1300
Kbzb
Shinoda
“Iceberg” Formation and Solubility Koro Shinoda Department of Chemistry, Faculty of Engineering, Yokohama National University, Ooka-2, Minamiku, Yokohama, Japan (Received October 29, 1976) Publication costs assisted by Yokohama National University
The solubility of paraffin chain alcohols, amines, hydrocarbons, rare gases, etc., in water is very small, so that a large entropy of solution is expected. Yet, the enthalpy and entropy of solution of these solutes at room temperature are small or negative. This abnormal solubility behavior has been explained coherently taking into account iceberg formation of water molecules surrounding the solute molecules. The enthalpy and entropy of solution of hydrocarbons in water determined from the temperature dependence of solubility were divided into contributions due to mixing and to iceberg formation of solvent. It is concluded that the enthalpy of mixing of solute with water is as large as expected from widely different intermolecular forces, but is largely cancelled by the enthalpy decrease due to iceberg formation of water. Thus, the apparent enthalpy of solution is slightly positive, zero, or negative around room temperature (0-80 “C). Unlike currently accepted views on so-called hydrophobic bonding, it is concluded that the slight solubility of these solutes in water is mainly the effect of a large positive enthalpy of mixing, which at lower temperature is diminished (and the solubility promoted) by a large negative enthalpy of iceberg formation in the surrounding water. The small temperature dependence of solubility of nonelectrolytes in water at room temperature occurs because in that temperature range the large negative enthalpy of iceberg formation cancels the large positive enthalpy of mixing. Enthalpy loss due to iceberg formation of water is larger than the corresponding entropy loss, so that iceberg formation is not the entropy effect. These conclusions are widely applicable to the solubility behavior of most substances in water, including biocolloids.
Introduction The enthalpy, entropy, and Gibbs free energy of solution of a second component from a pure liquid state to a solute state are expressed as
Ac2
A H , - TAg2= = R T In a2 = R T In ( p 2 / p f ) (1) where u2 is the activity relative to the pure liquid, and p 2 and p : are the vapor pressures of the second component in equilibrium with the solution and pure liquid 2, respectively. The entropy of dissolution of a liquid (second component) in a liquid for regular solution is
AS,
= -R In x 2 (L2 in L,) (2) where x2 is the solubility of the second component expressed as mole fraction.’ If the mutual solubility of a liquid-liquid mixture is small, the vapor pressure of the solute is close to that of the pure liquid, i.e., In a2 = 0 and we obtain
R T In (p2/p;)
0 = A g 2 + R T In x2
(3)
It is evident from eq 3 that the enthalpy of a solution is large if the solubility is small. However, the enthalpy of aqueous solutions of many substances, as determined from the temperature dependence of the solubility
(4) is generally small or even negative a t 10-25 “C. Two examples of alcohols in water are shown in Figure l.2-4 In order to explain this important abnormality, Le., a large entropy of dilution, -R In x2, and a small or negative entropy of solution, R(a In x2/a In T ) ,Frank and Evans postulated that water molecules surrounding solute molecules form frozen patches or microscopic icebergs.O The solute molecule brings about an increase in the total The Journal of Physical Chemistry, Vol. 81, No. 13, 1977
amount of “order” in the water.6 In the present paper, the apparently abnormal solubility behavior of solutes in water is explained coherently by adoption of the concept of iceberg formation of water molecules. Several misinterpretations concerning hydrophobic bonding are elucidated.
Correlations among Solubility Curves The logarithm of solubility vs. the reciprocal of temperature is linear in ordinary solutions just as is the logarithm of vapor pressure vs. the reciprocal of temperature. The slope multiplied by -R is equal to the enthalpy of solution. Below the melting point of a solute, the solubility decreases more rapidly and the slope discontinuously increases in the amount AH: and AS:.
Ag2(S2in L,) = A g 2 ( L 2in L1) + AHzf
AS,(S2 in L , )
=
-R In x2 + AS:
(5)
(6)
The solubility curve deviates downward as compared to that of a supercooled liquid in liquid. Contrary to this, the solubility curve may deviate upward if solvent molecules surrounding the solute partially solidify or form icebergs, because the change in properties of the surrounding solvent molecules is reflected upon the partial molal quantity of a solute in dilute solution. The extent of partial solidification of solvent molecules surrounding the solute may increase with decreasing temperature and thereby provide an increasing negative enthalpy term. Thus, the slope of the solubility curve may also decrease progressively. The temperature dependence of these solubility phenomena are illustrated in Figure 2.
