Medium Effects for Single Ions in Acetonitrile and Ethanol-Water Solvents Based on Reference-Electrolyte Assumptions Orest Popovych, Allan Gibofsky, and David H. Berne Department of Chemistry, Brooklyn College of the City University of New York, Brooklyn, N . Y . 11210 Medium effects, my, of several electrolytes in acetonitrile and ethanol-water solvents were calculated from new and literature data. In ethanol-water solvents, medium effects for single ions were estimated using the three assumptions that the values of log my of tetraphenylarsonium tetraphenylborate, tetraphenylphosphonium tetraphenylborate, and triisoamyl-n-butylammonium tetraphenylborate, respectively, can be divided equally between their anions and cations. In acetonitrile, only the first two assumptions were applied. Excellent agreement was observed between the first two assumptions, while the third deviated from them by up to0.5 unit in log my. According to all three estimates of the medium effects for the proton, the basicity of ethanol-water mixtures is greater than that of the pure solvents and passes through a maximum. For ethanol-water solvents, the liquid-junction potentials at their interfaces with aqueous KCI and the potentials of the standard hydrogen electrodes referred to the aqueous SHE were calculated.
THEMEDIUM EFFECT, is a measure of the difference between the free energy of a solute i in its aqueous (,Gio) and nonstandard states: aqueous (sGio) sGio -
=
RT In mYt
For 1 :1 electrolytes, In
= In my*2 = (In
,r++ In
7 n ~ - )
(1b)
where m ~ + , and are the medium effects of the cation, the anion, and the electrolyte, respectively. In previous communications from this laboratory (1, 2 ) it was shown how knowledge of medium effects for single ions enables us to formulate solvent-independent ion-activity scales (such as pH) and emf series and to evaluate liquidjunction potentials at the interfaces of different solvents. These questions as well as the many extrathermodynamic methods of estimating medium effects for single ions have also been the subject of a comprehensive critical review by one of us (3). One of the most promising methods to date is based on the assumption that the medium effect of an “ideal reference (1 :1) electrolyte’’-composed of very large symmetrical ions as similar in size and structure as possible-can be divided equally between the anion and the cation. Because the reference ions must not be susceptible to appreciable specific interactions with the solvents, their choice so far has been restricted to large tetraalkyl and tetraaryl ions, where the bulky organic groups presumably shield the central atom from the solvent (4). A more detailed discussion of the criteria for selecting reference ions can be found in the review (3). In earlier studies, we employed triisoamyl-n-butylammoniurn tetraphenylborate (TAB BPh,) as a reference electrolyte in methanol and an isopropanol-toluene mixture (1) and in (1) 0. Popovych, ANAL.CHEM., 38, 558 (1966). (2) 0. Popovych and A. J. Dill, ibid., 41, 456 (1969). (3) 0. Popovych, Crit. Rec. Anal. Chem., 1, 73 (1970). (4) E. Grunwald, G. Baughrnan, and G. Kohnstarn, J . Amer. Chem. Soc., 82, 5801 (1960).
ethanol-water solvents (2), Le., the assumption was that log m ~ T A B = log mYBPh4. In the present study, medium effects for ions in acetonitrile and ethanol-water solvents are estimated by the tetraphenylarsonium tetraphenylborate (Ph4As BPh4) and the tetraphenylphosphonium tetraphenylborate (Ph4P BPhJ assumptions, i.e., that log mYPh,A. = log mYBPh4 and log mYPhrP = log mYBPh49 respectively. While the choice of TAB BPhl was based on the equality of the Stokes radii of its ions (1-.3), the PhlAs BPh, and Ph,P BPh, assumptions are founded on the structural similarities of the counterions. No firm values are available for the sizes of the tetraphenyl ions, the literature estimates ranging from 4.2 to 5.5 (3). This study enables us to compare the three reference electrolytes as applied to ethanolwater solvents and two of them, in acetonitrile. Unfortunately, the relatively high solubility of TAB BPh4 in acetonitrile (0.5707 molal at 25 “C) renders its application in that solvent impractical, because calculated activity coefficients would be unreliable at that concentration. PhrP BPh, received its initiation as a reference electrolyte in dioxane-water mixtures (4). The PhrAs BPh4 assumption has been applied by Alexander, Parker, and their associates (5,6) in many solvents, including acetonitrile, but not in the ethanol-water systems. In their studies, however, the medium effects (termed “solvent activity coefficients” and referred to methanol rather than water as the standard medium) were calculated from concentration solubility products, with no corrections for incomplete dissociation and activity coefficients. Also, some of their calculations were based on values for the solubility products of AgBPhr, a rather unstable salt in many solvents, for which reliable pKsp values in water and methanol have not been determined until recently (7). The results in references (5, 6) are reported to one decimal place in log In an effort to improve on the above results, we have carefully determined the solubilities of several key electrolytes in acetonitrile with greater emphasis on analytical precision and accuracy. Activity coefficients in acetonitrile were estimated from the Debye-Hiickel equation with ionsize parameters. For ethanol-water solvents, we made use of thermodynamic ion-activity products determined in this laboratory (8, 9).
