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On the influence of ionic strength on the equilibrium constant of an ion-molecule reaction
A-125 J. Chem. TherPnodynamics1979,11, 1145-l149
On the influence of ionic strength on the equilibrium constant of an ion-molecule reaction ALFRED J. SMETANA and ALEXANDER
I. POPOVa
Departmentof Chemistry,Michigan State University, East Lansing,Michigan 48824,U.S.A. (Received22 September1978; in revisedform 15 March 1979) Concentrationformationconstantsfor the 18-crown-6-sodium ion complexin anhydrous methanolsolutionsweremeasured asa functionof the ionicstrengthof thesolution.TheK, valuesremainedreasonablyconstantfor Z, Q 0.05moldmb3At higherionic strengths the Kc valuesbeginto decrease. The infinite-dilutionformation constantwas2.2 x 104.
1. IntroductioIl Experimental measurementsof equilibrium constants of ionic reactions in solutions involve the vexing problem of activity corrections. A very common practice is to do the measurements at a high and constant ionic strength. If alkali salts are used for maintaining high ionic strength, they can sometimes participate in the reactions (particularly in complexation reactions) and, in addition, at high concentrations even in aqueous solution some ionic association can occur. It is preferable (although more difficult) to measure the concentration constant at several ionic strengths and to extrapolate the results to ionic strength of zero. Another procedure, although not as effective as the extrapolation method, is to calculate the activity coefficients using an appropiate form of the Debye-Hiickel equation. On the other hand, for ion-molecule reaction of the type M+ +L = ML+, (1) where the thermodynamic equilibrium constant is given by
K th
=
4ML+MM+ML+)
=
~AML+MM+ML),
(21
it is generally assumed that r(ML+) =y(M+) and that r(L) = 1. Thus the concentration equilibrium constant KC is assumed to be essentially equal to the thermodynamic constant Kth. However, it is obvious that the fist approximation is valid only within the validity of the Debye-Hiickel limiting law, i.e. for I, < 10B3 mol dmW3 in aqueous solutions and at much lower ionic strength in non-aqueous solvents with an intermediate or low value of the dielectric constant. At ionic strengths wher(: the exact form of the Debye-Hiickel equation: -loglOYi
=
A.ZfI~‘2/(1 fBrJ~‘2),
(3)
@To whomcorrespondence shouldbe addressed. OOZl-9614/79/121145+05 %01.00/O
0 1979AcademicPressInc. (London)Ltd.
1146
A. J. SMETANA
AND A. I. POPOV
is valid, the activity coefficients of the uncomplexed and of complexed metal ions are not equal since the ion-size parameters r will be different, presumably with r(ML+)>r(M+). In addition, at higher ionic strengths the activity coefficient y(L) of the neutral ligand will not be equal to unity. In recent years a number of investigators, including us, have been studying complexes of alkali cations with a variety of macrocyclic ligands such as crown ethers or cryptands, by many different physicochemical techniques.(‘) The formation constants of such complexes have been invariably reported as products of concentrations. It was of interest to us to test the validity of the above practice. Since the values of r(ML+) and r(M+) are generally unknown and since it is not possible at present to calculate precisely the variation of the activity coefficient of a neutral molecule as a function of the ionic strength of the solution, concentration formation constants were determined for the reaction: Na+ + 18C6 = Na. 18C6*, (4) where 18C6 represents 1g-crown-6 :
in methanol
solutions at (298.15 + 0.1) K at various ionic strengths.
