- Email: [email protected]
The osmotic and activity coefficients of lithium, sodium, and potassium trifluoroacetates and a discussion of the ionization of trifluoroacetic acid
A-243 J. Chem. Thermodynamics 1982, 14, 215-219
The osmotic and activity coefficients of lithium, sodium, and potassium trifluoroacetates and a discussion of the ionization of trifluoroacetic acid OSCAR D. BONNER Department qf Chemistry, The University qf South Carolina, Columbia, South Carolina 29208, U.S.A. (Received 19 September 1980; in revised form 14 August 1981)
Osmotic and activity coefficients are reported for solutions of lithium, sodium, and potassium trifluoroacetates. Trends are compared among these salts and the corresponding acetates and trichloroacetates. Estimates of the ionic activity coefficients of the parent acid are discussed.
1. Introduction The author has reported the osmotic and activity coefficients of the lithium,“’ sodium,‘2’ and potassium(r) trichloroacetates in connection with studies of the ionization of trichloroacetic acid. The various studies of this acid are of interest in that an ionization constant of about 0.2 mol. kg-r is obtained from the usual measurementsof hydrogen-ion molality in fairly dilute solutions while a constant in the range of 2 to 5 mol. kg-’ was obtained by Covington’3’ from measurementsof the trichloroacetate-anion molality by Raman spectroscopy. A bibliography of previous work is given in Covington’s article. The author confirmed’2’ the Raman results of Covington using the C-Cl band as an internal standard. An ionization constant of 4 to 8 mol. kg- 1 was reported (3) for trifluoroacetic acid in the same paper and it was noted that previously reported values, obtained by measurementsof hydrogen-ion molality in dilute solutions, were much smaller. The difficulty in the calculation of a thermodynamic constant for each acid is the lack of knowledge of the ionic activity coefficients. I have attempted to measure the stoichiometric activity coefficients of these acids by the isopiestic technique but both are volatile in aqueous solutions and this is not possible. Even had these measurements been feasible, the measured coefficients would not be those which were desired. Just as the measurement of the activity coefficients of the salts of trichloroacetic acid was undertaken so that they might be used to estimate the ionic activity coefficients of the parent acid, the reported results for the trifluoroacetate salts will be used. 0021-9614/82/030275+05
$01.00/O
Q 1982 Academic
Press Inc. (London)
Limited
276
0. D. BONNER
2. Experimental Reagent-grade trifluoroacetic acid was obtained from Fisher Scientific Company and distilled, the middle fraction being retained. A portion of the acid was almost neutralized with reagent-grade lithium, sodium, or potassium carbonate in aqueous solution. Each solution was then evaporated in a vacuum desiccator containing sulfuric acid in one dish and solid sodium hydroxide in another. This removed both the water and the slight excess of trifluoroacetic acid. The salts were recrystallized from (methanol + ether). The lithium salt is quite soluble in these organic solvents and the recrystallization is difficult. The recrystallized salts were then dried under vacuum, first in the presence of H,S04 and then of P,O,. The molar masses were checked by passing a solution of a known mass of the salt through an ion exchange resin in the acid form and titrating the eluent with standard sodium hydroxide. The salts were found to be anhydrous and the molar masses which were found agreed with the calculated values within the error of the titration (0.1 to 0.2 per cent). The isopiestic equilibration of solutions was carried out in the manner which has previously been describedt4) in detail. As usual, equilibrium was obtained in 24 h to 10 d depending on the molality of the solution.
