B. G. KYLEAND T. A I . REED,111
6170
solution (0.0144 g. Mn/ml.) and weights of manganese carbonyl were sealed in glass ampoules under nitrogen: 1 2 3 Sample Vol. ketyl soln. (ml.) 9.85 8.0 9.90 I V t . Mn*(CO)lo (g.) 0.4212 0.2443 0.2358 Molar ratio (ketyl: carbonyl) 2.38 3 34 4 29 Color after 2 days Orange Orange Orange-red
4 7.56 0.1469 5.27
Red
After standing for two days a t room temperature, the tubes were opened and the infrared spectra of the solutions were obtained. The 5.0 p (manganese carbonyl) band was strongest in sample 1 and much weaker in the other three samples. Although the data are not subject to quantitative interpretation, i t appears t h a t somewhat in excess of 2.38 moles of manganese benzophenone ketyl will react with one mole of manganese carbonyl. I n order to study the products of the ketyl-carbonyl reaction, two hydrolysis experiments were carried out. I n
[CONTRIBUTION FROM
THE
Vol. 80
the first experiment, a 20-ml. sample of the THF-ketyl solution was poured into 100 ml. of 10% acetic acid. The solution was extracted with ether, a n d the extract was washed with 5% potassium bicarbonate solution and with water. T h e ether was distilled, and the residue was analyzed by infrared spectroscopy. In the second experiment, 2.5 g. of manganese carbonyl was dissolved in 20 ml. of THF-ketyl solution, and the mixture was let stand for 30 minutes. The molar ratio of carbonyl to ketyl was 1.22. T h e solution was hydrolyzed, worked up and analyzed in the same manner as the control experiment with ketyl alone. The hydrolysis product from the control experiment contained 15% benzophenone and i 9 y o benzpinacol, while the hydrolysis product from the reaction of manganese carbonyl with the ketyl solution contained 24% benzophenone, 23 % benzpinacol and about 50:; mnnganese carbonyl. These data show that benzophenone is produced by the reaction of the ketyl with manganese carbonyl. DETROIT20, ~ I I C I ~ I G A S
DEPARTNEXT O F CHEMICAL EXGINEERING, LNIVERSITY
O F FLORIDA]
Free Energy Relations in Fluorocarbon-Hydrocarbon Systems BY B. G. K Y L EAND ~ T. &/I.REED,I11 RECEIVED JUXE 25, 1958 The mutual solubility curves have been determined for 14 fluorocarbon-hydrocarbon systems. The equations of Hildebrand fail to predict consolute temperatures of these systems although consolute compositions are satisfactorily predicted. Examples are given which show t h a t the agreement between observed and calculated consolute temperature is not a good criterion for testing the applicability of the Scatchard-Hildebrand theory. The total vapor pressures of some fluorocarbonhydrocarbon mixtures were measured in the two liquid phase region. It is shown t h a t excess free energies of mixing in binary fluorocarbon-hydrocarbon systems can be estimated quite well from mutual solubility data through the use of Van Laar equations. An empirical correlation is also presented for the estimation of excess free energies of mixing or consolute temperatures in fluorocarbon-paraffin hydrocarbon systems from properties of the pure components. This correlation is based on a negative excess entropy of mixing a t constant volume.
Experimental Materials.-Most of the hydrocarbons used in this work were obtainable commercially in a reasonable degree of purity and were not further purified. T h e pllysical properties of these compounds are listed in Table I along wit11 the reported literature values.
fluorocarbons have been reported in the literature; these are in I. Perfluorocyclic Oxide (C8F160).-This material was the major constituent in "Fluorochemical 0-75'' manufactured by the Minnesota Mining and ?rlanufacturing Company. I t is believed that this fluorocarbon is a five- or six-membered
TABLEI PHYSICAL PROPERTIES OF MATERIALS Compound
%-Heptane Methylcyclohexane Toluene Carbon tetrachloride 2-Butanone Perfluoroheptane (C7Fls) Perfluorocyclic oxide ( CsFleO) 1-Hydroperfluoroheptane (C7FljH) Peduorotributylamine [( CaFo)tN] Methyl peduorooctanoate [C7F1sCOOCH31
Refractive index '25' Expt. Lit.
1.3852 1,4206 1,4567 1.3761 1.2A9.1 1,2770 1.2700 1,2906 1,2033
-Density Expt.
1.385112 1.42058:: ..... 1 ,45733 1.376432 1,25818' ..... 1,27186
..... .....
0,6798 ,76811 ,86232 1.5844 0.7995 1,7258 1.7633 1. i 2 3 3 1,8772 1.6967
'2SC (c. 'mi.) Lit.
