ON T H E SOLUBILITY OF PAR.AFFIK-CH.4IK COMPOUSDS A. BONDI’ International Lubricant Corporation, New Orleans, Louisiana Received September 17, 1846
The large body of experimental data on the solubility of paraffi-chain compounds of higher molecular weight which has recently become available (9, 12) offered the opportunity to study the thermodynamics of solutions of this interesting group of materials in more detail than has previously been possible. I. THE FREE ENERGY OF YI?XKG AS A MEASURE OF THE SOX-IDEALITY OF SOLCTIONS
The information which we wish to derive from solubility data is the degree to which the distribution of particles in the solution deviates from randomness and the magnitude of the interaction energy between solvent and solute, or, in short, the degree t o which the solutions deviate from Raoult’s law. The solubility of solids-for systems following Raoult’s law-is to a good approximation :
where AH, = heat of fusion of solute, T, = melting point of solute ino K., 2‘ = temperature (OK.) a t which the solubility a2 is measured, R = gas constant. (The only approximation made here is the neglect of the temperature dependence of AH,, given by the specific-heat difference between the solid and the liquid states of the solute. The few recent specific-heat data (9) of normal paraffis, when applied to this calculation, produce a perceptible reduction in the slope of the “ideal” solubility line at the low-temperature end. The apparently quite low degree of accuracy of the solubility data at the lowest temperatures, as well as the paucity of reliable specific-heat data for most of the compounds to be discussed, militated strongly against the use of a temperature correction for AH,, which would complicate the calculation vithout benefitting the significance of the results. The magnitude of the error, introduced by this approximation a t about 5OoC. below the melting point, is of the order of < -30 per cent in a, which will affect log y only insignificantly.) Figures 1 and 2 illustrate the manner in which actual solutions follow, or deviate from, equation 1. We obtain a convenient numerical expression for the “non-ideality” of a solution by defining an excess free energy of mixing: AF, = R T l n y
(2)
In figures 3 to 9 A F m is presented in such a manner that one can compare the effect of molecule size and type (of solvent and solute) upon non-ideality a t 1
Present address: Shell Development Company, Emeryville, California 891
892
A . DOh’DI
equal molar concentrations of solute. Before entering into a detailed discussion of these diagrams it should be pointed out that the figures given are not all of equal reliability, mainly because the heat of fusion data in the literature are both scarce and not always consistent. The most plentiful and reliable data are
FIG.1. Solubility of n-dotriacontane in various solvents
those on the hydrocarbons (9, 10, 16). The AH, data of the higher fatty acids are available, but not equally reliable. The most probable values mere selected by graphical interpolation of materially self-consistent data. The heat of fusion of cetyl alcohol was taken from the recent paper by Parks and Rowe (ll), and AH, of monocetylamine was obtained by measurement of the melting-point depression.
893
SOLUBI1,ITY OF PARAFFIN-CHAIh-COMPOUKDS
While the accuracy of the AH, values used may leave much to be desired, the internal consistency of the results obtained makes it very probable that better AH, values--once they become available-will not materially alter the over-all picture developed.
t N2
C
oc
I
i
I
i
I
I
I
loyT-
3’
32
FIG.2. Solubility
33.
34
I
35
36
of cetyl alcohol in various solvents
The sequence of i\F, values2 is on the whole about as one mould expect. Kormal paraffins in “inert” solvents, such as chloroform and carbon tetrachloride, show negative deviations from Raoult’s law which increase with their chain length, just as has been ohserved for the vapor pressure of such solutions (1). 9 T h e A F , graphs are presented in a n upside-down fashion in order t o be consistent with the direction of the solubility deviation from the “ideal” curve.
