2336
ERWIN K. BAUMGARTNER AND GORDON ATKINSON
Ultrasonic Velocity in Nonelectrolyte-Water Mixtures
by Erwin K. Baumgartner and Gordon Atkinson’ Department of Chemistry, University of Maryland, College Park, Maryland
20740
(Received October 26, 1970)
Publication costs borne completely by The Journal of Physical Chemistry
Aqueous solutions of propylene oxide, acetone,tetrahydrofuran,p-dioxane, and tert-butyl alcohol exhibit marked nonideal thermodynamic behavior in the concentration range 3-8 mol % organic solute. All of these solutes form solid clathrate hydrates of the well characterized “17 hydrate” structure. In order to investigate the possibility of a water stabilization into ordered, clathrate-like shells in these dilute solutions, we have measured the ultrasonic velocity in aqueous propylene oxide, tetrahydrofuran, and tert-butyl alcohol solutions at 10 and 25”. All systems show a maximum in the sound velocity in the mentioned concentration range. The adiabatic compressibilities were calculated from the measured velocities and known densities and show a minimum very near the clathrate composition (X,= 0.0556). It is shown that a simple two-state model suffices to explain the behavior seen in such systems in the low-concentration range.
Introduction It has been observed by several workers that aqueous solutions of propylene oxide (PO), acetone (A), tetra-
hydrofuran (THF), p-dioxane (D), and tert-butyl alcohol (TBA) exhibit anomalous water properties near 3-8 mol % solute. A very good account of these results can be found in a paper by Clem and coworkers.’ Since these solutes all form solid clat]hrates with water a t concentrations near 5 mol % solute,2 corresponding to a composition consisting of (1 organic molecule) e 1 7 HzO, it has been suggested that the dilute aqueous solutions consist of solute molecules stabilizing adjacent water into ordered, hydrogen-bonded shells, similar to clathrate “cages.”lIa Using these ideas, Glew was able to explain, a t least qualitatively, the marked nonideal behavior of these solutions in this concentration range. l o a The velocity of ultrasound, v, in a solution is related to the adiabatic compressibility through eq 1
vz = 1/psCl
(1)
where d is the density of the solution and pB is the adiabatic compressibility.
ps
=
-1/V(bV/bP),
ternary mixtures of two clathrate formers with water a t 25 and 10”.
Experimental Section Apparatus. The sound velocity mas determined by the “sing-around” technique,8 using a NUS Laboratory Velocimeter Model 6100, which works a t a fixed frequency of 3.6 RIHz, together with a Beckman Universal EPUT Meter Model 7350R. The temperature of the solutions was maintained constant to better than =k0.002”by means of a Leeds and Northrup thermostatic oil bath (RIodel4956). The error in velocity measurements has been estimated to be less than 0.03%. Solutions. All solutions were made up with deionized water. They were prepared at the required concentrations by weight. The organic solutes, tetrahydrofuran (Chromato quality from Matheson Coleman and Bell), propylene oxide (Eastman), and certified tert-butyl alcohol (Fisher Scientific Co.) were used without further purification. The data in tabular form can be obtained on request from the senior author (G. A.).
(2)
The stabilization of water molecules by the organic solute would be expected to decrease the compressibility of the solution1 and since the density in these systems changes very smoothly with the concentrationj4v6it could be expected that the ultrasonic velocity would show a maximum at the concentration where the stabilization of mater into clathrate shells is a maximum (X,= ‘/18). I n fact, this behavior has been observed in A-H20,6 D-H20,687and TBA-H206 solutions. I n order to further investigate these ideas about water stabilization in nonelectrolyte-water mixtures, we have measured the velocity of ultrasound in the PO-H20 and THF-H20 systems a t 25 and 10” and in the TBAT h e Journal of Physical Chemistry, Vol. 76,N o . 16, 1971
HzO system a t 10”. We have also examined equimolar
B.