A
EXPERIMENTAL
Materials. The preparation and purification of KPi, KBPh4 (IO), TAB BPh, (II), TAB Pi, LiCl (12), Ph,As Pi (5) R. Alexander and A. J. Parker, ibid., 89, 5549 (1967). (6) R. Alexander, E. C . F. KO, A. J. Parker, and T. J. Broxton, ibid., 90, 5049 (1968). (7) I. M. Kolthoff and M. K. Chantooni, Jr., private cornrnunication, 1971. (8) A. J. Dill and 0. Popovych, J. Chem. Eng. Data, 14,240 (1969). (9) D. H. Berne and 0. Popovych, J. Chem. Eng. Data, in press. (10) 0. Popovych and R. M. Friedman, J. Phys. Chem., 70, 1671 (1966). (11) M. A. Coplan and R. M. Fuoss, ibid., 68, 1177 (1964). (12) A. J. Dill and 0. Popovych, J. Chem. Eng. Data, 14, 156 ( 1969). ANALYTICAL CHEMISTRY, VOL. 44, NO. 4, APRIL 1972
811
Electrolyte Ph4As Pi PhrP Pi KPi KBPhd RbBPha CsBPh4 Ph4As BPh4 Ph4P BPha KCl RbCl RbBr RbI TlCl ( I 7) TlBr ( I 7 ) TI1 ( 1 7 ) TlSCN (17) TlNOa ( 1 7 ) TlClOa (17) Molarities
Table I. Solubility Products and Medium Effects of Electrolytes in Acetonitrile at 25 "C Acetonitrile PK (CHsCN) PK (Hz0) c, M x 102 f*2 (molal) (molal) log m Y 7.99 0.249 2.58 8.92 (9) -6.34 f 0.04 8.38 0.244 2.55 8.70 (9) -6.15 f 0.04 1.05 0.510 4.03 3.41 (8) +0.62 f 0.04 5.33 0.298 2.85 7.53 (8) -4.68 i 0.04 1.70 0.455 3.66 8.54 -4.88 f 0.04 1.68 0.456 3.67 8.80 -5.13 f 0.05 ... ... ... -11.63 i 0.08 (calcd) ... 5.68 - 17.13icalcd) -11.45 f 0.08 (calcd) 0.025 (16) 0.889 7.04 -0.90 ( 1 ) +7.94 0.023 (16) 0.893 7.11 -1.31 (17) $8.42 0.22 (16) 0.717 5.24 -1.13(17) $6.37 0.242 2.83 -1.21 (17) +4.04 6.2 (16) 3.19 x lO-5= 1.00 12.99 3.76 +9.23 4.25 x 10-6" 1.00 12.74 5.47 f7.27 8.07 x 10-5a 1.00 12.19 7.19 +5.00 9.04 x 10-3" 0.94 8.11 3.77 +4.34 5.03 x 10-20 0.86 6.66 1.32 +5.34 3.31a 0.42 3.33 1.12 +2.21 .
.
I
and Ph4P Pi (9) have been described. RbBPh4, CsBPh4, and Ph4P BPh4 were prepared from the chlorides (Alfa Inorganics, Inc.) and purified by the same procedure as the potassium salt. Tetraphenylgermane (Ph4Ge), tetraphenylmethane (Ph4C), and tetraphenylsilane (Ph4Si) (Alfa Inorganics, Inc.) were purified by triple sublimation. Methanol (IO) and ethanol-water solvents (12) were purified as before. Acetonitrile (Spectroquality, The Matheson Co.) was refluxed for 24 hours over CaH2 and then distilled slowly, collecting the middle fraction. Spectrophotometric Determination of Solubilities. Ultraviolet spectra were recorded on a Cary Model 14 spectrophotometer. The molar absorptivity, e, of the picrate maximum at 369 nm in acetonitrile was determined on solutions of KPi, Ph4As Pi, and Ph4PPi of accurately known concentrations, yielding values of 1.695 X 104, 1.696 X 104 and 1.689 X lo4, respectively. Similarly, using solutions of RbBPh4 and CsBPh, in acetonitrile, we obtained for the BPh4- peaks at 266 nm and 274 nm the e values of 3203 and 2082, respectively, reproducible to about 2-3 ppt. Beer's law was obeyed. For solutions in methanol (IO), ethanol, and water (8) we used the values of B determined in this laboratory earlier. Saturated solutions of Ph4As Pi and Ph4P Pi in acetonitrile were prepared by ultrasonic generation followed by shaking of the suspensions at 25.00 "C using apparatus and procedures already described (8, 9). Ultrasonic generation was omitted for the tetraphenylborates in all solvents in order to avoid possible decomposition. After several days of equilibration, aliquots of the saturated solutions were analyzed spectrophotometrically. Shaking for an additional week produced no changes in the absorbances, within the experimental error of about 1 % or less. The solubilities of RbBPh, and CsBPh, in ethanol were determined at a series of concentrations of added LiCl ranging from about 2 to 200 times the solubility of the electrolytes. The average relative precision of the solubility determinations was 0.6% for the picrates and 1 for the tetraphenylborates. Differential Thermal Analysis. The purified solids KBPh4, RbBPh4, CsBPh4, TAB BPh4, Ph4As Pi, Ph4P Pi, KPi, Ph4Ge, Ph4C, and Ph,Si were individually equilibrated with water, methanol, acetonitrile, ethanol, and 50 wt ethanol in water (with the exception of Ph4Ge, Ph4C, and Ph4Si with water) under indentical conditions as used for their solubility determinations. The suspensions were filtered and the solids dried by suction in air. The wetted samples were analyzed in air us. glass beads as the reference material in a Du Pont 900 Differential Thermal Analyzer. Thermograms 812
ANALYTICAL CHEMISTRY, VOL. 44, NO. 4, APRIL 1972
were obtained over the range of 20-240 "C at a sensitivity of 0.2 "C/inch. RESULTS AND DISCUSSION Acetonitrile. Table I lists molar solubilities, C, of some electrolytes in acetonitrile, both those determined by us and the more reliable literature values, the calculated activity coefficients, f* *, the corresponding molal pK's in acetonitrile and water, and the medium effects with their standard deviations. Unless otherwise referenced, the data were obtained in this study. The solubilities of RbBPh4 and CsBPh, in water were redetermined to be 5.42 X 10-5M (+2%) and 4.01 X 10-bM ( i 4 %), respectively. These were combined with values offiZ from the Debye-Huckel limiting law to arvalues. According to literature data, rive at their pK (HzO) the tetraphenylborates and perchlorates of alkali-metal ions (13) and of several tetraalkylammonium ions (14) are completely dissociated in acetonitrile. We therefore assumed complete dissociation in the calculation of the pK (CHaCN) values for other electrolytes as well. Activity coefficients, f; for individual ions in acetonitrile were calculated from the Debye-Huckel equation in the form -log f
=
1.64C1'2
1
+0.485~C~'~
where the ion-size parameters, a, were approximated as before Values of a = 5 A were adopted for the tetraphenyl ions, a = 3 A, for the alkali-metal and the picrate ions, and a = 2.5 A, for the halide ions (14, 15). Fortunately, logfis not a very sensitive function of a, changing by only a few hundredths per 1 A for the solutions studied here. Assuming that the error in f would be that resulting from a change in a by 1 A, the relative precision of the solubility products in acetronitrile was calculated to be about 10%. To convert from molar (not tabulated) to molal pK's, either (15) by Stokes radii.
