Studying Odd-Even Effects and Solubility Behavior Using a,w-Dicarboxylic Acids Hugh D. Burrows University of Coimbra, 3049 Coimbra, Portugal Surprise can play a valuable role in teaching. In a general chemistry experiment on solvent extraction, my students were required to determine the partition coefficient that expresses the distribution of a dicarboxylic acid between water and an organic solvent. They did this by titrating the aqueous phase with base both before and aRer extraction ( I ) . We had been using solutions of succhic acid. I wanted to broaden the experiment and lower the likelihood of student collusion, so I was interested in replacing the succinic acid with other dicarboxylic acids. However, on consulting the Handbook of Chemistry a n d Physics (2)I was surprised to fmd the following entries for solubility in water for the first few members of this series. oxalic acid malonic acid succinic acid giutaric acid adipic acid
HOzCCOzH soluble CHz(C0zH)z very soluble HOzC(CHz)zCOzH slightly soluble HO~C(CHZ)~COZH very soluble HOzC(CHz)420zH slightly soluble
ever, the wealth of other material now included has led to its exclusion from most current textbooks. As a check on ignorance about the effect, try this simple question on your colleagues. Anhydrous (glacial) acetic acid is normally a solid in cold weather. Will propionic acid be solid or liquid under the same conditions? Depending on your feelings about your colleagues, send them either scuttling into the snow with a bottle of propionic acid, or to the library to find the answer! Applications of the effect, however, are from trivial, and ignorance of it can lead to much wasted research effort. I t is not uncommon to read articles aboutattempts made to increase the "hydrophobicity"of a molecule by introducing a n extra methylene group. Researchers involved frequently become perplexed on learning that their results offer no simple interpretation. For such studies, one should normally use a series with either an even or an odd number of carbon atoms in the chain. Examples and Applications of Odd-Even Effects Observed Physical Propeflies
This proved to be a n example of a n odd-ven effect, in which physical properties of straight-chain aliphatic compounds, such as solubilities and melting points, alternate with the numher of carbon atoms in the chain. This has long been known (31, and it was formerly included in standard texts of physical chemistry (4,5). How-
I begin my discussion with the simplest series of compounds. Figure 1 contains plots of the melting and boiling points of the straight-chain hydrocarbons in the series from methane to eicosane (CZoHe) as function of chain length. Polymorphism, with different melting points, is frequently shown by these compounds (6). Using a consis-
Figure 1. Melting and boiling points of the straight chain aliphatic hydrocarbons.
F gdre 2. Traple polnts (c rc es), atent neals ofIJS on (nexagonsjand logarithm of me prce in ao ars per gram (sq~ares) of tne slraght chain monocarboxylic acids
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Table 1. Fany Acid Compostion of Some Typical Oils (53)' Percentage of total fany acid content Saturated acids (CH3(CHz)nC02H) n=
10
12
14
16
18
unsaturated acids other
palmitoleic
oleic
linoleic
linolenic
other
45.4 18.0 10.5 2.3 0.4 14.6 0.4 7.5 trace coconut oil 1.4 10.2 3.9 1.5 49.6 34.3 corn oil 19.0 24.1 47.4 0.2 linseed oil 6.3 2.5 0.5 olive oil trace 6.9 2.3 0.1 84.4 4.6 42.7 10.3 palm oil 1.4 40.1 5.5 soybean 0.1 9.8 2.4 0.9 0.4 28.9 50.7 6.5 0.1 oil sunflower 5.6 2.2 0.9 25.1 66.2 seed oil The dataclearly show why mrn oil, olive oil, or sunfloweroil are preferableto mconut oil or palm oil for anyone likely to have acholestorol problem.
