S. D. CHRISTIAY, E. NEPARKO ANI) H. E. AFFSPRVCTNG
442
Yol. 64
TABLE IV CONSTANTS FOR EQUATION 1 System
t,
+ + +
Ethanol benzene Methanol benzene Methanol benzene
oc.
45 25 45
An
a AQ
Ai
uAi
A%
978 580 799
4
554 407 448
24 39 17
473 351 466
10 4
a Az
31 47 19
A3
478 247 434
uA3
74 111 47
aAH
3 4 2
susceptible to error through heat exchange than that used in the original ethanol benzene studie~.~ The heat of mixing of methanol benzene at
20" has been measured by Scatchard, Ticknor, Goates and ?tlcCartney12 who fitted their data to eq. 1 with four parameters, A. = 600, 8 , = 250, A s = 550, A 4 = 800. Since they omitted A 2 and we omitted A , exact comparison of their parameters TABLE V with ours is impossible. However, Table V shows a t 20" fits well with ours MIXING IN ALCOHOL BENZENE that their value of AH,, at25and45". SYSTEMS AHmax, Acknowledgments.-We wish to thank Dr. I. cal. mole-' a t m Ref. Brown of C.S.I.R.O., Melbourne for helpful discussion and for sending us his unpublished results. 159 0.30 12 Our thanks are also due to Mr. D. B. Myers of this 179 .30 This work department for the computer program used in the 237 .30 This work least squares treatment of the results. 287 .31 This work
+
+
MAXIMUMHEATSOF t,
Alcohol
OC.
Methanol
20 25 45 45 45 45
Ethanol 1-Propanol 1-Rntanol
+
320 340
.3 .35
11 11
112) G. Scatchard, L. €3. Ticknor. J. R. Goatrs and E. R . l l c Cartney, J. .4?n. Chem. Soc., 74, 3721 (1952).
A NEW METHOD FOR THE DETERAXISATION OF ACTIVITY COEFFICIENTS OF CO&XPONEYTSI N BINARY LIQUID IUIXTURES' BY SHERRILD. CHRISTIAN, EDWARD XEPARKO AXD HAROLD E. AFFSPRCXG The University of Oklahoma, Norman, Oklahoriin Recezved October 6, 1969
A new, extremely rapid method is described for the determination of activity coefficients of components in binary liquid mixtures, based on measurement of total pressure and equilibrium vapor density alone. Partial pressures and activities are calculated directly from the measured pressure and density values and solution mole fractions are computed from the constant temperature, constant pressure form of the Gibbs-Duhem equation, which may be written -d In az/(d In al d In a z ) = z,, where a2 and a1 are the activities of components 1 and 2, respectively, and 21 is the mole fraction of component 1 in the liquid phase. Methods are given for curve-fitting experimental activities to obtain the best analytical expressions for activity coefficients as functions of zl. The apparatus consists of a fused silica gas density balance suspended directly above the thermostated solution container and connected to a closed-end manometer. For each concentration, total pressure is measured, vapor density is determined from the position of a pointer on the balance and vapor temperature is measured. Concentrations are changed between readings by distilling in one of the pure components through a ground-glass valve. No liquid samples or vapor samples are collected and the apparatus is closed from the atmosphere during an entire run, covering half the concentration range. Results of measurements made on several binary organic systems are reported.