2. Experimental Sodium perchlorate (G. F. Smith) was dried at 423 K. Tetrabutylammonium hydroxide (TBAH, Matheson, Coleman, and Bell) was obtained as a 25 mass per cent solution in methanol and was used as received. Flame emission analysis showed that its con) centration was less than 10e6 mol dme3 of Na and of K. 18-crown-6 (18C6, Aldrichwas purified by first forming the solid acetonitrile. 18C6 complex.(2) The adduct was precipitated from an 18C6 solution in acetonitrile by cooling the solution in an (acetone + ice) bath. The solution was filtered rapidly and the weakly bonded acetonitrile was removed under vacuum. The resulting product was further purified by recrystallization from methanol. The final crystals had a melting temperature of 310 to 311 K, lit. 312 K.(2) Methanol (Fisher, ACS grade) was purified by distillation over magnesium turnings. The mass fraction of water in the purified solvent was found to be less than 75 x 10m6 by Karl Fischer titration. 3. Measurements Potentiometric titrations were done using the Corning NAS 11-18 sodium-ion electrode which was preconditioned to methanol as described by Frensdorff.(3) A methanolic (silver + silver chloride) reference electrode, was used with saturated KC1 as the supporting electrolyte; this electrode was constructed with a “thirsty
INFLUENCE
OF IONIC STRENGTH
ON ION-MOLECULE
1147
REACTIONS
quartz” junction (Corning Vycor brand 7930 acid-leached quartz) which seems to show a much lower transfer of potassium ion into the test solution than any other junction. The output from the electrodes was measured by means of a high-impedence operational amplifier potential-follower (input impedence greater than 1012 a) connected to an Analogic 2546 digital voltmeter. Potentials could be read in a range of f 2.00 V with f. 0.1 mV accuracy. Titrations were carried out in an all-glass cell thermostatted at (298.15 rt 0.1) K. The titrant was added from 2 cm3 or 5 cm3 microburets. The titration cell, while essentially airtight, was not purged with nitrogen to avoid solvent losses. To reduce the electrical noise, the titration assembly was enclosed in a grounded Faraday cage. An air-driven magnetic stirrer was used for solution mixing since electrical stirrers introduced electrical noise into the titration assembly. The titrations were performed in the following manner: with the electrodes in place, 20 cm3 of a tetrabutylammonium hydroxide (TBAH) solution in methanol (the supporting electrolyte at a given ionic strength) was temperature equilibrated for 30 min. This solution was then titrated with a methanolic solution of sodium perchlorate, (at the same ionic strength) generating the electrode-calibration curve. The resulting solution was then back titrated with a solution of the ligand (18C6), again at the same ionic strength. A typical titration curve is shown in figure 1. Only the points after the equivalence point were used in the calculation of the formation constants. The results were analysed using a nonlinear least-squares program KINFIT4(4’ to fit the calibration curve, and a general equilibrium-solving program MINIQI.JAD76A(5) for the calculations of the formation constants. -120-
/
I
1
I
1
1
/
I
I
I
I
I
I
I-
-lOO-
-80 k E
do-
&
,e,ve#eNe’
-do,eNe
-20 -
Oe’ 0
l’
/
1
I
0.4
t
I
0.8
I
1.2
1.6
I
2.0
Y,i,/cIn3 FIGURE 1. Titration curve of sodium perchlorate with 18C6 in methanol measured at Z, = 0.40 mol dmd3; electromotive force E against the volume of the t&ant. The arrow indicates the equivalence point. 71
1148
A. J. SMETANA
AND A. I. POPOV
It was assumed that TBAH was indeed an “inert” electrolyte for the following reasons. The decadic logarithms of the formation constants of 18C6 complexes with dimethylammonium and diethylammonium cations in methanol solutions are 1.76 and 0.85 respectively@) and, therefore, one would not expect any complexation of the TBA ion by 18C6. In addition, precise electric conductance studies of ionic association in anhydrous methanol by Kay et al(‘) could not detect ion-pair formation in tetrabutylammonium chloride solutions. Similar results for TBAH do not seem to be available in the literature but it seems reasonable to conclude that also in this case the extent of ion pairing at best would be very small. 4. Results and discussion Concentration equilibrium constants for reaction (4) were obtained at different ionic strengths. The results are shown in table 1 and figure 2. It is seen that in the ionic strengh range of 0.005 to 0.05 mol dmm3 the value of the concentration formation constant remains reasonably constant and close to the value of Kth. At higher ionic strengths, however, K, begins to decrease appreciably. Since y(L) TABLE 1 Concentration formation constants Kc for the reaction: NaC104 + 18C6 = 18C6-Na+ -j- CIO, in methanol at (298.15 & 0.1) K at various ionic strengths Z, Z,/mol rlme3 log,&, a
0.005 4.33
0.01 4.32
0.03 4.30
0.05 4.29
0.08 4.21
0.10 4.28
0.20 4.22
0.30 4.17
0.40 4.13
0.50 4.09
a The uncertainity in log,,K, is zt 0.02.