Enthalpy of Mixing of Hydrocarbons in Water The surface tension, y, of liquids is a direct measure of intermolecular forces. For saturated hydrocarbons, whose intermolecular forces are purely dispersion forces, yz = 20-26 dyn/cm. For water, y1 = 72.8 dyn/cm, which is
1301
"Iceberg" Formation and Solubility
TABLE I: Analysis of the Enthalpy and Entropy of Solution of Liquid Hydrocarbons in Water at 25 " C (First Approximation)a Solute AR,b = Agz(H bonds) t nARi AS: = R l n x , t Ayz(H bonds) + n A q Ti$ K V,, cm' t 5 8 0 = 8100 7520 + 1 . 9 = 15.4 t 7.2 20.7 363 89 C6H6 7.9 - 23.6 365 107 CH3C6H5 t640= 9260 - 8620 + 2 . 2 = 17.9 + C2H5C6H, t 4 0 0 = 10500 - 10100 t 1 . 4 = 20.4 + 8.4 - 27.4 370 123 a Numerical values in Table I are not accurate, but are indispensable to drawsemiquantitative or qualitative conclusions. Enthalpy of solution = AH, = -R_[a In x J a ( l / T ) ] , , a ; entropy of solution = AHJT; enthalpy [entropy] of mixing(H bonds interaction) = AH,(H bonds) [AS,(H_bonds ] ; e_ntropy of dilution = -R In x , ; enthalpy of iceberg formation = nASi; mean cal/mol. cal/(deg mol). 'Ti = tegpezture of iceberg formation = Ti = a d i / a S i ; Molar volume at 25 " C = V,. A Hi/aSi.
I
-
\
4'
22
1
I
2.6
30
I
I
i/T
I
34
I / T x IO'
Flgure 1. Solubility of hexanol and heptanol in water as a function of temperature.
the sum of the contributions of dispersion forces and hydrogen bonding interactions. The interfacial tension between water and saturated hydrocarbons, 712,is about 50-52 dyn/cm a t 20 "C. Introducing these values into the Fowkes's equation, which relates the interfacial tension to surface tensions of respective components 712
=
71
+ 72 - 2(7,d7P2
(7)
Fowkes can evaluate the contribution of dispersion forces to the surface tension of water, which is yld = 21.8 f 0.7.7 This value is close to that of saturated hydrocarbons, Le., the dispersion energy per unit volume of water is close to that of the hydrocarbon. Hence, the enthalpy of mixing of hydrocarbons with water is mostly due to changes in the hydrogen bonding interaction in the water surrounding the solute. In dissolution of saturated hydrocarbons in water, the destruction of hydrogen bonding interactions and the formation of "icebergs" in the water surrounding the solute molecules may be the dominating processes. The enthalpy and entropy of solution of sparingly soluble hydrocarbons in water is expressed as follows: A S z = AHz(H bonds)
A S 2 = -R In
+ nA&
+ ASz(H bonds) + nasi
(8)
(9) Where nARi (nASi) is the change in the partial molal enthalpy (entropy) of the solute due to iceberg formation of n moles of solvent, M 2 ( Hbonds) [AS2(Hbonds)] is the partial molal enthalpy (entropy) of the solute due to the decrease in hydrogen bonding interactions, and -R In x2 is the entropy of dilution. The extent of iceberg formation of the solvent (as shown by the value of n) will diminish with a rise in temperature, and the enthalpy of solution, -R[a In x2/a(l/T)], should approach a more constant value. The enthalpy of solution a t the temperature at which iceberg formation disappears XZ
Flgure 2. Schematic diagram of the correlations among the solubility vs. temperature curves of solid in liquid, liquid in liquid, and liquid in liquid accompanied with iceberg formation of solvent. The logarithm of solubility vs. 1/ Tis nearly straight, but the slope suddenly increases below the melting point of solute and the solubility of solid deviates downward compared that of the supercooled liquid. In the case when solvent molecules surrounding solute form icebergs with the consequent decrease in enthalpy of solution the solubility of solute will deviate upward. The slope, a In x,/a (1/ T) will decrease gradually according to the increase in iceberg formation at lower temperature as shown in dashed curve.
(-160 " C ) may be evaluated as follows: a l n x = A g 2 = A n z ( H bonds)
a(l/T) a t 160 "C A g 2 / T = A S , = -R In xz + ASz(H bonds) a t 160 "C
(11)
Once AH2(H bonds) and AS2(H bonds) are determined, n u i or nASi may be evaluated from the solubility and the temperature dependence of the solubility a t any temperature with eq 8 and 9.
Analysis of the Temperature Dependence of the Solubility of Hydrocarbons in Water The solubilities of aromatic hydrocarbons in water are known up to 250 "C or ~ 0 . The 8 ~ ~logarithms of solubilities vs. the reciprocal of temperature are plotted in Figure 3. The temperature dependence of solubility, -a In x 2 / a ( l / T ) , increases a t higher temperatures and it becomes almost constant at -160 " C where iceberg formation of water seems mostly to disappear. If there is no iceberg formation, the enthalpy of solution, Le., the slope, may be nearly constant. The straight lines in Figure 3 express the solubility of the respective liquid hydrocarbons in water assuming no iceberg formation. The enthalpy and entropy of solution of liquid hydrocarbons in water a t 25 "C are calculated from the temperature dependence of the solubility and shown in Table I. The enthalpy of solution, AH2(H bonds), is obtained from the slope of straight lines in Figure 3, then the enThe Journal of Physical Chemistry, Vol. 81, No. 13, 1977
1302
2
Kbzd Shinoda 200180 I60 140
120 I00 l
l
I
80 i
60
40
1
1
l
1
20 1
"C
8
3
-
52'
and Figure 3 are useful to demonstrate that the small solubility of hydrocarbons in water results mainly from the large positive enthalpy of mixing, and the enthalpy of iceberg formation is largely cancelled by the accompanying entropy decrease at 25 "C, and that the solubility increase from the solid lines to the experimental curves in Figure 3 is due to the iceberg formation. This conclusion is opposite to that of Nemethy and Schera a, who concluded iceberg formation depressed solubility.' Recent findings by Patterson and Barbel3 are consistent with the present conclusions. Ideal entropy of mixing is used in the present systems, because the simplified Flory-Huggins entropy is certainly an overestimate in these
,
24
I
28
I/T x
32
36
103
Figure 3. The solubility of aromatic hydrocarbons in water as a function of reciprocal temperature.
