Control and Measurement
S. D. Christian, H. E. Affsprung, J. R. Johnson, and J. D. Worley University o f Oklahoma Norman
of Water Activity
The quantitative removal of water from chemical systems is difficult t o achieve. It is equally difficult to maintain systems a t accurately known relative humidities. The present communication describes equilibration techniques which may be used t o dry organic solutions or t o bring them to a known water activity in a short period of time. These techniques may also be used with volatile solutes other than water. Recently we have been investigating the effect of dissolved water on the association equilibria of hydrogen-bonding solutes in organic solvent^.'^ Although the partition or distribution method is suitable for studies a t nearly unit water activity, we wanted to study systems a t other fixed activities of water. Cousequently, we wanted to develop a solute isopiestic equilibration technique, in which the volatile solute. water, would be distributed by vapor contact between a phase of known water activity and the organic solution. We expected equilibration to take place slowly (since solvent isopiestlc methods are slow) but were surprised to find that a constant water activity is attained in solvents such as benzene or CCll within a few hours. The solute isopiestic apparatus is shown in Figure 1. Bottle B is a chemical reagent bottle of approximately 1500 ml capacity, to which is cemented a 6-in. test tube T. I n thermostating the device, the test tube fits over
Figure I. Solute ikopiestir oppmratus.
a vertical metal rod in a constant temperature bath, allowing the bottle to float in an upight position. The 100 ml beaker C contains a solution or solid of known relative humidity-for example; aqueous CaC13, a crystalline hydrate, or a drying agent such as Mg(C1032. Solution D, outside the beaker, is the phase to be -
--
Thia research was supported in psrt by the National Institutes Health. 1 CHRISTIAN, S. D., AIIFSPRUNQ, H. E., AND TAYLOR, S. A., J. Phya. C h a . , 67,187 (1963). ~TAYLOR, S. A,, CIIRIBTIAN, S. D.,
AND
APPSPRUNG,H. E.,
presented st the Southwest Regional Meeting of the American Chemical Society, Dallas, Texas, December, 1962.
equilibrated a t the known, constant water activity. I n closing the system from the atmosphere, a piece of aluminum foil is molded over the top of the bottle, and the cap is placed over it. Air is not removed from the apparatus, and no provision is made for stirring either the solutions or the vapor.3
0
10
23
Equilibretion time (hours) Figure 2.
Equilibration rate data
(2dODI.
Typical equilibration rate data are shown in Figure 2, for an experiment in which nearly d ~ benzene y was used for solution D, and an aqueous solution of CaCla of water activity 0.905 was placed in beaker C. Formal concentrations of water in benzene, f,, (determined by Karl Fischer method, with coulometric end point) are plotted versus equilibration time. It appears that equilibrium has been attained in less than 10 hoursthe half-life for the process is roughly 1hour. Encouraged by the success of the equilibration technique, we decided to attempt to solve another critical problem involving water. I n near infrared spectral studies (using the Beckmann DK-1 extended range spectrophotometer) we could detect small, variable concentrations of water in CCl, solutions, no matter how carefully we handled them. Therefore, we constructed hollow caps which would contain a drying agent and fit the tapered neck of the spectrophotometer cells; one of these caps is depicted in Figure 3. Water vapor can transfer from the solution in the cell, through the vapor phase, t o the drying agent P. a Note that in solvent isopiestic studiesit is virtually mandatory toremove air and tostir thesolutions. See, for example:DAILEY, G. W., ETAL., J. CBEM.EDIIC., 38, 28 (1962), and BAES,C. F.,
J . Phya. Chem., 66,1629 (1962). Volume 40, Number 8, August 1963
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419
Figure 4 is a rate curve for the drying of a CClr solution in a 2 cm cell (initially containing a water concentration of 0.0071 M) using PzOs as the desiccant. The absorbance of the peak a t 2.671 microns (on a log scale) is plotted versus time. It was determined that Beer's law is obeyed a t this wavelength; a molar absorptivity of 29 liter mole-' cm-' was obtained for water concentrations in the range 0.002 to 0.010 molar. Figure 5 shows the dependence of absorbance on wavelength a t various times after attaching the drying cap to the spectrophotometer cell. The water fundamental frequencies a t 2.671 and 2.743 microns do not appear to shift with concentration, nor does the absorbance ratio of these peaks change as water is removed. It is seen from Figures 4 and 5 that the desiccation process is very rapid, haviug a half-life for removal of water of about 57 minutes in this experiment. I n practice we use two drying caps; one on the reference cell and the other on the cell containing the solution being investigated. It is possible, of course, to equilibrate solutions a t arbitrary water activities by placing constant humidity solutions in the drying cap. Note that this technique for controlling water activity obviates the need for dry-box manipulations.
