HEKRY’S LAWSTUDIES OF
2895
SOLUTIONS OF JvATER IN ORGANIC SOLVENTS
of T2 DNA at 37” is about 2 min/niolecule or 6 X sec/base pair.24 The similarity of this time to the other time constants in Table I1 suggests that orientational effects involved in “stacking” may be rate limiting rather than hydrodynaniic resistance to unwinding of the strands as suggested by C r ~ t h e r s unless , ~ ~ hydrodynamic effects are also responsible for the rate of the dye interactions, which seems unlikely. However, a t present the relationship between dye interactions and DNA base interactions is quite speculative. For the sake of comparison, the characteristic time constants of these nucleic acid interactions are included in Table 11. The nature of the forces involved in base and dye interactions is still riot certain; presumably, hydrophobic, dipolar, and T-T interactions are all involved.
The interaction of acridine dyes with polymer m o l e cules is still not clearly understood. Obviously, the nature of the binding sites and the conformation of the macromolecule are important among the many factors which influence the “stacking” interactions. Intermolecular complex formation occurs a t rates approaching those characteristic of diffusion-controlled processes. The results presented in Table I1 indicate that the phenomenon of “stacking” occurs relatively slowly and may be controlled by the rate of orientation of dye and polymer into a favorable interaction position. Similar interactions may be of importance in DSA replication. ~~~
(24) D. M. Crothers, J. Mol. Biol., 9, 712 (1964).
Henry’s Law Studies of Solutions of Water in Organic Solvents’
by W. L. Masterton and M. C. Gendrano Department o j Chemistry, University o j Connecticut, S t o r m , Connecticut
(Received M a r c h 7 , 1966)
A study of the relationship between activity and concentration of water in benzene, chloroform, and 1,Bdichloroethane gives evidence for association of water molecules in the latter two solvents. The data in these solvents can be explained adequately in terms of an equilibrium between water monomer and dimer.
Introduction A survey of recent literature shows some disagreement concerning the association of solute water molecules in nonhydrogen-bonded organic solvents. Gordon, et u Z . , ~ found that the apparent molal volume of water dissolved in benzene and toluene at 60-70” decreases with increasing concentration. Attributing this effect to association, Gordon calculated that at 90% of saturation at 67”, the molecular weight of water dissolved in benzene is approximately 45. On the other hand, Christian, et U Z . , ~ report that solutions of water in benzene at 25” obey Henry’s law, a behavior which seems to preclude extensive association. The same sort of evidence is cited4 to indicate the absence of association of water in carbon tetrachloride solu-
tion. However, these authors note, in solutions of water in 1,Zdichloroethane, a pronounced curvature in the plot of concentration of water vs. activity. This is attributed to association of water molecules. I n particular, it is stated that the data are most readily interpreted in terms of an equilibrium between mono-
(1) Abstracted in part from the M.S. Thesis of M. C. Gendrano, University of Connecticut, Oct 1965. (2) M. Gordon, C. Hope, L. Loan, and R. Roe, Proc. Roy. Sac. (London), A258, 215 (1960). (3) S.Christian, H . Affsprung, and J. Johnson, J . Chem. SOC.,1896 (1963). (4) J. Johnson, S.Christian, and H . Affsprung, ibid., 1 (1965).
Volume 70, N u m b e r 9
September 1966
2896
mer and trimer or monomer and tetramer.5t6 Recently, we have undertaken a thermodynamic study designed to give information concerning molecular interactions in solutions of water in organic solvents. As a part of that study, we have conducted isopiestic measurements siniilar t o those of Christian, et al., on solutions of water in benzene, chloroform, and 1,2-dichloroethane. We find, as did these authors, that solutions of water in benzene obey Henry's law, while solutions of water in 1,2-dichloroethane deviate from Henry's lam in a manner which is most readily interpreted in terms of association of water molecules. The same sort of evidence indicates that water in chloroform solution is associated to approximately the same extent as in 1,2-dichloroethane.
W. L. MASTERTON AND ,If. C. GENDRANO
titrations were carried out in an atmosphere of dry nitrogen.
