,700 3.97 0,550 3.74 0.460 0,600 0.400 3,45 0.750 0.250 3.23 0,100 3.06 0,900 1.000 0.000 2.97
4.16 4.13 3.96
3.72 3.43 3.21 3.06 2.95
...
n-Te tradecane
. . ... ...
log Pp
0.950 0.900 0.800 0.700 0.800 0.800 0.726
...
3.78
3.74 3.61 3.41
...
3.06 3.40 0,600 3.19 0.760 2.89 0.550
0.700 0.400 2.96 0,250 . I .
0,600 . . . 0.480 2.73 0'.300 2.75 0,150 2.94 ... 0..zoo 0,040 2.85 0.600 2.29 0,300 . . . 0,500 . . . 0,320 2.31 0,200 2.34 0.040 2.40 0.400 2.15 0.100 2.24 1.906 0.500 0,333 2.00 0.260 0,360 1:+i6 0,200 1.760 1.760 0,080 0.400 1.630 ... 0.300 0,150 0,060 1 :is5 0,250 1.470 0.300 0.260 1 290 0.100 1.326 0.060 1.340 0.100 1,213 1,130 0.100 0.040 1.045 .
:
I
.
...
3.78 3.72 3.59
3.40
...
3.18 3.39 3.17 2.88
...
2.94
...
...
2.71 2.86 2.91 2:83 2.26
...
2:32 2.32 2.38 2.10 2.21 1.892 1.982 1;694 1.734 1.730
1.607 ... 1 :b67
1.452
1 :is2 1.321 1.337 1.213 1.138 1.045
-5319/T
+ 8.494
.,.
(17)
...
...
Ternary Values
0.020 0.030 0.050 0.050 0.050 0.150 0.246 0.054 0,100 0.100 0.150 0.050 0.124 0.150 0.400 0,050 0.100 0.300 0.190 0.060 0,200 0.100 0.100 0.500 0,050 0.700 0,200 0,200 0.170 0.350 0,100 0.600 0.800 0,050 0.100 0.700 0,040 0.920 0.300 0.100 0,200 0.500 0.300 0,200 0.230 0.450 0.200 0.600 0.140 0.820 0.300 0.300 0.200 0.700 0.400 0.100 0.333 0.333 0.350 0.400 0.460 0.200 0.400 0.400 0.370 0.550 0.100 0,500 0.200 0.500 0.450 0.400 0.440 0.500 0.200 0.530 0.600 0.100 0.690 0.050 0.600 0.300 0.350 0,590 0.700 0.200 0.800 0.100 0.920 0.040
=
, .
4.55 4.06 3.90 3.71 3.45 3.11 3.20 3.36 3.21 2.84 2.74 2.93 2.88
2.66 2.72 2.79 2.76 2.67 2.60 2.26 2.42 2.19 2.31 2.32 2.39 2.14 2.23 1,900 1.990 1.891 1.701 1.740 1.738 1.630 1.582 1.608 1.583 1,472 1.424 1.304 1.346 1.346 1.228 1.146 1.050
...
1-Hexadecene
1,967 1.680 1.412 1.345 1.220 1.060 1 207 i:iso 1.120 1.298 1.271 1.298 1.200 1.178 1.160 1.042 1.052 1.040 1.000 1:05z 1.056 1:074 ,.. 1.076 ... 0.935 ... 0.940 1:025 1 002 0.997 1.005 ... , . . 0,941 0:iiz 0:iiz 0.959 0.811 0.792 0,820 0.822 0 :792 0 :774 0,770 0.793 0:787 0.790 0:805 0.773 0.795 0.788 ,.. 0.744 ... 0.748 ... ...
:
1.520 1 503 1.487 1.472 1.415 1.393 1.310 1.288
log PB = -6003jT
(18)
:
I
.
where T =
...
.
0:6i8
... ...
... ...
0 :is0 0.567 0.578
...
0:535 0.576 0.668
0 'Si0 ,..
o:iio ...
Naphthalene-n-Tetradecane
.1436 -
T
+ 5.602
0.720
0.894 0:301 o:ici5 0.663 0.254 0 . 2 6 3 0.656
0.625 0.811 0.660 . . . 0.625 0.593 ,.. 0.576 0 :558 0.620 0.564 0.640 0.577 0.660 . . . 0.557 0.543 01536 0.580 0.594 0,590 0,679 0.625 , . .
OR.
