would coordinate PAN more strongly than cobalt. However, certain metal ions and anions still interfered, as shown in Table 111. Copper(I1) was the most serious interference in 95 ethanol, and this interference was not reduced by switching to absolute ethanol solvent as with some other metal ions. The mechanism of the fluorescence quenching is not clear although Goldstein, Manning, and Menis (14) found that copper(I1) was also the most serious interference in their spectrophotometric determination of cobalt(II1) with PAN. As might be predicted from the large stability constant of nickel(I1)-PAN in water, nickel(I1) interferes seriously in 95 ethanol, but this interference is reduced in absolute ethanol. Aluminum(II1) interferes seriously in 95 ethanol, but its interference is dramatically reduced in absolute ethanol solvent. The fluorescence of aluminum(II1)-PAN in the latter solvent is not a factor since the 440 interference filter does not pass this emission. When present in fivefold excess, the halide ions did not appear to differ in their ability to quench the fluorescence of cobalt(II1)-PAN. However, when they were present in twentyfold excess, the initial fluorescence intensity was reduced from 45 to 5 units by iodide, from 45 to 11 units by bromide, and was essentially unchanged by the chloride ion. This may be
the result of the so-called heavy atom effect (1) observed in fluorescence quenching. The sulfate and phosphate ions (Table 111) as well as the acetate, oxalate, sulfite, and nitrite ion appeared to quench the fluorescence of cobalt(II1)-PAN very effectively. It appears likely that many of these ions quench the fluorescence by replacing one or more PAN ligands in the coordination sphere of cobalt(II1) to produce some nonfluorescent species. Although this procedure is only slightly more sensitive than the colorimetric PAN procedure (14) which has a lower limit of 0.1 ppm, it is of theoretical interest in that it appears to be the first direct fluorometric procedure for cobalt. The procedure also has some advantages in that it can be used for the determination of cobalt in the presence of iron(III), cadmium(II), nickel(II), and aluminum(II1) without the preliminary separation and the use of citrate in the colorimetric procedure (14).
RECEIVED for review June 21,1968. Accepted December 9,1968. (14) G. Goldstein, D. L. Manning, and 0. Menis, ibid., 31, 192 (1959).
Individual Activities of Sodium and Chloride Ions In Aqueous Solutions of Sodium Chloride Adam Shatkay and Abraham Lerman Isotope Department, The Weizmann Institute of Science, Rehovot, Israel The emf’s in aqueous solutions of NaCl were measured with a Na glass electrode and a Ag/AgCI electrode, each opposed by a calomel electrode, and opposing each other. A procedure was followed which yields reproducible results despite the change of Eo of the electrodes. The liquid junction potentials were calculated by the Henderson equation. Activity coefficients of the neutral NaCl and of the individual ions were calculated and compared with y*h-acl and with y c l - and yKa+obtained with the Maclnnes assumption. The potentiometric behavior observed is consistent with the use of the Maclnnes assumption and with the liquid junction potentials calculated.
THEUSE of individual ionic activities is attracting considerable attention in the investigation of biological and mineral systems, and in analytical chemistry (1). Such individual activities are measured with reversible ion-specific electrodes. In practice, the electrodes are reversible only within some limited range of concentration of the relevant ion; furthermore their specificity in the presence of other ions is not perfect and is difficult to assess (2, 3). Usually the behavior of an electrode is studied by either of the following methods: The cation-reversible electrode is opposed by an anionreversible electrode; the activity measured is that of the (1) G. Eisenman, editor, “Glass Electrodes for Hydrogen and Other Cations,” Marcel Dekker, N. Y., 1967, Chapters 11-19. (2) A. Shatkay, J . Plzys. Chem., 71,3858 (1967). (3) A. Shatkay, Biophys. J., 8,912 (1968). 514
ANALYTICAL CHEMISTRY
thermodynamically well defined neutral species, and no liquid-junction potentials have to be considered. However, the individual contributions of each of the two electrodes are difficult to separate. The electrode is opposed by an “inert” reference electrode -e.g. calomel electrode; the activity measured is that of the individual ion [this can be disputed on theoretical grounds (41; the uncertainty due to the liquid junction potential is also introduced. A combination of the above two methods was attempted in a recent investigation of the phosphate electrode (5). When such methods are applied to complex systems the intepretation is difficult. An attempt is now made to apply such methods to a system for which considerable information is already available, so that the consistency of the results can be checked. EXPERIMENTAL
Analytical grade NaCl was used. The water was triply distilled. All the solutions were saturated with analytical grade AgC1. The electrodes used were Beckman glass sodium electrode No. 39278, Beckman Ag/AgCl electrode No. 39261, and Radiometer Type K 401 saturated KC1 calomel electrode. The emf‘s were measured with a Metrohm E 388 compensator potentiometer, with a precision of hO.1 mV. The (4) F. Helfferich, “Ion Exchange,” McGraw-Hill, New York, 1962 p 140.