,
0.679512 .765062 .862302 1,5 M 3 0.79970* 1.71802' . . . . . ... .. ..... ..... ,
--1
Ilxpt.
R tr.
a t m . ( " C.~-Lit.
95.4 100.9 110.7
98.42i2 100.0342 110.(i2;i2
...
.....
i9.6 82.1 102.8
i9.5g2 82.5''
E,4
177.6 liiO.8
Five fluorocarbon compounds were used in this work. The physical properties of these compounds are also listed in Table I. The physical properties of some of these
..... 94-935 _ .. . . ... . .
oxygen-containing ring with side chains. This material first was fractionated in a laboratory distillation column. The center cut from this fractionation was further purified by a n azeotropic distillation with n-heptane. (1) Department of Chemical Engineering, Kansas S t a t e College. The fluorocarbon thctj mas separated from the n-heptanr hIanhattan, Kansas. by cooling the azeotrope to Dry Ice Temperature where the (2) .4merican Petroleum Institute Research Project 41, "Selected liquid phases were found t l j have very low mutual solubility. Values of Properties of Hydrocarbons," National Bureau of Standards, T h e perfluorocyclic oxide now freed fronl the small Washington, D. C., 1950. amount of remaining qz-heptane by redistillation. This (3) J. Timmermans, "Physio-Chemical Constants of Pure Organic purified material exhibited only one peak when subjected to Compounds," Elsevier Publ. Co., ?Jew York, S. Y. chromatographic analysis using a partitioning liquid fou!~d (4) G. D. Oliver, S. Blumkin and C. TV. Cunningham, T H I S J o ~ R - to be especially go(,d a t resolving fluorocarbot~ mlxN A L , 73, 5722 (1951). tures.6 ( 5 ) E. P. McLaughlin and R. 1,. Scott, J. P h y s . ,"!C 6 0 , 674 ~~-- (1956).
(i;j
1'. hf. Reed, 111,
,11!u/.
( ' h e n . , SO, 221 ( l Y 5 8 !
FREEENERGY RELA4TIONSIN
Dec. 5 , 1958
6171
FLUOROC~4RBOiY-HYDROCARBON SYSTEMS
Perfluoroheptane (C7Fls).-This material was a constituent of “Fluorochemical 101” marketed by The Minnesota Mining and Manufacturing Company and was purified by the same procedure as perfluorocyclic oxide. A chromatographic analysis of this material revealed only one peak. Perfluorotributylamine [ (C4Fg)~N] .-This material was the center cut obtained by fractionation of Minnesota Mining and Manufacturing Company’s “Fluorochemical li-43 .” Chromatographic analysis revealed that this material was a mixture of several components, probably isomers. 1-Hydroperfluoroheptane (C7FlaH).-This material was prepared by Dr. H . C. Brown in these laboratories by the dicarboxylation of the sodium salt of perfluorooctanoic acid. This material was purified by fractional distillation. Methyl Perfluorooctanoate (C,HlsCOOCH3).-This compound was prepared by Dr. H . C. Brown from perfluorooctanoic acid and was purified by fractional distillation. Solubility.-The solubility apparatus consisted of a heavy-walled glass test-tube clamped between two stainless steel flanges by means of four bolts. A Teflon gasket placed between the open end of the tube and the top flange was used to seal the tube. A thermocouple, which passed through the top flange, was used to measure the temperature of the mixture. The whole tube assembly was immersed in a n oil- or water-bath, which provided the necessary temperature control. The unmixing temperature of a known binary mixture was determined by heating the mixture until the two liquids were completely miscible, then cooling the solution slowly while shaking and observing the temperature a t which the second liquid phase appeared. T h e solubility curves on Fig. 1-5 were obtained by plotting the unmixing tempera-
Fig. 2.-Binary
solubility curves, systems containing C7FijH.
60
401
50
40
30
T(OC).
-
T (“C).
20 -
30
20
IO
Fig. 1.-Binary
I
I
I
I
I
I
I
TOLUENE ,-e-,
7
B Cflle-C7H,REF: IO
,
\
//
I
0.5 MOLE FRACTION O F HYDROCARBON.
I
solubility curves, systems containing C7F16.
turecomposition data. For comparison the data of Hildebrand, Fisher and Benes? for the two perfluoroheptane systems are also plotted on Fig. 1. T h e small differences between the present data and that of Hildebrand, et al., could be due to the difficulty in accurately determining unmixing temperatures caused by opalescence or due to the differences in composition of the perfluoroheptane used. Total Vapor Pressure.-A dynamic still, shown on Fig. 6, was used for these measurements. The still was designed so that vigorous boiling and low liquid level would prevent superheating while the insulating vapor space would prevent any appreciable heat loss by the vapor in the inside tube. During operation of the still under equilibrium conditions, no condensation was observed inside the inner tube. A calibrated thermocouple was used to measure the vapor temperature. The still was connected to a vacuum system containing a mercury manometer which could be read to the nearest tenth of a millimeter by use of a cathetometer. As a check on the performance of the still, the total pressure of the system 2-butanonewater was determined a t two (7) J. H. Hildebrand, B. B. Fisher and H. A. Benesi, THISJOURNAL,
a , 4348 (1950).