(1) D. E.Glew, D. Mak, and N. S. Rath in “Hydrogen-Bonded Solvent Systems, A. K. Covington and P . Jones, Ed., Taylor and Francis, London, 1968. (2) TBA does not form solid clathrates with water, but it does form them in the presence of a help gas like HxS. The formula is 2H2S. TBA. 17H20.1 (3) M. J. Blandamer, D. E. Clarke, N . J. Hidden, and M. C. R. Symons, Trans. Faraday Soc., 64, 2691 (1968). (4) J. Timmermans, “The Physioo-Chemical Constants of Binary Systems,” Vol. 4, Interscience, New York, N. Y., 1960. ( 5 ) R. Signer, H. Arm, and H . Daeniker, Helv. Chim. Acta, 52, 2347 (1969). (6) Ch. J. Burton, J . Acoust. Sac. Amer., 20, 186 (1948). (7) K. Arakawa and N. Takenaka, Bull. Chem. SOC.Jap., 42, 5 (1969). (8) R. Garnsey, R. J. Boe, R. Mahoney, and T . A. Litovitz, J . Chem. Phys., 50, 5222 (1969).
2337
ULTRASONIC VELOCITY IN NONELECTROLYTE-WATER MIXTURES
-
? 1.6
PO/H20
o_ 1.5
.
*.
o
V P)
$ IA
-
:25"C : 10°C
0 :
e :
'f' 1.5 0 X
25'C 10°C
Y
X " x ~ XPO ~ ~ +
8 ri
I
> 1.3
THF/PO/H 20 .
TBA/PO/H20. o : e :
0.1
0.3
0.5
0.7 -X
0.9
Po
\
X"XTBA+XPO
Figure 1. Concentration dependence of ultrasonic velocity for the propylene oxide-water system at 25 and 10".
9
2S°C 10°C
TBA/THF/H20. o : e :
25°C IOOC
I.6
0 I(
J
< E
,
1.5
0.1
0.2
I
X-X,TBA+,XTHF
0.3
6.4
-x
> 1.4
Figure 4. Concentration dependence of ultrasonic velocity for ternary mixtures of organic solutes in water at 25 and 10".
1.3 0.1
03
0.5
0.7
-.+
0.9
'THF
Figure 2. Concentration dependence of ultrasonic velocity for the tetrahydrofuran-water system a t 25 and 10".
The concentration dependence of ultrasonic velocity in the water-rich region for ternary mixtures of organic solutes in water, using equimolar concentrations of both solutes, is depicted in Figure 4. The mixtures studied were: THF-PO-H,O, TBA-PO-Hz0, and TBATHF-H20 a t 25 and 10".
Discussion
0.1
0,3 0,s 0.7 -X
0.9
T BA
Figure 3. Concentration dependence of ultrasonic velocity for the tert-butyl alcohol-water system at 276 and 10'.
Results The concentration dependence of ultrasonic velocity for the systems PO-H20 and THF-H20 at 10 and 25" and a t 10" for TBA-H20 is given in Figures 1-3. We have included in Figure 3 Burton's data6 measured at 27". The curve corresponding to TBA-H20 a t 10" has been interrupted a t X z = 0.85 because of the appearance of two phases.
Using very extensive nuclear relaxation data, Hertz9 has pointed out that clathrates certainly do not exist in solution as rigid, long-lived hydration spheres. Yet Hertz's results also show a marked decrease in the diffusion coefficient of the water near the solute. At the same time the organic molecule is freer t o rotate in the water than it was in the pure solute. It seems useful then to consider that the "guest" solute molecule causes fluctuations in the thermodynamic properties of the "host" water in the region near the "guest." It should be emphasized that for both ultrasonic velocity and absorption, the effects seen are maximized by solutes with the greatest ratio of hydrocarbon group to hydrophilic group. The ultrasonic absorption peak in dilute aqueous TBA solutions has been explained with the clathrate water-shell rn0de1,~but the same explanation seems to fail in A-H20, THF-H20, and D-HzO solutions, where the ultrasonic absorption peak occurs a t a molar fraction (9) E. von Goldammer and H. G. Hertz, J. Phys. Chem., 74, 3734
(1970).