(13) R. L. Kay, B. J. Hales, and G. P. Cunningham, J . Phys. Chem., 71, 3925 (1967). (14) J. F. Coetzee and G. P. Cunningham, J. Amer. Chem. SOC., 87, 2529 (1965). (15) J. F. Coetzee and J. J. Campion, ibid., 89, 2513 (1967). (16) T. Pavlopoulos and H. Strehlow, 2. Physik. Cltern., 202, 474 (1954).
_ _ _ _ _ ~
Table 11. Medium Effects of Single Ions in Acetonitrile at 25 "C (Molal Scale) Alexander, Parker, et al. Coetzee et al. Ion
This study
...
" Li+ Na+ K+ Rb+ cs+ Tl+
...
... 1.08 =t0.07 0.88 + 0.07 0.63 f 0.07 1.88
...
Ag+
c1BrI-
6.86a 7.54b 5.49 3.16 3.46 2.46 0.33 -0.48 f 0.07 -5.81 0.04 -5.72 f 0.04
NOSSCNclod-
PiPh4As+ = BPh4PhdP+ = BPh; a From KC1. b From RbCl. Ferrocene assumption. d Pha As BPh4 assumption.
*
(6)
(5) ...
...
...
...
0.8
-0.2
0.0
-0.3 ...
-5.2 8.3 5.8 3.4
-5.6
...
...
3.3 -1.1 -5.8
... ...
...
2.3
(3)
...
... ...
... ...
mYPhrPBPh4
= log
mYPhiPPi
+ log mYKBPh4
... -3.8(nd, -6.7 (20)
...
3.7 1.4 1.8 0.8 -1.4 -2.6
...
...
...
... ...
...
...
...
The resulting medium effects of the reference electrolytes were split equally between the individual ions, according to the assumption that either log mYPh4As
=
log mYBPh4 =
'/Z
1%
mYPhcAsBPh4
(5a)
or log mYPhrP = log m7BPh.l =
'12
log m Y P h r P B P h r
(5b)
Complete error analysis was carried out on the pK values determined in this study and the standard deviations in the values of log for electrolytes and single ions calculated by the method of propagation of errors are specified in Tables I and 11. In acetonitrile, log mYBph, was found to be - 5.81 0.04 and -5.72 0.04 based on Equation 5a and 5b, respectively. The average value of -5.76 0.05 was used to calculate the log m ~ for ' the ~ remaining ions in Table I1 as follows :
*
*
+
log mYM = log rnYXBPh4 where M log mYPi
= =
- log mYBPh4
'/?(log mYPh4AePi
+
log mYPhdPPi log m
~ c* i
- 2 log mYBPhr) (6b)
log ~ Y K C I- log m Y K or log mYRbCl
where X
=
(64
K+, Rb+, Cs+
- log m Y R b
(6~)
- log m Y R b
(64
- log m ~ x av )
(6e)
log ~ Y T I A- log ~ Y T I
(60
log niYX = log mYRbX
- log mYKPi (4a)
...
5.6
...
...
-0.6 -5.8
...
...
... ...
... ...
3.2
...
5.0
Kolthoff et al. (20) 5.1 (20)
(18)
...
...
Br-, I-
log m
and log
-3.0 8.0
(19)
...
3.7
+ log mYKBPh4
... ...
