J. Phys. Chem. t987, 91, 1687-1690
1687
Precise Density Measurements of Aqueous Solutlons of Mixed Nonpolar Gases Noel Bignell CSIRO Division of Applied Physics, Sydney, Australia 2070 (Received: November 6, 1985; In Final Form: August 26, 1986)
An experiment is described which measures the change in the density of water, Ap, on being saturated with various gases at different temperatures in the range 3-25 O C . The gases used were argon, hydrogen, and a mixture of the two containing a fraction X of argon. It is shown that the equation Apmi,(f) = XApA,(t) (1 - X)Ap,,(t) should be obeyed under conditions of ideal dilution but the results indicate that it is not. This is discussed in the context of similar work and the result is attributed to a long-range hydrophobic interaction.
+
Introduction Aqueous solutions of nonpolar gases represent the simplest systems exhibiting hydrophobic interactions. These have been the subject of much study in recent years,I not only because of their intrinsic interest and their involvement in the understanding of water itself but also because they almost certainly have a significant part to play in the stability of biological systems.2 Rontgen suggested as long ago as 1892 that water contained “ice molecules” and though this cannot be literally true it is thought that there exist regions of local order. The basic source of the anomalous properties of water is that it is a hydrogen-bonded liquid, which gives it a great variety of possible interconnecting geometries. In ice, which exists in many forms, most of the bonds are complete but, even in the liquid, it is thought that about 80% are still intact at 0 O C . This is so high that continuous networks of bonds exist throughout, so that water resembles a gel. When ice melts some bonds are broken and others strained, allowing the volume to be reduced, a process which continues with rising temperature and permits further contraction in volume until 4 OC after which the normal expansion accompanying bond rupture predominates. The accounts of Stillinger3 and Angel14 are good introductions to recent work in this field. In a molecular dynamics computer simulation Geiger, Rahman, and StillingerS studied two inert solute particles and 214 water molecules and found orientational preferences reminiscent of the structure in clathrate hydrates. Alagona and T a d used a Monte Carlo method to simulate a dilute solution of argon and found a first solvation shell which contained about 17 water molecules. Stillinger3 suggested several possible clathrate-type cages and Bignell’ measured the volume occupied per solute molecule for argon and found some of the cages had too large a volume, but one, composed of 15 water molecules arranged as two parallel pentagons on either side of the solute with links coupling vertices, had the same volume as measured. Hydrophobic hydration, as the structuring of water molecules around a nonpolar molecule is called, is accompanied by a lowering of entropy and, by associating, two such structures are able to minimise this effect. This is the basis of the hydrophobic interaction. Geiger, Rahman, and Stillinger5 found such a tendency to associate. Pangali, Rao, and Berne* found a minimum in the potential of mean force corresponding to a water molecule lying between the two solutes. Rapaport and Scheragaq in a long simulation involving 339 water molecules and 4 solute molecules
failed to find any tendency for the solute molecules to aggregate. Speedylo has looked at the often pentagonal structures found in water by computer simulation studies and has argued that pentagonal rings of hydrogen-bonded water molecules are self-replicating. In a later paper Speedy and Mezei” argue that pentagons in water have a tendency to form correlated clusters. The pairing of cavities on either side of the plane of the pentagons and their clustering were thus said to account for the phenomenon of hydrophobic hydration. The concentration of solute molecules used in computer simulation studies is about 100 times that which is possible in saturated solutions. One argon molecule in 30 000 water molecules at 10 OC is a saturated solution at atmospheric pressure so that it might be thought that there would be no interaction between solute molecules. If this assumption is made then a relation can be derived between the change in density of water when saturated with a mixture of two gases, ApM, and the two values observed separately with each gas, ApA and ApB ApM(t) = XAPA(t)
where X is the fraction of gas A in the mixture. This relation, and the assumption on which it is based, that the solute molecules are noninteracting, has been tested experimentally for argon and hydrogen and this experiment is described. The results of this experiment show that the equation above is not obeyed.