\, 0.5 MOLE FRACTION OF HYDROCARBON. I
0 Fig. 3.-Binary
/
I
0
solubility curves, systems containing C~Fi~COOCHa.
temperatures. These values compare favorably with the reported literature valuess as shown in Table 11.
TABLE I1 CHECKR U NI X TWO-LIQUJD PHASE STILLSYSTEM: S-BUTANOSE-WATERS --Ref. Pressure, mm.
760 500
--This
8------.
Pressure,
Temp.,
O C .
73.3 62.0
work----.
mm.
Temp. “ C .
768 503
73.6 62.0
Consolute Temperatures The consolute temperatures and compositions of twelve systems reported in this work are listed in Table I11 along with the consolute temperature and (8) D. F. Othmer and R. F. Benenati. Ind. En8. Chcm.. a 7 $ 299 (1945).
(i1'72
\yol.so
H . G. KYLEAND T. 11. REED,I11
1201
I
I
I
GROUND GLASS JOINT
100 -
80 -
/'I
60 -
p-
'1 rd
I
THERMOCOUPLE WELL
T(*C).
40
-
20 -
I
0
I
I
50 MOLE PERCENT OF HYDROCARBON.
Fig. 4.-Bin:iry solubility curves, systems containing CaFlcO. I
I
140-
120 -
Fig. 6.--Tno
liquid phase still
and 6 is the solubility parameter defined a s 4 3 1 where A E v is the energy of vaporization. Suhscript one (1) refers to the hydrocarbon. TABLE 111 THE COMPARISON O F CALCULATED A S D OBSERVED COSSOLUTE TEMPERATTRES ASD COMPOSITIONS
100 -
System
CeHjCHrC8Fi60 CsHiCHa-(GFg)sS CGHjCH3-C,Fi;>H n-CTHi6--CjFioO n-CiHic-CTFijCOOCH3 n-CjH~e-CjFljH n-CrHis-( C4Fg)aS CsHiiCHrC8Fi80 C6HtiCHrCiFijCOOCHa CeHiiCHa-CjFijH CClr-CsF160 CHaCOC2Hj-CsFicO
80 T(*CI. 60 -
40 -
20 -
I
0.5
0
I.o
MOLE FRACTION OF HYDROCARBON.
I'ig.
HEATERS
100
:i.--Biiiary
solubility curves, systems containing (C~FQ)~T.
cornposition as calculated from the equations of Hildebrantl"
T e m p , OK. Obsd. Eq.l
,--Composition-Obid. Erl.L'
377 ti60
0. 7 3 .82
0 . 77
--
.Xi
. t;)
.71
:Eo
2iii 130
.ii;
3IKi
X1
, I 3 .(i7
:'03
RR
. ii:i
1
2% 1s9
.i j l ,iO
.71
. -I J
.71 . 73
.GS
.(is
.80
.78
c-
,81
:18lj
115 :309
338 :118 32,i ?21 Xi9
124 140 292 300
.iJ
,
ri!)