Introduction Most previous vapor pressure methods for determining activity coefficients of components in volatile binary liquid mixtures have made use of the relations
and calculate y1 and y2 directly from equations 1 and 2. In recent years a number of techniques have been developed for determining activity coefficients from measurements of p and x1 a l ~ n e . ~ . ~ The application to these data of an independent y1p = p , ; (1 - v d p = pz (1) relation, the Gibbs-Duhem equation, permits the and pll(zlp1~)= 71; PSAl - z1)pzO = yz (2) calculation of pl and p z and, hence, yl.and y2. where x1 and y1 are mole fractions of component Thus, one may write (again assuming ideality of the 1 in the liquid and vapor phase, respectively; vapor phase and ignoring the effect of T-arintion pl and p2 are partial pressures of components 1 in total pressure on activities) and 2 above the equilibrium mixture; pl0and pzoare p , + p 2 = p ; xld In p , + z2d In p 2 = 0 the vapor pressures of pure 1 and pure 2; p is the and these two equations involve only the two total vapor pressure and y1 and yz are the activity unknown pressures, p , and p,. The mathematical coefficients of components 1 and 2.2 A common procedure is to determine p , z1and y1 experimentally analysis is somewhat complicated in most procedures of this type, and experimentally it usually (1) Presented before the Division of Physical Chemistry, 136th is necessary to remove liquid phase samples after National Meeting of the American Chemical Society, Btlantic City, N. J., Sept., 1959. (2) Equations 1 and 2 assume ideality of the vapor phase.
(3) G. Scatchard, Ann. Rev. Phvs. Chem., 3, 259 (1952) (4) J. A . Barker, Aust. J. Chem., 6 , 207 (1953).
April, 1900
A
l COEFFICIENTS ~ ; ~ OF ~ COMPONENTS ~ ~ IN ~ BINARY ~ LIQUIDMIXTCRES
each pressure determinat,ion for subsequent analysis. The method described here involves the determination of total vapor pressure and vapor composition alone, followed by the applicat'ion of the constant t,emperature, constant pressure form of the Gibbs-Duhem equation for the calcul 2.t'1011 of solution concentrat,ions and, consequently, activity coefficients. The assumption is made throughout that the vapor phase is ideal and that the variation in total pressure does not affect the activitI. Mochel, J . An. Chem. Soc., 62, 712 (1940).
,n
To wioncrntc
443
SYSTEM
/
G
L Fig. 1.-Activity apparatus. nent 1 into the sample tube and degassing by a number of freezing-thawing cycles. The ground glass valve is closed and component 1 is frozen with liquid air. The system is swept out with dry air several times to eliminate vapors of component 1 . Component 2 is introduced into the vessel (E) through one arm of the Y-tube, which can be blown open or closed by heating with a torch. The system is thoroughly degassed and the pressure and pointer deflection for pure component 2 are recorded. An increment of component 1 is added by removing the liquid air and heating gently with a torch until the liquid boils vigorously, the magnetic valve being held open by a permanent magnet supported outside the tube. Component 1 is frozen again, the system is evacuated briefly and the pointer position, gas temperature and pressure readings are recorded. Increments of component 1 are added in this manner until an entire run, covering half the concentration range, is completed. The other half of the concentration range is covered in an analogous manner. It should be noted that once the pure components are degassed and the system is evacuated, no air is admitted during the rest of the run. Bttainment of equilibrium vapor composition is so rapid that no drift of pointer position occurs if the entire apparatus is allowed to stand. Not only pressure equilibrium, but diffusion equilibrium as well appear to be reached within three or four minutes after addition of a component to the solution. C. Materials .-All liquids were Reagent Grade organic compounds, purified by distillation through a 30-plate Oldershaw column a t reflux ratios in excess of 10 to 1. Only middle fractions varying less than 0.1O in boiling point were collected.