Experimental Details The philosophy of the measurement is to make as few changes as possible between the gas-free measurement and the saturated measurement. Thus the same water sample is used for both measurements and it is saturated with the gas in the sample cell while it and the rest of the apparatus are held at the temperature of measurement. The water is initially made gas-free by prolonged boiling and is stored under its own vapor pressure. Before transferring it to the sample chamber it is brought to approximately the working temperature to avoid volume hysteresis effects in the float. A large excess is prepared and transferred, the initial portion flowing to waste to ensure that the sample retained is uncontaminated by air. The small changes in density between the gas-free sample and the same sample saturated with gas were measured with a magnetic float. This apparatus has been described in detail elsewhere12and consists of a 126-mL glass float, containing a small magnet, which is held submerged in the sample of water by the field of a current-carrying circular coil. The float is sensed optically and held in a fixed position by variation of the current in the coil. When this changes by Ai, the change in density Ap is given by
(1) Faraday Symp. Chem. SOC.1982, 17. Ben-Naim, A. Hydrophobic Interactions; Plenum: New York, 1980. (2) J. Phys. Colloq. C7 1984, 45. ( 3 ) Stillinger, F. H. Science 1980, 209, 451. (4) Angell, C. A. Recherche 1982, 13, 584. (5) Geiger, A.; Rahman, A.; Stillinger, F. H. J. Chem. Phys. 1979, 70, 263. (6) Alagona, G.; Tani, A. J . Chem. Phys. 1980, 72, 580. (7) Bignell, N.J . Phys. Chem. 1984, 88, 5409. (8) Pangali, C.; Rao, M.; Berne, B. J. J. Chem. Phys. 1979, 71, 2982. (9) Rapaport, D. C.; Scheraga, H. A. J . Phys. Chem. 1982, 86, 873.
0022-3654/87 , ,/2091-1687$01.50/0 I
+ (1 - X)&B(t)
(10) Speedy, R. J. J . Phys. Chem. 1984, 88, 3364. (11) Speedy, R. J.; Mezei, M. J . Phys. Chem. 1985, 89, 171 (12) Bignell, N. J. Phys. E 1982, 15, 378.
0 1987 American Chemical Societv -
1688
The Journal of Physical Chemistry, Vol. 91, No. 6, 1987 Ap = cAi
where c is a constant depending on gravitational acceleration, the volume of the float, the strength of the magnet, and the geometry of the coil-magnet system. This geometry has been chosen so that the magnet is (3/2)1/2rfrom the plane of the coil, where r is its radius. For this condition coil temperature changes have a negligible effect on the value of c. A continuous series of readings of the voltage across a standard resistor is made with a digital voltmeter under computer control and the mean of each 1000 readings is printed. This mean changes progressively until temperature equilibrium is reached. Then the mean of readings taken over about 30 min (about 16OOO) is taken to represent the current in the gas-free sample. The appropriate gas is then bubbled through the sample cell for about 15 h, a time shown to be sufficient for saturation. A further series of means and a final mean representative of the sample saturated with gas are taken as before. In previous experiments a dificulty was experienced when the sample temperature was above the laboratory temperature, due to convection currents disturbing the float. These currents have been suppressed by winding a small heater on the emergent stem of the sample cell in order to create a zone of slightly higher temperature than the sample. The gas mixture was prepared in an aluminum gas cylinder which had been evacuated. The cylinder was wrapped in an insulating material and a platinum resistance thermometer strapped to the side was used for temperature measurement. Pressures were measured with a Digiquartz pressure transducer which gives the pressure to 0.01% from a quadratic expression in its frequency output. First argon was admitted and after equilibration the temperature and pressure readings were taken. Then hydrogen was admitted and again, after equilibration, temperature and pressure readings were taken. The argon used was 99.99% and the hydrogen 99.5% pure.
Theory Consider a solution of nAr,nH, and nw moles of argon, hydrogen, and water of molar weights MAr,MH, and Mw and partial molar volumes VAr,FH, and Fwat a temperature t O C . The volume V and mass M of the solution are given by 'v = nArvAr nHFH nwvw
+ + M = nArMAr + nHMH + nwMw
The density of this solution is M / V and that of pure water Mw/Vw where Vw is the molar volume of water and is here assumed to be equal to the partial molar quantity. The difference in density, ApM, between the solution and pure water is given by
Bignell and from Henry's law nAr/(nw
+ nAr + n
~ =) KArX(p - PwdJ)
where KAr is a proportionality factor which will depend on the temperature but very little on the pressure P. Since nAr+ )'1H