...
where s is a nonaqueous solvent. Equation 3 is strictly valid only when the solid phase in equilibrium with the saturated solutions is identical for both solvents, i.e., when no crystal solvates are formed. Because suspicion has been raised (17) that crystal solvates might be forming with tetraphenylborates, all electrolytes and uncharged solutes studied by us were tested for the presence of solvates by differential thermal analysis. The differential thermograms recorded over the temperature range of 20-240 "C for the solids wetted alternately with water, acetonitrile, methanol, ethanol, and 50 wt ethanol in water were horizontal straight lines, indicating an absence of solvates in all these solvent-solute combinations. Of course, one canot be sure that the same conclusion can be extended to the alkali-metal halides (16) and the thallium (I) salts (18), for which the data in Table I were taken from the literature. Because the solubilities of Ph4As BPh4 and Ph4P BPh4 in water are too low for reliable spectrophotometric determinations, their medium effects were obtained by the usual (2) indirect calculation: log mYP4AsBPhr = log mYPhcAsPi
6.76 4.90 3.38 2.87 2.54
8.7 6.2 3.8
the solvent density [0.777 g/ml for acetonitrile (Is)],or the actual solution densities were used when available (16). Medium effects for electrolytes, log were calculated from Equation 3 log m~ = pK ( s ) - pK (HzO)
Izmaylov (21) 5.5 1.8 2.5 1.4 1.6 1.1
~
=~ (log l mYTlX
where X = C1-, Br-, I-
- log mYKPi (4b)
log ~ where A
(17) A. J. Parker and R. Alexander, J . Amer. Chem. Soc., 90, 3313 (1968). (18) J. F. Coetzee and J. J. Campion, ibid., 89, 2517 (1967). (19) J. F. Coetzee, J. M. Simon, and R. J. Bertozzi, ANAL.CHEM., 41, 766 (1969). (20) I. M. Kolthoff and F. G. Thomas, J. Phys. Chem., 69, 3049 (1965). (21) N. A. Izmaylov, Dokl. Akad. Nauk S S S R , 149, 1364 (1963).
=
Y A =
NOs-, SCN-, clod-
Different calculation paths are also possible using these or additional data and the results obtained by them may vary, as exemplified by the values of log rnYci in Table 11. Similarly, the results from this study and from the work of Alexander, Parker, and their associates differ somewhat, even though they are all based on the PhlAs BPh4 assumption and start ANALYTICAL CHEMISTRY, VOL. 44, NO. 4, APRIL 1972
813
~~
~
Table 111. Medium Effects of Electrolytes, log ,y, in Ethanol-Water Solvents and Methanol at 25 "C(Molal Scale) Wt
2
ethanol in water
Ph4AsPi Ph4PPi TAB Pi KPi -0.461 f 0.006 -0.466 i 0.006 -0.200 f 0.005 0.19 i 0.02 - 1 . 1 7 4 i 0 . 0 0 8 -1.134f0.008 -0.521iO0.O05 0 . 2 6 f 0 . 0 3 -2.11 rtO.01 -2.103i.0.006 -1.205fO.005 0.18i.0.02 -2.916f0.007 -2.978&0.007 -2.022i.0.006 0.10&0.02 73.46 i O . 0 2 50.0 -3.48 f 0 . 0 1 -2.725f0.009 0.02fO.02 -3.82 i 0 . 0 1 60.0 -3.87 f O . 0 1 -3.19 f 0 . 0 1 0.22f0.03 70.0 -4.08 +Oo.O1 -4.015i.0.009 -3.52 f0.03 0.36&0.02 -4.13 i 0 . 0 1 -4.040dz0.009 80.0 -3.76 f O . 0 4 0.85iO.02 -4.05 i. 0.01 90.0 -3.936f 0.006 -3.92 f 0 . 0 4 1 . 7 3 f 0.02 -3.56 i 0 . 0 2 -3.96 i.0.03 100.0 -3.723+0,009 2.66zkO.02 pK (H20) 8.92 ( 9 ) 8.70 (9) 7.31 (8) 3.41 (9) pK(CH3OH) 3.91 3.86 ... 4.25 ( I ) a There is no error in the second decimal of log ,,,YKCI and for most values of log ,,,YHCI. 10.0 20.0 30.0 40.0
out with identical values of log &fBPh, = -5.8. Such discrepancies are a reflection of the accuracy of experimental data used in the calculations and do not invalidate a given reference-electrolyte assumption, just as perfect agreement among the results calculated by different paths would not prove its validity. For example, some of the discrepancies in the above comparison can be traced to differences in the pK values adopted for the calculations. in Table I1 are based on assumpOther estimates of log tions already reviewed ( 2 , 3 ) . Izmaylov's (21)results obtained by an extrapolation method are in fair agreement with those derived from reference-electrolyte assumptions. A positive value of log m y means a lower solvation energy (tighter solvation) in water than in acetonitrile. This is the case for most small ions and is particularly accentuated for the halide ions, whose solvation depends on strong H-bonding which is available in water, but not in acetonitrile. The negative values of log m y for the silver ion and for the large organic ions are in agreement with their known preferential solvation by acetonitrile. Ethanol-Water Solvents. The medium effects of electrolytes studied here and their standard deviations are compiled in Table I11 at even ethanol-water compositions. Reported here for the first time are the values of log mYPh,A& and log m Y p h 4 p p i calculated oiu Equation 3 from their thermodynamic ion-activity products determined by us (9). Another addition to our data in 100% ethanol is the value of log These Were nLYRbBPi14 = -0.94 and Of log m')'cssPh, = -1.15. calculated from their pK (H20) values in Table I and the thermodynamic pK (C2H50H)values of 7.60 and 7.65, respectively, determined from the variation of soubility as a function of ionic strength. Some of the values for the medium effects of KBPh4,KPi, and TAB Pi previously reported from this laboratory (2) were changed slightly because of a recalculation of their solubility products and a few redeterminations of their solubilities. In the case of HCl and KCI, the values of log m y previously reported ( 2 ) were retained. A complete error analysis was carried out for all electrolytesolvent combinations studied and the standard deviations of log m y are include in all the results. The medium effects for the reference electrolytes Ph4As BPh4, Ph4PBPh4, and TAB BPh4were calculated from Equations 4a, 4b, and an analogous expression involving TAB Pi, respectively. Values of log m ~were ~ then ~ estimated h by all three assumptions, as expressed by Equations 5a, 5b, and the equality log ~ Y T A B = log m Y B P h r , respectively. The corresponding results are listed in Table IV, together with the 814
ANALYTICAL CHEMISTRY, VOL. 44, NO. 4, APRIL 1972
KBPha -0.215 f 0.009 -0.598i.O.009 -1.188iO.009 -1.86 i.O.02 -2.25 f O . 0 2 -2.51 f 0 . 0 1 -2.45 i.O.02 -2.16 f 0 . 0 2 -1.62 f 0 . 0 7 -0.96 f 0 . 0 2 7.53 (8) 5.02 ( I )
KCP 0.27 0.60 0.98 1.39 1.85 2.37 2.95 3.62 4.72 6.12
...