FIGURE 2. A plot of log,,K, for the 18C6*Na+ complexation the solution.
reaction against ionic strength of
INFLUENCE
OF IONIC
STRENGTH
ON
ION-MOLECULE
REACTIONS
1149
increases with increasing ionic strength, the decrease in K, indicates that the variation in the ion-size parameter is a more important factor than the variation in y(L). Extrapolation of our results to infinite dilution yields log,,& = 4.34 in goodagreement with the 4.32 obtained by Frensdorff (3) also from potentiometric measurements, and the 4.36 obtained by Izatt et al. from calorimetric measurements.(*) The results given in table 1 were used to fit the distance of closest approach r(ML+) for the complexed metal ion to the Debye-Hiickel equation. Values of 0.40,0.45, and 0.50 nm were assumed for the distance parameter of the solvated sodium ion and the KINFIT program was used to fit the results; the corresponding values of r(ML+) were calculated to be (0.80 & 0.09), (0.92 + 0.05), and (1.04 + 0.07) nm. The authors gratefully acknowledge the support of this work by a grant from the National Science Foundation, and the help of Professor A. Vacca of the Institute of Inorganic Chemistry, University of Florence, who supplied us with the MINIQUAD program. REFERENCES
1. Popov, A. I. ; L&n, J.-M. Physicochemical Studies of Crown and Cryptate Complexes in Chemistry of Macrocyclic Compounds, Melson, G. A. : editor. Plenum: New York, N. Y. 1979. 2. Gokel, G. W.; Cram, D. J.; Liotta, C. L.; Harris, H. P. ; Cook, F. L J. Org. Chem. 1974,39,2445. 3. Frensdorff, H. K. J. Am. Chem. Sot. 1971,93, 600. 4. Dye, J. L.; Nicely, V. A. J. Chem. Educ. 1971, 68, 443. 5. (a), Sabatini, A.; Vacca, A.; Gans, P. Talanta 1974,21, 53 ; (b) Gans, P.; Sabatini, A.; Vacca, A. Znorg. Chim. Acta 1976, 18, 237. 6. Izatt, R. M.; I&t, N. E.; Rossiter, B. E. ; Christensen, J. J. Science 1978, 199, 994. 7. Kay, R. L.; Zawoyski, C.; Evans, D. F. J. Phys. Chem. 1965, 69,420s. 8. Izatt, R. M.; Lamb, J. D.; Maas, G. E. ; Asay, R. E.; Bradshaw, J. S.; Christensen, J. J. J. Am. Chem. Sot. 1977,99,2365.
On the influence of ionic strength on the equilibrium constant of an ion-molecule reaction ALFRED J. SMETANA and ALEXANDER
I. POPOVa
Departmentof Chemistry,Michigan State University, East Lansing,Michigan 48824,U.S.A. (Received22 September1978; in revisedform 15 March 1979) Concentrationformationconstantsfor the 18-crown-6-sodium ion complexin anhydrous methanolsolutionsweremeasured asa functionof the ionicstrengthof thesolution.TheK, valuesremainedreasonablyconstantfor Z, Q 0.05moldmb3At higherionic strengths the Kc valuesbeginto decrease. The infinite-dilutionformation constantwas2.2 x 104.
1. IntroductioIl Experimental measurementsof equilibrium constants of ionic reactions in solutions involve the vexing problem of activity corrections. A very common practice is to do the measurements at a high and constant ionic strength. If alkali salts are used for maintaining high ionic strength, they can sometimes participate in the reactions (particularly in complexation reactions) and, in addition, at high concentrations even in aqueous solution some ionic association can occur. It is preferable (although more difficult) to measure the concentration constant at several ionic strengths and to extrapolate the results to ionic strength of zero. Another procedure, although not as effective as the extrapolation method, is to calculate the activity coefficients using an appropiate form of the Debye-Hiickel equation. On the other hand, for ion-molecule reaction of the type M+ +L = ML+, (1) where the thermodynamic equilibrium constant is given by
K th
=
4ML+MM+ML+)
=
~AML+MM+ML),
(21
it is generally assumed that r(ML+) =y(M+) and that r(L) = 1. Thus the concentration equilibrium constant KC is assumed to be essentially equal to the thermodynamic constant Kth. However, it is obvious that the fist approximation is valid only within the validity of the Debye-Hiickel limiting law, i.e. for I, < 10B3 mol dmW3 in aqueous solutions and at much lower ionic strength in non-aqueous solvents with an intermediate or low value of the dielectric constant. At ionic strengths wher(: the exact form of the Debye-Hiickel equation: -loglOYi
=
A.ZfI~‘2/(1 fBrJ~‘2),
(3)
@To whomcorrespondence shouldbe addressed. OOZl-9614/79/121145+05 %01.00/O
0 1979AcademicPressInc. (London)Ltd.
