Transfer Energies and Solute-Solvent Effects in the Dissociation of Protonated "Tris" in N-MethylpropionamideMethanol Solvents Yobou Bokra' and Roger G. Bates Department of Chemistry, University of Florida, Gainesville, FL 326 1 1
Earlier investigations have shown that the addition of either methanol or N-methylproplonamlde (NMP) to an aqueous solution of tris(hydroxymethy1)aminomethane (Tris) decreases the pK of Tris-HC lnitlally, after which pK reaches a minimum and rises to values in pure methanol and NMP that exceed those in pure water. Qualitatively, the course of the pK curve is similar in the two binary solvent systems despite the fact that MeOH decreases the dielectric constant while NMP raises it. Solubility and emf methods have now been used to determine the individual transfer energies of Tris, Tris-hydrochloride, and HCI between water and NMPMeOH mixtures (dielectric constants from 32.6 to 176) and to derive the pK at 25 OC from them. Again It is found that the pK passes through a minimum when the mole fraction of NMP in the mixture is about 0.4. The pK in binary mixtures of the three solvents H20, MeOH, and NMP is discussed in terms of preferential solvation.
It is now a well recognized fact that the dissociation of weak acids and bases in mixed solvent media is a function not only of electrostatic effects related to the charge type of the acid-base pair but is also influenced profoundly by specific solvation of the acid, its conjugate base, and the proton. The relative effectiveness of the two components of the solvent mixture in stabilizing these individual species can often be revealed by emf and solubility measurements. Tris(hydroxymethy1)aminomethane ("Tris") and its hydrochloride are particularly well suited for studies of this sort, as they are solid substances of moderate solubility in many common mixed solvent media. In earlier papers, we have reported the pK of Tris-H+ in water ( I ) , N-methylpropionamide (NMP) (2), and in water-methanol mixtures ( 3 ) .Recently, solubilities of Tris and Tris hydrochloride and emf measurements of hydrochloric acid solutions were utilized to calculate the pK of protonated Tris in mixtares of water and NMP ( 4 ) .The results also serve to illustrate the manner in which the equilibrium constant reflects the specific interaction of the two types of solvent molecules with the three solute species. The work has now been extended to the water-free binary solvent system methanol-NMP. The combined data give a complete picture of the acid-base behavior of Tris-H+ in all two-component solvent systems formed from water, methanol, and NMP, varying in dielectric constant from 32.6 to 176. The emf and solubility methods used in this investigation followed closely those by which the individual transfer energies of Tris, Tris-HC1, and HC1 from water to NMPH20 mixtures were determined ( 4 ) . If A C t o ( i )is the standard molar Gibbs energy change for the process i(in MeOH) = i(in NMP-MeOH)
(1)
Fulbright-Hays Scholar 1974. On leave from the Universitk d'Abidjan, Ivory Coast. 1110
ANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
the difference in pK for Tris-H+ is given by [AG,"(Tris) + psK - PmK = 2.3026RT AG,O(HCl) - AG,"(Tris-HCl)]
(2)
where the subscripts s and m refer, respectively, to the NMP-MeOH mixed solvent and to pure MeOH. One can therefore use transfer energies to calculate the dissociation constant in the mixed solvents if that in pure methanol is known. Furthermore, the values of AGto for process 1 are indicative of the effectiveness of the two components of the solvent in stabilizing the individual reactants and products and thus offer an insight into the reasons for the effect of a change in solvent composition on the equilibrium constant.
EXPERIMENTAL The Tris base used was of primary standard grade, recrystallized once from water and dried in a vacuum desiccator a t room temperature before use. A commercial lot of Tris-hydrochloride was also purified by a single recrystallization. The hydrochloric acid was doubly distilled. Methanol was distilled before use. The purification of the NMP and the techniques for the measurement of solubility and emf have been described in the earlier paper ( 4 ) . The properties of NMP, methanol, and the solvent mixtures are summarized in Table I. The densities of the solvent mixtures were determined in a pycnometer, and the dielectric constants were measured with an a-c bridge incorporating a General Radio impedance comparator and a General Radio precision decade capacitor. The cell used had a cell constant of about 0.002 cm-'. The data for the pure solvents were obtained from the literature: MeOH (5); NMP (6).The Debye-Huckel constants were calculated from natural constants, the density, dielectric constant, and the thermodynamic temperature by the usual formulas (7).