...
HCla 0.13 f 0.01 0.25 0.37 0.47 0.62 0.79&0.01 1.12 1.57 2.21 5.13
...
...
standard deviations calculated by the method of propagation of errors. The differences between the results obtained by the Ph4As BPha and the Ph4P BPh4 assumptions in ethanolwater solvents are not statistically significant. A borderline significance could be claimed only in the case of 100% ethanol, where the values of log mYBPh4 estimated from the two assumptions (Ph4P BPh4-Ph4As BPh4) differ by 0.08 f 0.02. The corresponding difference in acetonitrile was 0.09 f 0.06. In methanol, the molar solubilities of Ph4As Pi and PhaP and 1.416 X rePi determined by us are 1.341 X spectively, from which the (molal) pK's were calculated to be 3.91 and 3.86. [For both electrolytes we adopted a = 0.94 and f** = 0.48, assuming the same association constant of -10 as for R4N+ picrates (11) and using the previously reported calculation for the activity coefficients (IO)]. Using the pK's for KBPh4 and KPi in methanol previously reported from this laboratory ( I ) , we calculated the log mYPh,AsBPh' and log mYPhrPBph4 values for methanol from Equations 4a and 4b to be -8.36 and -8.19, respectively. Again the difference between the values of log mYBPh4 from the two assumptions is 0.08. Nevertheless, given the present status of this art, we feel justified in using the average values of log m y B p h , for the calculation of medium effects of other ions. It is noteworthy that when the standard state for the medium effects is adopted in 100% ethanol rather than water, the differences between the Ph4As BPh4 and the Ph4P BPh4 assumptions virtually disappear for acetonitrile and methanol. Thus, in acetonitrile log mYPhdA8BPhr and log mYPh4PBPhr become -4.29 and -4.27, respectively, and in methanol they are - 1.02 and - 1.01, respectively. Furthermore, ethanol and methanol do not discriminate between the tetraphenyl cations and the TAB+ ion, since log mYTABBPhr in methanol (os. ethanol reference) is also -1.02. On the other hand, the difference between the estimates of log m Y s p h 4 from the tetraphenyl-cation assumptions and the TAB+ assumption us. water as the reference is appreciable, reaching a maximum discrepancy of almost 0.5 log unit (Table IV). These results suggest that, within the experimental error of the A pK determinations, the solvents acetonitrile, ethanol, and methanol do not discriminate among the reference cations Ph4Pt,Ph4As+and TAB+ (although we have no data for TAB+ in acetonitrile) and that any differentiating action may be a function of interactions with water. Coetzee and Sharpe (22) cautioned against the assumptions (22) J. F. Coetzee and W. R. Sharpe, J. Phys. Chern., 75, 3141 (1971).
Table IV. Medium Effects, log m ~ of, Reference Electrolytes and Reference Ions at 25 "C (Molal Scale) in Ethanol-Water Solvents and Methanol Assumptions
10.0 20.0 30.0 40.0 50.0
60.0 70.0 80.0
90.0 100.0 CHIOH
-0.87 -2.04 -3.48 -4.95 -5.75 -6.60 -6.89 -7.14 -7.40 -7.34 -8.36
f 0.02
-0.88 i 0.02
f 0.03 f 0.02 f 0.03 f 0.03 f 0.03
-2.00 -3.47 -4.88 -5.72
10.03
f 0.03 f 0.07 f 0.03
i 0.03 f 0.02 f 0.03 f 0.03 -6.56 f 0.03 -6.83 f 0.03 -7.05 f 0.03
-7.28 f 0.07 -7.18 i 0.03 -8.19
-0.61 -1.38 -2.57 -3.98 -4.99 -5.92 -6.33 -6.77 -7.27 -7.58 -8.60
Table V. Medium Effects, log
+ 0.02
f 0.03 f 0.02 f 0.03 f 0.03
i 0.03 i. 0.04 f 0.02 f 0.08 f 0.04
(2)
-0.44 -1.02 -1.74 -2.47 -2.87 -3.30 -3.44 -3.57 -3.70 -3.67 -4.18
f 0.01 f 0.02 f 0.01 i 0.01 f 0.02 f 0.02 f 0.02 i 0.02 f 0.04 f 0.01
-0.44 -1.00 -1.74 -2.44 -2.86 -3.28 -3.41 -3.52 -3.64 -3.59 -4.10
f 0.01 f 0.02 f 0.01 f 0.01 i 0.02 f 0.02 f 0.01 f 0.01 f 0.04 f 0.02
-0.30 -0.69 -1.29 -1.99 -2.50 -2.96 -3.17 -3.38 -3.63 -3.79 -4.30
f 0.01