( 5 ) A. Shatkay, Anal. Biochem., in press.
solutions were maintained at 25 i 0.1 “C in a thermostated jacket. They were stirred on introduction into the apparatus, but on reaching the equilibrium temperature the stirring was stopped, and the measurements were made in unstirred solutions. The measurements were carried out till the drift in emf was less than 0.1 mV/hr.
Table I. Experimental EMF’S Obtained with Various Combinations of Electrodes emf (mV) Chloride us. Sodium cs. Sodium us. chloride mxaa calomel calomel (molal) (&I, calomel) (Exs, e a ~ a m e ~ ) (EN~cI)
RESULTS AND DISCUSSION
The emf in aqueous solutions of pure NaCl of varying molality was measured using a sodium electrode against a chloride electrode, and also using each of the above electrodes against a saturated KCl calomel electrode. Employing the IUPAC convention Chapter I], the three emf‘s obtained with ideal reversible electrodes can be expressed respectively by the three following equations (where E designates the emf, a the activity, the subscripts refer to the ions, and the superscript 0 indicates a standard state; Ej represents the liquid junction potential between a solution and the saturated KCl bridge; R , T , and F are the gas constant, the temperature, a n d the faraday):
[(a
ENaCi
=
Ec\ -
= Eocl
ENS
RT F
- - In acl
-
RT F
-
EONa
= E ” N ~ CI In aNaCl
- RT - In a N s F (1)
(3) As already stated by authors who had investigated the activity of a salt using a glass cation-specific electrode us. a reversible chloride electrode (7), the term E ” Nin~ Equation 1 “does not remain constant for long periods or for a wide range of solution concentrations.” They have succeeded, however, in evaluating satisfactorily the activity coefficients [y*NaCl] by using the differential form of Equation 1, thus dispensing with E”, and then integrating (introducing an integration constant by the use of the Debye-Huckel equation). Such a procedure requires high accuracy, especially if the value of 2RT/F is reduced to RT/F on investigation of single ion activities, and reduced even further when the ions are polyvalent. Another successful attempt to calculate activity coefficients despite the uncertainty of EON^ was made by Eisenman (8) who obtained consistent slopes even though each series of measurements yielded different values of emf. While this method is useful when an uninterrupted continuous run can be made along concentrations close to each other, it does not yield the reproducible results which are necessary in many electrochemical investigations. It appears thus of interest to ascertain whether reproducible results can be obtained even when E” changes. The effect of time and concentration on E O N * was therefore studied, to augment the data already available on the subject (8). (6) D. J. G. Ives and G. J. Jam, “Reference Electrodes,” Academic Press, New York, 1961. (7) P. B. Hostetler, A. H. Truesdell, and C. L. Christ, Science, 155, 1537 (1967). (8) G. Eisenman, “The Electrochemistry of Cation Sensitive Glass Electrodes,” in “Advances in Analytical Chemistry and Instrumentation,” C. N. Reilley, Ed., Interscience, New York, 1966.