Treatment of Data A. Calculation of Activities.-The vapor density d of the equilibrium vapors is determined directly from the position of the pointer on the silica balance. In the case of systems of components which obey the ideal gas law, the activity of each component may be calculated from the expressions and al = p , / p l O ; a? = ( p - pl)/p?O
(4)
where is the average molecular weight of the vapors, MI and Mz are the molecular weights of pure components 1 and 2, and al and az are the activities of components 1 and 2 . In the case of systems in which one component dimerizes (e.g., the system CCl4-CH3COOH) expressions corresponding to (3) and (4) may be written in terms of the dimerization constant K D and the partial pressure of the monomer of the as-
S. D. CHRISTIAN, E. NEPARKO AND H. E. AFFSPRUNG
444
Vol. 64
tion of x1 according to the equation
1.0
-(d In n 2 / d x l * ) ( d I n al/dxl*) - ( d In u2/dxI*j
"
(8)
It can be shown that for systems deviating but slightly from ideality
0.8 *
T:
For this reason, the function xl* = (1 - u2)/(2.a1 - a2) was chosen for use in equation 8 as the independent variable. Defining yl* =
ul/xl* and yz* = a 2 / ( 1 - xi*)
(10)
one can determine analytical expressions of t'he type In
0.2
Ti* =
- xl*)z
(I
*4ixl*i i=O
and
1
0.0
In
0.0 Fig.
0.2 0.4 0.6 0.8 1.0 Activity of carbon tetrachloride, A z . 2.--Activities of the system benzene-carbon tetrachloride.
1.o
ye* =
x1*2
~ i z ~ * i
directly from experimental values of al and a2.' Actually, only one of the expressions in (11) need be used, since it is obvious that once either yl* or yz* is fit as a function of xl*, the other y* is determined by equations 10. Equations 10 can be differentiated to give d In al/dxl* = d In yl*/clxl*
0.8
EXPERIMENTAL VALUES
and
d
d In a2/dxl* = d In ye*/dxl*
d
2 0.G
8
FROM BEST ANALTTICAL FIT OFDATA
-
B
L-
-
I D E A L CURVE
-
0.2 -
Activity of carbon tetrachloride, A2. 3.--Activities of the system n-hexane-carbon tetrachloride.
sociating compound, pl. Thus dRT =
;Vp = p1Jf1
+ 2 K D p i 2 d f , + ( p - pi
- Knp12)M2 (5)
and (11
= pi/plo;
uz = ( p
- p1
- K ~ p i ~ ) / p z O (6)
where the assumption is made that monomers and dimers, once formed, obey the ideal gas law. Similar expressions may be developed for systems in which both components associate in the vapor phase. B. Calculation of Liquid Composition.-The constant temperature, constant pressure form of the Gibbs-Duhem equation may be rearranged t u give --d In az/(d In al - d In a z ) = xi
(7)
The determination of In a2 and In a1 as functions of any arbitrary variable, zl*, would allow the calcula-
+ l/rl*
- 1/(1 - xi*)
(12)
From equations 11 and 10, expressions for d In yl*/dxl* and d In yz*/dxl* can be calculated and substitut,ed into equations 12. Hence, application of equation 8 mill yield x1 as a function of XI* and the activity coefficients y1 and yzmay be calculated. Results A. System C6H6-CC14.-For t'he system benzene (1)-carbon tetrachloride (2) a t 20°, the following analytical expressions have been obtained In
Fig.
(11)
i=O
yl* =
0.14(1
-
and xi
=
xi*
(13)
Table I lists the experimental activities, al a,nd u2; zl; calculated activity coefficients, ylcalCd and y2ca1cd; and calculated activities, alcalcd and a C a l c d . from equation 13. Also given for reference are activity values calculated from a smoothed extrapolation of the data of Scatchard, et u Z . , ~ which were taken a t temperatures ranging from 30 to 70". Figure 2 shows experimental values of al and u2 and the solid line representing the calculated al us. a2 curve? as well as the ideal curve. (6) Note t h a t for a n ideal solution, 2 1 = ai and zz = uz, making relation (9) a n identity. Systems deviating not greatly from ideality .a)*and In yf = A n % , normally follow the relations In yi = A ( 1 from which 7 1 zz 1 A(l a)*, ai zi A m ( l - z1)2andat i3 (1 zi) .4zi2(1 21). Substitution of these values for ai and uz into equation 9 verifies t h a t
-
+
+
-
21
+
-
75
(1 - a2) (1 - ad (1 - a,)
+
(7) The form of equations 11 is suggested by the relations commonly used to express activity coefficients as afunction of solution mole fraction. Although XI* and yi* are not the actual mole fraction and activity coefficient, they ordinarily will not differ considerably from these variables, and the expressions in (11) are thus convenient for curve-fitting data. For a discussion of these power series expansions of In y. see J . H. Hildebrand and R. L. Scott, "The Solubility of NonElectrolytes," Reinhold Puhl. Coip., New York, K . Y., 1950, Chapter
111.