f 0.02 f 0.01 f 0.01 f 0.01 f 0.02 f 0.02 f 0.02 f 0.04 f 0.02
0.14 0.32 0.45 0.47 0.36 0.33 0.25 0.16 0.04 -0.16 -0.16
for Single Ions in Ethanol-Water Solvents at 25 "C
z
Wt ethanol in water 10.0 20.0 30.0 40.0
K' PiClH+ Ph4+a TAB+ Ph4+ TAB' Ph4+ TAB+ Ph4+ TAB+ O.lOfO.01 0 . 0 5 f 0 . 0 2 0 . 1 9 i 0 . 0 1 0 . 0 8 f 0 . 0 2 -0.06fO.02 0 . 2 2 f 0 . 0 2 0 . 0 8 f 0 . 0 1 -0.02+0.02 0.17i0.02 0.19f0.03 0.51i0.02 0.06f0.03 -0.26f0.02 0 . 4 1 f 0 . 0 3 0 . 0 9 i 0 . 0 2 -0.14f0.03 0 . 0 9 i 0 . 0 1 0.4350.02 0 . 8 8 f 0 . 0 1 - 0 . 0 6 f 0 . 0 2 -0.5110.01 0 . 5 5 i 0 . 0 2 O.lOfO.01 - 0 . 3 6 f 0 . 0 2 0 . 6 0 f 0 . 0 4 0 . 1 3 i 0 . 0 2 -0.49i.0.02 - 0 . 0 3 f 0 . 0 2 0 . 7 9 f 0 . 0 4 1 . 2 6 f 0 . 0 2 - 0 . 3 2 f 0 . 0 4 -0.79fO.02 0 . 6 1 f 0 . 0 4 0 . 2 5 i 0 . 0 2 -0.61*0.03 50.0 -0.22fO.02 1 . 2 4 f 0 . 0 4 1 . 6 0 f 0 . 0 2 -0.62fO.04 -0.98fO.02 60.0 0 . 7 8 f 0 . 0 3 0 . 4 5 i 0 . 0 2 -0.55f0.03 - 0 . 2 3 f 0 . 0 2 1 . 5 9 f 0 . 0 3 1 . 9 2 f 0 . 0 2 -0.8OfO.03 - 1 . 1 3 f 0 . 0 2 0 . 9 7 i 0 . 0 4 0 . 7 2 1 0 . 0 3 - 0 . 6 3 f 0 . 0 2 -0.35f0.04 1 . 9 8 f 0 . 0 4 2 . 2 3 i 0 . 0 3 - 0 . 8 6 i 0 . 0 4 - 1 . 1 1 f O . 0 3 70.0 80.0 1 . 3 8 i 0 . 0 4 1.22f0.03 -0.54i0.02 -0.38i0.05 2.24f0.04 2.40f0.03 -0.67fO.04 -0.83fO.03 90.0 2 . 0 5 f 0 . 1 1 2 . 0 1 f 0 . 0 8 -0.32f0.05 - 0 . 2 9 f 0 . 0 6 2 . 6 7 f 0 . 1 1 2.71fO0.O8 - 0 . 4 6 i 0 . 1 1 - 0 . 5 0 i 0 . 0 8 100.0 2.67 f 0.04 2.83 f 0.03 -0.01 i 0.03 -0.17 f 0.04 3.45 f 0.04 3.29 f 0.03 +1.68 f 0.04 +1.84 i 0.03 a Based on the average of the Ph4AsBPh4 and the Ph4PBPh4 assumptions. Based on the TAB BPh4 assumption.
that Ph4As+, Ph4P+ and BPh4- ions experience equal solvation-energy changes upon "transfer" between pairs of solvents, on the grounds that these ions exhibit specific interactions with several solvents, including water, acetonitrile, ethanol, and methanol. The evidence for these solventsolute interactions was deduced mainly from the chemical shifts of the proton resonance of the solvents. It should be borne in mind, however, that it is difficult to translate NMR shifts in terms of energetics and that appreciable shifts may be associated with negligible free-energy changes. Moreover, NMR measurements are made on relatively concentrated solutions, where the large tetraphenyl ions constitute an appreciable volume fraction of the solution, leading to a perturbation of the solvent structure which may not occur at the extreme dilutions at which medium effects are typically determined. From a practical viewpoint the question is not the existence of such differentiating interactions per se, but rather their magnitude relative to the experimental error in the A pK values or similar data from which the medium effects are calculated. Our results show that any differentiation between the solvent-solute interactions for the Ph4As+and the Ph,P+ ions is at the most of the order of experimental errors in A pK's, but we can only infer that the same is truc.: for the BPh4- ion. The medium effects for ions other than the reference ions are listed for ethanol-water solvents in Table V. They were calculated using either the average value of log m ~ de-~ rived from the Ph4As BPh4 and the Ph4P BPh4 assumptions, or its value from the TAB BPh4 assumption. Although the results based on the TAB BPh4 assumption have already been
Table VI. Standard Potentials of Hydrogen Electrodes in Ethanol-Water Solvents Referred to ,Eo (H, H20) = 0 (Molal Scale, 25 "C) Wt
z
ethanol in water 10.0 20.0 30.0 40.0 50.0
60.0 70.0 80.0
,Eo (H, SH),mV TAB+b 5 -4 - 15 4 -4 - 30 -47 - 19 - 37 - 58 -47 -66.8 -65.7 -51 -49 -40 - 27 - 30 109 99.4 the average of the Ph4As BPha and the Ph4P BPh4 Phi+'
90.0 100.0 a Based on assumptions. Based on the TAB BPh4assumption.