thalpy change due to iceberg formation, n m i , is readily obtained using eq 8. The entropy change due to hydrogen bonding interactions, AS2(H bonds), is evaluated with eq 11,and n a g i is then obtained from eq 9. All these values are summarized in Table I. As the solubilities of water in the separated these hydrocarbons are so small, x = hydrocarbon phase can be assumed to be a pure phase." The numerical values in Table I are not accurate because of the long extrapolation assuming a constant slope and somewhat arbitrary temperature at which the slope is drawn. The enthalpy of mixing is approximately proportional to the molal volumes of respective alkanes, and the ratio of AA,/ASi = 360-380 K, mean temperature of iceberg formation analyzed at 25 "C, is nearly constant for all hydrocarbons examined. As iceberg formation proceeds above room temperature, this is a reasonable value as a first approximation. Kauzmann obtained a very low temperature, because he used AH2 for his calculation." The amount of enthalpy and entropy loss due to iceberg formation decreases with temperature rise and the ratio of these value is enhanced as would be expected. These relations support the consistency of the present theory. Unlike currently accepted views,11'12it is evident from Figure 3 and Table I that the enthalpy of mixing is a large positive value as would be expected on the basis of intermolecular forces. A small negative enthalpy of solution, m2,results from a large positive enthalpy of mixing and a large negative enthalpy of iceberg formation. Table I
The Journal of Physical Chemistry, Vol. 81, No. 13, 1977
Conclusion (1)The enthalpy of solution of hydrocarbons in water has a large positive value at temperatures above 160 "C, where iceberg formation of water molecules surrounding solute molecules becomes negligible. (2) The enthalpy of solution of hydrocarbon in water gradually diminishes with decrease in temperature due to a negative enthalpy of iceberg formation of the surrounding water molecules. (3) The small or negative enthalpy of solution of hydrocarbons at room temperature results from a large positive enthalpy of mixing (decrease in hydrogen bonding interaction of adjacent water) and a large negative enthalpy of iceberg formation. (4)The large negative standard entropy of solution also results from iceberg formation. (5) Iceberg formation is somewhat similar to a liquidsolid phase change. Such a phase change always involves both an enthalpy and an entropy changes. It is not an entropy process. (6) Solubility increases due to the iceberg formation. Namely, the actual solubility curve is shifted to higher concentration than the hypothetical solubility curve in which no iceberg formation occurs. References and Notes (1) J. H. Hildebrandand R. L. Scott, "Regular Solutions", Prentice-Hall, Englewood Cliffs, N.J., 1962. (2) F. Fontein, 2.fhys. Chem., 73, 212 (1910). (3) H. Fuhner, Berichte, 57, 510 (1924). (4) K. Kinoshita, H. Ishikawa, and K. Shinoda, Bull. Chem. SOC.Jpn., 31, 1081 (1958). (5) H. S. Frank and M. W. Evans, J . Chem. fhys., 13, 507 (1945). 161 A. Ben-Nalm. J. fhvs. Chem.. 69,3240 (1965). i7j F. M. Fowkes, J . fhys. Chem., 87,2538 (1963). (8) "API Technical Data Book-Petroleum Refining", 2nd ed, American Petroleum Institute, 1970. (9) A. N. Guseva and E. I. Parnov, Vestn. Mosk. Univ., Khim., 18, 76 (1963);Chem. Abstr., 58 9673f;R. L. Bohon and W. F. Claussen, J . Am. Chem. Soc., 73,1751 (1951);D. M. Alexander, J . fhys. Chem., 63, 1021 (1959). (10) C. Black, G. G. Joris, and H. S.Taylor, J . Chem. fhys., 18, 537 (1948). (11) W. Kauzmann, Adv. Protein Chem., 14, l(1959). (12)G. Nemethy and H. A. Scheraga, J. Chem. fhys., 36, 3401 (1962). (13) D. Patterson and M. Barbe, J . fhys. Chem., 80, 2435 (1976). (14) K. Shinoda and J. H. Hildebrand, J . fhys. Chem., 61, 789 (1957); 65, 1885 (1961). (15) Reference 1, pp 29-33 and 147-149.