3
3 8
2 3 5
10-3 10-3 10-2 x 10-2 x 10-2 10-1 x 10-1 x 10-1 x 10-1 1 2 3 5 6
x
1-157.6 +132.4 +103.4 $77.7 +54.3 +49.4 +34.4 $25.0 +14.0 -1.6 -17.1 -27.1 -42.9 -48.8
-32.1 -44.2 -62.9 -91.0 -114.3 - 120.0 -135.7 146.9 - 160.7 -178.6 -199.9 -214.5 -234.3 -244.5
-
+125.7 $88.2 $40.4 -13.8 -60.2 -70.6 - 101,8 -121.9 -146.5 -180.0 -217.1 -241,2 -277.1 -292.9
E o N ewas found to be stable within * O S mV during periods of up to 3 days. Thus during any single measurement the E” may be safely assumed to remain constant, within our experimental accuracy. On the other hand the effect of the change in concentration is considerable: the emf‘s were measured in NaCl solutions of increasing concentrations from lO-%n to 5m, and then backwards in solutions of decreasing concentration. This procedure was repeated a number of times. It was found that the previous history of the electrode affects considerably the emf, in particular in dilute solutions, where the emf obtained on approach from very dilute solutions may differ by some 50 mV from the emf obtained on approach from concentrated solutions. To overcome this difficulty, we employed the following procedure. Before each measurement of the sample and after each measurement, the relevant electrodes were tested in a reference solution (arbitrarily chosen as 0.lm NaCl). The reference emf of the AgjAgCl electrode us. the calomel electrode can be chosen arbitrarily, but we have taken the value of f49.4 mV, which is in line with the E’CI and Eoalomel of the well investigated electrodes (6). The emf of the Na electrode us. the calomel electrode must be chosen arbitrarily, as E’sv, depends on the construction of the electrode; we have chosen the value of - 120.0 mV, which was close to the emf’s measured with our electrode in a O.lm NaCl solution. The emf of the Ag/AgCl us. the Na electrode is determined by the previous two values as -70.6 mV. The average values of the two measurements were compared with the above reference emf’s, and the corrections were applied to the readings obtained in the sample solution. The results obtained are summarized in Table I. It should be emphasized that these results represent readings carried out over a period of one month, and that the sequence of the measurements was not regular. Thus the experimental readings of the same solution might vary by many millivolts, yet the corrected values were reproducible to within 1t0.4 mV. When the ENaclof Table I is plotted against log [msscl x T*N&i], using values of y*Nac1 taken from literature (g), a straight line is obtained, with a slope of 118.4 mV/log aNac1, corresponding exactly to Equation 1 ; see Figure 1, part I. The calculated values begin to deviate from the straight line only when ~ ~ N < ~ 6 C X I m. The behavior at such very dilute solutions will be considered later. Above 6 x 10-3nr the deviation of the calculated values from the straight line is within the experimental error. Such behavior suggests that (9) H. S. Harned and B. B. Owen, “The Physical Chemistry of Electrolytic Solutions,” Reinhold, New York, 1964. VOL. 41, NO. 3, MARCH 1969
515
50 w
50
-200
’+
t I
-3
I -I
I
-2
I
1
0
I
lop m ond lop(mr’)
Figure 1. I (circles)--Ev,cl; (squares)--EN a +
I1 (triangles)-Ecl-
;
[I1
Filled figures-experimental emf against molality. Open figuresexperimental emf against m X y*. Straight lines-theoretical Nernst slopes the activity coefficients can be calculated directly from the experimental data using Equation 1, To obtain a point of origin for the Nernst slope, we could use the emf of some sufficiently dilute solution, whose y* can be safely assumed as equal unity-e.g., NaCl 10-5m. Unfortunately, as stated above, at molalities below 6 X 10-3m the emf‘s do not appear to be reliable already at 10-2m. Thus an initial y* has to be chosen from literature. We have chosen the y * of 0.903 for a m solution (9). In this respect our procedure does not differ in principle from that of Hostetler (7) and of Eisenman (8), who also used one reference y* derived from values given in the literature. The activity coefficients so obtained are presented as closed circles in Figure 2, and compared with the values given in literature (curve 1 in Figure 2). It can be seen that the agreement with the literature values is good. It should be noted that an error of 0.5 mV corresponds to an error of about 1 in the value of y*, so that the deviations from the literature values are within