NOTES
molecules are lost from the advancing trihydrate front by diffusion into the porous interior. However, once the supply of water vapor is cut off, the surface blocks of trihydrate rapidly disappear as the loosely bound water is dispersed into the porous interior, where it then becomes more firmly bound. Hence there results the steep drop in A&-l as the relaxation time increases. The sharp decrease is arrested at about the same AQ-I value as the initial inflection at the beginning of rehydration, which provides further evidence that the firmly bound water corresponds to the monohydrate. After the arrest, the slow decrease in AQ-l to about 1.5 X is most probably due to there being insufficient water to form the monohydrate uniformly throughout the solid. After the last data point shown for curve B, the cell was kept isolated at 22" for 24 hr before being reconnected to the reservoir, but no marked changes in AQ-l were observed. This suggests that a transformation to a nonporous structure had occurred. This sample was then dehydrated under vacuum before being rehydrated to give curve C. With the latter, inflections following the initial rise are scarcely evident, perhaps as a result of the lower temperature and the consequent increase in relaxation time. I n spite of the narrowness of the data presented here, it is clear that the dielectric method may provide useful information concerning dehydration and rehydration of salt hydrates. Such a method has an advantage over the conventional gravimetric approach, in that changes in relaxation time can be followed.
1671
nonaqueous solvents. While the title tetraphenylborides and picrates acquired importance as reference electrolytes in definitive conductometric studies,l-B there was little information on their solubilities. Except for those of potassium picrate (KPi) in water and methanol' and of potassium tetraphenylboride (KBPh4) in water,& the solubilities are reported here for the first time. Concentration of tetraphenylborides and picrates in saturated solutions was determined by ultraviolet and visible spectrophotometry, respectively. Using the association constants reported for methanolic solutions by Fuoss and c o - ~ o r k e r s , ~ we* ~calculated ionic concentrations and activities for the saturated methanolic solutions, as well as the corresponding medium effects. Experimental Section Materials. Reagent grade chemicals were used unless otherwise specified. Methanol (Matheson, spectro grade) was refluxed over aluminum amalgam and distilled, rejecting the initial and final lo?&. Deionized water was redistilled. Sodium tetraphenylboride (Fisher, 99.7Oj,) was the starting material for the synthesis of other tetraphenylborides. KBPh4 was prepared by treating NaBPh4 with an excess of KCI in water; it was recrystallized three times from 3: 1 acetone-water and dried in vacuo at 80". Tetrabutylammonium tetraphenylboride (BUINBPh4) was synthesized as described in the literature.' Anal. Calcd: C, 85.52; H , 10.05; N, 2.49. Found for two batches: C, 85.52, 85.52: H , 9.85, 9.96; K, 2.50, 2.40. Triisoamylbutylammonium tetraphenylboride ((TAB)BPh4) and picrate ((TAB)Pi) were synthesized and purified essentially by the method of Coplan and F u o ~ s . Anal. ~ Calcd for (TAB)BPh4: C, 85.54; H, 10.35; N, 2.32. Found: C, 85.89; H, 10.36; N, 2.40. Tetrabutylammonium picrate (Bu4NPi) was prepared by exact neutralization of purified picric acid in water-methanol with methanolic Bu4NOH (Matheson, 25%) and purified by recrystallization from 90% ethanol-water mixture. KPi was prepared by treating stoichiometric amounts of purified picric acid with standard aqueous KOH. I
Achnowledgment. This research was supported financially by the U. s. Air Force through its European Research Office.
Solubilities of Potassium, Triisoamylbutylammonium, and
Tetrabutylammonium Tetraphenylborides and Picrates in Water and Methanol and
/
Their Medium Eflects at 25' (1) F. Accascina, S. Petrucci, and R. M. Fuoss, J . A m . Chem. SOC., 81, 1301 (1959).
by Orest Popovych and Robert 84. Friedman Department of Chemistry, Brooklyn College of the City University of New York, Brookllin 20, New York (Received October 4, 1966)
The solubilities reported here were determined as part of our study of medium effects for electrolytes in
(2) H. Sadek and R. M. Fuoss, ibid., 81, 4507 (1959).