. TX
The results shown in Table I11 follow the trend observed with many other fluorocarbori-hydrocarbon systems. Equation 2 predicts reasonable values of the consclute composition while equation 1 in most cases predicts values of the consolute temperature which are far too low. Only for the system peduorocyclic oxide-toluene does equation 1 predict the correct value of the consolute temperature. It should be mentioned t h a t although used often in the literature, the comparison of the calculated and observed consolute temperatures is not a good criterion for testing the applicability of the Scatchard-Hildebrand theory. If equations I and 2 predict the correct temperature and composition, this means that the first and second derivatives of the activity coefficient with respect to composition are equal to the corresponding derivatives of the activity coefficient as given by the Scatchard-Hildebrand theory. 'This is 21 nrwssary, but not a siif-
FREEENERGY RELATIONS I N FLUOROCA4RBON-HYDROCARBOX
Dec. 3 , 1938
ficient condition which must be met by the Scatchard-Hildebrand equation for activity coefficients, for i t is conceivable that two different functions could have equal first and second derivatives a t a given composition. This reasoning can be substantiated by comparing activity coefficients determined from binary solubility data with those calculated from the Scatchard-Hildebrand equations RT In y1 = VI(& RT In y? = V?(81 -
&)*+.2 6.)2+12
(3) (4)
The term 4 represents the volume fraction. Activity coefficients in two liquid phase systems can be calculated from equations 5 and G which state the conditions for equilibrium X l Y l = XI'Y1' x2y2
= X,'ys'
(6)
The primed quantities in equations 5 and 6 refer to the hydrocarbon-rich phase and the unprinied quantities refer to the fluorocarbon-rich phase. In many fluorocarbon-hydrocarbon systems forming two liquid phases, the mole fraction of hydrocarbon in the hydrocarbon-rich phase (XI') approaches unity a t low temperatures thus causing y,' to approach unity. By setting yl' equal to unity, equation 5 can be used with the solubility data to calculate the activity coefficient of the hydrocarbon in the fluorocarbon-rich phase (7,). The natural logarithm of y1 so calculated is compared in Table IV with values of In y1 predicted by equation 3 for three systems in which the observed and calculated consolute temperatures are in good agreement. TESTOF -Tc
THE
I 11
I11
-Solubility Eq. 1 1 i'C.) XI
(OK.)-
sys-
tema
TABLEIV COSSOLCTETEMPERATURE CRITERION
Obsd. 323.5 3n8 5 386
323 300 377
20 3 li1.l tiU.0
0 306 ,320 .2.5D
dataxl'
0 960 ,956 ,981
--In 71Eq. Eq. Ref. 5 3 1 , l i 0.913 10 1 09 ,900 10 ,977 This 1 34 work
I, perfluoromethylcyclohexane-chloroform; 11, perfluoromethylcyclohexane-benzene; 111, perfluorocyclic oxide-toluene.
6173
SYSTEMS
peratures. However, from consideration of consolute temperature alone, one would erroneously assume that the three systems listed in Table IV closely conformed to the theory. Excess Free Energy of Mixing The Scatchard-Hildebrand equations for the activity coefficients are similar in form to the Van Laar equations which are widely used in correlating and smoothing vapor-liquid equilibrium data. The Van Laar equations are
These Van Laar equations can be regarded as empirical versions of equations 3 and 4 where constants A and B are evaluated from experimental data. The relationships between equations 8 and 4, and '7 and 8 are .I= Vi(8i - 6?)'/11T
AIB =
VJL72
Van Laar constants, and subsequently activity coefficients and excess free energies of mixing can be evaluated from binary solubility data by the following method suggested by Carlson and Colburn .ll At a given temperature the conditions for equilibrium in a two liquid phase system can be expressed by equations 5 and 6. If it is assumed that the Van Laar equations correctly represent activity coefficients as a function of composition, then equations 7 and 8 can be substituted into equations 5 and 6 and the constants A and B can be evaluated. This prccedure can be repeated a t several temperatures, thereby establishing the temperature dependence of the Van Laar A and B. The above procedure was used to determine Van Laar constants for several systems of fluorocarbons and hydrocarbons for which the binary solubility data were determined. It was found that in all cases the Van Laar A's and B's were linear functions of temperature as shown in Fig. 7.
One would expect the same percentage difference between the logarithm of the activity coefficients as between the two consolute temperatures in Table IV since both T , and In yI are directly proportional to the ( 6 , - 62)2 term. Inspection of Table IV reveals that the percentage difference between the logarithms of the activity coefficients is much greater than between the consolute temperatures. If the assumption that yl' = 1 were inaccurate, it would cause values of yl as calculated from equation 5 to be lower than their actual values since these systems exhibit positive deviations from Raoult's law (71'> l ) . The actual values of y1 would then be higher than calculated from equation 5 which would cause even larger disagreement between the values of In 71 compared in Table IV. Since the values of T , and In y1 are compared a t different temperatures, the possibility arises that the system conforms to the theory in the range of the consolute temperature, but not a t other tem-
Before activity coefficients calculated from equations 7 and 8 were used, i t was necessary to determine their validity. This was done by measur-
(10) J. H. Hildebrand and D. R. F. Cochran, THISJOURNAL, 71, ?%(1949).
(11) H. C. Carlson and A. P. Colburn, Znd. Eitp Chem , 34, 581 (1942).
I
."
20
Fig. 7.-I'an
30
40 T(*C).
50
60
Laar constants versus temperature.