1146
A. J. SMETANA
AND A. I. POPOV
is valid, the activity coefficients of the uncomplexed and of complexed metal ions are not equal since the ion-size parameters r will be different, presumably with r(ML+)>r(M+). In addition, at higher ionic strengths the activity coefficient y(L) of the neutral ligand will not be equal to unity. In recent years a number of investigators, including us, have been studying complexes of alkali cations with a variety of macrocyclic ligands such as crown ethers or cryptands, by many different physicochemical techniques.(‘) The formation constants of such complexes have been invariably reported as products of concentrations. It was of interest to us to test the validity of the above practice. Since the values of r(ML+) and r(M+) are generally unknown and since it is not possible at present to calculate precisely the variation of the activity coefficient of a neutral molecule as a function of the ionic strength of the solution, concentration formation constants were determined for the reaction: Na+ + 18C6 = Na. 18C6*, (4) where 18C6 represents 1g-crown-6 :
in methanol
solutions at (298.15 + 0.1) K at various ionic strengths.
2. Experimental Sodium perchlorate (G. F. Smith) was dried at 423 K. Tetrabutylammonium hydroxide (TBAH, Matheson, Coleman, and Bell) was obtained as a 25 mass per cent solution in methanol and was used as received. Flame emission analysis showed that its con) centration was less than 10e6 mol dme3 of Na and of K. 18-crown-6 (18C6, Aldrichwas purified by first forming the solid acetonitrile. 18C6 complex.(2) The adduct was precipitated from an 18C6 solution in acetonitrile by cooling the solution in an (acetone + ice) bath. The solution was filtered rapidly and the weakly bonded acetonitrile was removed under vacuum. The resulting product was further purified by recrystallization from methanol. The final crystals had a melting temperature of 310 to 311 K, lit. 312 K.(2) Methanol (Fisher, ACS grade) was purified by distillation over magnesium turnings. The mass fraction of water in the purified solvent was found to be less than 75 x 10m6 by Karl Fischer titration. 3. Measurements Potentiometric titrations were done using the Corning NAS 11-18 sodium-ion electrode which was preconditioned to methanol as described by Frensdorff.(3) A methanolic (silver + silver chloride) reference electrode, was used with saturated KC1 as the supporting electrolyte; this electrode was constructed with a “thirsty
INFLUENCE
OF IONIC STRENGTH
ON ION-MOLECULE
1147
REACTIONS
quartz” junction (Corning Vycor brand 7930 acid-leached quartz) which seems to show a much lower transfer of potassium ion into the test solution than any other junction. The output from the electrodes was measured by means of a high-impedence operational amplifier potential-follower (input impedence greater than 1012 a) connected to an Analogic 2546 digital voltmeter. Potentials could be read in a range of f 2.00 V with f. 0.1 mV accuracy. Titrations were carried out in an all-glass cell thermostatted at (298.15 rt 0.1) K. The titrant was added from 2 cm3 or 5 cm3 microburets. The titration cell, while essentially airtight, was not purged with nitrogen to avoid solvent losses. To reduce the electrical noise, the titration assembly was enclosed in a grounded Faraday cage. An air-driven magnetic stirrer was used for solution mixing since electrical stirrers introduced electrical noise into the titration assembly. The titrations were performed in the following manner: with the electrodes in place, 20 cm3 of a tetrabutylammonium hydroxide (TBAH) solution in methanol (the supporting electrolyte at a given ionic strength) was temperature equilibrated for 30 min. This solution was then titrated with a methanolic solution of sodium perchlorate, (at the same ionic strength) generating the electrode-calibration curve. The resulting solution was then back titrated with a solution of the ligand (18C6), again at the same ionic strength. A typical titration curve is shown in figure 1. Only the points after the equivalence point were used in the calculation of the formation constants. The results were analysed using a nonlinear least-squares program KINFIT4(4’ to fit the calibration curve, and a general equilibrium-solving program MINIQI.JAD76A(5) for the calculations of the formation constants. -120-