RESULTS Solubility Measurements. The standard changes of Gibbs energy
A c t o for the processes
T r i s (in MeOH) = T r i s (in NMP-MeOH) (3) and Tris-HC1 (in MeOH) = Tris-HC1 (in NMP-MeOH) (4) were determined by measuring the solubilities of the Tris base and its hydrochloride in methanol and in NMPMeOH solvent mixtures. The solubilities of these substances in NMP have already been determined ( 2 ) . The data are summarized in Tables I1 and 111. In order to make valid comparisons for equal numbers of solvent molecules, the solubilities on the mole fraction scale were used in the calculations of free energies. The calculation of A c t o at 25 "C (in cal mol-') was accordingly made by the equation
where u = 1 when i is Tris and v = 2 when i is Tris-HC1. The subscripts m and s refer to methanol and to NMPMeOH solvents, respectively; x i is the mole fraction of i
Table I . Properties of N-Methylpropionamide-Methanol Solvents a t 25 "C D c b y e -Hu:kel constantsa
ivt
06
K.MP
0 20 40 60 80 100 a
Mole iraction, N M P
Mean molar mas5
Dielectric constant
Densit,/g m l - I
0 0.0842 0.1969 0.3555 0.5953 1
32.04 36.68 42.89 51.62 64.83 87.12
32.64 57.6 59.0 63.7 84.4 175.7
0.7866 0.8139 0.8432 0.8721 0.9008 0.9305
A
B
1.6860 0.7314 0.7179 0.6512 0.4336 0.1467
0.4521 0.3462 0.3481 0.3408 0.3008 0.2119
Scale of molality.
Table 11. Standard Gibbs Energy Change -1Gt"(B) for the Transfer of Tris(hydroxymethy1)aminomethane (B) from Methanol to NMP-Methanol Solvents Derived from Solubility Measurements at 25 "C Solubility of B
a
AG; ( B ) /
Wt M NMP
mol k g - l
m o l e iraction
fa
cal m o l - l a
0 20 40 60 80 100
0.2925 0.2344 0.1944 0.1334 0.0933 0.0602
0.00928 0.00852 0.00827 0.00684 0.00601 0.00522
1.009 1.008 1.008 1.007 1.006 1.005
51 69 182 259 343
0
Mole fraction scale.
and a is the ion-size parameter in A, taken to be 4.03.When this value of ti is used, Equation 7 yields correctly the known value (0.503) of y* in the saturated aqueous solution of Tris-HC1 (8).Although the solubility of Tris-HC1 in all of the solvents studied here is less than 6% of its value in water, it is likely that there is some ion pairing in methanol. The value of f* in the saturated solution in methanol (0.312) was calculated on the assumption that Bjerrum ion association exists. The details are given in a later section. Emf Measurements. The change of AGO for the transfer process HC1 (in MeOH) = HC1 (in N M P M e O H )
(8)
at 25 "C was derived from the standard emf E" of the cell
Pt; H,(g, 1 atm), HC1 ( n ? ) ,AgC1;Ag Table 111. Standard Gibbs Energy Change L G r 0 for the Transfer of Tris( hydroxymethy1)aminomethane Hydrochloride (BHCl) from Methanol to NMP-Methanol Solvents Derived from Solubility Measurements a t 25 "C S o l u b i l i q of BHCl \$'t
3
NMP
0 20 40 60 80 100 a
mol k g - l
m o l e fraction
0.3892 0.3648 0.3563 0.3471 0.3379 0.3523
0.02433 0.02606 0.02966 0.03459 0.04197 0.05783
A G~'(BHC~)I
f,
0.312 0.591 0.603 0.636 0.742 0.930
c a l rno1-l
0 -838 -1015 -1260 -1672 -2320
Mole fraction scale.
