XVI. Polarizabilities and Ionization Potentials
4- hydrocarbons as discussed under vapor-liquid equilibria
214 T. M. REED III o
FI G. 13. Gas solubilities.
F . VOLUME CHANGE ON MIXING
Experimental investigations reveal that not only is the enthalpy, entropy, and free energy of mixing in liquid hydrocarbon + fluorocarbon systems unusually large, but the volume changes on mixing are positive and exceptionally large as compared to those encountered in mixtures containing only hydrocarbons. The volume change on mixing in fluoro
carbon + fluorocarbon systems is essentially z e r o *1 3 7'1 8 3) . A calculation by Dunlap*4 1) indicates that the entropy of mixing may be accounted for by the change in volume on mixing using experimental values for the internal pressure or (dPjdT)v in the mixture. The enthalpy of mixing is accounted for by the refinements in the theory of Hildebrand*1 3 3) when
P H Y S I C A L C H E M I S T R Y O F F L U O R O C A R B O N S 215
216 T. M . REED III
experimental volume changes on mixing are included in the calculation. To complete the description of the thermodynamic behavior of mixtures containing a fluorocarbon and a hydrocarbon then requires that the volume change on mixing and the compressibilities be calculated.
In the following discussion it is shown that the volume change on mixing is in part proportional to the value of K given by Eq. (49), and thus that a large portion of volume changes encountered in fluorocarbon + hydrocarbon solutions arises from the same causes as those which give the large energies and excess free energies of mixing, namely, the failure of the geometric mean assumption, due to the large ratio of the ionization pot
entials of the constituent molecular species in the mixture.
The volume change on mixing, AV, is given by
AV = (dAGPldP)T. (55) The Gibbs free energy of mixing, AGp, is approximately
AGP ~ AAV - (AV)2/2pV, (56) as shown by Hildebrand and Scott*7 2). In this equation AAV is the
Helm-holtz free energy of mixing at constant volume, and /? and V are the com
pressibility and volume of the mixture. Inserting Eq. (56) in Eq. (55) and differentiating gives
(AF)2|-0/3-i AV = (8AAVI8P)T +
|-BP + 1
(57) if the change in AV with P is neglected. We now assume that (dASv/
8P)T = 0. Dunlap and Scott*40) have shown that the entropy of mixing at constant volume is essentially that for ideal solutions (random mixing) in the system H-CQFU + n — C6H14. With this assumption and the definition of A,
(dAAv/dP)T = (dAEvldP)T. (58)
Since AEV = Ev — £o> where Ev is the energy of the mixture at the same volume as the unmixed components, and EQ is the energy of the unmixed components,
(8AEV\ _ /8Ev\ /dV\ _ -v- /3Eoi\ / dV0i \
\ 8P ) T" \8V) T
\dp)
T£ \dvj
T\
8P ) TDefining a number n by
- nEjV = (dE/dV)T = TOL/P, (60)
and similarly for Eq. (59) becomes
( —A
dAE \ = NEVP - JntEotfa = npE0 + npAEv - 2«tEwfa. (61) 8P ITP H Y S I C A L C H E M I S T R Y O F F L U O R O C A R B O N S 217 Substituting Eqs. (58) and (61) in Eq. (57) gives
AV = npE0 + npAEv - 2niE^ i + F - ^ - 1 - ^ - + l j . (62) The first and third terms cancel each other approximately. That is,
npE0 £ ^tiiEoipoi or
Then
AV = nfSAEv + l i y - ["|p- + l j • (64) Approximately E = — AEV and using the relationships 60,
AV = (AEv/AEv)TxV + [(AV)2/2V] + l j . (65) A more approximate form of this equation frequently found in the litera
ture is obtained by replacing AEV by the energy of vaporization of the pure components, and AEV by AGPE, the excess free energy of mixing:
AV - (AGpE)T(xVI 2&Et». (66)
The latter two energies are equal, if the second term of Eq. (56) is neglected and ASV is assumed to be that for an ideal solution. By including the second term in Eq. (56) actually a better approximation might be
(AV)2 AGpE = AEV - £ - .
2
pv
With this substitution Eq. (65) becomes
AV = [AGpE + (AV)2l2pV]ToLVI^AEiV + [(AV)2/2V][8p-^8P + 1]
(67) By means of Eq. (67) it is possible to estimate the volume change on mixing at constant P and T from the experimental values of AGpE and the properties a, /?, and V. The function d/3- 1/£P is given by Eq. (20) and has a value of 8 for molecules obeying the (12, 6) potential junction.
For polyatomic molecules 8p~x\8P is larger than 8. A value of 11.2 was found for the hydrocarbons discussed earlier, and Scott*1 5 2) gives values of 10 to 11 for several other molecules.