B.G. KYLEAND T. A I . REED,I11
6li4
ing the total vapor pressure of the system in the two liquid phase region and comparing this measured pressure with the value calculated from equation 0 7r
=
XlPlOYl
+
2.4 -
(9)
X2P20Y2
Where P I o and pzo are vapor pressures of components 1 and 2 , and ir is the total vapor pressure. Since the total vapor pressure measurements were conducted in the two liquid phase region, the liquid composition could be determined from the temperature and the experimental binary solubility data. Using the vapor pressure data of components 1 and 2, and the activity coefficients as predicted by the Van Laar equation, the total vapor pressure of the two liquid phase mixture was calculated by equation 9. Values of the total vapor pressure as calculated by equation 9 are plotted ueysus temperature on Fig. 5-13 along with the experimental total vapor pressures for several systems. From Fig. S-13, it is seen that the Van Laar activity coefficients predict the total vapor pressures fairly accurately in these systems. The agreement between calculated and observed total vapor pressures is seen to be better a t lower temperatures.
1'01. 80
LOG TT. 2.2-
2.0
Fig. 10.-Total
LOG lT.
0
3.1
3.2 IOOO/T
3.3
3.4
vapor pressure plot; system perfluorocyclic oxide-carbon tetrachloride.
2'ol
OBSERVED CALCULATED
2.6 1.61 3 .O
LOG
I
I
3.1
3.2 IOOO/T.
o OBSERVED
Fig. 11.-Total
CALCULATED 2.21 3.0
Fig. 8.-Total
I
3.1
I
3.3
1 3.4
vapor pressure plot; system perfluorocyclic oxide-n-heptane.
I
3.2 lOOO/T.
I
3.3
-T-
3.0/--
--
vapor pressure plot; system perfluoroheptane-carbon tetrachloride.
I 2 6r
LOGT. 2.4
LOG
1 ~
1 I
i ~
2.21
imo Fig. 9.-Total
IT.
vapor pressure plot; heptane-n-heptane
It is recognized that although the Van Laar activity coefficients can predict the total vapor pressure, this is not definite proof of their validity, since there is an infinite number of combinations of y1 and y2 which will satisfy equation 9. ,4s a further check on the validity of the Van Laar activity coefficients, the excess free energies of mixing were calculated from the Van Laar equations usinp the reDorted binarv solubilitv data for the 0
2.o
system perfluoroFig. 12.-Total
0 0
2 .8
2.9
3.0 IOOO/T,
3.1
3.2
vapor pressure plot; sj-stem perfluorocyclic oxideetoluene.
systems n-pentane-perfluoro-n-pentane,'* n-butane-perfluoro-n-butane,13isooctane-perfluoroheptane' and n-hexane-perfluoro-n-hexane.lbExperimental excess free energies have been reported for ( 1 2 ) J. H Simons and 11 I3 1 ) u n l a p . J Chein P h > s , 18, 375 (1930). (13) J. H. Simons and J. 1". Mausteller, i b i d . , 20, 1516 ( I % ? )
Dec. 5, 1958
2.6
these s y s t e m ~ ~ and ~ - l ~are compared with the values calculated from the Van Laar equation and binary solubility data in Table V where i t can be seen that the two sets of values are in good agreement. TABLE V COMPARISON OF A P CALCULATED BY THE VAN LAAREQUATIOSS WITH LITERATURE VALUES i-OctaneXI, perfluommole heptane18 fracAF 5 , tion cal. mole-1 hydro- Van Literature carbon Laar
99 182 246 291 314 311 281 223 .9 131
0.1 .2 .3 .4 .5 .6 .7 .8
6175
FREEENERGY RELATICKS IN FLUOROCARBON-HYDROCARBON SYSTEMS
128 215 277 315 329 320 290 234 140
?&Butaneperfluoron-butane17 AF
6,
cal. mole-' Van Literature Laar
80 147 199 235 253 253 230 182 106
87 151 203 237 250 247 222 181 112
n-Pentaneperfluorowpentane's AF e, cal. mole-' Litera\'an ture Laar
87 160 214 255 280 272 248 197 116
101 181 240 274 295 292 265 217 134
+Hexane perfluoropi-hexane10 AF 6, cal. mole-' Van LiteraLaar ture
2.2 LOGTT.
I
I
I
t1
1.8'
3.0
I
I
I
3.1
3.2
3.3
3.4
1000/ 1.