3. Results The primary results are presented in table 1 and the osmotic and activity coefficients at round molalities are reported in tables 2 and 3. Osmotic coefficients were calculated from the relation : 4 = (vrefmreJvmMref. The results for sodium TABLE
1. Molalities
chloride
are those of Robinson
m of isopiestic
solutions
0.193,
0.189,
0.308 0.527 0.661 0.872 1.144 1.302 1.518 1.703
0.298 0.502 0.625 0.817
0.344 0.692 0.944 1.233 1.499
0.342 0.684 0.934 1.221 1.493 1.814 2.135 2.449 2.932 3.460 4.014 4.640 5.316 6.046 7.046 8.015
0.382 0.119 1.147
0.378 0.755
2.096 2.370 2.708 3.081 3.541 3.870 4.416 5.049 5.358
K ; TFA : trifluoroacetate KTFA
NaCl m/(mol
2.278 2.588 2.972 3.382 3.878 4.230 4.787 5.430 5.734
Activity
NaCl
LiTFA
1.091 1.443 1.752
at 298.15
and Stokes.“’
i%TFA kg-‘)
NaCl
1.542 1.892
(1)
1.068 1.210 1.410
1.811 2.160
1.575 1.675 2.001
2.380 2.828 2.984
2.212 2.636 2.793
1.799 2.091 2.406 2.776 3.iOO 3.623 4.065 4.504 4.933 5.497 6.007
ISOPIESTIC TABLE
nl
mol-kg-’ 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1.0 1.2 1.4 1.6 1.8
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8
m
4
NaTFA
K~FA
0.934 0.929 0.928 0.929 0.935 0.942 0.952 0.962 0.972 0.982
0.944 0.947 0.952 0.959 0.966 0.976 0.984 0.991 0.998
0.935 0.930 0.928 0.927 0.929 0.932 0.936 0.939 0.942 0.946 0.953 0.958 0.961 0.964
1.OQ7 1.020 1.033 1.046 1.058
1.001 1.020 1.040 1.059
3.
277
ON TRIFLUOROACETATES
Osmotic coefficients 4 at 298.15 K in solutions of modality m
LiTFA
TABLE
m mol.kg-’
2.
MEASUREMENTS
mol. kg-’ 2.0 2.5 2.8 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
4
NaTFA
KTFA
1.077
1.070
1.125
1.101
0.966 0.972
LiTFA
1.118 1.169 1.209
0.976 0.979 0.982 0.983 0.979 0.973 0.969 0.964 0.960 0.958 0.953
1.246 1.280 1.314 1.347
Mean ionic activity coefficients at 298.15 K in solutions of molality m
LiTFA
;‘t NaTFA
KTFA
0.781 0.740 0.718 0.704 0.698 0.695 0.696 0.698 0.703 0.708 0.720 0.736 0.754 0.773
0.794 0.768 0.756 0.753 0.753 0.756 0.760 0.764 0.768 0.774 0.786 0.801 0.816 0.831
0.783 0.742 0.717 0.704 0.694 0.687 0.682 0.679 0.677 0.616 0.674 0.673 0.671 0.670
In mol.kg-’ 2.0 2.5 2.8 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
LiTFA
;‘i NaTFA
0.793 0.851 0.913 0.997
1.044 1.116 1.192 1.269
0.847 0.892 0.917
KTFA 0.669 0.668 0.668 0.668 0.668 0.666 0.663 0.658 0.654 0.649 0.645 0.641 0.635
coefficients were calculated from the relation: f&f
In ;I = In Yref+ln R+2
(R - l)d ln((mrefyref)li2i.
