solution is obtained if the internal solution is similar in concentration to the test solution. Even in 5 to 6 m CaCh (log m y = l.O), Equation 1 is obeyed over a narrow range of activities if the internal solution and external solution are matched. In a second set of experiments, we attempted to measure the activity of calcium in mixed solutions containing sodium ion. The Orion electrode was used without any modification (internal solution O.lm CaC12) and the test solution consisted of NaCI-CaCIz mixtures at total ionic strengths of 1, 3, and 6m. In such mixtures the potential of the cell depends on the concentration of both NaCl (ml) and CaClz (mz).
E = E”
=
(RT/2F)In [mz(m1
+ 2m2I2yZls+ KmlYml + 2md2 y1z4I
(2)
where y12 is the mean activity coefficient of NaCl and yzl is the mean activity coefficient of CaClz in the mixed electrolytes and K is the selectivity ratio. Although the selectivity ratio for the calcium-sensitive liquid ion exchange electrode in the presence of Na+ is approximately in dilute solutions ( I ) , its behavior in the presence of interfering ions is much more complicated in concentrated solutions. Figure 2 shows the selectivity ratios calculated from our measurements. The activity coefficients 7 1 2 and 7 2 1 were taken from measurements made by the isopiestic and amalgam electrode methods (12, 13).
A relatively simple explanation can be made both of the (12) R. A. Robinson and V. E. Bower, J . Research National Bureau Standards, 70A, 313 (1966). (13) J. N. Butler and R. Huston, J. Phys. Chern., 71,4479 (1967).
deviation from Nernstian behavior when a CaClz rest solution differs widely in concentration from the reference solution, and the complex variations of the selectivity ratio in the presence of sodium ion (14). If species such as CaClR (where R is the decylphosphate group in the ion exchanger) are transported through the organic phase instead of CaRz at high chloride ion concentrations, this would have the effect of making the liquid ion exchange membrane permeable to chloride ion and would destroy the simple Nernstian behavior in CaClz solutions. The observed deviations from ideal behavior are in the predicted direction (Figure 1). Furthermore, the species CaClR would be expected to be more easily interchangeable with the species NaR, and the selectivity of the electrode for CaZ+over Na+, which depends on the formation of CaR2, decreases ( K increases) at high chloride concentrations, as we have observed. It should be pointed out that this explanation is speculative, and that other phenomena involving migration of species within the liquid ion exchanger, or “salting out” effects, might also be responsible for the observed deviations from ideal selectivity. Nevertheless, the present work has demonstrated unequivocally that this particular liquid ion exchanger is much less selective for calcium ion over sodium ion in concentrated solution, a result of practical importance for analytical chemistry. RECEIVED for review September 13, 1968. Accepted October 14, 1968. Work supported by the U. S. Department of the Interior, Office of Saline Water. (14) M. S. Frant and J. W. Ross, Jr., Orion Research Inc., Cambridge, Mass., personal communication, 1968.
Sodium Ion-Selective Electrode Studies of Ion Association in Solutions of Sodium Tetrametaphosphate and Trimetaphosphate Gary L. Gardner and George H. Nancollas Department of Chemistry, State University of New York at Buffalo, Buffalo, N . Y.
THENATURE and concentration of ionic species present in solutions containing alkali metal ions is of great importance, especially in biological systems. The ion-selective electrodes have a number of advantages in such studies since complexes involving these cations are usually present in small concentrations and difficult to characterize by the more conventional pH glass electrode indirect methods ( I ) . Relatively few studies have been made of ion-association involving sodium ions with anions. A new protonated species in sodium EDTA solutions, namely NaHEDTA2-, impossible to characterize by means of hydrogen electrode studies, was detected by Palaty (2) using a sodium ion electrode. Ion-pairs in sodium malate solutions have also been studied by this method (3) but the effect of ionic strength upon the association constant was not discussed. The potential of the sodium glass (1) F. J. C. Rossotti and H. Rossotti, “The Determination of Stability Constants,” McGraw-Hill, New York, 1961. (2) V. Palaty, Can. J. Chern., 41, 19 (1963). (3) G. A. Rechnitz and J. Brauner, Talanra, 11, 617 (1964).
202
ANALYTICAL CHEMISTRY
electrode varied with total ionic strength of the solution but in view of the 1-2 mV uncertainty reported by these workers (3), these variations were not analyzed quantitatively. An error of f30 was reported in the association constant determined for the sodium monomalate ion pair at an unspecified ionic strength. In a later paper ( 4 ) the sodium monocitrate complex was studied (at an approximately constant ionic strength) by a differential potentiometric method. The data were reported at an approximately constant ionic strength, but no attempt was made to calculate activity effects so that allowance could be made for the variation of ionic strength with citrate buffer ratio. In most studies using ion-selective electrodes, attempts have hitherto been made to calibrate the electrodes as concentration, rather than as activity probes. Although the constant-ionic-strength procedure is useful, especially where more than two complex species are formed simultaneously, the experimental data are directly comparable only with similar data obtained at the same ionic strength, and (4) G. A. Rechnitz and S. B. Zamochnick, ibid., p 1061.