To illustrate that Eq. (67) does in fact reproduce fairly well the large observed volume changes for fluorocarbon + hydrocarbon solutions, we repeat a calculation of AV obtained by Bedford and Dunlap*7) for
218 T. M. REED III
the system U-CQFU + H-CQRU at 0.5 mole fraction and 25°C. These authors used Eq. (66) and the experimental AGpE — 328 cal/mole to give AV = 3.82 ml per mole. The experimental AV is 4.84 ml per mole.
Using the second order term in Eq. (67) and j3 = 3 x 10~4 a t m -1 (ref. 40) and V = 165 ml per mole the following calculations may be made:
1.99 AGPE + {AVfjlPV = 328 + [(4.8)2/2(3 x 10"4)(165)]
82
= 328 + 57 = 385 cal per mole.
TaV/lLAEiv is obtained from Bedford and Dunlap's estimate of AV and Eq. (66) as 3.82/328 ml per cal. The first term in Eq. (67) is then (3.82/328)(385) ml per mole. The second term is
[(AV)2l2V][d^jdP + 1] = [(4.8)2/2(165)][12] = 0.84 ml per mole, so that Eq. (67) and these values
AV = 3.82 + 0.84 = 5.3 ml per mole. 385
328 F This compares favorably with the experimental value. Since it has already
been shown that AGpE may be computed using the K value of Eq. (49), it follows that essentially the same value of AV can be obtained without the experimental value for AGpE.
Thus the large volume change, on mixing observed for fluorocarbon + hydrocarbon mixtures arise at least in part from the same causes as do the large heats and excess free energies of mixing.
G . EFFECT OF MULTICENTERS OF INTERACTION
In the above paragraphs in this section we have been discussing the interaction between a hydrocarbon and a fluorocarbon molecule on the basis of a single-center spherically symmetrical force field. The Hilde
brand theory utilizes this model. The existence of multicenters of inter
action and of molecular structure have been ignored. In the actual problem there are effects in mixtures which arise from differences in interaction between unlike centers as well as effects which arise from the existence of multicenters of interaction on each molecule of an interacting pair of molecules. The first of these differences (as approximated by the single-center treatment) has been shown to arise from differences in molecular parameters (ionization potential and polarizability), and to give a weaker interaction between a fluorocarbon + hydrocarbon pair than exists between either a hydrocarbon + hydrocarbon pair or a fluorocarbon + fluoro
carbon pair.
P H Y S I C A L C H E M I S T R Y O F F L U O R O C A R B O N S 219 With respect to the effects arising from differences in the variety and kind of multicenters of interaction some comment has already been made under the discussion of the compressibility of mixtures (Sections VII and VIII). Reexamining the compressibility behavior of mixtures of a fluorocarbon with a hydrocarbon represented in Fig. 8, it is seen that the weaker energies of interaction between a pair of these molecules arising from the molecular parameters is also reflected in the compressi
bility behavior. A tangent line to the experimental curve H F on Fig. 8 at the pure hydrocarbon end intersects the pure fluorocarbon axis at a compressibility F' that is greater than that of the pure fluorocarbon.
The intercept F' is the compressibility of the fluorocarbon when inter
acting only with hydrocarbon molecules. Since the interaction energy under these circumstances is less than that for the fluorocarbon + fluoro
carbon interactions (because of the effects arising from the molecular parameters), the cell containing the fluorocarbon in the hydrocarbon surroundings is expanded over that for the fluorocarbon in fluorocarbon surroundings. This means that the compressibility should be greater for the fluorocarbon in hydrocarbon surroundings, as it is at F'. A part of the difference (H'H in Fig. 8) between the compressibility of the hydrocarbon in dilute solution and that of the hydrocarbon as a pure substance must also arise from the weaker interactions between the mole
cules. The remaining difference is then that due to differences in the num
ber of multicenter interactions.
XVIII. Separations of and with Fluorocarbons
Separation of close-boiling fluorocarbon compounds by liquid extrac
tion does not appear to be attractive, because the factors which alter the activity coefficient of one fluorocarbon with the third component are essentially the same for the other fluorocarbon with the third com
ponent. The only significant difference between the fluorocarbons might be the molar volume which has only a minor influence in the free energy of solutions. The selectivity of either of the two solvents, CCI4 or W-C7H16 in the separation of CsFieO + C7F16 is only about 1.1 at 30°C. This is lower than the relative volatility of 1.9*183) for this fluorocarbon binary in vapor-liquid equilibrium. Extractive distillation methods are unattractive for the same inherent reasons. Azeotropic distillation has been used to purify fluorocarbon mixtures*1 3 7'1 8 3). The advantage gained in this method appears to be that the number of theoretical plates in packed columns is greater when a hydrocarbon compound is present with fluorocarbons.