Results Data for the systems studied are presented in Table I, where the concentration of water in moles per liter (C,) is given as a function of the molality of calcium chloride and the activity of water (a,) derived therefrom. Each result represents the mean of a t least two determinations. Water analyses on duplicate samples showed an average deviation from the mean of slightly less than *0.0002. Values for the solubility of water in benzene and 1,Bdichloroethane at 25" (a, = 1) are in good agreement with the results of Christian, et al. (C, = 0.0349 in benzene, 0.1252 in 1,2-dichloroethane).3,5
Experimental Procedure The 1,2-dichloroethane used as a solvent was distilled through a 3-ft silver-coated column at a reflux ratio of 13. The refractive index of the distillate agreed with the literature value (nZo1)1.444) within =kO.OOl; nioreover, a vapor phase chromatogram showed only one peak. Reagent grade chloroforni, containing a small amount of ethyl alcohol, was purified by washing repeatedly with distilled water until the alcohol peak virtually disappeared from a vapor phase chromatogram. The purified chloroform was used immediately to avoid photocheniical decomposition. Thiophenefree benzene '\vas used without furt!ier purification. The organic solvents were equilibrated with pure water and with a series of aqueous solutions of calcium chloride ranging in concentration from 1 to G nt. The apparatus used was similar in all respects to that described by Christian, et al.337 Equilibration mas allowed to take pIace for at least 2 days with the entire apparatus immersed i:i a water bath held at constant temperature to within =tO.O5". After equilibration, the calcium chloiide solutions were analyzed by titrating weighed samples with silver nitrate. Preliminary experiments indicated that the concentration of calcium chloride changed by less than 1% during equilibration. The equilibrated organic phases were analyzed for \water by the Karl Fischer method (dead-stop end point). The Fischer reagent was standardized before each determination by titrating a sample of distilled imter introduced from a calibrated micrometer buret. Weighed samples of the organic phases, chosen so as to contain 10-40 nig of water (equivalent to 2-7 nil of Fischer reagent) , Ivere introduced from a syringe into the titration assembly. The inicroburet used for the titrations was read to *0.01 ml. Each of the openings t o the apparatus was protected from atmospheric moisture by phosphorus pentoxide drying tubes. All T h e Journal o j Physical Chemistry
~~
~~
Table I : Solubility of Water in Organic Solvents as a Function of Activity CaC12, CW
m
Benzene at 25' 0.0347 ... 0.0327 0.951 0,0299 1.898 0.0266 2.858 0.0227 3.701 0.0180 4.839 0.0133 5.838
aw
CW
CaClz, m
ow
1,000 0.948 0.871 0,767 0.662 0.518 0.407
Chloroform at 25' 0.0738 ... 1.000 0.0693 0.979 0.947 0.0632 1.978 0.864 0.0544 2.965 0.754 0.0455 3.940 0.631 0.0368 4.901 0.511 6.006 0.391 0.0275
1,2-Dichloroethane a t 25" 0.1264 .. . 1.000 0.1202 0.976 0.947 0.1084 1.926 0.869 0.765 0,0945 2.880 0.0791 3.800 0.649 0.0645 4.698 0.535 0.0488 5.802 0.411
1,Z-Dichloroethane at 5' 0.0696 .., 1.000 0.0637 1.073 0.940 2.025 0.857 0.0581 0.0500 3.004 0.745 0.0411 3.959 0.619 0.0323 4.945 0.488 0.0286 5.494 0,422
Water activities in calciuni chloride solutions at 25" were calculated from a seniieinpirical equation given by Lietzke and Stoughton* which reproduces the measured values reported by Stokesg with an average deviation of less than + 0.001. The calculation of water activities a t 5" is complicated by a lack of reliable isopiestic data for calcium ( 5 ) T. Lin, S. Christian, and H. Affsprung, J . Phys. Chem., 69, 2980 (1965). (6) J. Johnson, S. Christian, and H. Affsprung, J . Chem. SOC.,77 (1966). (7) S. Christian, H. Affsprung, J. Johnson, and J. Worley, J . C h e m . E d w . , 40, 419 (1963). (8) M. Lietzke and R. Stoughton, J . Phys. Chem., 66, 508 (1962). 41, 637 (1945). (9) R. Stokes, Trans. Faraday SOC.,
HENRY'S LAWSTUDIES OF SOLUTIONS OF WATER IN ORGANIC SOLVENTS
chloride solutions a t this temperature. The equation d_In_ a,_ --L - __ dT RT2
Table 11: Water Activities in CaClz Sulut,ions at 25 and 5" L,
m
cal/mole
1 2 3 4 5 6
- 20 - 50 - 120 - 300 - 500
...
a, a t
a,,. at
25'
50
0.945 0.861 0.750 0.623 0.499 0.391
and its activity, a,, consider a simple equilibrium be tween monomer and dimer.
