Thermodynamic Parameters Involved in ~ydrophobicInteraction A Laboratory Experiment Tony Aeris and Julius Ciauwaeri Biophysics Research Group. Department of Biochemistry, Universitalre Instelling Antwerpen. Universiteitsplein 1. 8-2610 ~ntwerpen,Belgium The hydrophobic effect and hydrophohic interactions have been quite controversial for a long time in general biochemical and bionhvsical literature. Kauzmann first introduced the term .'thehydrophobic bond" in hisnowclassiral review 11) and the rwenline hook '.The Hvdruohobir Effect" by '?;anford (2) has given a clear expianation of hydrophohic forces, their thermodynamic principles, and their molecular basis. Since then, more general handbooks on biochemistry (3) such as those on proteins ( 4 ) and on membranes (5) have discussed the implications of hydrophobic forces on the structure of hiosystems. The main point is that apolar molecules are forced toleave water mainly on the basis of entropic effects that allow the water molecules to have a more disordered structure in the absence of the apolar molecules. Therefore the nonpolar side chains of the amino acids cluster together inside the protein molecules; in the same way the apolar parts of the lipids and aoolar surfaces of the intrinsic membranes proteins aaere-gate to form the interior part of the membranes. A short review of the present problems in explaining the molecular details involved in hydrophobic forces has been discussed (6). We have set up some quitesimple experiments for our graduate students in biochemistry that demonstrate the basic properties of hydrophohic interactions and allow quantitative conclusions ahout the thermodynamic principles of the hydrophohic effect.
alcohol as a solution of alcohol molecules in itself, so we can write PHC= P'HC
+ RT WXHC.~ H C )
(3)
where we use the same quantities in the same units as in relation 2. Now, for the pure alcohol, the mole fraction of the alcohol equals 1,so that x ~ cf . ~ =c 1and eq 3 reduces to PHC = P'HC
(4)
If we now have a solution of an aliphatic alcohol in water in equilibrium with the pure aliphatic alcohol itself, the chemical potential of the alcohol in the two phases is the same, PHC= Pw
(5)
so that we have pDHC= pO, + R T in x, (6) We can now define the free enerw of transfer of a mole of solute from an aqueous solution to a pure hydrocarbon solution as a auantitative Darameter describine" the hvdrooho" . hicity of t i i s solute. . For the aliphatic alcohols, we can now consider the pure alcohol itself as the reference hydrocarbon solvent. Thus, we get from relation 6,
--
Theoretical Background
We consider the aliphatic alcohols 1-butanol and l-pentano1 as model systems for hydrophohic molecules. The thermodvnamic oronerties of these solutes in an aqueous s o h tioncan he described by the chemical potential ~i of the solute, which tells us how much the free enerw of the solution changes per mole of solute added to the system:
According to Tanford (2), we have for the alcohol, dissolved in water: where r.. #".
r,
f,
= t h e rhemiral potential of the dissolved alcohol in wnrer. = rhertantlnrdchcmical potential; if using molefrnrr~~nas cunccntraliun ut~its,thia polenrid represents the internal free energy of the solute molecules and the free
energy of interaction with the solvent molecules. =the mole fraction of the solute _- nurnlwr ol mdrs oisolurr .number of m c k of rc,lurt + n u r n l w of mules ol solvcnr
=the activity coefficient of the solute in water: in the present conditions, due to the limited solubility ofthe concerned alcohols, we can write f, = 1.
Using the same terms, we can handle the pure aliphatic
In order to get a quantitative idea about the hydrophobicity of the aliphatic alcohols 1-hutanol and 1-pentanol, we have to determine the mole fraction X, of the alcohols dissolved in water when in equilibrium with the pure alcohols: thiscan he done with reasonable accuracy by solubility studies of the alcohols in water in a simple way. Experimental A whole set of solutions of the alcohols (pro analysi grade) are prepared in water: For butanol we cover the range of 4.0 to 14.0 mL butanol per 100 mL solution in steps of 0.5-mL increments; for pentanol we cover the range of 0.50 mL to 5.00 mL per 100 mL solution in steps of 0.25-mL increments. These solutions are prepared at 20 "C and are kept at some constant temperature. Let us suppose that the solution a, (containing ai mL of alcohol) is clear and that the solution a;+~is opaque due to the presence of undissolved butanol or pentanol that forms drops of pure alcohol, then we accept that the soluhilitv of t h e d c o h k is given by
Here we introduce an experimental anoroximation whose size is determined by the solute increments of the different solutions: the smaller these increments the more accurate one can determine the solubility. In our case fbr butanol we take 0.5-mL increments and for pentanol 0.25-mL increments, which results in an uncertainty of 3%. Volume 63 Number 11 November 1986
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We calculate the mole fraction x, from the relation
va0~,,+ vz
(8)
vdUtion =
where V,lUt. is milliliters of hydrocarbon added and V2 is volume of water; if we have measured the amount of water we had to add to get the finalvolume of 100 mLsolution, this relation is correct. If we have accepted that VZ = Vso~ution V,,lUt, and we just have made a subtraction, then we have made an approximation because there is avolume changes in dissolving the aliphatic alcohol in water. We have V,wm = Xi&% where & is the partial specific volume, which is the change of the volume Vof the solution per gram of i added.