-
-
tent set from ref 7, it is obvious that boiling points follow a fairly smooth curve, whereas melting points show a somewhat irregular increase. Separate curves would be needed to fit the data for the odd and even members. As the chain length increases the differences become smaller, and are barely perceptible beyond decane. Similar effects, which are frequently more marked, are observed with derivatives of the straight-chain alkanes. In Figure 2, the triple points (temperatures at which solid, liquid, and vapor coexist) and enthalpies of fusion of the monocarboxylic acids are plotted against chain length. Much of the data is taken from a recent study (81, and it provides a good example of the value of precise thermodynamic data. A similar odd-even effect is observed with the melting points. For alkanoic acids and alkanes that have the same crystal structure (typically orthorhombic), the melting points eventually converge to that of an infinitely long hydrocarbon chain, such as polyethylene, which melts at 414.6 K (9).Various linear functions have been proposed that relate melting point and chain length (10). Do transition entropies show the same effect? Yes. However, enthalpies. entropies, and transition temperatures transifirsborder (sharp) are closely related. tion a t constant pressure, the free energy change a t equilibrium is zero according to
or-a
AG=Af-TAS and
Some Biochemical Considerations One can look for odd-even effects elsewhere, for example, in the prices of these compounds as a function of chain length. Figure 2 contains the logarithm of the 1990 price, in dollars per gram, for monocarboxyIic acids with purity greater than 99% (11).Two main points emerge. first, acetic acid is not the cheapest fatty acid. Second there is a dramatic odd&even effect for acids with eight or more carbon atoms in the chain that is closely related to the abundance of these acids in nature. The most common biological sources of fatty acids are glycerides and phospholipids, which contain only the acids with even chain lengths in significant amounts. This can be seen in Table 1, which lists the constituents of some common oils and fats. It is tempting to attribute this obser70
Journal of Chemical Education
vation to some preferred biophysical property of evenchain acids. However, there is little evidence for this. Biochemists are familiar with the bioaenesis of fatty acids, and they offer a more appropriate explanation that involves biosynthesis by addition of two-carbon units (12). In one proposed mechanism (13) ethanol is oxidized to acetaldehyde, which then combines with coenzyme A (CoA). Two molecules of CoA then yield acetoacetylCoA, which is reduced to butyrylCoA. Then either butyric acid is released, or other even-chain length derivatives are formed by successive condensations with acetylCoA.
CH,CHO + HSCoA 2CH,C@SCoA Z?
CH,CO-SCoA + Hz
CH3COCH2COSCaA+ HSCoA
(4) (5)
Other mechanisms have been proposed (141, but experiments using isotopically labelled acetate confirm that addition of the Cz unit is a major pathway to fatty acid formation in nature (15). This biological predominance of the compounds with even chain length finds application in environmental studies. Aliphatic hydrocarbons occur naturally due to the degradation of fatty acid derivatives. They also occur in the cracking of crude oil. However, the naturally occurring hydrocarbons show odd-even variations, while those from petroleum cracking do not. Thus, the two types are easy to distinguish in oil-pollution studies (16,17). Melting and Phase Changes Odd-even effects are observed in manv other svstems (18-22). These effects have important applications in ~olvmerchemistrv. where ~olvamides and ~olvesters with . . &n n u r n b e r s o f ~ 1 1 , ~ r o u are ~ shigher melting than rhose with odd numbers (23,.Although it isr(enerally preferable to have relatively high-meltingpolym~rs,low&ransition temperatures may be desirable to reduce the cost of orocessinn. With systems involving liquid crystals (e.g., nematic phases in display devices), there is particular interest in materials that form such phases close to room temperature. One method of "fme-tuning" liquid crystalline phasetransition temperatures, either from the solid or from the
-
isotropic liquid, is to vary the number of methylene groups, and various examples of odd-even effects in liquid crystalline systems have been presented (24). Other examples where odd-even variations are observed include Krafft points of detergents (251, optical aniosotropy (26) and solute ordering (27)in liquid crystals. One of the most pronounced odd-even effects is seen with the a,malkanedioic (dicarboxylic) acids, which show differences in melting points up to 90 'C between successive members (28).This effect also leads to the observed solubility differencesbecause solubility and fusion both involve breaking up the crystal lattice and thus are related theoretically (29). Theoretical Interpretation of the Odd-Even Effect Alternation of Bonds and Resonance The f r s t theoretical explanation (30)suggested that the odd-even differences arose from alternating strong and weak bonds along the chain. Subsequent moiels m&fied this bv introducine the idea of alternating - -positive and negat&e charges on carbon atoms ( 3 1 3 3 ) . Although these ideas seem somewhat contradictory to our current ideas on covalent bonding, they are closely related to the valence bond idea of resonance. Theoretical calculations (34) have shown that many of the odd-even variations can successfully be explained by resonance between singly and doubly bonded structures. In addition to treating straight-chain compounds, these models also explain the observed variations in melting points of the cycloparaffis. Studies on the closely related polysilanes (35)have also shown the value of such resonance calculations in explaining photodegradation product distribution. Solid Packing and End-Chain Interactions
However. the maior effect eausim this odd-even variation is more likely to he related to tge packing of the alkyl chain in the solid phase. Aliphatic chains are normally present in the solid (36) in-an all-trans configuration (Fig. 3). Muller (37)explained the odd-even effect as due to the fact that the terminal groups are trans to one
another in the even-chain series, but cis in the odd homologues of alkanes. This was contested by Malkin (38),who suggested that the essential feature responsible is the tilting of the zigzag carbon chains. Alternation is only observed when the chains are tilted with respect to the end-group planes. There are exceptions, and this generalization has been criticized (39).Although much of the criticism centered on Malkin's attempts to correlate melting points with X-ray that there is a~ structural it is~clear (7.40) ~~~determinations. ~ ~ ~ .~ , relationship between differences in packing in the solid state and the alternation of properties. In one of the clearest treatments of the problem, Larsson (41)has shown that the alternation can be correlated with the packing in the planes containing the end gmups. The various possible subcell structures in hydrocarbon chain systems were treated, and the packing of the terminal methyl groups was considered specifically.An increase in packing increases intermolecular interactions, notably van der Waal's forces. It also stabilizes the solid phase. When alternation of properties occurred there were differences between the oackine densities a t the interfaces between the chain en& for even and odd members. Although the arguments were for methyl groups, treatment for other groups will be similar. The importance of end-chain interactions also applies to the odd-even effect observed for nematic-isotropic phase transition (42). This was treated usine a self-consistent molecular field approach. Although the; transitions differ fundamentallv from meltine. -. as thev occur between two fluid phases, there are points in common. ~~~
~
~
An Experiment to Demonstrate the odd-~ven Effect Experiments consist of determining the solubility of a series of saturated solutions of dicarboxylic acids by titrating them with standardized sodium hydroxide solution, using phenolphthalein.