ACTIVITY COEFFICIENTS OF COMPONENTS IN BINARY LIQUIDMIXTURES
April, 1960
B. System n-Hexane-Carbon Tetrachloride.For the system n-hexane (1)-carbon tetrachloride ( 2 ) at 20°, these expressions have been obtained In
yl* =
0.18(1 - zl*)I and zl = xi*
In
nil*
=
0.35(1
-
and z1 = zl*
(15)
Figure 4 shows experimental results for this system. D. System Ethyl Acetate-Carbon Tetrachloride.-For the system ethyl acetate (1)-carbon tetrachloride ( 2 ) a t 20°, the analytical expressions (16) have been obtained 111
11*=
0.40(1
- x l * ) I and q
= zl*
1.0
(14)
Figure 3 shows experimental results for this system. C. System Benzene-n-Hexane.-For the system benzene (1)-n-hexane (2) a t 20°, analytical expressions have been obtained
445
0.8 *
T
m
$ 0.6 d
P + L.
2 0.4
.e
>
.e 42
4 0.2
(16)
Figure 5 s h o m experimental results for this system. 0.0
TABLE I SYSTEM C6Hs-CClr DEPENDENCE OF ACTIWIIESA X D A C T I V I T Y C O E F F I C I E N T S O N LIQUID hIOLE F R A C T I O N AT 20" a1
1,000 0.937 ,878 ,797 .759 ,688 ,648
,029 .592 ,519 ,517 ,469 ,319 .2GO ,204 ,107
.ooo
a2
XI'
y+d
0 000 1.000 1.000 .OB9 0.937 1 . 0 0 0 ,133 ,877 1.002 ,214 795 1.006 ,266 ,753 1 . 0 0 8 ,333 ,681 1.014 ,379 ,638 1.019 ,402 ,615 1.022 ,444 ,577 1.025 ,520 ,499 1.036 ,523 ,497 1.037 ,570 ,447 1 . 0 4 6 ,699 ,307 1.OG8 ,756 , 2 4 8 1.083 .812 ,191 1.094 ,099 1 . 1 2 3 ,902 1.000
,000
yienlod
1.131 1,114 1,092 1 083 1.067 1.059 1.054 1.048 1.035 1.035 1,028 1.013 1.009 1.005 1.001 1.000
a@Cd al(S) a*@) 1.000 0.000 1 , 0 0 0 0.000 0.937 .071 0.937 ,071 ,879 ,137 ,879 ,136 ,800 223 .799 ,224 ,760 267 ,759 ,267 ,690 ,340 ,691 ,339 650 ,383 ,649 ,383 ,628 ,406 .628 ,404 .594 .443 .591 ,443 ,517 ,518 ,517 ,518 ,515 ,521 ,514 ,520 ,467 ,568 ,466 ,568 ,328 ,702 .328 .702 ,262 ,759 ,262 ,758 .209 ,813 ,208 ,813 ,111 ,902 ,109 ,903 ,000 1.000 ,000 1.000
0.2 0.4 0.6 0.8 1.0 Activity of n-hexane, AI. Fig. 4.-Activities of the system benzene-n-hexane. 0.0
a+d
Discussion The method presented here for the determination of activity coefficients has a number of important advantages. First, it is extremely rapid, making it possible to determine activities and activity coefficients of both components in a binary mixture, over the entire concentration range, in a period of less than a day. Second, the problem of reaching equilibrium is not nearly so difficult as in methods depending on the condensation and analysis of vapors bled from the equilibrium mixture. (The apparatus used here, which had an 80 mm. Pyrex tube connecting the vapor density balance and the liquid solution, seemed t,o allow almost instantaneous attainnieiit of equilibrium-no drift of the balance pointer was ever observed during runs.) Furt,her, compounds which react with water vapor or air can be kept under their own vapor pressure t,hroughout an entire run. Another advantage is that the system may be used in the determination of vapor densities and, hence, association constants, of compounds which associate in the yapor phase. Thus, corrections may be made for the formation of associated species, which is one of the factors leading to deviation of the vapors from ideality. The precision of the met.hod appears to be a function of the sensitivitit,y of the vapor density
-.