(2)
s 0
The molality ratio R is m,,,/m. The extrapolation of R from its value in the most dilute solution to a value of 1 at infinite dilution presented no problem becausethe solutions are well behaved ; i.e. R is not far from 1 and approaches 1 in a predictable manner. In a plot, no experimental point lay off the curve by more than 0.002 with the average deviation being less than 0.001. The uncertainty in the osmotic coefficients is, therefore, about 0.1 per cent. In the calculation of the activity coefficients from
278
0. D. BONNER
equation (2), the In yref and In R terms are known with the same precision. By choosing a proper reference solute, such that (R- 1) z 1 in dilute solutions, the contribution of the integral is so small that an error of 10 per cent does not affect the value of the activity coefficient. 4. Discussion The mean ionic activity coefficients of the trifluoroacetate salts at any molality are Na+ > Li+ > K+ except for the very dilute solutions where the activity coefficients of the lithium and potassium salt are essentially the same. This may be compared with the acetates for which the order is K+ > Na+ > Li+ and the trichloroacetates for which the order is Li+ > Na+ > K’. The order of the coefficients for the acetates is typical of the behavior of salts of weak carboxylic acids. The order for the trichloroacetates is the same as that of the salts of strong acids such as HCl, HClO,, erc. The order for the trifluoroacetates is that which would be expected for an acid of intermediate strength. This poses an interesting problem in the light of the values reported for ionization constants in the introductory portion of this paper, since the activity coefficients of the trifluoroacetates indicate that the parent acid is weaker than trichloroacetic acid. The author has suggested (l’ that trichloroacetic acid is, indeed, ionized to the extent which is suggested by the Raman measurements but appears to be much weaker by other measurements because of rather extensive ion pairing in the form of hydrogen bonding between the hydronium ion and the chloride atoms of the trichloroacetate ion. A similar phenomenon should occur in solutions of trifluoroacetic acid and this will also account for the range of ionization constants reported for this acid. What conditions are necessary, however, for the trifluoroacetic acid solutions to have a greater molality of carboxylate ion as measured by Raman spectroscopy even though the activity coefficients of the salts indicate that it is a weaker acid than trichloroacetic? The ionization constant, K, is expressed as K = (@-I+ )m(A-)/WM))
{fi(HA))2/jU-M),
(3)
where f+(HA) represents the mean ionic activity coefficient of the acid HA. The symbolf, is used to represent the mean ionic activity coefficient of weak acids while y+, the mean stoichiometric activity coefficient, is normally used for strong acids and au salts since they are considered to be completely ionized. The results reported in this paper indicate that for all of the salts, the coefficients are larger for the trichloroacetates. Furthermore, the trends indicate that the coefficients of the trichloroacetic acid should be appreciably larger than those of trifluoroacetic acid in the molality range in which the Raman measurements were made. It is, therefore, possible that the value of the quotient m(H+)m(A-)/m(HA) could be smaller for trichloroacetic acid than for trifluoroacetic acid and yet the values of the ionization constant K would be reversed. We should now determine whether this possibility is reasonable. If an acid is partially ionized, the degree of ionization will be increased if the hydronium ion is removed from solution by bonding to (or ion pairing with) another group. The extent of the increased ionization of the weak acid depends not only on the strength of the acid but also on the strength of the hydronium ion
ISOPIESTIC
MEASUREMENTS
ON TRIFLUOROACETATES
279
association with the second group. In the case of these two acids the hydronium ion must be more strongly ion paired with the trichloro-group than with the trifluorogroup. This would seem to be improbable if one considers only electronegativity. There is evidence, however, that the relative polarizabilities of the two groups is more important than their relative electronegativities. The tetramethylguanidinium cation can form ion pairs by means of hydrogen bonding with the three anions discussed in this paper. The values’6.7’ of the activity coefficients y+ of the tetramethylguanidinium acetate, trifluoroacetate, and trichloroacetate a
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
Banner, Bonner, Covington, Bonner, Robinson, Bonner, Bonner, Hanstein.
0. D.; Prichard, P. R. J. Solution Chem. 1979, 8, 113. 0. D.; Flora, H. B.; Aitken, H. W. J. Phys. Chem. 1971, 75, 2492. A. K.; Freeman, J. G.; Lilley, T. H. J. Phys. Chem. 1970, 74, 3773. 0. D. J. Chem. Thermodynamics 1979, 11. 559. R. A.; Stokes, R. H. Trans. Faraday Sot. 1949, 45. 612. 0. D. Physiol. Chem. Phys. 1980, 12, 38. 0. D. J. Solution Chem. 1980, 9. 877. W. G.; Davis, K. A.; Hatefi, Y. Arch. Biochem. Biophys. 1971, 147, 534.