reported (2), they are being reproduced here due to the slight changes resulting from revised values of the medium effects for some of the electrolytes. The values of log my in Table V were calculated for the K+, Pi-, and C1- ions from Equations 6a, 6b, and 6c (using KCl), respectively. ~Thehmedium effects for the proton were calculated as log m~~ = log m ~ ~ c llog m ~ For ~ comparisons ~ . with the literature values, the reader is referred to a previous communication devoted to the TAB BPh4 assumption (2). It is obANALYTICAL CHEMISTRY, VOL. 44, NO. 4, APRIL 1972
*
815
~
~~~~~
~
~~~
Table VII. Liquid-Junction Potentials between 3.5M Aqueous KCI and Buffers in Ethanol-Water Solvents at 25 log m'YH (interpolated) Ph,+= TAB+
z
Wt ethanol in water
( E j - log ,,,YH) (23)
0.0 16.2 33.2 52.0 73.4 85.4 100.0
0.003 0.086 0.221 0.196 -0.032 -2.91
(I
O.Oo0
0.00 0.08 -0.12 -0.68 -0.83 -0.53 1.68
pH units
0.00 -0.17 -0.61 -1.02 -1.03 -0.66 1.84
Ph4+
TAB+
0.00 0.08 -0.03 -0.46 -0.63 -0.56 -1.23
0.00 -0.17 -0.52 -0.80 -0.83 -0.69 -1.07
O C
millivolts PHr+ TAB+ 0 5 -2 -27
- 37
-33 -72.8
0
- 10 -31 -41 -49 -41 -63.3
Based on the average of the Ph4AsBPh4and the Ph4PBPh4 assumptions. Based on the TAB BPh4 assumption.
tions and other physicochemical properties in mixed solvents in general, has been presented (2,3). Using the values of log m~~ in Table V, any paH* value, referred to infinite dilution in a given ethanol-water solvent, can be converted to its counterpart on a single paH scale, referred to the aqueous standard state:
ti
+I h=
E
-
For example, in 100% ethanol, a solution of a given pa^*
P 0
0
0
-I ,
I
I
,
I
0
0
,
I
50 WT X ETHANOL
I
I
IC
will have a pa^ lower by 1.84 units (TAB BPh4 assumption) or 1.68 units (Ph4As BPh4, Ph4P BPh4 assumptions), Le., it will be more acidic than an aqueous solution of the same nominal pH. Similarly, the values of log m~~ enable us to refer the standard potentials of the hydrogen electrode (SHE) in any ethanol-water solvent to the SHE in water as their arbitrary zero point (2): (H, SH) =
Figure 1. Medium effects for proton in ethanol-water solvents The curve represents results based on the average of the Ph4AsBPha and the Ph4P BPh4 assumptions. Circles are values derived from the TAB BPh4assumption
vious that in a given solvent the difference between the medium effects of any ion calculated by the TAB BPh4 assumption on the one hand and from the average of the Ph4As BPh4 and the Ph4P BPh4 assumptions on the other hand will be exactly equal to the difference between the estimates of log mYBPh4 by these two assumptions. For ethanol-water solvents, this difference ranges from 0.0 to 0.5 unit in log (Table IV). Regardless of which reference-electrolyte assumption is used, however, the all-important values of log exhibit the same characteristic pattern as a function of ethanol-water composition (Figure 1). At low ethanol contents, values of log remain around zero, then become negative, reaching a minimum at about 65-70 wt ethanol, and finally rise steeply to a positive value in 100% ethanol. Thus, the present findings using the Ph4AsBPh4 and the Ph4P BPh4 reference electrolytes, confirm the earlier conclusions (2, 3) based on TAB BPh4 alone. As bulk liquids, ethanolwater mixtures are more basic than either water or ethanol, with the maximum basicity occurring at the minimum in log m ~ Also, ~ . liquid water is more basic than liquid ethanol. A more detailed interpretation of this characteristic behavior of log m ~ which ~ , is also similar to the behavior of acidity func816
ANALYTICAL CHEMISTRY, VOL. 44, NO. 4, APRIL 1972
[H, HzO)
+
0.05916 log m~~ (at 25 "C) (8) where [H,SH) is the potential of the SHE in solvent SH on the aqueous emf scale, i.e., referred to the SHE potential in water, (H, H20),as being zero volts. Values of (H, SH) calculated via Equation 8 are compiled in Table VI. Any conventional potential, referred to the arbitrary zero point of the SHE in a given solvent, can be converted to its counterpart on the aqueous scale by adding to it algebraically the value of (H, SH) characteristic of that solvent. Thus, in 100% ethanol, all potentials undergo a positive shift of about 0.1 volt when transferred from the nonaqueous to the aqueous emf series. It is well known (2,3) that the emf of a cell composed of an aqueous and a nonaqueous SHE is a function of both the log m~~ and the liquid-junction potential, Ej. This function is involved in the interpretation of pH measurements made in nonaqueous solvents with electrodes standardized against aqueous buffers. Bates, Paabo, and Robinson (23) have determined experimentally values of (& - log m ~ for~ dilute ) buffer solutions in ethanol-water solvents in contact with 3.5 M aqueous KCI, where Zi (in pH units) is the liquid-junction error in a pH measurement, which is essentially equal to the E, at the nonaqueous (buffer)-aqueous (3.5 M KCl) interface.