our experimental error. Since the submission of this paper the results of Schindler and Walti have been published (IO). These authors have measured uKscIalso employing Na glass electrode and Ag/ AgCl electrode, but only in the concentration range of 0.14m to 2.2m. They have thus partly avoided the difficulty of the change of E ’ N ~with concentration. They have shown that their values of U N ~ C are I in good agreement with the results of osmotic measurements. Unlike the curve of log us. emf, the values of emf obtained for the sodium and the chloride electrodes against the calomel electrode d o not yield a constant slope when plotted against log mx.cl y *X*CI, see Figure 1, parts I1 and 111. For the sodium electrode the slope is about 68 mV/log my* in (10) P. Schindler and E. Walti, Helu. Chim. Acta., 51 539 (1968). 516
ANALYTICAL CHEMISTRY
solutions above lm, decreases t o about 60 at O.lm, and falls t o obviously low values for solutions more dilute than 10-2m. For the chloride electrode the slope is about 47mV/log my* in the concentrated solutions, and decreases toward the concentrated solutions, and decreases toward the constant value to 10-3m. of about 59 for solutions between The deviation from Nernstian behavior of the two electrodes when opposed by a calomel electrode can be due to nonideal behavior of the electrode, to the neglect of the liquid junction potential in Equations 2 and 3, to the use of y * N a C I for yNa and ycl, or to any combination of the above factors. These possibilities will be discussed in detail. The liquid junction potential has been treated clearly by MacInnes ( ] I ) , though a rigorous treatment requires the use of nonequilibriurn thermodynamics. The application of liquid junction potentials to the single ion activity of hydrogen has been discussed by Bates (12), who advocates the use of the Henderson equation. In his calculations Bates uses the limiting equivalent conductivity of the ions instead of the mobilities appearing in the original Henderson equation (13, 14). This has been done, as little information on mobilities at useful concentrations was available, and as the approximation was assumed not to be serious (15). It is more correct to use the conductivity values a t the concentrations of the solutions investigated-Le., XK and Xcl of KC1 at 4.lm, and X C and ~ NaCl at the experimental varying molalities. We have calculated these conductivities using the equivalent conductivities of KCl and of NaCl and their transport numbers, listed in the literature (16,17). Using the above values, the Henderson equation can be written as
where C i s concentration in moles per liter of solution. Ej has been calculated using Equation 4 for solutions of NaCl up to 7m, and is plotted against log mXaC1in Figure 3. The value of E, so calculated is approximately constant at -4.5 mV between m N a C l 7 and 3, increasing almost linearily with concentration to 0 mV at m N a C l = 0.2~1,and then increases logarithmically to infinity at m N & l = 0. The behavior of Ej at high dilution is a direct consequence of the form of the Henderson equation, in which E, tends to 03 as CNsCltends to 0. For the values given in Equation 4, the increase of the emf is about 1.1 mV per tenfold decrease in the concentration of NaCl. The limitations of the Henderson equation have been discussed in the literature quoted above ( 9 , 11-16), but the implication of infinite potentials at high dilutions has not yet pointed out explicitly, to the best of our knowledge. A calculation of the E, using the limiting equivalent conductivities, as suggested by Bates (12,15), yields results which almost coincide with those obtained through the use of Equation 4, thus justifying his approximation (Figure 3). Recently a novel method has been suggested t o calculate Ej (18). The method is applicable t o solutions more dilute (1 1) D. A. MacInnes, “Principles of Electrochemistry,” Dover,
New York, 1961, Chapters 13-14. (12) R. G. Bates, “Determination of Ph,” Wiley, New York, 1964,
Chapter 111. (13) P. Henderson, 2.Phys. Chem., 59 118 (1907).
(14) P. Henderson, ibid.,63 325 (1908). (15) R. G. Bates, private communication, NBS, Washington, D. C., 1968. (16) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” Butterworth, Bethesda, Md., 1965. (17) R. Parsons “Handbook of Electrochemical Constants,” Butterworth, Bethesda, Md., 1959. (18) R. G. Picknett, Trans. Faraday Soc., 64 1059 (1968).