330
328
In Table V values of the excess free energy of mixing as calculated by the Van Laar equation are a t slightly lower temperatures than the reported literature values. However, in fluorocarbon-hydrocarbon systems, the excess free energy of mixing has not been found to be strongly dependent on temperature since the temperature derivative, the excess entropy of mixing a t constant pressure, has been reportedz0 to be less than 1 cal. mole-' degree-' a t a mole fraction of one half. Since values of the excess free energy of mixing are in the range of 300 cal. mole-l a t a mole fraction of one half, a change of 30' would result in less than a 10% change. Because the deviations between observed total vapor pressures and total vapor pressures calculated from the Van Laar equation appear larger a t higher temperatures, the excess free energy should be calculated from Van Laar constants determined a t lower temperatures in the region of relatively low mutual solubilities. Excess Free Energy Correlation For systems of fluorocarbons and paraffin hydrocarbons i t is possible to estimate the excess free energy of mixing or consolute temperature from a knowledge of molal volumes, solubility parameters and ionization potentials of the pure components. The correlation is based on published binary solu(14) C. R. Mueller and J. E. Lewis, J . Chem. Phys., 2 6 , 286 (1957). (15) R. G . Bedford and R. D. Dunlap, THISJ O U R N A L , 80, 282 (1958). (16) Van Laar constants evaluated from solubility d a t a a t 17'. Literature values determined from vapor-liquid equilibrium measurements a t 30' (ref. 14). (17) Van Laar constants evaluated from solubility d a t a a t 220'K. Literature values were calculated by the authors from reported values of A & and 422 which were average values determined from vaporliquid equilibrium measurements in t h e range of 223 to 260'K. (ref. 13). (18) Van Laar constants evaluated from solubility d a t a a t 262%. Literatme values were calculated by the authors from reported values I A& which were average values determined from vaporof A ~ and liquid equilibrium measurements in the range of 262 to 293'K. (ref. 12). (19) Van Laar constants evaluated from solubility d a t a a t 6 " . Literature values determined from vapor-liquid equilibrium measurements a t 25' (ref. 15). (20) A tabulation of these excess entiopies for several Buorocarbonhydrocarbon systems has been reported by R. L. Scott, J . Phys. Chem., 6 2 , 13G (19.55).
Fig. l3.-Total
vapor pressure plot; system perfluorocyclic oxide-methl Icyclohexane.
bility data and excess free energy of mixing data and was established in the following manner. Reedz1has shown that by omitting the geometric mean assumption and the assumption of no volume change on mixing the Scatchard-Hildebrand theory accurately predicts heats of mixing in fluorocarbonhydrocarbon systems. By omitting the geometric mean assumption and retaining the condition of no vclume change on mixing the energy of mixing a t constant volume (AEVxf) can be written =
+
(xlT.'I
- 61)'
%v2)[(61
in which fI fr, =
f 26162(1
-fIfD)1@1+2
+ +
= 2(1112)1~~/(L 1 2 ) 12(d*20/dll"~/~l[l d*20/d1*01 I
(10)
and Il and I2 are ionization potentials and d,? and d2z0 are the distances between centers of nearestneighbor molecules. An approximation of d22°/dlf can be obtained from the cube root of the molal volume ratio. Hildebrandg has shown that the Helmholtz free energy of mixing a t constant volume (U,)is approximately equal to the Gibbs free energy of mixing a t constant pressure (AF). If i t is further assumed that the excess entropy of mixing a t constant volume (AS,.) can be expressed by equation 11, then the excess free energy of mixing is given by equation 13 AS," =
-z(Xlvl
AF* = (1
+
+ ZT)(xii'i +
- 62)'
f 26162 (1 - fIfD)l@l'$2 (11) ~2Vz)[(61- a,)* 261641 fIfD)l@l'$2 (12)
X?T.'2)\(6i
+
-
Equation 12 can be rewritten to give AFe
where K
=
(1
(XII/,
+ xzI7z)K+i@2
+ Zr)[(61- 6
~
f) ?618:(1 ~
(12a)
- frfr,)]
Equations 12 and 12a are merely empirical forms of the Scatchard-Hildebrand equation for the excess free energy of mixing. The constant K and subsequently the correlation factor 2 was evaluated by fitting~. equation 12 to published free energy data. The majority of published data for fluorocarbonhydrocarbon mixtures, however, is published as (21) T. M. Reed, 111, i b i d . , 59, 425 (1955).