where Aw; is the mass in grams of the added component i. By just making a simple subtraction Vz = V,i -V h and thus accepting no volume change in mixing the two components, solute and solvent, the maximum deviation is 0.5% in the applicable concentration range (7). By using the appropriate densities and molecular weights of the two com~ o n e n t s .the mole fraction of the solute can he calculated irom relation 8. Onlv simple equipment need he used: volumetric flasks and pipette;, a carefully thermostated waterbath, and a reasonable sharp eye, which must differentiate between clear and opaque solutions. Results Our students measure the solubility and calculate the corresponding AGo,..,fe, a t different temperatures: they usually try 1 ' C (ice-water bath), 25 ' C (room temperature)
30
325
350
Journal of Chemical Education
(9) AG(T)'tran8re,= mOtrsDarer - T.AS"ma~er where the enthalpy change of transfer AHDt,..fer and ASot,a.,sf.. can he considered as constant, so that a linear graph of AGo,,fe, as a function of the absolute temperature Tallows the calculation of the slope and of ASot,.f.,. From and the the AG" a t some defined temperature G(Tx)ot~a~,~e, calculated ASot,..fer, the AHo, re. can be calculated:
(see Figure 1).Alternatively
so that a graph of AGo,,.,~er/Tas a function of l/Tallows the direct calculation of AHot,.,,~er. In the same way, from the AG(T,)o,a..rer a t some defined temperature T, and the AH0,,..fe, determined from the graph, the ASo, rer can now be calculated (see Figure 2).
If t h e students compare their results of AGotr...rer, AHot,,,fer, and ASDt,.,rer with the rigorous values from literature (Z),they usually obtain the following results: The AGo,..,,.fe, (298 K) does agree within 5% with the rigorous value of -2400 eallmdl for 1-hutanol and -3222 callmal for 1AH',,,. c. and AS',,.,. re, both are positive and demonrtmte the entropydriven basis of hydrophobic forces. The agreement wth rigorous values is now more qualitative because the 5%mismatch of the AGDt,an.r., can result in a 20%mismatch of ASo and AHD. They usually obtain a value close to 800 eallmol for the difference between G"u,.f.r for 1-pentanoland 1-butanol;this value is very close to the magic number of 825 callmol, which is the increase in hydrophobicity if the apolar part of a hydrophobic molecule is increased bv one -CH7- unit (2). They are surprised to find that the solubility of a hydrophobic molecule decreases on increasing the temperaturesince they have demonstrated the omosite with maw chemicals in their chemistry experiments. ~ h ealso i can understand now why same aggre..rates.. such as TMV virus. fall mart if thev. are out . into the cold room nlthough morr of their hiorhemirnl~are stored in the cold room in order to protect them agomat denatwarion and devada-
375
'/rr.KI."b Figure 1. AGO for me transfer of butanol hom water to pure butanal. Solubility measurements have been done at 2.0.9.0, 16.0, 19.5, 23.0, 29.5.37.0, and has been calculated. 47.5 OC. From the molar solute fradian, lhe AGO, From the graph AGO,.,, versus Ta ASOmsfm of 14.5 callmol deg K can be deduced (see relation 7). From the AGO(298 K) of -2375 callmol and lhe just deduced ASOmwh, of +14.5 callmal deg K. a AHOmwtm of +I950 cal/mol can be calculated. 994
and 50 "C (where volumetric flasks covered with parafilm still can be used). The results can now he interpreted in two ways:
Figure 2. The same data as far Figure 1 have been used to make a graph AGO,,a..,m/T versus t/T. From this, a A,*, of 1960 catlmol has been deduced (seerelation 8). From lhe AGO(298 K h , , of -2375 callmol. and the just deduced AHD,,a.,b, of 1960csl/mol.a ASOmsqmof 14.6callmol deg K can be calculated.
1979:Chsp 3.
Literature Cited
(5)
( I ) Kaurmann. W.Adu.ProkinChem. 1959.14.1. (2) Tsnfod, Ch. "The Hydrophobic Effect";Wi1.y: New York. 1973. (3) Metzler, D. E:'Biochemistry"; Academic NewYork, 1977: C h a ~ 4 . (4) S~hulr.G. E.; &hirmer. R. H. ."Principles of Protein StructureM:Springer: Berlin,
(6)Franks. F. Nofure 1977,270,386, (7) Hi1debrand.J. H.:Smfl, R. L. "The Solubilityof N o n e l e ~ o l m s " Dover: ; New York,
H O U ~ I ~ YM.
D.: stanlev, K. K. '
'
~ of ~~ i ~~ ~ Membranes"; o~ ~ ii ~ ~dwiley: NW
umk,1982: Chap 1. 1964 Chaps.
Volume 63
Number 11
November 1986
995