(HzO)?
2H20
where 1 is the differential heat of dilution, was used to estimate water activities a t 5" from accurately known values a t 25". The results a t rounded molalities of calcium chloride are given in Table 11.
CaClz,
2897
0.945 0.859 0.745 0.614 0.481 0.368
The equilibrium constant for dimerization, K , may be written as
K
=
Interpretation of Data To investigate the effect of association upon the relationship between the concentration of mater, C,,
(3)
where C1 and CZrepresent the concentrations of monomer and dimer, respectively. The total concentration of mater, C,, is
c,
= C1
+ 2C2
(-2)
or, from (3)
c,
+ 2KC12
= C1
(5) Soting that water vapor is monomeric and assuming that the monomer in solution obeys Henry's law C1
Values of 1 were interpolated from literature data.l0>l1 Unfortunately, the heat of dilution of calcium chloride is strongly dependent upon both concentration and temperature; as a result, the 1 values in Table I1 may Le in error by as much as 2075. Although variatiorls in have little effect upon water activities in dilute solution, an error of 20% in G nz calcium chloride mould change the activity of water in this solution at 5" by 0.005. I n calculating water activities, the small amount of organic solvent transferred to the aqueous phase during equilibration was neglected. This is entirely justifiable when the equilibrating medium is pure water. For example, the niole fraction of water in a solution saturated with chloroform is known to be 0.999. If Raoult's law is obeyed, the activity of mater in this qolution would he 0.999, O.lYc less than that given in Table I. This error is negligible compared to the uncertainty in the inea~uredvalue of the concentration of water . I t is more difficult to estimate the effect of dissolved organic solvent on the activity of water in calcium chloride solutions. However, the solubility of the organic liquid can be expected to decrease with increasing salt concentration. This was confirmed qualitatively from vapor phase chromatograms of the aqueous phases; the peaic associated with the organic solvent was considerably reduced in the more concentrated calcium chloride solutions.
Cg/C,2
=
(6)
ka,
where k is the Henry's law constant. Substituting ( 6 ) in ( 5 ) gives
C,
ka,
=
+
(7)
In the more general case, where the nionoiiier is in equilibrium with a polymeric species containing n niolecules of water it is readily shown that
C,
=
ka,
+ nKk"a,"
(9)
From eq 7 or 9, it is clear that if only monomer is present ( K = 0), the concentration of water \vi11 be a linear function of its activity. If, on the other hand, significant association occurs, the data will be better fit by a polynomial in a,. I n such a case, the equilibrium constant for association can be calculated from the coefficients of the equation relating C, to a,. The data for the benzene solutions can be fitted by a least-squares technique to the linear equation
C,
=
0.0343a,
(10)
The average deviation of an experimentally determined concentration from the value predicted by this equation is =t0.0002, the estimated experimental error in C,. If one attempts to fit the data with a second-degree polynomial of the form
C,
=
Aa,
+ BaN2
(11)
(10) J. Hepburn, J . Chem. Soc., 562 (1932). (11) W. Tucker, Phil. Trans. Roy. Soc.. A215, 338 (1019)
V o l u m e 70, S u m b o r 9
September 1966
2898
W. L. MASTERTON AND M. C . GENDRANO
the coefficient of the quadratic term is extremely small (0.0003), and the average deviation remains *0.0002. Increasing the degree of the polynomial to 3 or 4 (Le., 7~ = 3 or 4 in eq 9) does not improve the fit. Thus, our data show no evidence for association of water molecules in benzene solution. The situation in chloroform solutions of water is quite different. Fitting the data to an equation of the same form as (10) gives
C,
=
0.0729~~
(12)
The average deviation here is zkO.0006, three times the estimated error in C,. &foreover, the deviations at low water activities (