and f i is its activity coefficient on the mole fraction scale. The activity coefficients f i for Tris and Tris-hydrochloride in these solvents have not been measured. They were estimated as follows. For undissociated Tris, yi (molality scale) in the saturated aqueous solution (molality 5.78 mol kg-') is 1.005 (8). The solubility of the free base is much smaller in both methanol and NMP than it is in water; consequently, yi was taken to be 1 in these solvents and in their mixtures. The desired activity coefficient f i was calculated from y i by the usual formula fi
= Yi(l
(A)
as a function of solvent composition by the equation AGta(HC1) = 23061(,E0
- ,E")
where the units of the transfer energy are cal mol-l. The standard emf Eo of this cell for the two solvents MeOH (9-11) and NMP (2, 12) is already known. The molality ( m )of HC1 in each of the mixed solvents was 0.01 mol kg-l. The values of sEo for the solvent mixtures were calculated by the equation E" = E
+
0.11831 log (?i?y,)
(10)
with the use of yi derived from Equation 7. The ion-size parameter a was taken to be 4.5 A, a value consistent with that found for HCl in water ( 1 3 ) , NMP (12), and several mixed solvents. A t m = 0.01, however, the calculated transfer energy is not highly sensitive to the choice of value for a. For example, if A = 6 8, had been chosen instead of a = 4.5A, the value of AG," (HCl) a t 40 wt % NMP would have changed by only 6 cal mol-'. T r a n s f e r Energies a n d pK Values. The values of AG," given in Tables 11, 111, and IV relate to the general process of type 1, as set forth specifically in Equations 3,4, and 8. In other words, they are all referred to the free energy in pure methanol. The corresponding values for the process
+ 0.001 V M ' I I ? ) i (in H,O) = i (in NMP-H,O)
in which M' is the mean molar mass of the solvent, m is the molality of solute, and v is 1 for Tris and 2 for Tris-HC1. The mean activity coefficient y+ (scale of molality) for Tris-HC1 in NMP-MeOH mixtures was calculated by the Debye-Huckel equation
where m is the molality of salt in the saturated solution
(11)
are given in Table V. These results were obtained by adding the values of AG," (i) for the process i(in H,O) = i (in MeOH)
(12)
to those for process 1 given in the tables. The standard free energies of transfer from water to methanol can be derived from the solubilities of Tris and Tris-HC1 in these two solANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
*
1111
0
1 M~OH-NMP~ I
I
I
0.25
0.5
0.75
1
'NMP Flgure 1. Standard Gibbs energies of transfer AG," from water to
0
MeOH-NMP solvent mixtures (mole fraction scale) as a function of solvent composition
0.25
0.5 0.75
1
x2 Figure 2. p K of Tris-H+ as a function of solvent composition in the binary systems H20-MeOH, H20-NMP, and MeOH-NMP
Table IV. Standard Gibbs Energy AGIO for the Transfer of HCl from Methanol to NMP-Methanol Solvents Derived from Emf Measurements of Cell A at 25 "C N t n , hh4P
E/Va
ECIV
E'IV
ACt"(HCl)/
(molality)
( m o l e fraction)
cal mol-'
0 ... -0.0099' 20 0.3463 0.1022 40 0.3740 0.1301 60 0.3961 0.1528 80 0.4065 0.1653 . .. 0.16724d 100 0 Molality of HC1 = 0.01 mol kg-1 ence (9).d Reference (12).
-0.1867 0 -0.0677 -2745 -0.0318 -3573 0.0005 -4317 0.3248 -4876 0.04184 -5270 Mole fraction scale. Refer-
vents and (for HC1) from the values of E" for cell A. The solubility of Tris in water is 5.780 mol kg-' ( 3 ) and in methanol is 0.2925 mol kg-' (see Table 11). The latter value can be compared with 0.2952 mol kg-' found by Kundu, De, and Das ( 1 4 ) .On the mole fraction scale, then, AG,"(Tris) for process 12 is 1426 cal mol-'. For Tris-HC1, the solubility decreases from 6.75 mol kg-' in water ( 2 ) to 0.3892 mol kg-' in methanol (see Table 111). Hence, AG," (Tris-HC1) for process 12 is 3294 cal mol-' on the mole fraction scale, including a correction of 66 cal mol-' for ion pairing. The standard emf E" of cell A is 0.2224 V for the 'water solvent (23) and -0.0099 V in methanol (91, giving AGto(HCl) = 4674 cal mol-' (mole fraction scale) for process 12. The standard transfer energies referred to the water solvent (process 11)are plotted in Figure 1 as a function of the composition of the NMP-MeOH mixed solvent. When the transfer energies l G t " ( i ) are referred to water instead of to methanol, their combination with the aid of Equation 2 leads to values of p,K - p,K, where w refers to the aqueous solvent in which the pK of Tris-H+ is well known ( I , 15). These differences are listed in Table V and converted to pK on the molality scale (pK = 8.075 in water a t 25 "C). I t is now possible to compare the change of pK with composition in the binary solvent system NMPMeOH with that in the systems H20-MeOH ( 3 ) and H20NMP ( 4 ) .This comparison is shown in Figure 2. The mole fractions of BHCl given in Table I11 of the earlier paper ( 4 ) are in error, although the solubilities in mol kg-' are correct. The transfer energies in the last column should read 1112
ANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
(from top to bottom), 0, 95, 246, 518, 850, and 974 cal mol-'. Small changes in AGO and A S o (Table VI, Ref. 4 ) for the mixed solvents result, and pK a t 20, 40, 60, and 80 wt % NMP should be increased by 0.01, 0.02, 0.03, and 0.05 unit, respectively.