The osmotic and activity coefficients of lithium, sodium, and potassium trifluoroacetates and a discussion of the ionization of trifluoroacetic acid OSCAR D. BONNER Department qf Chemistry, The University qf South Carolina, Columbia, South Carolina 29208, U.S.A. (Received 19 September 1980; in revised form 14 August 1981)
Osmotic and activity coefficients are reported for solutions of lithium, sodium, and potassium trifluoroacetates. Trends are compared among these salts and the corresponding acetates and trichloroacetates. Estimates of the ionic activity coefficients of the parent acid are discussed.
1. Introduction The author has reported the osmotic and activity coefficients of the lithium,“’ sodium,‘2’ and potassium(r) trichloroacetates in connection with studies of the ionization of trichloroacetic acid. The various studies of this acid are of interest in that an ionization constant of about 0.2 mol. kg-r is obtained from the usual measurementsof hydrogen-ion molality in fairly dilute solutions while a constant in the range of 2 to 5 mol. kg-’ was obtained by Covington’3’ from measurementsof the trichloroacetate-anion molality by Raman spectroscopy. A bibliography of previous work is given in Covington’s article. The author confirmed’2’ the Raman results of Covington using the C-Cl band as an internal standard. An ionization constant of 4 to 8 mol. kg- 1 was reported (3) for trifluoroacetic acid in the same paper and it was noted that previously reported values, obtained by measurementsof hydrogen-ion molality in dilute solutions, were much smaller. The difficulty in the calculation of a thermodynamic constant for each acid is the lack of knowledge of the ionic activity coefficients. I have attempted to measure the stoichiometric activity coefficients of these acids by the isopiestic technique but both are volatile in aqueous solutions and this is not possible. Even had these measurements been feasible, the measured coefficients would not be those which were desired. Just as the measurement of the activity coefficients of the salts of trichloroacetic acid was undertaken so that they might be used to estimate the ionic activity coefficients of the parent acid, the reported results for the trifluoroacetate salts will be used. 0021-9614/82/030275+05
$01.00/O
Q 1982 Academic
Press Inc. (London)
Limited
276
0. D. BONNER
2. Experimental Reagent-grade trifluoroacetic acid was obtained from Fisher Scientific Company and distilled, the middle fraction being retained. A portion of the acid was almost neutralized with reagent-grade lithium, sodium, or potassium carbonate in aqueous solution. Each solution was then evaporated in a vacuum desiccator containing sulfuric acid in one dish and solid sodium hydroxide in another. This removed both the water and the slight excess of trifluoroacetic acid. The salts were recrystallized from (methanol + ether). The lithium salt is quite soluble in these organic solvents and the recrystallization is difficult. The recrystallized salts were then dried under vacuum, first in the presence of H,S04 and then of P,O,. The molar masses were checked by passing a solution of a known mass of the salt through an ion exchange resin in the acid form and titrating the eluent with standard sodium hydroxide. The salts were found to be anhydrous and the molar masses which were found agreed with the calculated values within the error of the titration (0.1 to 0.2 per cent). The isopiestic equilibration of solutions was carried out in the manner which has previously been describedt4) in detail. As usual, equilibrium was obtained in 24 h to 10 d depending on the molality of the solution.