too many different values of I have been used. It is clearly desirable to be able to determine thermodynamic association constants (ionic strength, I -+ 0) so that all systems are directly comparable and for this purpose, activity coefficient terms can be evaluated from the ionic strength by means of suitable extended forms of the Debye-Hiickel relationship (5). The application of the activity corrections is particularly important for ion association reactions involving high valent ions. In the present work, the sodium ion electrode has been used in solutions of condensed phosphates to study the interaction between sodium ions and tri- and tetra-metaphosphate anions. These systems have been investigated by a precision conductivity method by Monk and his co-workers (6) and it was therefore possible to compare the present method with one in which measurements were made under conditions of high dilution. The conventional glass electrodes responsive to hydrogen ions have been used in a number of precise studies of ion association involving anions of weak acids and emf values reproducible to better than 0.1 mV have been achieved by rigorous experimental technique and by careful standardization of the electrode systems (7-9). In this work, the same standards are applied to the sodium ion glass electrode in order to yield meaningful thermodynamic association constants.
to age in water at 50 "C for at least twelve hours before use. Sodium glass electrodes were aged in 0.1M sodium chloride solution for 48 hours and the electrode systems were standardized before and after each experiment using several concentrations of sodium chloride covering the concentration range of interest. It was possible to reproduce a Nernstian slope of 58.40 mV/log axa unit to within 1 0 . 3 mV throughout this work by careful preconditioning of the electrodes and by washing with test solution before each measurement. Activity coefficients of z-valent ions, fi, were calculated using the Davies extended form of the Debye Hiickel equation (11) (3)
In a typical titration, standardization in situ was first carried out by adding sodium chloride solution to the cell and then without removing the electrodes, additions of sodium tri- or tetrametaphosphate solutions were made. The pH of the cell solutions was always within 6.7 f 0.2 during the experiments, considerably larger than pNa, indicating a negligible degree of hydrolysis and hydrogen ion interference. A similar conclusion was reached by Monk (6) from his conductance studies. By frequent standardization of the electrode systems, it was possible to correct the measured emf values for a small drift in E" with time of about 0.02 mV per hour.
EXPERIMENTAL
RESULTS AND DISCUSSION
AR reagents and grade A glassware were used, and solutions were prepared with doubly distilled water; carbon dioxide was excluded by bubbling with nitrogen gas. Sodium tetrametaphosphate kindly given by Albright and Wilson Ltd. Birmingham, England, was used without further purification. A sample of sodium trimetaphosphate donated by Monsanto Chemical Co. was recrystallized once from water. The phosphate solutions were analyzed for sodium ions by passing through Dowex 50-W ion-exchange resin in the hydrogen form and titrating the liberated acid with sodium hydroxide. Measurements were made at 25 =k 0.05 "C in cells with liquid junction: Glass electrodes/solution under study/calomel electrode
(1)
and without liquid junction: Glass electrodes/solution under study, Cl-/AgCl/Ag
The measurement of sodium ion activity in phosphate solutions and the application of meaningful activity coefficient corrections is a problem of great importance. Friedman (12) has suggested that the sodium selective glass electrode is poisoned in a normal phosphate buffer solution, but no evidence was found in the present study for abnormal behavior in the condensed phosphate solutions or in an orthophosphate buffer solution. The results of the potentiometric measurements over the entire ranges of concentration could be interpreted in terms of the formation of the sodium monometaphosphate ion pairs Nap( l-n) where P represents trimetaphosphate (n = 3) or tetrametaphosphate (n = 4). The concentrations of ionic species in the solutions were calculated from equations for total sodium ion concentration, (4)
(2)
Emf values, measured with a Leeds and Northrup Type K 3 potentiometer using a Victoreen picometer (model 474) as null detector, were reproducible to *O.l mV. A Beckman sodium ion glass electrode (Type 39278) used in the initial stages of the work, was later replaced by the Beckman cationic electrode (39137) because the latter showed a much smaller drift of E" with time. The calomel electrodes were used either with the fiber type junction (Corning type 476001) or else with an intermediate junction consisting of a J-tube filled with potassium chloride agar gel. Diffusion of potassium chloride into the cell solutions with these types of liquid junction was always less than 10-6gram ions of K+ per hour. Silver-silver chloride electrodes prepared by the thermal electrolytic method previously described (IO) were allowed (5) G. H. Nancollas, "Interactions in Electrolyte Solutions," Elsevier, Amsterdam, 1966. (6) C. B. Monk,J. Chem. Soc., 413 (1949). (7) . . J. R. Brannan and G. H. Nancollas, Trans. Faraday SOC.,58, 354 (1962). (8) S . Boyd, A. Bryson, G. H. Nancollas, and K. Torrance, J . Chem. Soc., 7353 (1965). (9) A. Chughtai, R. Marshall, and G. H. Nancollas, J, Phys. Chem., 72,208 (1968). (10) V. S . K. Nair and G. H. Nancol1as.J. Chem. Soc., 4144 (1958).