894
A. BOND1
In alcoholic solutions the opposite is the case, A F , increasing markedly in the positive direction with increasing chain length, as is easily understandable. Keeping the molecular weight constant and comparing the effect of varying the
\
\\
-Z M X
-m
+IO00
00001
0 001
001
01
FIG.3. A F m curves of paraffin hydrocarbons in chloroform 0 AFm C A mole
+IO00
C I -.-----
IO
FIG.4. Al;, curves of normal paraffin hydrocarbons In isopropyl alcohol
functional group, Ive observe in carbon tetrachloride the largest AFm values for the alcohol, the fatty acid and the primary amine following in close succession, while the hydrocarbon alone shows negative deviations from ideality. This observation speaks against the existence of the alcohol, the fatty acid, and the amine as double molecules in solution. In case they existed as double molecules,
I
I
0 -
I
I *2ooo
I
I 1
+w
1
---I
A '
cu
Fm
mol(
l I
O0O1 N t -
001
01
IO
890
A . I3OSDI
carbon has the highest AF,,, value, but it is rather surprising to observe that the sequence of the other three compounds is the same in isopropyl alcohol as in
FIG.7. AF, curves of normal f a t t y acids in cyclohexane
+3000
p; ____
0001 N1-
001
e
01
-
I
-IO
FIG 8 AF, curves of normal f a t t y acids in methyl alcohol
carbon tetrachloride. The behavior of the fatty acids in cyclohexane solutions and in methyl alcohol is just as expected, the deviation from ideality increasing with the length of the paraffi chain in the ratter, and decreasing in the former.
897
SOLUBILITY OF PARAFFIN-CHAIN COMPOUNDS 11. THE ORIGIN OF THE DEVIATIOXS FROM RAOULT'S LAW
Negative deviation from Raoult's law, which cannot be accounted for by the cohesive energy difference concept ( 5 ) , have become of considerable interest during the past decade owing to their frequent occurrence with polymer solutions. Guggenheim (4) proposed a rigorous mathematical treatment of the case of large solute among smell solvent molecules, which has recently been applied to the vapor-pressure data of a number of paraffin-chain compound solutions
I -
ICYcloherane .
+IO00
1
'-PrOP O H n butyl OH
I
4
+ 2000-
I
MeOH
I
t3000
AeOH
0 0001
0001
001
I
01
FIG 9 AF, curves of stearic acid in various solvents
(2). He derives for completely flexible (or completely stiff) chain-like molecules the following equation:
where a1 = activity of solvent; N , , ATB = number of molecules of solvent and solute, respectively; r A , TB = number of sites occupied by molecules A or B ; 2 = z = number of nearest neighbors of any one site; zp, = T,(Z - 2) number of sites neighbors of the T , sites n-hich are occupied by a molecule of type i, excluding sites occupied by the next elements of the same molecule, i.e., zp, is the number of sites which are neighbors of a molecule of type i. The x and p are defined by
+
X = QnNa/(QANa
+ QBNB);
p
= { ( I- 2X)'
-k 4 ~ ( 1- X)e2YAB'k)t
where uAB= the contribution of each pair of sites to the intermolecular potential energy, so that the energy of mixing
898
A. BOND1
For the “semi-ideal” case, when AE, = 0, the second bracket term of equation 3 becomes equal to unity. If we calculate the activity of carbon tetrachloride and cyclohexane3in the presence of n-dotriacontane under the assumption of AE, = 0 by equation 3, we obtain for %‘ the curve G in figure 1. The shape and position of this curve suggest that the negative deviation of this solution from Raoult’s law can be accounted for ivithout the need of special assumptions of energy (1) or of entropy (15) of mixing effects. The same applies to the n-hexadecane systems. The activities calculated from the vapor-pressure data of the same systems (1) are equally well accounted for by use of equation 3 (see reference 2). In reality, then, not Raoult’s law but Guggenheim’s modification of it should be accepted for the definition of the reference solution in order to take into account large differences in molecule size betneen solvent and solute. As in all cases under consideration in this