TABLE \'I I ) . ~ T A ITSSOI U ESTABLISHTSG EMPIRICAL CORRELATIOS FOR EXCESS F R E EEYER(;\, 'l'ype ui
data
Free energy Solubility SolubilitjSulubility Solubility Solubility Solubility Solubility Solubility Solubility Solubility SolubilitLSolubility Free energy Free energy
I
I
I
\
I
\
9
4.0-
equation 1
Values of the correlation factor Z for fifteen systems are listed in Table VI along with the method of obtaining K. The correlation factor Z is plotted 26162(1 - . f ~ f ~1 in ) w s u s the quantity [(6[ Fig. 14. Values of the excess free energy of mixing or consolute temperature can be estimated from Fig. 14 and equations 12 and 13 for systems of fluorocarbons and paraffin hydrocarbons. Systems containing benzene, carbon tetrachloride and chloroform could not be so correlated. Although the experimentally determined values of Z deviate from the correlation line. values of K calculated from the correlation deviate from the experimentally determined K values by an avera deviation of 7?ls and a maximum deviation of 20 -1lthough the correlation is based predoniinaritly on consolute temperature data which are less reliable than free energy data for the evaluation of K , 2 6i t should be useful as an estimate of the free energy in a fluorocarbon-parafin hydrocarbon system. I t should be noted that this correlation is based on a negative excess entropy of mixing at constant volume. Test of Free Energy Correlation
+
2 2.0-
\O
rr)
0
v
N
1.0-
binary solubility data. For these systems the constant k' was determined from a modification of
This correlation can be used t o predict the consolute temperature for the system perfluoro-7z-llexane-~z-hexane. Data for this system have been published recently b\Bedford and Dunlap16 who found the consolute temperature to be 296'K. Using their reported molal volumes a 1 ~ 1 solubility parameters ( V I = 131, T'? = 202, 61 = '7.32, = 5.88), the ionization potential of n-hexanel' ( 1 1 = 10.43), and using the method of ReedZ*to estimate the ionization potential of perfluoro-n-hexane (12 = 17.8) from the polarizabilityzY (a = 14 X the calculated value of [(& - &)2 261612(1 - frj'n)] was found t o be5.71. Using Fig. 14 the value of 2 was found to be 0.58 This resulted in a value of 1 2T = l . l T 3 and K = 6.71. Using K equal to 6.71 the consolute temperature as calculated from equation 13 I n s found to be 29OoK. This value compares favorably with the observed value of 296°K. This value of K , however, predicts I F 0 = 268 cal. mole-'
( 2 2 ) J. A . Pieff and J. B. Hickman. J . P h y s . Chem., 59, 42 (1955). (23) J. B. Hickman, TnIs J O U R N A L , 76, 2879 (1953). f 2 4 ) J. B. Hickman, ibid., 77, 6154 (1955). (2.5) R. Dunlap, R. Digman and J. Vreeland, Abstracts of Papers, 124th 5Ieeting American Chemical Society, Chicago, September, 1953.
(26) This fact has hecn rect,gnired lip I< I , . Scott J . Phys. 62, 131-1 (I95Sj. (27) R . E . Honig, ibid., 1 6 , 105 (1943). (28) T. h I . Reed, 111, ibid., 6 9 , 128 (1955). 129) J. H . Simons and J €3 H l c k m a n , i b i d . , 66, 420 (1952).
01
1
I
I
I'
+
Fig. 14.-Free
energy correlation for fluorocarbons and paraffin hydrocarbons.
+
('11??;1
Dec. !5, l!L5h
ELECTRONIC TR~INSITIONS IN METHYL FLUORIDE IXD IX FLUOROFOR~RI 6177
a t x = 0.5, quite a bit lower than the reported value of 328 cal. mole-’. Since it has been notedz6 that values of K calculated from solubility measurements and vapor-liquid equilibrium measurements are sometimes quite different and since the majority of the data used to establish the correlation were solubility data, it is not surprising that the consolute temperature was predicted more accurately than the excess free energy.
Conclusions Reliable values of the excess free energy of mixing in fluorocarbon-hydrocarbon systems can be
[CONTRIBUTIOS FROM THE
DEPARTMEXT OF
calculated from mutual solubility data through the van L~~~ equation. Where mutual solubility an estimate Of the data are not free energy of mixing in fluorocarbon-paraffin hydrocarbon systems can be obtained from an empirical correlation if the molal volumes, solubility parameters and ionization potentials of the pure compounds are known. MASHATTAN,
KAXSAS
CHEMISTRY, UNIVERSITY OF ROCHESTER]
Electronic Transitions in Methyl Fluoride and in Fluoroform’ BY SUZANNE STOKES~ AND 9. B. F. DUNCAN RECEIVED MAY19, 1958 Electronic spectra of CH3F and of CHF3 have been obtained in absorption in the vacuum ultraviolet region. The electronic transitions are fitted to series which converge to ionization potentials of the molecules. Vibrational structure associated with two of the transitions is interpreted. rl correlation of electronic terms in the series of molecules CHI, CH3F, CH2F9, CHF3 and CFI is presented.