3. Results The primary results are presented in table 1 and the osmotic and activity coefficients at round molalities are reported in tables 2 and 3. Osmotic coefficients were calculated from the relation : 4 = (vrefmreJvmMref. The results for sodium TABLE
1. Molalities
chloride
are those of Robinson
m of isopiestic
solutions
0.193,
0.189,
0.308 0.527 0.661 0.872 1.144 1.302 1.518 1.703
0.298 0.502 0.625 0.817
0.344 0.692 0.944 1.233 1.499
0.342 0.684 0.934 1.221 1.493 1.814 2.135 2.449 2.932 3.460 4.014 4.640 5.316 6.046 7.046 8.015
0.382 0.119 1.147
0.378 0.755
2.096 2.370 2.708 3.081 3.541 3.870 4.416 5.049 5.358
K ; TFA : trifluoroacetate KTFA
NaCl m/(mol
2.278 2.588 2.972 3.382 3.878 4.230 4.787 5.430 5.734
Activity
NaCl
LiTFA
1.091 1.443 1.752
at 298.15
and Stokes.“’
i%TFA kg-‘)
NaCl
1.542 1.892
(1)
1.068 1.210 1.410
1.811 2.160
1.575 1.675 2.001
2.380 2.828 2.984
2.212 2.636 2.793
1.799 2.091 2.406 2.776 3.iOO 3.623 4.065 4.504 4.933 5.497 6.007
ISOPIESTIC TABLE
nl
mol-kg-’ 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1.0 1.2 1.4 1.6 1.8
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8
m
4
NaTFA
K~FA
0.934 0.929 0.928 0.929 0.935 0.942 0.952 0.962 0.972 0.982
0.944 0.947 0.952 0.959 0.966 0.976 0.984 0.991 0.998
0.935 0.930 0.928 0.927 0.929 0.932 0.936 0.939 0.942 0.946 0.953 0.958 0.961 0.964
1.OQ7 1.020 1.033 1.046 1.058
1.001 1.020 1.040 1.059
3.
277
ON TRIFLUOROACETATES
Osmotic coefficients 4 at 298.15 K in solutions of modality m
LiTFA
TABLE
m mol.kg-’
2.
MEASUREMENTS
mol. kg-’ 2.0 2.5 2.8 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
4
NaTFA
KTFA
1.077
1.070
1.125
1.101
0.966 0.972
LiTFA
1.118 1.169 1.209
0.976 0.979 0.982 0.983 0.979 0.973 0.969 0.964 0.960 0.958 0.953
1.246 1.280 1.314 1.347
Mean ionic activity coefficients at 298.15 K in solutions of molality m
LiTFA
;‘t NaTFA
KTFA
0.781 0.740 0.718 0.704 0.698 0.695 0.696 0.698 0.703 0.708 0.720 0.736 0.754 0.773
0.794 0.768 0.756 0.753 0.753 0.756 0.760 0.764 0.768 0.774 0.786 0.801 0.816 0.831
0.783 0.742 0.717 0.704 0.694 0.687 0.682 0.679 0.677 0.616 0.674 0.673 0.671 0.670
In mol.kg-’ 2.0 2.5 2.8 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
LiTFA
;‘i NaTFA
0.793 0.851 0.913 0.997
1.044 1.116 1.192 1.269
0.847 0.892 0.917
KTFA 0.669 0.668 0.668 0.668 0.668 0.666 0.663 0.658 0.654 0.649 0.645 0.641 0.635
coefficients were calculated from the relation: f&f
In ;I = In Yref+ln R+2
(R - l)d ln((mrefyref)li2i.