paper, such a change in the reference curve would cause but a small change in AFm ( < 500 cal. per mole) and would also leave the relative position of the curves in figures 3-9 essentially unaffected, such recalculation would not reveal any qualitatively neiv features and \vas therefore deemed unnecessary at this time. Negative deviation from Raoult’s law due to specific interaction between solvent and solute has been observed in the aliphatic series only for the system amines-chloroform. Rlonocetylamine in this solvent has a t .V2 0.02, At‘” = -500 cal. per mole. From Marvel’s data (7) one extrapolates for this system AH,,, $1200 cal. per mole. This would give an entropy change AS,,, +5 E.U. for the mixing process. Qualitatively all these changes point in the direction of molecular compound formation. They involve such small changes in thermodynamic properties, however, that the association must be a very loose one and hardly comparable with the solvates known among aromatic compounds. The positive deviations from Raoult’s law are for those systems for which ASm = 0 (regular solution), most often explained as due to differencesin cohesive energy density (AIEYBII/V)of the pure components. If the premise of the equivalence of all configurations of the segments of all component molecules on any of the available sites, which underlies equation 3, is fulfilled, wAB should indeed be independent of the molecule-size difference between solvent and solute and should be expressible as a function of
-
-
N
just as in the case of simple spherical molecules for which the Hildebrand function ( 5 ) has been derived. Since in that case the activity coefficient is given by
* In view of their rigidity, both of these molecules were considered as occupying one site each, the size of which was for geometrical rea~onsconsidered as equal t o four methylene group, so that rA 1, r. = 8; z w a 8 taken 88 8.
-
SOLUBILITY OF PARAFFIN-CHAIN COMP0UNI)S
899
where $1 = volume fraction of solvent, N i / N 2 = y2should a t a fixed concentration (and in solvents of a narrow molar volume range) be a function of AEJVI only. The plots of log y2 us. (AE1/Vl)* in figures 10, 11, and 12 show that this condition is not fulfilled in the solutions under consideration. The activity coefficient is a function not only of the differences in cohesive energy density but also of molecular s t r ~ c t u r e . One ~ can, indeed, discern a definite grouping of solvents: (1) The solvents made up of molecules of small polarization anisotropy, such as cyclohexane, carbon tetrachloride, chloroform,
LO-
/
DI-PI-OH
OEIOAc
10SVOPC e-109
x 9ENZE%E
O-
Is'io 10. Plot of activity coefficient y2 of n-dotriacontane in various solvents (at .V? 0 02) as a function of the cohesive energy density difference.
-
and benzene ; (2) the dipoles containing molecules of considerable polarization anisotropy (strong orientation tendency such as aliphatic ester, ethers, ketones) ; and (3) the alcohols. This grouping is about what one mould expect intuitively from the neglect of entropy changes in the correlation. We can then calculate the exrcss entropy of mixing from
4 Here, a s well a s in the following discussions, all comparisons are made at solute ooncentrations of N 2 mole per cent, which is below the concentration at which interpenetration of the randomly configurated chains (6)or common possession of one solvent neighbor site by two solute molecules would occur in the case of the largest molecule-size differences of this series.
900
A . BOND1
Most of the presently available data involve alcohols. The recent calorimetric work of Parks and Rowe (11) permits calculation of AH,,, of cetyl alcohol
I
O
-10
yt 86
E)&-(#I-
20
30
FIG.l l . Plot of activity coefficient Y S of stearic acid in various solvents ( a t 5': a function of the cohesive energy density difference.
FIG.12. Plot, of activity roefficient y2 of cetyl alcohol in various solvent.8 (at S: as s function of t,he r.ohesive rnergy demity differenre.