The binary equilibrium constant equations with estimated average errors are
:
01703
4-8.920
0:247 0.224 0.278 0.232 0.224 0.208 0.235
0:248
0.224 0.276 0.251 0.223 0.208 0.234
01248 01246
o:i& o : i h
0.212 0.206 0.226 0.221 0.235 0.236
where T =
O
R.
(19)
INDUSTRIAL AND ENGINEERING CHEMISTRY
348
Vol. 46, No. 2
TABLEVIII. Temp., 0
F.
397.9 377.1 354,n 347.7 343.6 339.8 335I5 334.n 446,i 41s.n
369.0 364.9 340.0
334.0
0 . nno n.200
0 . m
1 , non 0 . son
Exptl.
o.non
n.980 n .558
1.onn 0.664 0.275
0.717 0.783 0.833
n,393 n.300 n . son n.zoo 0.933 0.067 1 .nnn n nnn
0.883 I ,000
Kz
0.431
0 . m
0.607 n.700
n.nnn n.isn n. 500 n ,649
71
1 2
21
0.269 0.197 0.158 n.111
0.898 n.958
n ,046
1. oon
n.nnn
0.636 n.843
.., , . .
... ...
0.898 0.968
i.nnn
0. non
o.noo
i',
Exptl.
K-3
o.an
n. 169 n ,i o i
0.040
n.nnn
n.nnn
0.533 0.530
0.832 n.891
0.844
1.002
0.968 1.000
n.9in
n.m
CI&IG Binary
446I7
439,O 431,l
418.1 404.6
397.9
. . ... ...
... ...
...
n.onn 0.152 n, 300
o.om 0,262
n.oon
0.272
0.477 0.481 0.712 n,727 0.882 0.916 0.980 1.om
0.531 0,809
1.nno
Ternnrs 7'alucs
441.7 435.2 430.2 424,4 424,O
417.9 416.8
416.3 413.1 411.4 406, 8 403 7 402.4 I
402.1 400.1
400,i 398.8 395,s
395.6 391.5
n.020 0.050
n.n5n o.ns4 n.ion
0.150 0.124
n. n5n
n. loo
0,190
n, 200 n.ion n.nm n ,200 0.170 n.inn n. n5n n.1on n ,040 n. 300
389.3 387.5 357.n
n.200
384.4
0.140
386.0
383,n 380.8 377.2 377.2 369.9 3G8.1
367.3 366.5 365.5 362.1 361 .0
359.4
357.3 355 6
0.300 n.230
n.mn
0.300
n.zon
0.400
0.333 0.350 0.450 0.400
0.370 0.son 0 . jon
0,450 0 . -140 0.550 0.600
n,690 o.Gon 349.7 n 590 345.4 0 . $00 341.8 n. 800 350.2
330.1
336 6
log
'
=
n. 920
o.oan
n.w n:ibQ o ,203 0.187 0.186 n.103 0.195 n. 194 n,200 n,341 0.340 0 . 3 4 5 0.467 n:3io 0:39.g 0.397 n. 170 0.169 0.168 0.319 0.317 0.321 0.549 n, fi47 0.539 n, 5 4 s 0 ik6 0.ij 1 0.293 ... n. 144
n:i&
0 . n5n 0.150
0.246
n . m 0 . njn 0.150
o.4no n.300 0 .n
a n.ino n. 5nn n ,700 n.zm n. 350 n . Goo
0:467 0.275
0:iBr 0.286
0.147 0 . 1 4 6
0.700
n. 920 o.inn
o,ii4 n:ii3 0.685
0 . m 0.200 0.450 0 . 6nn 0.820
,..
0:532
n,?no n.(no n.ion
0.333 0.400
o.mn
n . a n. inn
n.znn 0.400 n.m n ,200 n.inn 0 .o m n.300
n: 763
.
,..
n:kin
0.799
0 is4
n:8k6 0.794
0.793 n ,549
n
912
0.962
0.053
0'. ii7
0'. ii6
...
...
...
0.523
6y+ =
6.610
where T = R. n-Tetradecane-l-Re~adecelie
5310 + 6.193 + Ektimated average error = 2%
0.528
...
0.753 0.187
o:bi,
:. . .
0.329
0 602
0.104
n:bba
n b8i
0.882
o:i&
nIiS5
0.138 n 267 0.670
n, 454 0 658
0.531
...
0,081
0.464 0:&Z 0.33