(2)
s 0
The molality ratio R is m,,,/m. The extrapolation of R from its value in the most dilute solution to a value of 1 at infinite dilution presented no problem becausethe solutions are well behaved ; i.e. R is not far from 1 and approaches 1 in a predictable manner. In a plot, no experimental point lay off the curve by more than 0.002 with the average deviation being less than 0.001. The uncertainty in the osmotic coefficients is, therefore, about 0.1 per cent. In the calculation of the activity coefficients from
278
0. D. BONNER
equation (2), the In yref and In R terms are known with the same precision. By choosing a proper reference solute, such that (R- 1) z 1 in dilute solutions, the contribution of the integral is so small that an error of 10 per cent does not affect the value of the activity coefficient. 4. Discussion The mean ionic activity coefficients of the trifluoroacetate salts at any molality are Na+ > Li+ > K+ except for the very dilute solutions where the activity coefficients of the lithium and potassium salt are essentially the same. This may be compared with the acetates for which the order is K+ > Na+ > Li+ and the trichloroacetates for which the order is Li+ > Na+ > K’. The order of the coefficients for the acetates is typical of the behavior of salts of weak carboxylic acids. The order for the trichloroacetates is the same as that of the salts of strong acids such as HCl, HClO,, erc. The order for the trifluoroacetates is that which would be expected for an acid of intermediate strength. This poses an interesting problem in the light of the values reported for ionization constants in the introductory portion of this paper, since the activity coefficients of the trifluoroacetates indicate that the parent acid is weaker than trichloroacetic acid. The author has suggested (l’ that trichloroacetic acid is, indeed, ionized to the extent which is suggested by the Raman measurements but appears to be much weaker by other measurements because of rather extensive ion pairing in the form of hydrogen bonding between the hydronium ion and the chloride atoms of the trichloroacetate ion. A similar phenomenon should occur in solutions of trifluoroacetic acid and this will also account for the range of ionization constants reported for this acid. What conditions are necessary, however, for the trifluoroacetic acid solutions to have a greater molality of carboxylate ion as measured by Raman spectroscopy even though the activity coefficients of the salts indicate that it is a weaker acid than trichloroacetic? The ionization constant, K, is expressed as K = (@-I+ )m(A-)/WM))
{fi(HA))2/jU-M),
(3)
where f+(HA) represents the mean ionic activity coefficient of the acid HA. The symbolf, is used to represent the mean ionic activity coefficient of weak acids while y+, the mean stoichiometric activity coefficient, is normally used for strong acids and au salts since they are considered to be completely ionized. The results reported in this paper indicate that for all of the salts, the coefficients are larger for the trichloroacetates. Furthermore, the trends indicate that the coefficients of the trichloroacetic acid should be appreciably larger than those of trifluoroacetic acid in the molality range in which the Raman measurements were made. It is, therefore, possible that the value of the quotient m(H+)m(A-)/m(HA) could be smaller for trichloroacetic acid than for trifluoroacetic acid and yet the values of the ionization constant K would be reversed. We should now determine whether this possibility is reasonable. If an acid is partially ionized, the degree of ionization will be increased if the hydronium ion is removed from solution by bonding to (or ion pairing with) another group. The extent of the increased ionization of the weak acid depends not only on the strength of the acid but also on the strength of the hydronium ion
ISOPIESTIC
MEASUREMENTS
ON TRIFLUOROACETATES
279
association with the second group. In the case of these two acids the hydronium ion must be more strongly ion paired with the trichloro-group than with the trifluorogroup. This would seem to be improbable if one considers only electronegativity. There is evidence, however, that the relative polarizabilities of the two groups is more important than their relative electronegativities. The tetramethylguanidinium cation can form ion pairs by means of hydrogen bonding with the three anions discussed in this paper. The values’6.7’ of the activity coefficients y+ of the tetramethylguanidinium acetate, trifluoroacetate, and trichloroacetate a
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
Banner, Bonner, Covington, Bonner, Robinson, Bonner, Bonner, Hanstein.
0. D.; Prichard, P. R. J. Solution Chem. 1979, 8, 113. 0. D.; Flora, H. B.; Aitken, H. W. J. Phys. Chem. 1971, 75, 2492. A. K.; Freeman, J. G.; Lilley, T. H. J. Phys. Chem. 1970, 74, 3773. 0. D. J. Chem. Thermodynamics 1979, 11. 559. R. A.; Stokes, R. H. Trans. Faraday Sot. 1949, 45. 612. 0. D. Physiol. Chem. Phys. 1980, 12, 38. 0. D. J. Solution Chem. 1980, 9. 877. W. G.; Davis, K. A.; Hatefi, Y. Arch. Biochem. Biophys. 1971, 147, 534.