The Journal of Physical Chemistry, Vol. 76, No. 16, 1971
2338 near 0.5.6*10-12The same problem seems to arise in the PO-HZO system, since vr7e have found13 that there is no maximum in the 3-8 mol% concentration range. The ultrasonic absorption ip this system tends toward a maximum a t higher concentrations but since there is a phase separation a t X z N 0.15, there is no way to tell a t which concentration the real maximum would occur. An interpretation in terms of concentration fluctuation gives an explanation of this apparent inconsistency. Ultrasonic absorption phenomena due to concentration fluctuations have been analyzed by Solovyev and coworkers.14 They find that the amplitude of the excess sound absorption as a function of Xz is a complex function of the second derivatives of the volume, enthalpy, and free energy of the system with respect to X2. Only when the volume factor is dominant, as it has been shown to be in TBA-H20 solutions,16does the ultrasonic absorption give a peak at around the same concentration as does the ultrasonic velocity. In the other systems, the situation is much more complicated and the absorption is a result of the combination of the three mentioned thermodynamic properties. Ultrasonic velocity is easier to interpret, since it depends only on the compressibility of the system. As is shown in Figure 1, we have indeed found a distinct maximum for the PO-H2O system at X z ‘v 0.08. The same behavior has also been observed for THF-H20 and TBA-H20 solutions, as depicted in Figures 2 and 3. It can be observed in these figures that the velocity maxima are always higher and sharper at lower temperatures. This is entirely consistent with the water-shell stabilization model. It has been suggested by Hertz9 that the structuring in the water-rich region might be due to association of organic molecules. I n order to test this possibility, we have measured the concentration dependence of ultrasonic velocity in the dilute concentration region for ternary mixtures of organic solutes in water, where the concentrations of both organic solutes were equimolar. The results, shown in Figure 4,do not seem to indicate the suggested association of organic molecules, since the observed maxima correspond quite well to a linear superposition of the maxima corresponding to each solute, at the same total concentration, measured separately. If there were distinct association between organic molecules at low concentrations, one should expect that the ultrasonic velocity maxima would depend much more on the nature of the solute. We have tried to explain the obtained ultrasonic velocity vs. concentration curves with a simple twostate model. In the concentration range 0 5 XZ 5 0.0556 we assume that each solute molecule is surrounded by water molecules forming a clathrate-like structure, in the sense discussed above, and that the water molecules not involved in the host structures behave like ordinary water. It is assumed also in this model that the compressibility of the guest molecule is zero The Journal of Physical Chemistry, VoE. 76, N o . 16, 1971
ERWIN K. BAUMGARTNER AND GORDON ATKINSON since it occupies a “hole” in the water but does not fill it. Basically, this model implies that we are dealing with an ideal two-state solution. Our aim is to calculate the isoentropic compressibility for it. The expression commonly used for this purpose is the followingle”-c (3) where p a is the volume fraction of the ith component and Postthe isoentropic compressibility for the pure component i. It has been recently shown” that this expression is only an approximate one and that the correct one is Psid
=
PTid
-
TVid(aid)2/Cpld
(4)
where / 3 is~the~isothermal ~ compressibility for an ideal solution, which is correctly calculated by an averaging over volume fractions (eq 3), and V i d , a i d , and C,,, are the molar volume, the thermal expansivity, and the heat capacity at constant pressure for ideal solutions. Tiid and C,, are calculated by a molar fraction average and a i d by a volume fraction average. The use of correct eq 4 requires the knowledge of a! and C, for a clathrate structure and for the components PO, THF, etc., which are not known at the present. Therefore, having estimated an error in plC (see below) by using the approximate expression less than 2%, which is smaller than the extent of our trust in the primitive model, we decided to use approximate eq 3 for our purposes. By means of the described two-state model, we compute the molar volume P and the approximate adiabatic compressibility for the solution
P = [(l- X,) - 17Xz]V1° + 17XzV1’ (5) where P1O = molar volume of “free” water and VlC = molar volume of “cage” water.
+
ps = 1/P[(1- l8XZ)Vl0pl0 17X2VlcPlc] (6) where p t = adiabatic compressibility of “free” water and plC = adiabatic compressibility of ‘