-
-
0.02)
0.02)
in methyl and butyl alcohols. At 25°C. and N? of 0.0055 (in methanol) and 0.0109 (in butanol) one obt,ains from their data AHm = -1940 cal. per mole and - 850 cal. pb?r mole, respectively. This gives, after reasonable temperature
SOLUBILITY OF PARAFFIN-CHAIN COMPOUNDS
-
-
90 1
correction, at the corresponding saturation line concentration AS,,, -12 E . U . and - 5 E.u., respectively. Extrapolation of K. L. Wolff’s (18) data for AHm to cetyl alcohol in cyclohexane gives AHm - 3 kg.-cal. per mole and AS, - 13 E.U. Reasonable extrapolation of the data for solution of hydrocarbon in alcohol to the system n-dotriacontane-isopropyl alcohol leads to AH,,, -2.5 kg.-cal. and A S m -20 E.U. The pronounced negativity of Ah‘, suggests that in these solutions-or a t least in the immediate neighborhood of the solute molecules-there is a more orderly arrangement than in the pure solvent. Such an enhanced state of order can be well visualized to mean that the small alcohol molecules (in the cetyl alcohol-methanol and in the dotriarontane-isopropyl alcohol systems) on the neighbor sites nearest to the parafin chain are oriented with their alkyl groups toward the paraffin chain in order to minimize the potential-energy differences between each other. This arrangement is similar t o Frank’s (3) *‘icebergs”around non-polar solutes in aqueouq
-
-
-
N
TABLE I ,Solubility, ezcess free energy of m i z i n g , and non-ideal portion of the heat of solution of normal f a t t y acids in u!ater (calculatedjrom data b!/ Ralslon and coworkers (18)) AFDI
cni. per mole
3590
Myristic nrid
’
0 GO
’ ~
I 02 2.70
x x
10-6 10-8
ml pcr nsnir
-930
4im
-880
5780 8530
+6,850 -t5,470
6000 9.540
___
+8,900
+11.OGO
systems. The numerical relation between the AS, values and the entropy of fusion of these alcohols suggests, however, that the alcohol molecules in our case do not form “frozen patches” around the solute but should be merely preferentially orientated. Further subst,antiation of the reality of t,his picture by additional independent experimental data (such as calorimetric and \raporpressure measurements) and possibly x-ray diffraction measurements, as well as rigorous analysis, could be interpreted to mean that there is essentially only a quantitative but no qualitative difference between “true’’ and “mirellar” solution. The solubility of fatty acids in water has an extremely small temperature coefficient. As a result we find R(alny/al/T) to be very strongly positive (table 1). At the extremely small concentrations involved, the term depending on (alnf/ac), is probably not very important,. We may therefore expect AS, to be either very small-if negative-or even sensibly positive. The latter would indicate that fatty acids, just like other electrolytes, produce an increased
902
A . HOXDI
state of disorder in the surrounding water structiire (3) by coulombic effects and by their large ion radius. SUMMARY
Published data of the solubilities of a number of paraffin-chain compounds in common solvents are analyzed for deviations from Raoult’s law. These deviations from ideality are expressed as excess free energy of mixing, AF,,,. Plots of AF,,, us. concentration are presented which permit detailed discussion of the relationship between chemical constitution of the solute and its solubility as well as of the specific interactions between solvent and solute. The negative deviation from Raoult’s law (higher than “ideal” solubility) of long-chain paraffin hydrocarbons in cyclohexane and carbon tetrachloride could be accounted for as due to molecule-size differences between solvent and solute alone by application of Guggenheim’s solubility theory. This result indicates complete random configuration of the segments of all components in such systems. The positive deviations from Raoult’s law (lower than “ideal” solubility) of most paraffin-chain compounds (alcohols, acids, amines) in the common solvents are shown not t o be accountable from differences in cohesive energy density alone, but must also be due to