The solubility in m o m can be calculated from the volumes of acid and sodium hydroxide, the NaOH concentration, and the stoichiometry If solubilities are required per unit mass of solution, or in mole fractions, solutions can be weighed before titration, or densities can be determined. Table 2. Quantities of Dicarboxylic Acids and Sodium Hydroxide Used for Solubility Determinations Acid
I
Weight (g)usedto prepare 1 L of saturated solution
Volume of solution pipetted (mL) for titration with ca. 20 mL of NaOH solution (1 M)
trans
oxalic acid maionic acid succinic acid glutaric acid adipic acid maieic acid fumaric acid 'AS the dihydrats. Alternatively, titrate with 0.1
.-. -. ..-.
10 lb
15
zb 1od 1 15d M
NaOH solution, and
use ten times
this
""LlrnP
I
'Due to the hiah con of this reaoent. it is oreferabie to use smaller Mlumes
Figure 3. (a) Trans and gauche conformers of mbutane; (b)ail-trans zig-zag configuration of n-octane.
Volume 69 Number 1 January 1992
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With g e n e r a l chemistry s t u d e n t s , no a t t e m p t a t temperature control was made, and solubilities were determined a t room temperature. An obvious extension would be to thermostat solutions a t a series of temperat u r e s , allowing d e t e r m i n a t i o n of thermodynamic parameters. Saturated solutions of the acids are prepared by dissolving the acid or anhydride in hot water and allowing the solution to cool, so that the solution will be in equilibrium with the solid acid. We have used the saturated dicarboxylic acids (oxalic to adipic) and the unsaturated maleic and fumaric acids. Convenient quantities are given in Table 2. Titrations were carried out usina a 1-mom solution;; sodium hydroxide, standardized-with potassium hydrogen phthalate (indicator: phenolphthalein (43)). .Caution: Csual precoutionr shuuld bc obiewed wth such c~,rwenrmtedNaOH solutions. 'The). ore corrosive n n d rerdllg nhsorh CO, from the otmoaphere Thcy tend to nctack glass, causinfglass buret stopcocks to stick (43). The supernatant saturated solution of each acid is pipetted into a n Erlenmayer flask. About 20 mL of water and a few drops of phenolphthalein are added, and the solution is then titrated with the standardized sodium hvdroxide solution. added from a 25-mL buret. "~ Care is taken tu avoid pipetting crystals of the solid. Due to the laree differences in solubilities, different volumes of t h e acid: a r e required, a s indicated i n Table 2. If solubilities are to be determined a t elevated temperature, pipets should be preheated to prevent solid precipitating.