R. M. Fuoss and E. Hirsch, ibid., 8 2 , 1013 (1960). R. W. Kunze and R . M. Fuoss, J . Phys. Chem., 67, 911 (1963) M. A. Coplan and R. M. Fuoss, ibid., 68, 1177 (1964). J. F . Skinner and R. M.Fuoss, ibid., 68, 1882 (1964). A. Seidell, "Solubilities of Inorganic and Metal Organic Compounds" D. Van Nostrand Co., Inc., New York, N. Y., 1940. (8) R . T. Pflaum and L. C. Howick, Anal. Chem., 2 8 , 1542 (1956) (3) (4) (5) (6) (7)
Volume 70, Number 6
May 1966
1672
NOTES
Table I: Solubilities of Electrolytes in Methanol and Water and Their Medium Effects at 25'
Electrolyte
KBPh4 KPi (TAB)Pi BurNPi (TAB)BPha
BuaNBPh
a
See ref 8.
-Solubility, Hz0
1.74 x 10-4 1.78 x 10-4" 2.42 x 2.41 X 2.26 x 10-4 1.21 x 10-3 1 . 4 x 10-7? (obsd) 1.08 x 10-7 (calcd) 3.4 x lo-? (obsd) 2.59 x 10-7 (calcd)
C, molea/l.-
CHaOH
a in CKaOH
3.11 x 10-3
0.958
2.94
x 10-8
5.86
x
10-6
-2.300
8.58 x 10-8 1.03 x 10-zb 0.392 0.873 3.60 x 10-3
0.951
4.37
x
3.46
x
lo-&
+l.lOl
0.680 0.589 0.930
4.92 x lo-* 1.35 x 1.17 x 10-14
0.940
6.69
2.58
x 10-3
----Ion-ectivity
H20
x
product, (Caf*!2----CHaOH
Medium effect, log mjf* (es 3)
10-4
10-14
1.23 x 3.70 x 10-2 7.36 x 10-6
-5.398 -4.438 -8.799
x
-7.839
4.62
10-6
See ref 7.
The product was recrystallized three times either from water or from methanol and was used for solubility determination in the corresponding solvent. Purity of all salts was monitored by their spectra and electrolytic conductances in methanol. Xeasurenzcnts. Saturation was achieved by shaking the salt suspensions on a Burrell wrist-action shaker in water-jacketed flasks through which water was circulated from a 25.00 =t0.01' bath. About 2 weeks of vigorous shaking was found to be sufficient for saturation. The saturated solutions were filtered through Gelman Metricel filters of 0.20-p pore size in a filtration syringe. Aliquots of the filtered solutions were immediately diluted (if necessary) with the solvent to proper spectrophotometric range and their spectra were recorded on a Cary spectrophotometer Model 14. -411 work with tetraphenylborides was carried out in thoroughly deaerated solutions and containers. In spite of all precautions, however, (TAB)BPhd and Bu4NBPhr usually decomposed upon prolonged equilibration mitk water, so that reliable results for their solubilities in water were difficult to obtain directly. Fortunately, the presence of decomposition could be readily recognized from the accompanying drastic changes in the ultraviolet spectra. Since hydrolytic decomposition of tetraphenylborides is known to be rapid in acid solutions, we attempted to measure the solubility of Bu4NBPh, and (TAB)BPh, in aqueous 10-5 ;M NaOH. This method was successful part of the time. The Journal of Physical Chemistry
Results and Discussion Spectrophotometric analysis of most tetraphenylboride solutions took advantage of their characteristic ultraviolet peaks at about 266 and 274 mp which are independent of the associated cation. At the two maxima, the molar absorptivities a were found to be 3.25 X lo3 and 2.06 X lo3 in water, and 3.00 X lo3 and 2.12 X lo3 in methanol, respectively. Similar values were reported for acetonitrile-water mixtures.8 Only the extremely dilute solutions of BuJVBPh4 and (TAB)BPhl in water had to be analyzed in the more intense, though less characteristic, region of the spectrum at 225 mp (a = 2.22 X lo4). Rlolar absorptivities of the picrate ion in mater and methanol were determined from the absorbance of KPi and (TAB)Pi to 1 X M range. For solutions in the 2 X the broad picrate maximum a t -355 mb, a was found to be 1.44 X lo4and 1.56 X lo4in water and methanol, respectively. Beer's law was obeyed throughout. The results in Table I were obtained as follows. Molar solubilities, C, were calculated from the above absorptivities and from the observed absorbances of the saturated solutions. For niethanolic solutions, the degrees of ionic dissociation, a ) were calculated from the literature values of the corresponding association constant^.^^^ Once the ionic concentration CCY was known, the conventional niean ionic activity coefficients frt (molar scale) were estimated from the Debye-Huckel equation, which for methanolic solutions at 25" assumed the form
NOTES
1673