The difference between the boiling points of the two fluorocarbons is essenti
ally the same as (if not larger than) the difference between the boiling
220 T. M. REED III
points of their respective azeotropes with a given hydrocarbon. The advan
tage gained here is one involving the dynamics of the operation of the distillation column (which involve diffusivities, viscosities, surface tensions, etc.), rather than one gained through any thermodynamic effect*182).
The number of theoretical plates in packed laboratory columns distilling hydrocarbons is twice that found when distilling fluorocarbons.
Fluorocarbons have been found useful as entrainers in the azeotropic distillation of hydrocarbons*2 6'9 7). In agreement with the qualitative predictions of Eq. (42) ''the lowering in the boiling point of a hydrocarbon with a fluorocarbon as one component will increase as the hydrocarbon component is changed in the following order: paraffin hydrocarbon, cycloparaffin hydrocarbon, and aromatic hydrocarbon"*9 7). Mixtures of close-boiling straight chain and branched chain paraffin hydrocarbons may be separated by the preferential entrainment of the straight chain hydrocarbons in azeotropic distillation of the hydrocarbon mixture with a fluorocarbon as entrainer*2 6). In this application the fluorocarbon should have a normal boiling point within at least 40°C, and preferably within 20°C, above or below, the normal boiling point of the hydrocarbon.
Azeotropic temperatures and compositions of hydrocarbon + fluoro
carbon mixtures are given in Ref. 97. Aldehydes are selectively entrained by fluorocarbons in azeotropic distillations of mixtures of aldehydes and aliphatic hydrocarbons*25). The azeotrope between benzene and 2, 3-di-methylpentane is broken by distillation from liquid containing tributforyl-nitride*8 8).
Fluorocarbon carboxylic acids have been found to dissolve selectively hydrocarbons in solvent extraction in the following order of decreasing solubility: aromatics, isoparaffins, normal paraffins, and cycloparaffins*148).
In contrast to this order of selectivity of hydrocarbon type is that of the solvent selectivity of the fluorocarbons. The fluorocarbon alkanes extract from liquid solution of hydrocarbons those hydrocarbon molecules which are relatively rich in hydrogen content*14). Saturated molecules may be removed by this process from mixtures containing saturated, aromatic, and unsaturated molecules. This selectivity of the fluorocarbon alkanes conforms qualitatively to the predictions of Eq. (42).
Gas liquid partition chromatography [see Keulemans*82) as a general reference to this technique] is a powerful means for separating fluoro
carbons, particularly mixtures of isomeric fluorocarbons. The isomers of C 5 F 1 2 and of C 6 F 1 4 have been separated from one another by this tech
nique [Reed*1 3 9)]. Homologs of the fluorocarbons and fluorocarbon deriva
tives have been separated on fluorocarbon stationary phases and on hydrocarbon stationary phases by Reed et a/.*1 3 5'1 3 6'1 3 9), and by Evans and Tatlow*4 6). The most effective stationary phase utilized for the isomer
PHYSICAL CHEMISTRY OF FLUOROCARBONS 221 separation is 0.4 gm w-hexadecane (W-C16H34) per gm of 3 5 to 80 mesh acid-washed Chromosorb.
A recommended preparative scale chromatographic column is 16 meters long and 0.5 in. inside diameter, aligned in the vertical direction and packed with 2050 gm of the above-mentioned n-hexadecane-coated Chromosorb. For the C5 and C6 separations this column was operated at 25 to 30°C with a nitrogen carrier gas flow rate of 108 ml/min at the exit, which was at atmospheric pressure.
The ethyl ester of the Kel-Facid Cl(CF2CFCl)3CF2COOH is a very good stationary liquid phase for both fluorocarbon and hydrocarbon separations when prepared as 0.2 gm of ester per gm of Chromosorb.
The relative partition coefficients of the C6F14 isomers in ra-hexa-decane are the same as on the Kel-F acid ester: namely W-C6F14, 1.0;
2-CF3C5F11, 1.05 to 1.1; 3-CF3C5F11, 1.15 to 1.2; and (CFs^CjFg, 1.27. Each isomer behaves essentially the same as all the other isomers when in solution in either solvent, even though activity coefficients in w-hexadecane are 10 times larger than in the Kel-F acid ester at 25°C. This behavior again illustrates that the selectivity of a solvent is independent of the nature of the solvent in separating saturated fluorocarbon. No investigations of this problem have yet been made for unsaturated fluoro
carbons.
Campbell and Gudzinowicz*2 2 a) have resolved SF4, SF6, S O F 2 , and
S2F10 by gas-liquid chromatography at 33°C using columns 15 to 20 ft long packed with 3 3 % by weight No. 3 Kel-F oil on 35- to 80-mesh Chromosorb W. This packing is also satisfactory for resolution of a mixture containing CF4, C2F4, C3F6, CVCI0-C4F8 and iso-C4F8 at 33°C.