total phosphate concentration
and electroneutrality [Na+l
+ ["I
= n[P-"I
+ ( n - 1) [NaP('-')] + [Cl-I
(6)
Sodium ion activities were converted to concentrations by means of Equation 3 and in the case of cell 2 appropriate corrections were made for the silver-silver chloride electrode potential. Corrections for the glass electrode response to the very small concentrations of silver ions in the solutions never amounted to more than 0.10 mV. The thermodynamic association constants for the reactions Na+
+ P*e Nap('+
(11) C. W. Davies, "Ion Association," Butterworth, London, 1962. (12) S . M. Friedman, "Methods of Biochemical Analysis," D. Glick, Ed., John Wiley and Sons, Inc., Vol. 10, 1962. VOL. 41, NO. 1, JANUARY 1969
e
203
TM
x
Table I. Sodium Trimetaphosphate Ion-Pair Formation at 25 "C Values at each ionic strength represent single results Mole I-' T~ x 103 I x 102 [Na+]X lo8 [NaP('-")] X lo4 0.4240 0.3530 2.291 0.1653 0.7714 0.5560 3.310 0.3344 1.086 0.7370 4.225 0.5509 1.900 1.210 6.605 1 .0350 2.132 1.343 7.278 1.2110 2.308 1.442 7.780 1.444 2.426 1.505 8.109 1.659 2.543 1.564 8.419 2.070 2.738 1.687 9.023 1.832 2.796 1.699 9.121 2.588
108
2.307 3.343 4.280 6.708 7.399 7.925 8,274 8,626 9,207 9.380 Mean K = 25.1
3.5 mole-'
Table 11. Sodium Tetrametaphosphate Ion-Pair Formation at 25 "C Values at each ionic strength represent single results Mole 1-1 T~ x 103 T~ x 103 I x 102 [Na+] X IO3 [NaP(l-")] X IO4 2.809 0.4459 0.5167 2.730 0,7942 3.018 0.4977 0.5691 2.940 0.7813 3.410 0.5974 0.6527 3,293 1.168 3.521 0.6246 0.6791 3.402 1.196 3.954 0.7348 0.7821 3.819 1.355 4.116 0.7745 0.8095 3.949 1,669 4.4927 0.8704 0.9039 4.323 1.688 4.919 0,9769 0.9854 4.687 2.317 5.136 1.0332 1,044 4.913 2.235 5.250 1.0600 1.064 5.007 2.434 5.586 1.1450 1.143 5.329 2.569 5.926 1.2310 1.224 5.659 2.664 6.369 1.3443 1.316 6.050 3.193 6.324 1.331 1.306 6.012 3.118 1.414 6.456 3.352 6.791 1.449 1.573 6.565 4.544 7.019 1.755 1.518 6.923 4.292 7.352 1.590 7.954 1.988 1.791 7.460 4.944 1.981 8.276 5.824 8,858 2.214 2.180 9.103 6.393 9.742 2.436 14.54 3.636 3.135 13.29 12.51 16.31 4.078 3.538 14.96 13.48 18.55 4.638 3.986 16.92 16.30 22.99 5.747 4.815 20.67 23.25 Mean K = 133.3 f 10.1 1. mole-'
were obtained by successive approximation for the ionic strength
I
=
0.5 ( n T p
- (2n - 1)
+ [Na+l + [Cl-I}.
The results are given in Tables I and I1 for sodium trimetaphosphate and tetrametaphosphate, respectively. The association constants in Tables I and I1 may be compared with the values obtained by Monk (6), 23 1 mole-' for NaP30g2-and 114 1 mole-' for NaP4OIz3-. The agreement is satisfactory in view of the difficulties involved in the conductance method as applied to unsymmetrical electrolytes. Uncertainties in the values to use for the mobilities of the charged ion pairs are considerable, especially with the high charge-type ions of interest in the present systems. Some experimental measurements were also made using the sodium ion glass electrode in solutions of sodium orthophosphate. Although the existence of the ion pair NaHP04- was 204
K,1 mole-' 29.6 25.8 25.9 21.2 20.9 22.3 24.0 28.3 22.0 31.1
ANALYTICAL CHEMISTRY
K,1 mole-' 146.4 120.1 145.6 139.0 123.6 146.8 121.9 149.7 129.4 137.2 129.2 119.2 129.2 127.3 120.3 143.4 141.8 126.2 128.1 121.1 144.7 128.4 132.2 149.5
proposed by Smith and Alberty (13), Bates (14) in his extensive hydrogen electrode cell measurements with sodium phosphate buffers, could find no evidence for the presence of this species. The results of the present work support the conclusion of Bates; within experimental error, no difference could be detected between total and free sodium ion concentrations within the range [Na+l = 5 X lo-' to 5 X 10-8 and to [HP042-] =
RECEIVED for review July 15, 1968. Accepted September 19, 1968. Studies aided by Contract N00014-66-'20227 (NR 105-419) between the Office of Naval Research, Department of the Navy, and the State University of New York at Buffalo. (13) R. M. Smith and R. A. Alberty, J. Phys. Chem., 60,180 (1956). (14) R. G. Bates and S. F. Acree, J. Res. Natl. Bur. Srd., 30, 129 (1943).