/
I
1
I
1
1
/
I
I
I
I
I
I
I-
-lOO-
-80 k E
do-
&
,e,ve#eNe’
-do,eNe
-20 -
Oe’ 0
l’
/
1
I
0.4
t
I
0.8
I
1.2
1.6
I
2.0
Y,i,/cIn3 FIGURE 1. Titration curve of sodium perchlorate with 18C6 in methanol measured at Z, = 0.40 mol dmd3; electromotive force E against the volume of the t&ant. The arrow indicates the equivalence point. 71
1148
A. J. SMETANA
AND A. I. POPOV
It was assumed that TBAH was indeed an “inert” electrolyte for the following reasons. The decadic logarithms of the formation constants of 18C6 complexes with dimethylammonium and diethylammonium cations in methanol solutions are 1.76 and 0.85 respectively@) and, therefore, one would not expect any complexation of the TBA ion by 18C6. In addition, precise electric conductance studies of ionic association in anhydrous methanol by Kay et al(‘) could not detect ion-pair formation in tetrabutylammonium chloride solutions. Similar results for TBAH do not seem to be available in the literature but it seems reasonable to conclude that also in this case the extent of ion pairing at best would be very small. 4. Results and discussion Concentration equilibrium constants for reaction (4) were obtained at different ionic strengths. The results are shown in table 1 and figure 2. It is seen that in the ionic strengh range of 0.005 to 0.05 mol dmm3 the value of the concentration formation constant remains reasonably constant and close to the value of Kth. At higher ionic strengths, however, K, begins to decrease appreciably. Since y(L) TABLE 1 Concentration formation constants Kc for the reaction: NaC104 + 18C6 = 18C6-Na+ -j- CIO, in methanol at (298.15 & 0.1) K at various ionic strengths Z, Z,/mol rlme3 log,&, a
0.005 4.33
0.01 4.32
0.03 4.30
0.05 4.29
0.08 4.21
0.10 4.28
0.20 4.22
0.30 4.17
0.40 4.13
0.50 4.09
a The uncertainity in log,,K, is zt 0.02.
FIGURE 2. A plot of log,,K, for the 18C6*Na+ complexation the solution.
reaction against ionic strength of
INFLUENCE
OF IONIC
STRENGTH
ON
ION-MOLECULE
REACTIONS
1149
increases with increasing ionic strength, the decrease in K, indicates that the variation in the ion-size parameter is a more important factor than the variation in y(L). Extrapolation of our results to infinite dilution yields log,,& = 4.34 in goodagreement with the 4.32 obtained by Frensdorff (3) also from potentiometric measurements, and the 4.36 obtained by Izatt et al. from calorimetric measurements.(*) The results given in table 1 were used to fit the distance of closest approach r(ML+) for the complexed metal ion to the Debye-Hiickel equation. Values of 0.40,0.45, and 0.50 nm were assumed for the distance parameter of the solvated sodium ion and the KINFIT program was used to fit the results; the corresponding values of r(ML+) were calculated to be (0.80 & 0.09), (0.92 + 0.05), and (1.04 + 0.07) nm. The authors gratefully acknowledge the support of this work by a grant from the National Science Foundation, and the help of Professor A. Vacca of the Institute of Inorganic Chemistry, University of Florence, who supplied us with the MINIQUAD program. REFERENCES
1. Popov, A. I. ; L&n, J.-M. Physicochemical Studies of Crown and Cryptate Complexes in Chemistry of Macrocyclic Compounds, Melson, G. A. : editor. Plenum: New York, N. Y. 1979. 2. Gokel, G. W.; Cram, D. J.; Liotta, C. L.; Harris, H. P. ; Cook, F. L J. Org. Chem. 1974,39,2445. 3. Frensdorff, H. K. J. Am. Chem. Sot. 1971,93, 600. 4. Dye, J. L.; Nicely, V. A. J. Chem. Educ. 1971, 68, 443. 5. (a), Sabatini, A.; Vacca, A.; Gans, P. Talanta 1974,21, 53 ; (b) Gans, P.; Sabatini, A.; Vacca, A. Znorg. Chim. Acta 1976, 18, 237. 6. Izatt, R. M.; I&t, N. E.; Rossiter, B. E. ; Christensen, J. J. Science 1978, 199, 994. 7. Kay, R. L.; Zawoyski, C.; Evans, D. F. J. Phys. Chem. 1965, 69,420s. 8. Izatt, R. M.; Lamb, J. D.; Maas, G. E. ; Asay, R. E.; Bradshaw, J. S.; Christensen, J. J. J. Am. Chem. Sot. 1977,99,2365.