0
0.8
EXPERIMENTAL
VALUES
T
2+ -9 0.6 h
t
5
% 0.4
.-+h>
.e U
FRON BEST ANALYTIC4 F I T OF DATA
IDEAL
CURVE
0.2
0.0 0.0
0.2 0.4 0.6 0.8 1.0 Bctivity of carbon tetrachloride, AI. Fig. 5.-Activities of the system ethyl acetate-carbon tetrachloride.
balance. Although it is possible to construct a silica balance capable of detecting a change in vapor density of less than g. such a balance would be thrown completely off scale during a run involving binary systems whose components have high vapor pressures and widely different molecular weights. The balance used here m s capable of determining average molecular weights in the range of 50 to 200, at a total pressure hetween 50 and 150 mm., to within &0.50/0. The one system for which it was possible to make detailed comparison of results obtained here with previously reported values was the system C6H6CCI,. From Table I it can be seen that the activity values calculated from the present data, by the curve-fitting technique described, and those calculated from the data of Scatchard, Wood and Xlochelj agree in general to within 0.001. The
F. S. KARN,J. F. SHULTZ AND R. B. ANDE~ZSON
446
directly measured values of activity appear to be in general in agreement with those of Scatchard, et al., to within 0.004. While the activity values obtained by this method are by no means as precise as those of Scatchard and co-workers, the agreement
Vol. 64
between those data and the data reported here is satisfactory. Acknowledgment.-T he authors are indebted to the National Science Foundation for support of the work described in this paper.
KISE'I'ICS OF THE FISCHER-TROPSCH SYKTHESIS O S I R O S CATLILYSTS. PRESSGRE DEYEKDENCE ASD SELECTIVITY OF SITRIDED CATALYSTS BY F. S. KARX,'J. F. SHULTZ' ASD 1%.13. A ~ D E R S O X ' Central Experiment Station, Bureau os Mines, Pzttsburgh, i'ennu. Reeezved October 7, 1858
The variations of rate and selectivit,y of the Fischer-Tropsch synthesis on nitrided fused iron cat,alysta :is a funct,ion of operating conditions have been studied. With HZ 1CO feed, t,he integral rate compared a t constant conversion of Hz GO was found to vary with the operating pressure to about the first power. However, a t any given operating pressure the differential reaction rate decreased more rapidly than t,he partial pressure of synthesis gas as the conversion was increased indicating that the rate is inhibited by reaction products. The relative usage of hydrogen to carbon monoxide decreased with increasing conversion, passed a minimum and then increased. Apparently water is the principal primary product and carbon dioxide is produced by subsequent n-ater-gas-shift reaction. Methane formation decreased initially m+th increasing conversion but subsequently increased. The olefin cont,ent of CZand CShydrocarbons decreased with conversion. When the hydrogen content of the feed was increased, the relative usage of hydrogen to carbon monoxide, tbe production of methane increased, and the olefin content of CZand Cahydrocarbons decreased. This xork is a part of Federal Bureau of Mines investigations of processes for converting coal to liquid fuels.