DISCUSSION The value of pK in pure NMP (8.83) given in Table V is that found by careful emf measurements ( 2 ) .The combination of transfer energies described in the previous section led to a value of 8.90. Similarly, the value in pure methanol (10.38) is to be compared with 10.34 obtained by the emf method ( 1 4 ) and with 10.43 calculated from transfer energies without consideration of ion pairing between Tris-H+ and C1-. Figure 1 shows that NMP stabilizes both HCl and Tris-HC1 strongly. I t also raises the dielectric constant of the solvent mixture; hence, it seems unlikely that ion pairing is of consequence in any of the NMP-MeOH mixtures. A correction for ion pairing in the methanol solution saturated with Tris-HC1 was made with the aid of the Bjerrum-Fuoss theory of ion association ( 1 6 ) . The ionization constant Kd of the ion pairs is given by (13)
where N is the Avogadro constant, a the ion-size parameter (taken to be 4 X lod8 cm) and b is related to a and to the Bjerrum critical distance q by
b =
29 - = - a560 at25T a a€
(14)
where t is the dielectric constant. Equation 13 therefore leads to a value of 0.085 for Kd. The fraction of ionization a in the saturated solution of Tris-HC1 ( m = 0.3892 mol kg-') can thus be calculated from the mass law. The mean activity coefficient yfof the free ions needed for the calculation was derived by Equation 7 using the molality of free ions ( a m ) instead of the stoichiometric molality ( m ) and the Bjerrum critical distance ( q = 8.6 A) in place of 8 . By successive approximations, a was found to be 0.58 and yf= 0.524. From thermodynamics, it can be shown that ayf = y,, where yf,unlike the stoichiometric activity coefficient y,,is based on the molality am of free ions. In this way, the value o f f * in the saturated solution of Tris-HC1 in metha-
Table V. Standard Gibbs Energy Changes AGt" for the Transfer of Tris, Tris-HC1, and HCI from Water to NMP-Methanol Solvents. pK for Tris-H+ at 25 "C A G t o (BHC i)/
AGtO(B)/
M't 96 h M P
cal mol-'
"
c a l mol-'
"
AG~"(HC~)/ c a l mol-' a
0 1426 3294" 4674 20 1477 2456 1929 40 1495 2279 1101 60 1608 2034 357 80 1685 1622 -2 02 100 1769 974 -596 a Mole fraction scale. * Molality scale. Corrected for ion pairing. Reference (2).
no1 was found to be 0.312 instead of 0.330 as given by Equation 7 for complete ionization of the salt. The correction for ion pairing in methanol amounts to 66 cal mol-' in the transfer energies given in the last column of Table I11 but is without effect on the values given in Table V that are referred back to water, except those for the pure methanol solution. The pK value in methanol is lowered from its uncorrected value (10.43) by 0.05 unit. These effects are scarcely larger than the accuracy of the methods and measurements on which pK depends. A reduction of f* from 0.330 to 0.312 would result if a in Equation 7 were changed from 4.03 to 3.67 8, without introducing the concept of ion pairing. In view of the fact that the choice of 4.03 8, was based on activity coefficients measured in water, an uncertainty of 0.4 8, in the value chosen for NMP-MeOH solvents cannot be considered inordinately large. It is clear from Figure 1 that Tris base displays little preference for NMP over MeOH but prefers water to either. It is also evident that both water and NMP are much more effective than methanol in stabilizing HC1 in solution; of the two, NMP is slightly more effective than water. Although Tris-HC1 also prefers water and NMP over methanol, there is a preference for water over NMP in this case. The separation of the two lower curves of Figure 1 reflects the magnitude of AGto(Tris-H+) - AGto(H+),a quantity free from the influence of anion solvation (17). In pure methanol, Tris-H+ is stabilized by solvation more strongly than H+, but as NMP is added to the solvent, preferential solvation of H+ becomes increasingly important. The difference in solvation energies amounts to 1 to 2 kcal mol-' when the mole fraction of NMP exceeds 0.2. Unfortunately, measurements of this type can