The electronic energy levels, obtained from a study of vacuum ultraviolet spectra, of a number of halogen derivatives of methane have been reported recently. The present investigation is a continuation of this work, and the vacuum ultraviolet absorption spectra of CH3F and CHF3 are presented here. Experimental Details The CHBFwas obtained from Dr. W. F. Edgell of Purdue University. He reported that the infrared spectrum of the compound showed that no impurities were present. Another sample of CH3F was prepared following the procedure given by Edgell.4 d mass spectrographic analysis indicated that the second sample contained about O . O F J ~of~ a n impurity which had a mass of 28. This impurity was probably nitrogen or possibly ethylene. Fluoroform was obtained from the Kinetic Chemicals Division of du Pont de Iiemours Company, who stated that the sample showed no impurities by mass spectrographic analysis. This statement was confirmed independently by a mass spectrum determined here. T h e spectra were photographed in the first order of a vacuum grating spectrograph.6 The grating, of one meter radius of curvature, was ruled 30,000 lines per inch on a two inch surface, and was mounted a t about normal incidence. T h e dispersion was equal to about 8.32 fi./mm. The slit was about 0.1 mm. wide. Eastman Kodak Company SWR film was used. Most of the spectra appeared a t very low pressures. I n such cases the vapor was introduced directly into the spectrograph through calibrated volumes to a known pressure and was separated from the background source only by the slit. The light source was operated a t about 0.5 mm. of He, and while some He diffused through the slit, none of the absorbing gas was lost during a n exposure.
The Lyman continuum was used as a background for absorption spectra. It was operated by periodic discharge, once a second, of a one microfarad capacitor, charged to about 15,000 volts. Helium gas a t a pressure of about 0.5 mm. was used as a carrier gas. Sarrow emission lines of carbon, silicon and atomic oxygen6 occurring in this source were used as wave length standards. The continuum was satisfactory except in the region 1000 to 840 A. where the strongest absorption of oxygen occurs. This oxygen probably originated from decomposition of quartz vapor from the capillary where the discharge occurred and could not be eliminated. This region in the methyl fluoride spectrum was investigated in detail with a hollow cathode copper discharge. The numerous well resolved lines of the Cu 1: spectra in this source allowed a point by point plot of the contours of absorption in this region which was shown to be continuous. T o investigate the possibility-of weak absorption a t longer wave lengths than about 1300 A . , pressures greater than 0.5 mm. of absorbing gas were required. For this purpose a n uncondensed discharge in hydrogen was used, separated from the absorbing gas in the spectrograph by a LiF window. Absorption coefficients in this region were determined a t Lmve lengths of lines in the hydrogen molecular spectrum. Intensity maxima of broad continuous bands were measured from microphotometer tracings. The estimated error in these measurements was about 5 to 8 A. When hydrogen lines or copper lines served as the background, band envelopes were found by plotting the absorption coefficients against wave lengths. The band maxima were read from these curves to about 5 to 10 B.,depending on the breadth near the maximum. For sharp vibrational bands the error in measurement was about 10 cm.?.
Description of Spectra The observed electronic transitions in the two molecules are shown in Fig. I where relative intensities, derived principally from appearance pressures are plotted against wave number. Further details are reported below concerning the behavior of the transitions with change of pressure. Methyl Fluoride.-This molecule was studied over the pressure range of 0.003 to 2.6 mm. The spectrum consisted of five electronic transitions, one ~
(1) P a r t of a dissertation submitted by Suzanne Stokes t o the
Graduate School of t h e University of Rochester in partial fulfillment for the requirements of t h e degree of Doctor of Philosophy. This work was supported in p a r t by t h e Office of Ordnance Research, U. S. Army, under contract DA-30-llj-ORD-728(C,20) with t h e University of Rochester. Reproduction in whole or in p a r t is permitted for a n y use of t h e U. S . Government. (7) Eastman Kodak Company Fellow, 1956-1937. (3) C. R . Zobel and A. B. F. Duncan, THISJ O U R N A L , 11, 2611 (19.58). Reference t o previous work on related molecules will be found in this reference. (4) W. F. Edgell and L. Parts, ibid., I T , 4899 (1955). (3).G. Moe and A. B. F. Duncan, i b i d . , 1 4 , 3136 (1952).
(6) J. C. Boyce and J. T. Moore, “Provisional Wavelength Identification for Vacuum Ultraviolet,” Massachusetts Institute of Technology, 1941. (7) 8. G. Sbenstone. Phrl. Trans. Roy. Soc., 8286, 195 (1936).