+
+
d recent paper2 from the Bureau of Mines, U. S. Department of the Interior, described the variatioiis of rate of the Fischer-Tropsch synthesis with feed gas composition, flow and temperature (225-255") on reduced and nitrided fused-iron catalysts. The present paper considers rate as a function of operating pressure on nitrided iron catalysts and the selectivity of the process. Frye, Pickering and Eckstrom3 studied the synthesis of iron at 300-330". For many cata,lysti the interpretation of kinetic data was difficult, as variation of operating variables produced an instantaneous change in rate followed hy a timedependent change that was attributed t o a change of composition of the active surface. I n the preseiit and previous investigations, the variation of operating variables produced no significant timedependent changes in rate; the observed rate n-a'i constant after the period of time-1 to 3 hourarequired to purge the system. Our results indicate that the time-dependent changes in rate are not important in studies a t temperatures below 260 or 270". Experimental Apparatus and experimental procedures mere describcd previously.2 Studies on pressure dependence were mndc with 6- t o 8-mesh nitrided iron catalyst D-3001 Tvith 1H2 1CO gas a t 240'. At each pressure the conversions of Hz CO and exit gas composition were detcrrnined as a funrtion of spare ~ e l o c i t y . ~Tests were m:tdc in th(1 order: 21.4, 14.6, 11.2 and 7.8 atm. To maintain the period of operation rrlatively short, feiwr (=.perimmtal determin:! tions \ v m n i d r than in thr prri ious work t o
+
+
(1) U. S. Department of t h e Interior, Bureau of Mines, Region V, Pittsburgh, Pa. (2) F. S I i a r n , B. Seliernan. 3 . F. Shulta and R. B. Anderson, T H I s JOT.RXAL. 62, 1030 (1933). (3) C. (; E'rye, 11. I,. Picliering a n d 11. C. Eckstroiii, i b i d . , 62, 1308 (1958). (4) Space velocity is defined as volumes (9.T.P.) ~ J C T bulk v o l u ~ n c of catalyst per hour.
avoid progrcssivc changes in catalytic activity; nevertheless, the activity increased slightly in the course\ of the experiments.
Results 1. Pressure Dependence of Rate.-Plots of exit gas composition and Conversion of H2 CO, x, against reciprocal space velocity were similar to those reported previously2 for 1H2+1C0 gas on nitrided iron catalyst at 240". Plots of the first-order empirical equation, -1n (1 - z)= kX-l, where S is the space velocity and 1~is a rate conetant which is e q u J to the differential reaction rate a t zero coiiversioii, T O , were linear over a wide range of conversions as shown in Fig. 1. If the rate equation can be separated into the form T = g ( x ) h ( P ) , where P is the system pressure, then (xS),= k'h(P1, where (xS),are values of X S determined at coiistant values of .I:as pressure is varied, and k' is a constant." Double logarithmic plots of J T X ) against ~ P are presented in Fig. 2 for values of x of 0, 0 2 . 0.4 and 0 6. The limiting d u e s of T S a+ s -+ 0 iq obtained from the slopes of the curves of I'ig. 1 Thc plot5 for coiistant conwwiom can he approximated hy a straight line. Slopes of the lines, as determined by least~quarehmethods. vere 0 '35, 0.(32, 0.97, 0.94 for valut+ of s c>f 0, 0.2, 0.41 and 0.0, respectively, and averaged 0.94. Thus II(I') E Po Figure 3 prweiits double logarithmic plot+ of the tlifferential rc:wtion mte ir = dn. ds-') determined hy graphical diffcrcwtiatioii for thc1 prewire-dependence beries :ii a fimction of thci cum of the partial pressures of I&+ CO for conversions varying from 0 to 0.81. In the course of tests at each presbiac the rate \-:tries npproximatcly as (p11? pco) as the p3rti:il pre+ure i. clcclc:~sed 1)s
+
+
(-2)
h =
.isoIr 1 ri(r) 1
dE,
't
function on13 ot r