solubility differences are also consistent with Larsson's views of increased packing in end-group planes (41). To confirm that effects in the solid state are dominant, s t u d e n t s can a t t e m p t to correlate solubilities with parameters such a s melting points (2, 28), densities (2), and pK,'s of the acids (47). The only other property showing alternation is the melting point, although there is no simple correlation. p he lack of alternation in thc densities ofthe solids may, at firsr, ieem surprising. Howtwer, the properries that should be considered are the molar volume and the rrystal structure. Urttcr students should he encouraged to refer to literature data 48,49 on crystal structures of dicarboxylic acids. One result that surprised me was that more than 50%of students thought that there should be a correlation with t h e pK,'s. Perhaps the students did this experiment around t h e same time they were learning solubility products in general chemistry and thought that there should be a connection between the equilibria for acid-base dissociation
~
Results and Discussion Tvoical results for the logarithm of the solubilities (in g/L) of the first five carboxylic acids are presented as a function of carbon chain leneth in Fimre 4. They clearly show the odd-even variation. Our &dents' expeEimental values are in eood ameement with literature data (28,44, 45). Even thepoorest students manage to get big differen: ces, in which the odd members always show higher solubilities. We would expect the trans unsaturated acid (fumaric acid) to have a iower solubility than the cis maleic acid if we accept Muller's suggestion (37)that the lower solubility of the e;en members G d u e to stronger lattice interactions when the carboxylate groups are in a trans configuration in the crystal. This is observed experimentally (Fig. 41, and it forms the basis of a nice experiment (46) that separates these two compounds after photoisomerization. The A.
-
and the precipitation
Care must be taken in emphasizing to students the importance of the separation of the solid phase in the second case. With more advanced students. study of solubility a t different temperatures provides reisonable values fo;enthalin molaltties vies of solution M,I.Solubilities are ziven im). The enthalpy (50) is given by
where T is temperature (Kelvin), and f2 is the activity coefficient of the solute. Assuming that the activity coeff~cient term is negligible
which is calculated simply from the slope of a plot of ln m against llT. Values obtained in this way compare well with those obtained calorimetrically (51). I n wnclusion, I feel that the odd-even effect provides a satisfying way of introducing students to a large area of chemistry t h a t encompasses both classical thermodynamics and applied aspects. General chemistry students who have tried the ex~erimentreacted favorably, and I feel that this experimenf. would be useful in practic& courses durine the first year or later. The experiment is o p e n - e n d e d , a n d we have extended i t to-studies of solubilities in organic solvents using solvent extraction. Data can be compared with literature values (52).
Figure 4. Logarithm of solubility (in giL) of the straight chain a.mdicarboxylic acids in water. Also included is data for maleic (square) and fumaric (triang1e)acids.
72
Journal of Chemical Education
Acknowledgment I am grateful to my Qulmica Laboratorial project students a t the University of Coimbra for testing the experiments; to S. &ao Adeyemi of Obafemi Awolowo University, Nigeria, for indicating the application of the effect in environmental studies; and to the reviewer for valuable comments. Financial support from INIC is gratefully acknowledged.