yield only sums or differences of solvation energies. The solvation energy of the proton, which would constitute a measure of solvent basicity, is not accessible by experimental means. The patterns of solvent-solvent and solute-solvent interaction are, of course, reflected in the solvent effect on pK shown in Figure 2, but a detailed interpretation of the curves cannot be given. The pK (that is, p,K) for protonated Tris (BH+) in a solvent containing any binary mixture of water, methanol, and NMP or one of these solvents alone is related to that (p,K) in pure water by (compare Equation 2) 2.3026 RT(p,K-P&
=
A G f o ( B ) - [AGto(BH*) - AGfo(H')] (15) When either MeOH or NMP is added to the water solvent, AGtO (B) increases steadily at a slow rate, demonstrating the superior stabilization of the base afforded by water or hydrogen-bonded cosolvent. The term enclosed in brackets
p,K-p,K"
2.06 0.70 0.23 -0.05 -0.10 0.15
PK
*
10.38 9.08 8.68 8.48 8.53 8.83d
in Equation 15 likewise has a positive sign. Its value passes through a maximum, however, as the proportion of water in the solvent mixture becomes small. It is evident from Figure 1 that NMP stabilizes HC1 somewhat more effectively than does water. Nevertheless, it is not possible to conclude that H+ prefers NMP to water in the absence of any information concerning anion stabilization by these two solvents. The combination of the two terms on the right of Equation 15 therefore leads to the minimum in pK observed for many weak acids of charge type BH+,B in alcohol-water solvents (17, 18).When the base B prefers the alcohol over water, AGto(B) decreases as alcohol is added, but a minimum in pK is still observed (17, 19). In NMP-MeOH mixed solvents, the shallow minimum is also caused by a decrease in the term enclosed in brackets in Equation 15 as NMP is added. It is highly likely that NMP is more basic than MeOH; hence, the observed decrease in the bracketed quantity must reflect an increased stabilization of Tris-H+ in NMP-rich media. Some support for this view is found in the values for AGto (Tris-HC1) in NMP-water solvents ( 4 ) , but once again the unknown effects of anion stabilization and solvent-solvent interactions prohibit an unequivocal conclusion to be reached.
LITERATURE CITED (1)R. G. Bates and H. E. Hetzer, J. Phys. Chem.. 65, 667 (1961). (2)E. S. Etz, R. A. Robinson, and R. G. Bates, J. Solution Chem., 2, 405 (1973). (3)P. Schindler, R. A. Robinson, and R. G. Bates, J. Res. Nat. Bur. Stand., Sect. A, 72, 141 (1968). (4)R. G. Bates, J. S.Falcone, Jr., and A. Y. W. Ho, Anal. Chem., 46, 2004 (1974). (5) R. G. Bates and R. A. Robinson, in "Chemical Physics of Ionic Solutions," E. E. Conway and R. G. Barradas, Ed., John Wiley and Sons, New York, 1966,Chap. 12. (6) T. B. Hoover, Pure Appl. Chem., 37,581 (1974). (7)R . G. Bates, "Determination of pH," 2nd ed.. John Wiley and Sons, New York, 1973,pp 248-249. (8)R. A. Robinson and V. E. Bower, J. Chem. Eng. Data, 10, 246 (1965). (9)I. T. Oiwa, J. Phys. Chem., 60,754 (1956). IO) J. M. Austin, A. H. Hunt, F. A. Johnson, and H. N. Parton, unpublished work cited by R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," 2nd ed. revised, Butterworths, London, 1970,Appendix 8.2. 1 1 ) K. K. Kundu, A. L. De, and M. N. Das, J. Chem. SOC.,Dalton Trans., 373
(1972). 12) E. S.Etz, Ph.D. thesis, Clarkson College of Technology, 1974. 13) R. G. Bates and V. E. Bower, J. Res. Nat. Bur. Stand., 53,283 (1954). 14) K. K. Kundu, A. L. De, and M. N. Das, J. Chem. SOC.,Dalton Trans., 386 (1972). (15)S. P. Datta, A. K. Grzybowski. and E. A. Weston, J. Chem. SOC., London, 792 (1963). (16)R. M. Fuoss, J. Am. Chem. SOC.,80,5059 (1958). (17)R. G. Bates. J. Nectroanal. Chem.. 29. l(1971) (18)C L deligny. Rec Trav Chfm Pays-Bas, 79,731 (1960) (19)R Gaboriaud, Ann Chfm (Pans) Ser 74, 2, 201 (1967)
RECEIVEDfor review January 6, 1975. Accepted February 21, 1975. This work was supported in part by the National Science Foundation under Grant MPS73-05019 A01.
ANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
1113