Reasonable values of the ion-size parameter d in methanol were adopted or estimated from the results of Fuoss and c o - w o r k e r ~ ; they ~ ~ ~ were 7, 6 , 5.5,and 4.5 for R4NBPh4,R4NPi, KBPh4, and KPi, in that order. For aqueous solutions, a was assumed to be unity and the Debye-Huckel activity coefficients were estimated using, for most cases, Kielland’sg ion-size parameters. For Bu4N+, TAB+, and BPh4-, the parameters were estimated from Nightingale’s datal0 to be 9.4,10, and 10,respectively. While the use of the Debye-Huckel equation for saturated (TAB)Pi and BueNPi in methanol (ionic strengths 0.267 and 0.514, respectively) is open to criticism, it is not nearly so objectionable here as it would be for common electrolytes, composed of small ions. Solvation, which is the primary cause for deviations from the Debye-Huckel law a t higher concentrations, is known to be negligible for ions of the size of TAB+, BudN+, and Pi-. For the Pi- ion (which is the smallest one of the three) the solvation number was actually determined to be zero in several solvents, including methanol. l1 The medium effect for an electrolyte J*2 is a measure of the free-energy change upon transferring 1 mole of the electrolyte from its standard state in water to its standard state in the nonaqueous solvent, methanol in this case. For a uni-univalent electrolyte
AGO
= 2RT In
mf*
(2)
and Jk2 can be obtained from the ratio of ionic activities a& in saturated aqueous and nonaqueous solutions, designated by subscripts w and s, respectively.
We resorted to this calculation because the two tetraalkylammonium tetraphenylborides were found to be susceptible to hydrolytic decomposition, which, coupled with their extremely low solubilities, would tend to make a direct solubility determination in water unreliable. The above calculation also leads to a possibly novel method of determining indirectly the solubility of a compound in a solvent in which it is too unstable for a prolonged equilibration required in a direct solubility determination. Thus, the solubilities of (TAB)BPh4 and Bu4NBPh4 in water were derived with the aid of eq 3 from their calculated medium effects (eq 4) and their measured activities in methanol. The accuracy of the indirect procedure could be improved, of course, if the activities of the tetraalkylammonium picrates in saturated methanolic solutions were determined by some method more suitable for solutions of the order of lo-’ M than solubility measurements coupled with the Debye-Huckel law. However, an advantage of the indirect solubility determination lies in the fact that it can be checked via medium effects in any number of solvents.
Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. (9) J. Kielland, J . A m . Chem. Soc., 59, 1675 (1937). (10) E. R. Nightingale, J. Phys. Chem., 63, 1381 (1959). (11) P. Walden and E. J. Birr, 2.Physik. Chem., A153, 1 (1931).
Effects of Divalent Cations on Multiionic Diffusion across a Weak-Acid Membrane’
The medium effects in the last column in Table I were calculated using eq 3. The striking feature of most medium eff ectJs (in logarithmic form) determined here is their negative sign, reflecting the fact that distribution of their ions favors the nonaqueous phase, despite the somewhat, reduced dissociation and activity coefficients in the latter. Medium effects for most electrolytes are positive. It should be noted that the medium effects for (TAB)BPh4 and for Bu4NBPh4 were obtained indirectly from those of other salts (eq 4). The indirect calculation takes advantage of the additivity of individual ionic medium effects in logarithmic form, e.g. log rnf(TAB)BPhr = log mf(TAB)Pi -k log mfKBPhr - log mfKPi
(4)
by T. M. Ellison2 and H. G. Spencer Department of Chemistry, Clemson University, Clemson, South Carolina (Received October 26, 1065)
The accumulation of divalent cations in weak-acid membranes has been shown to reduce appreciably the interdiffusion flux of univalent cations across the memb r a n e ~ . ~I n this investigation the flux ratios are reported for multiionic systems of the type: 0.0500 M (1) Presented to the Southeast-Southwest Regional Meeting of the American Chemical Society, Memphis, Tenn., Dec 1965. (2) To whom correspondence should be addressed: Research and Development Directorate, U. S. Army Missile Command, Redstone Arsenal, Ala. (3) H. G . Spencer and T. M. Ellison, J. Phys. Chem., 69, 2415 (1965).
Volume 70, Number 6
M a y 1966