considerable excess entropy of mixing, AS,,,. Some numerical values of AS,,, of systems involving alcohols were estimated. All of these were strongly negative, suggesting that insolubility may be proportional to the degree of specific orientation of solvent molecules in ,the immediate neighborhood of the solute molecule which is required to minimize the potential energy between them. The solubility data of fatty acids in water differ markedly from those of nondissociating systems and suggest as the cause both positive heats and positive excess entropy of mixing, closely resembling the behavior of some inorganic ionic systems. REFERENCES
(1) BERGER, G.:Itec. trav. chim. 17, 1029 (1938). (2) BONDI,A.: To be published. (3) FRANK, H. S.: J. Chem. Phys. 18, 507 (1945). E. 9.: Proc. Roy. SOC.(London) Ala,206,213 (1944). (4) GUGQENHEIM, (5) HILDEBRAND, J. H.:The Solubility of Non-electrolytes. Reinhold Publishing Corporation, New York (1936). (6) HULBURT, H. M., et al.: Ann. N . Y . Acad. Sci. 44, 371 (1943). (7) MARVEL, C. S.: et al.: J. Am. Chem. Sac. 80, 1337 (1938). (E) MARVEL, C. S., et al.: J. Am. Chem. SOC.61, 3550 (1939); 62, 2273, 3109 (1940;68, 2-54 (1941). (9) MAZEE,R . W.:T.O.M. Reel No. 79, p. 2504 et seq. (10) PARKS, G. S.,AND HUFFMAN, H. M.: Ind. Eng. Chem. 19,1138 (1931). (11) PARKS,G.S.,AND ROWE,R. D.: J. Chem. Phys. 14, 507 (1946). (12) RALSTON, A. W.,AND COWORKERS: J. Org. Chem. 7, 546 (1942);8. 344, 473 (1943);9, 68,102, 201, 259, 267, 319, 329 (1944);10, 170 (1945). (13) ROTRMUND, V.:Ld8lichkeif und Ldslichkeitsbeeinflussun~. J. A. Barth, Leipsig (1907).
PHOTOELECTRIC SPECTROPHOTOMETRY
903
(14) HEIDELL. A , : Solubilities of Organic C o m p o u n d s . D . Van Nostrand Company, S e w York (1911). (15) STAVERMAN, A . J., A X D COWORKERS: Rec. trav. chim. 60, 76,327, 610 (1941). (16) UBBELOHDE, A . R . , A K D OLDHAM, J. W. H . : Trans. Faraday Soc. 34, 282 (1938). (17) WILLIAMOS,A . T . : Trans. Faraday Soc. 40, 421 (1944). (18) WOLFF,I i . L., A N D COWORKERS: Z.physik. Chem. B36, 237 (1937); B46, 287 (1940).
PHOTOELECTRIC SPECTROPHOTOMETRY THEPERFORMANCE OF A QUARTZ DOUBLE MONOCHROMATOR IX AN IMPROVED AND MOREVERSATILE PHOTOELECTRIC SPECTROPHOTOMETER] F. P. ZSCHEILE2 Department of Agricultural C h e m i s t r y , P u r d u e U n i v e r s i t y Agricultural E x p e r i m e n t S t a t i o n Lafayette, I n d i a n a Received December 9,1946
A photoelectric spectrophotometer was described by Hogness, Zscheile, and Sidwell in 1937 (6) as a much more sensitive, accurate, and rapid instrument than the first of its type reported by Zscheile, Hogness, and Young (21). In 1937 construction was started on a third spectrophotometer, which operates on the same general principles as the second instrument (6) but which embodies certain refinements of construction and arrangement and is much more flexible and versatile in performanoe. Illloreover, it is built about a large quartz MiillerHilger double monochromator, indicated earlier (6) as the i d 4 optical instrument for transmittancy measurements. This permits very exhaustive studies on scattered radiant energy and the effect of various slit widths on absorbancy (log,, I o / I ) values. This paper describes the performance of this assembly and the results of rigorous tests for scattered radiant energy, with emphasis on the monochromator and photocell employed. Some of this work supplements the report on the earlier assemblies (6, 21).
I. DESCRIPTION OF EXPERIMENTAL EQUIPMENT Figure 1 shows the entire spectrophotometer except the galvanometer scale, which is back of and above the operator. Figure 2 s h o w the contents of the photocell chamber with the vacuum cylinder removed (it appears in figure 1 as a vertical cylinder between the absorption cell chamber and the amplifier control panel). Figure 3 is a diagram of the principal parts of the assembly. Journal Paper No. 275, Purdue University Agricultural Experiment Station. address: Division of Agronomy, College of rlgriculture, University of California, Davis, California. 1
* Present