'
1.4
I
I
I
I
0.6
o
r m
1 t
I
1
-4t
A
-5 -3
A
-2
-1
l o g mNaCL -3
-2
I
0
*I
l o gmNoCL
Figure 2. Curves: 1. Y * S A ~ ~from literature; 2. YCI = y*~tcl calculated from literature; 3. YN* = (y*N-aCJ2/y*KC1 calculated from literature Circles-hTaC1; Triangles-CI-, open-without E,; filledcorrected for E,; Squares-Na +, open-without E3; filled-corrected for Ej
than 10-2m; the values obtained for NaCl do not differ significantly (less than 0.5 mV) from those given in Figure 3. From the above considerations it appears that for NaCl l 0 - h the liquid junction potential should be about +4 mV, while for 10-2m it should be about f 3 mV. The experimental deviations at 10-3mfrom the Nernst values for C1- are about 1 mV, and for Na+ are about 25 mV (see Figure 1, parts I1 and 111). It is thus obvious that the effect of the liquid junction potential on the calomel electrode in this range of concentrations cannot account for the behavior of the sodium-calomel electrode pair. On the assumption that the sodium electrode is reversible to Na+ even at m N a C 1 as low as the activity coefficient of Na+ would have to be about 3, which is incompatible with any convention as to single ion activities. Thus it appears quite clear, on comparison of parts 1-111 of Figure 1 in the dilute range, that the Ag/AgCl behaves as a reversible electrode for C1- up to the dilution of 10-3m, while the Na+ glass electrode is unreliable below the dilution of lO-%n. It should be noted that this conclusion cannot be reached on consideration of part I alone: the good behavior of the Ag/AgCl electrode masks the defects of the Na electrode, so that the anomalous behavior becomes noticeable only below 6 x 10-3m, and even there is not as pronounced as in part 111. Such masking can have an even greater effect when the concentration of the two species at the opposing electrodes is unequal--e.g., in the case of phosphoric acid (5) or of mixed electrolytes. The calculation of y * ? ~ ~and c l its comparison with the values listed in literature has been described above. In a similar way ysa and ycl were calculated for the range of concentrations in which the Na and C1 electrodes appear to be reliable. The calculations used Equations 2 and 3 with E, taken from Figure 3, and similar calculations were done ignoring Ei. The results are presented in Figure 2: the open squares and triangles represent the y y Band ~ C (respectively) I without correction for El, while the closed figures represent the values obtained using
Figure 3. Liquid junction potential between saturated KCI solution and NaCl solutions of varying molality Calculated using Equation 4. Curve 1-calculated using limiting conductivities; Curve 2-calculated using the conductivities corresponding to the ionic concentrations the E,. The continuous curves in Figure 2 represent the y* taken from literature (curve l), and the individual activity coefficients calculated using the Maclnnes assumption : ycl = ~ * ; X C I (curve 2), and 7 x a = ( T ~ K ~ c ~ ) ~ / T ~ -(curve K C I 3). It can be seen that the activity coefficients of Na+ without the corrections for E, are erratic in the concentration region of 10-'m to l m ; after the correction for Eithey favour slightly obtained using the MacInnes assumption. These rethe 7YNa sults are at variance with those of Hyman (19) whose results are compatible with the assumption of y~~ = y*Sacl. The activity coefficients of C1- without the correction for Ej have improbably low values. After correction for E j they follow closely the ycl obtained using the MacInnes assumption. As the Henderson equation assumes concentration profiles at the liquid junction which may differ greatly from the experimental profiles, the E3 of Figure 3 can serve only as a rough guide. The deviation of yci from the theoretical curves at mNaCI< 10-lrn corresponds to an error of about 2 mV; thus the experimental error in the measurement of ECItogether with the possible error in E, calculated with the Henderson equation might account for the discrepancy. Garrels [Chapter 13 in Ref(])] has noted that and yIcobtained using glass electrodes are slightly higher than the coefficients obtained using the MacInnes assumption. This applies to the results not corrected for E,. After the correction, yNnvalues are slightly lower than the values of curve 3 in Figure 2. It is seen, therefore, that the use of y* instead of ysaand ycl does not yield consistent results, either with direct experimental data or with the emf's corrected for Ei; the neglect of E3 emphasizes the difference between the use of y* and the individual activity coefficients; and finally, the use of the MacInnes assumption and of the Henderson equation yields a consistent description of the behavior of NaCl when measured with Na and C1 electrodes. RECEIVED for review July 29, 1968. Accepted September 27, 1968. Work performed under Grant No. NIDR 5 x 5121 of the National Institutes of Health, U.S. Public Health Service. (19)
E. S. Hyman, ANAL. CHEM.,34 365 (1962). VOL. 41, NO. 3, MARCH 1969
517