(23) R. G . Bates, M. Paabo, and R. A. Robinson, J. Phys. Chem., 67, 1833 (1963).
With the aid of the values of log lo^^ from Table IV, we were able to evaluate the corresponding liquid-junction potentials (Table VII). While it is difficult at this time to make a final choice between the TAB BPh4 and the combined PhrAs BPh4-Ph4P BPh4 assumptions for the estimation of medium effects for single ions, we tend to favor the latter on the grounds that for the solvents studied here, log mYPh& = log mYPh,P, which in
turn makes the assumption of their equality to log seem very plausible.
mYBph4
RECEIVED for review October 8, 1971. Accepted November 24, 1971. Presented at the Division of Analytical Chemistry, 157th National Meeting, ACS, Minneapolis, Minn., April 1968. Work supported in part by the National Science Foundation under Cirants GP-9417 and GP-25906.
~~
~
Solubilities and Medium Effects of Tetraphenylgermane, Tetrapheny Imethane, a nd TetraphenyIsiIane in AcetonitriIe, Methanol, and Some Ethanol-Water Solvents David H. Berne and Orest Popovych Department of Chemistry, Brooklyn College of the City Unicersity of New York, Brooklyn, N . Y . 11210
According to a model of ion solvation, the medium effect, log of a lar e ion can be approximated by or a structurally analogous unthe sum of the log charged molecule and a Born electrostatic term, log m y (Born). Medium effects of tetraphenylgermane, tetraphenylmethane, and tetraphenylsilane referred to standard states in ethanol were calculated from their solubilities in acetonitrile, methanol, and ethanol-water solvents containing 60-100 wt % ethanol at about 10 wt % intervals. The solubilities were determined at 25 O C by UV spectrophotometry. When the medium effects of the tetraphenyl compounds are added to the corresponding estimates of log (Born) for an ion with r = 4-5 A, the results are in fair-to-good agreement with the observed values of l/* log m y for the tetraphenylborates of tetraphenylarsonium, tetraphenyl phosphonium, and triisoamyl-n-butylammonium in the ethanol-water solvents and methanol, but not in acetonitrile. This discrepancy may be due to an appreciable difference between the energies of iondipole interactions in acetonitrile and ethanol.
9
THESOLVATION ENERGY of an ion has been formulated by many as a composite of electrostatic and neutral contributions (1). As applied to solvation-energy differences, AGO, or medium effects, log between pairs of solvents, this formulation dates back at least to Bjerrum and Larsson (2). The “distribution coefficients,” as they called the medium effects, were thought to consist of 1) an electrostatic part given by the Born equation (3), 2 ) a non-electrostatic, or neutral part, equivalent to the medium effect of an uncharged molecule structurally analogous to the ion, and 3) another part comprising those ion-solvent interactions unaccounted for by 1) and 2). The difference between the Born solvation energies for one mole of ions in a nonaqueous solvent and in water is: AG”(Born) = ,Go
- ,Go
=
Nz-2eZ 2r
its Born component becomes In
N z 2e
(Born)
(D, l- &)
= 2 RTr
(3)
In the above equations, subscripts w and s denote aqueous and nonaqueous solvents, respectively, r is the ionic radius, D is the bulk dielectric constant of the solvent, and the other symbols have their usual meanings. According to Bjerrum and Larsson, the neutral component of the solvation-energy change for an ion, AGO (neut), could be equated to the corresponding AGO of an obvious molecular analog (such as benzoic acid for the benzoate ion) or of an isoelectronic noble gas. The latter approach was revived recently by Haugen and Friedman (4,who adopted He, Ne, Ar, Kr, and Xe as the neutral analogs of Li+, Na+, K+, Rb+, and Cs+, respectively. In a different version of the above “inert-gas assumption,” Alfenaar and De Ligny (5) preferred size to electronic structure as the criterion for assigning neutral analogs to alkali-metal and halide ions. Values of AGO (neut) corresponding to the crystallographic radii of the ions were interpolated from a plot of AGO for the transfer of noble gases and other nonpolar solutes from water to methanol as a function of r z of the solutes. Of course, the results obtained by the two versions of the “inert-gas assumption” would not agree. The need for a third component of amediumeffect in the Bjerrum and Larsson formulation stems from the failure of the simple Born equation to account for the solvationenergy terms associated with ion-dipole, ion-quadrupole, dipole-dipole, ion- (induced dipole) and dispersion interactions, which are functions of r--2, r-3, r--3, r - 4 , and P , in that order (6). Together with the Born charging term, which is proportional to r - l , they express the total electrostatic part of the solvation energy of an ion as a power series in r-l. Thus, for any ion which undergoes no specific interaction
and since the medium effect is defined by
~
~~
~
(1) 0. Popovych, Crit. Rer. Anal. Chem., 1, 73 (1970). (2) N. Bjerrum and E. Larsson, Z. Physik. Chem., 127, 358 (1927). (3) M. Born, Z . Physik., 1,45 (1920).
(4) G. R. Haugen and K. L. Friedman, J. Phys. Chem., 12, 4549 (1968). (5) M. Alfenaar and C. L. De Ligny, Rec. Truu. Chim. Pays-Bus, 86, 929 (1967). (6) J. S. Muirhead-Gould and K. J. Laidler, in “Chemical Physics of Ionic Solutions,” B. E. Conway and R. G. Barradas, Ed., Wiley, New York, N.Y., 1966, Chapter 6. ANALYTICAL CHEMISTRY, VOL. 44, NO. 4, APRIL 1972
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