coutrast to those prevailing in solvent isopiestic experiments, where large volumes of solvent must be transferred at very small mean activity differences. Experiments analogous to partition studies can be performed using equilibrators of the type shown in Figure 1. A volatile solute, such as ethanol or acetic acid, may be distributed between two solvents, which need not be immiscible. If the concentration of solute is determined in both solutions, and if the relation between solute activity and concentration is known in one of the solutions, the dependence of activity on concentration in the other solution call be inferred.
2.59
2.62
2.65
2.68
2.71
2.74
2.77
2.80
wavelength (mirronr) Fw.re 5.
Figure 3.
Absorbance rrrver for wofer 'n CCI. 01 26' at vor'ors vimes during the orling process. Scam were m o m ot t h e $ 0. 1 1 mn., 22 min., 37 mi.. 57 m:n.. 1 hr. 2 3 min. .no I hr. 57 min. after olacinp the drying coo on the rpectropholometer d l .
Drying cap for spectrophotomder cell
The surprising rapidity with which equilibration takes place in the experiments described here can be explained in t,erms of two factors-the large average activity difference between the constant humidity phase and the organic solution, and the relatively small total amounts of water which must be transferred to or from the organic phase. These conditions are in direct
Even if the solvents are somewhat volatile, equilibrium will be reached with respect to the volatile solute before significant quantities of solvent have been transferred. It is interesting to speculate how the properties of the volatile solute would affect the rate of equilibration, using equilibrators similar to the one pictured in Figure 1. The following rate equation might be expected to hold for the equilibration process: dcSDldt= k(paC - pSD)
(1)
where paC represents the constant partial pressure of solute in the solution in C, peD is the variable partial pressure of the solute in solution D, t is equilibration time, and k is a function of the geometry of the equilibrator and the diffusion coefficients of the solute in the solution and vapor phases.& If Henry's law is valid for solution D, ceDcan be replaced by csD = ( P , ~ / P , ~csD." )
(2)
where can.- represents the final concentration of solute in D, corresponding to the equilibrium partial pressure paC. Substituting this expression into equation (I),the rate equation becomes dmDldt = k ( ~ . ~ / c , ~ ~ " ) (p ,paD) ~
(3)
Equation (3) may be integrated to yield l n ~ ~ . ~ / (-p pSD)1 . ~ = k(~,~lc.~~")t 0.01
1 0
1
2
3
4
5
6
(4)
where it has been assumed that initially peD = 0. The half-life for equilibration is
time (hours) Absorbonce at 2.671 microns verwr drying time. Points a, x were token fmm 0 to 1 abrorbmcy, 75 to 125% tronrmirrion
Figure 4.
0 md
and 90 to
420
/
100%tronmissim xdes rerpcrtively.
Journal of Chemical Education
T h e farm of equation (1)is suggested by the dabin Figure 4.
indicating that the total time required t o reach equilibrium will be directly proportional to the final solute concentration in D, and inversely proportional to k and to the equilibrium partial pressure of the solute. The constant k should change relatively little for a variety of solutes in a given equilibrator, since diffusion coefficients are not so strongly dependent on molecular geometry and functionality as are vapor pressures and solubilities. Thus, the rate of transfer of a slightly volatile solute would not be prohibitively slow if the ratio paC/c.D."(i.e., the Henry's law constant) were sufficiently large. The approximate relation
t,,, (solute X) =
tt/,(water)
Ka (water) Kn (solute- X)
(6)
where K,(water) and K,(solute X) are the Henry's law constants for water and solute X, should be useful in predicting whether or not the present technique would be suitable for equilibrations with a given solute-solvent system. Equilibrators such as those described here were used to demonstrate that water exists primarily as the monomer in benzene and CCl4 solutions.' CE~STIIN, 6 . D., AEPSPRUNG,H. E., J. Chern. Soc., 1963,1896.
AND
JOHNBON, J. R .
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