25. Tsataamni. F.: Pegiadov-Koentj"pou1". S.: Demettis, G.J Am. Oil Chem. Soe. 1387.64, 144P1447. 1. Palmer, W G. Expanmental Physlml Chemistry; 2nd ed; Cambridge University 26. Lalame, J. R.; Rayel, J. C.: Duguay, B.: Routiere, A,; Viani. R. Chem. Phys. 1986, Prehp: 1962; pp 136153. 107 998999~ 2. Weast, R. C.. Ed.; Handbook of Chemiafry o d Physics, 64th ed.; CRC: BoeaRaton, 27. Emsley, J . W.; Luckh-t, G. R.; Timini B. A. Chem. P h y s Letts. 1985,114,19-23. FL 198L1984: pp CGS576. 28. Markley, K S. in ThePatty Acids; Msrkley. K. S., Ed.; Interscience: New York, 1960; 3. Ba8yer.A. Ben Dtseh. Cham Ges 1877,lO. 12861288. Vol. 1, p 96. 4. See, for example, Glasstone, S. ?!enbook ofPhysieol Chemistry. 2nd ed: van 29. See. for a m p l e , ref4, p 644. Noatrand: New Ywk, 1940, p 402. 30. Bisch,O.Z. Physik. C h . l S W , 5 0 , 4 3 4 . 5. The only reference I have came across in the chemical education literature is 31. F d k , K.G. J. Am. Chem. Soe 1910.32.1637-1654. Oldroyd, D. R. Sehmi Sci. Re". 1968,50,86%863. 32. Cuy, E.J. J A m . Cham Soc 1920.42.503-514. 6. Maroncelli, M.; RngQi, S.; Strsuas, H. L.; Snyder, R. G. J. Am. Chem. S a . 1982. 33. Paulr H. Z.ZAnom. Chem 1922.119.271-291: ChemAbs. 1922.16.3561. 104,62374247. andreferen- therein. 34. c ~ R R E . ;Walter. ~.yEyring,H. J . ' h . ~ h S; ~ ~ 19'39.61. . 18761886. 7. B r o a d h u t , M. 0. J.Rra Nafl Bur Standards AlSBZ. 6 6 k 241-249. 35. Michl, J ; Downing, J . w.; Karatsu, T;M c h i e y , A. J ; Peg*, G ; wauraff. G.M ; 8. Sehaake.R.C. F:van Miltenhurg,J. C.;deKruif,C.G. J . Chem Themodyn. 198% Sw~yalrumaran,R.; Miller, R. D. Purp Appl. Chem. 1988.60.959472. 14. 763-769: 771-778. 36. WymK R. 0 . W. Crydal Structure; h d ed.;Interscience: New York, 1966;Vol. 5, pp 9. Nagle, J. F.; Goldstein, M. Macmmobcules 1 9 s . 16,264362652. sna.a*o lo. See, for example, Zaeharia, H. M. Cham. Phys EpIds 1977,18,221-231. 37. Muller, A. Pmc Roy.Soc LondonA 1929,124,317321. 11. Sigma Chemicd Company: St Louis,1990. 38. M d k i n , T J Chem. Soc. 1931.27962805. 12. Sh?cLland, K. P. in Blog8"esis ofNofuml Compounds; P Bemfeld, Ed.; p e w m o n : 39. Chapman, D. Chem. R w l382,62,43%456, and references therein. Oxford, 1963; Chapter 3. 40. von Sydow, E.Arkiu Kmd 1956,9,231-254. 13. The reverse r e a d o n hap recently k e n disnused in fhia Jovrnal in relation to me41. Lanron. K J. Am. Oil Chem Soe 1966,43.559662. taboliam: Bodner, 0. M. J . Chem. Educ. 1986.63, 676677. 42. Marcella, S. J. Cham. Phys 1974,60.35993604. 14. For a recent review see Wakil. S. J.: Stoops, J. K.: Joshi, V. C. Ann. RPUBiockm. 1970; 43. See,forerample,Laitinen,H.A.,ChemicdAnoiysis;McOraw-Hill:NewYor*; 1983.52.537479. Chapter 5. 15. Spe,fmexample,Popjalr,G.;Freneh.T.H.;Hunter,G.D.;Martina,AJ.PBiakm. 44. Aftan6 E. C.; Doumani, T F Ind. E n g Chem. 1949,41,2015;1017. J 1951,43,612618. 45. Apelhlat, A: Manzumla, E. J. Chem. Thprmodyumics 1987, 19, 317-329. 16. Bray, E. E.: Evans. E. D.Clpochim. Casmochim. Ado 1961.22, Z 1 5 . 46. Castm, A. J.;Ellenkrger,S.R.; Slnka, J . P J. Chem Educ. 19g9, 60, 521. 17. Rogere, M. A,: Koona, C. B. in Ongin and Refinins of Petroleum; MeGrath. M. G.: 47. A1hert.A: 5ejeant.E. P Thei%termimtim oflonizotion Constants, 2nd ed.; ChapCharles. M. E., Eds.: Advances in Chemietty Series 103; Ame"can Chemical man and Hall: Londm, 1971: p 89. Society: Washington, DC, 1971; pp 67-80. 48. Momison, J.D.: Monteath Robertson, J. J. Chem. Soe 1949,980-936: 987-982:99b 18. Pamr, P: Spier, H.L.J Am. Oil Chem. Soc. 1988.45336342. 1w1: 1001-1008. 19. Adeoeun, S. 0.: Sime, S. J. T h a m h i m . A c t o 1678,27,319-327. 49. Gaedkoop, J. A.; MseGillaw, C. H.&o Cryst 1967,1O, 125-127. 20. Lutton, E. S. in The Fatty Aeds: Markley, K S., Ed.; Interscience: New York, 1967; 50. Williamson, A. T. l h m . Fumdq S a . 1944,40,421436. Vol. 4, Chapter 22. 51. Apelblat,A. J. Chem. T h o d y n . 1986,18,351357. 21. Rakrtson,P. W J. Chem. Soc 1919. 115. 1210-1223. 52. See,for example,Dauies, M.; Gri€litha, D. M.L.Tmns. Faraday Soe. 1353,49,140522. H8rgert.A J . k n s . Fomdoy Soc 1537,63,55S560. 1410. 23. Bunn,C. W. JPolym. Sei. 1855,16,323-343. 53. Farman. G. D., Ed.: Handbmh ofBiakmisfry a n d Makulcrr Biology: Lipid% C a r 24. Toyne, K. J. in Thermotmpic Liquid Crystals; Gray, G. W , Ed.: SCIIWiley: bohydratw Siemids. 3rd ed.: CRC: Cleveland, 1975; pp 502-503. Chiehester, 1987; Chapter2.
Literature Cited
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